rebasing for gitea

main
Michael Winter 5 years ago
commit 128a0fc928

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GNU GENERAL PUBLIC LICENSE
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a history of the domino problemo
essential details of the contents of this repository are outlined in the score/documentation at: https://www.unboundedpress.org/scores/a_history_of_the_domino_problem_score.pdf
note that all large files are within the attachment for the code release here at: https://gitea.unboundedpress.org/mwinter/a_history_of_the_domino_problem/releases
as more extensive documentation of the interface is written it will be posted here in this README.

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// Include the AccelStepper library:
#include <AccelStepper.h>
// Define stepper motor connections and motor interface type. Motor interface type must be set to 1 when using a driver:
// Set stepper 1 pins
#define m1LimitNegPin 2
#define m1LimitPosPin 3
#define m1DirPin 4
#define m1StepPin 5
#define m1PowerPin 6
// Set stepper 2 pins
#define m2LimitNegPin 9
#define m2LimitPosPin 10
#define m2DirPin 11
#define m2StepPin 12
#define m2PowerPin 13
#define motorInterfaceType 1
// Create a new instance of the AccelStepper class:
AccelStepper m1Stepper = AccelStepper(motorInterfaceType, m1StepPin, m1DirPin);
AccelStepper m2Stepper = AccelStepper(motorInterfaceType, m2StepPin, m2DirPin);
unsigned long previousMillis = 0;
unsigned long currentMillis = 0;
void setup() {
pinMode(m1PowerPin, OUTPUT);
pinMode(m1LimitNegPin, INPUT);
pinMode(m1LimitPosPin, INPUT);
pinMode(m2PowerPin, OUTPUT);
pinMode(m2LimitNegPin, INPUT);
pinMode(m2LimitPosPin, INPUT);
Serial.begin(115200);
// Set the maximum speed in steps per second:
m1Stepper.setMaxSpeed(200);
m1Stepper.setAcceleration(100);
m1Stepper.setCurrentPosition(0);
m2Stepper.setMaxSpeed(200);
m2Stepper.setAcceleration(100);
m2Stepper.setCurrentPosition(0);
}
int integerValue=0;
bool negativeNumber = false; // track if number is negative
char incomingByte;
void loop() {
currentMillis = millis();
int m1EorNeg = digitalRead(m1LimitNegPin);
int m1EorPos = digitalRead(m1LimitPosPin);
int m2EorNeg = digitalRead(m2LimitNegPin);
int m2EorPos = digitalRead(m2LimitPosPin);
if (currentMillis - previousMillis >= 1000 == true ) {
Serial.println("------Stepper 1------");
Serial.print("m1EorPos:");
Serial.println(m1EorNeg);
Serial.print("m1EorNeg: ");
Serial.println(m1EorPos);
Serial.print("m1CurPos: ");
Serial.println(m1Stepper.currentPosition() * -1);
Serial.print("m1TarPos: ");
Serial.println(m1Stepper.targetPosition() * -1);
Serial.println("");
Serial.println("------Stepper 2------");
Serial.print("m2EorPos: ");
Serial.println(m2EorNeg);
Serial.print("m2EorNeg: ");
Serial.println(m2EorPos);
Serial.print("m2CurPos: ");
Serial.println(m2Stepper.currentPosition() * -1);
Serial.print("m2TarPos: ");
Serial.println(m2Stepper.targetPosition() * -1);
Serial.println("");
previousMillis = currentMillis;
}
// limit switch logic for stepper 1
if ((m1EorNeg < m1EorPos) && (m1Stepper.targetPosition() > m1Stepper.currentPosition())) {
m1Stepper.setSpeed(0);
m1Stepper.moveTo(m1Stepper.currentPosition());
digitalWrite(m1PowerPin, HIGH);
} else if ((m1EorNeg > m1EorPos) && (m1Stepper.targetPosition() < m1Stepper.currentPosition())) {
m1Stepper.setSpeed(0);
m1Stepper.moveTo(m1Stepper.currentPosition());
digitalWrite(m1PowerPin, HIGH);
} else if (m1Stepper.targetPosition() == m1Stepper.currentPosition()) {
digitalWrite(m1PowerPin, HIGH);
} else {
digitalWrite(m1PowerPin, LOW);
m1Stepper.run();
}
// limit switch logic for stepper 2
if ((m2EorNeg < m2EorPos) && (m2Stepper.targetPosition() > m2Stepper.currentPosition())) {
m2Stepper.setSpeed(0);
m2Stepper.moveTo(m2Stepper.currentPosition());
digitalWrite(m2PowerPin, HIGH);
} else if ((m2EorNeg > m2EorPos) && (m2Stepper.targetPosition() < m2Stepper.currentPosition())) {
m2Stepper.setSpeed(0);
m2Stepper.moveTo(m1Stepper.currentPosition());
digitalWrite(m2PowerPin, HIGH);
} else if (m2Stepper.targetPosition() == m2Stepper.currentPosition()) {
digitalWrite(m2PowerPin, HIGH);
} else {
digitalWrite(m2PowerPin, LOW);
m2Stepper.run();
}
if (Serial.available() > 0) { // something came across serial
integerValue = 0; // throw away previous integerValue
negativeNumber = false; // reset for negative
while(1) { // force into a loop until 'n' is received
incomingByte = Serial.read();
if (incomingByte == ' ') break; // exit the while(1), we're done receiving
if (incomingByte == -1) continue; // if no characters are in the buffer read() returns -1
if (incomingByte == '-') {
negativeNumber = true;
continue;
}
integerValue *= 10; // shift left 1 decimal place
integerValue = ((incomingByte - 48) + integerValue); // convert ASCII to integer, add, and shift left 1 decimal place
}
if (negativeNumber)
integerValue = -integerValue;
integerValue = -integerValue; // this makes up for the fact that things are backwards
m1Stepper.moveTo(integerValue);
integerValue = 0; // throw away previous integerValue
negativeNumber = false; // reset for negative
while(1) { // force into a loop until 'n' is received
incomingByte = Serial.read();
if (incomingByte == '\n') break; // exit the while(1), we're done receiving
if (incomingByte == -1) continue; // if no characters are in the buffer read() returns -1
if (incomingByte == '-') {
negativeNumber = true;
continue;
}
integerValue *= 10; // shift left 1 decimal place
integerValue = ((incomingByte - 48) + integerValue); // convert ASCII to integer, add, and shift left 1 decimal place
}
if (negativeNumber)
integerValue = -integerValue;
integerValue = -integerValue; // this makes up for the fact that things are backwards
m2Stepper.moveTo(integerValue);
}
//delay(100);
}

1
gds/.gitignore vendored

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*.gds

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import pya
import os
base_dir = os.path.dirname(os.path.abspath(__file__))
ly1 = pya.Layout()
ly1.read(os.path.join(base_dir, "..", "gds", "alignment_marks_overlapped.gds"))
ly2 = pya.Layout()
ly2.read(os.path.join(base_dir, "..", "gds", "image_overlapped.gds"))
ly1_top_cell = ly1.top_cell()
tmp = ly1.create_cell("Image")
tmp.copy_tree(ly2.top_cell())
ly1_top_cell.insert(pya.CellInstArray(tmp.cell_index(), pya.Trans(3, False, 0, 0)))
ly1.rename_cell(ly1_top_cell.cell_index(), "All")
ly1_top_cell.flatten(1)
ly1.write(os.path.join(base_dir, "..", "gds", "image_with_alignment_marks_overlapped.gds"))
ly1 = pya.Layout()
ly1.read(os.path.join(base_dir, "..", "gds", "inverted_tonality", "alignment_marks_overlapped_inverse.gds"))
ly2 = pya.Layout()
ly2.read(os.path.join(base_dir, "..", "gds", "inverted_tonality", "image_overlapped_inverse.gds"))
ly2.top_cell().transform_into(pya.Trans(3, False, 0, 0))
processor = pya.ShapeProcessor()
processor.boolean(ly1, ly1.top_cell(), 0, ly2, ly2.top_cell(), 0, ly1.top_cell().shapes(0), 1, False, False, True)
processor = pya.ShapeProcessor()
processor.boolean(ly1, ly1.top_cell(), 1, ly2, ly2.top_cell(), 1, ly1.top_cell().shapes(1), 1, False, False, True)
ly1.write(os.path.join(base_dir, "..", "gds", "inverted_tonality", "image_with_alignment_marks_overlapped_inverse.gds"))

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import pya
import os
base_dir = os.path.dirname(os.path.abspath(__file__))
# init vars
pixel_size = 20
shift_mult = 5
image_size = 4266 * pixel_size * 100 #calculate this directly (4266 and 4242 for shift_mult 5 and 3, respectively)
image_size_half = image_size / 2
image_dist = (shift_mult * 3 * 2 + 2) * pixel_size * 100
object_border = 0
#print(image_dist)
# create layout
layout = pya.Layout()
layout.dbu = 0.01
top = layout.create_cell("Top")
layer1_index = layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_index = layout.insert_layer(pya.LayerInfo.new(2, 0))
layer3_index = layout.insert_layer(pya.LayerInfo.new(3, 0))
layer4_index = layout.insert_layer(pya.LayerInfo.new(4, 0))
layer5_index = layout.insert_layer(pya.LayerInfo.new(5, 0))
# wafer limits
wafer = layout.create_cell("Wafer")
wafer_circle_limit = layout.create_cell("CIRCLE", "Basic",
{ "actual_radius": 75000, "npoints": 256, "layer": pya.LayerInfo(5, 0)} )
wafer1_cell_border = layout.create_cell("DONUT", "Basic",
{ "actual_radius1": 67500, "actual_radius2": 75000, "npoints": 256, "layer": pya.LayerInfo(1, 0)} )
wafer2_cell_border = layout.create_cell("DONUT", "Basic",
{ "actual_radius1": 67500, "actual_radius2": 75000, "npoints": 256, "layer": pya.LayerInfo(2, 0)} )
wafer.insert(pya.CellInstArray(wafer_circle_limit.cell_index(), pya.Trans(0, 0)))
wafer.insert(pya.CellInstArray(wafer1_cell_border.cell_index(), pya.Trans(0, 0)))
wafer.insert(pya.CellInstArray(wafer2_cell_border.cell_index(), pya.Trans(0, 0)))
limit_region = pya.Region(wafer_circle_limit.begin_shapes_rec(layer5_index))
wafer1_fill_region = pya.Region()
wafer1_fill_region.insert(pya.Box(-7500000, -6850000 + 1750000, 7500000, -1 * (6850000 + 1850000))) #mount area fill
frame_width = 300000
square_width = 2000000
wafer1_fill_region.insert(pya.Box(image_size_half, image_size_half, image_size_half + square_width, image_size_half + square_width)) #encoder
wafer1_fill_region.insert(pya.Box(image_size_half, -1 * image_size_half, image_size_half + square_width, -1 * (image_size_half + square_width))) #encoder
wafer1_fill_region.insert(pya.Box(-1 * image_size_half, image_size_half, -1 * (image_size_half + square_width), image_size_half + square_width)) #encoder
wafer1_fill_region.insert(pya.Box(-1 * image_size_half, -1 * image_size_half, -1 * (image_size_half + square_width), -1 * (image_size_half + square_width))) #encoder
wafer.shapes(layer1_index).insert(limit_region & wafer1_fill_region)
wafer2_fill_region = pya.Region()
wafer2_fill_region.insert(pya.Box(-7500000, 6850000 - 1750000, 7500000, 6850000 + 1850000)) #mount area fill
wafer2_fill_region.insert(pya.Box(image_size_half, image_size_half, image_size_half + square_width, image_size_half + square_width)) #encoder
wafer2_fill_region.insert(pya.Box(image_size_half, -1 * image_size_half, image_size_half + square_width, -1 * (image_size_half + square_width))) #encoder
wafer2_fill_region.insert(pya.Box(-1 * image_size_half, image_size_half, -1 * (image_size_half + square_width), image_size_half + square_width)) #encoder
wafer2_fill_region.insert(pya.Box(-1 * image_size_half, -1 * image_size_half, -1 * (image_size_half + square_width), -1 * (image_size_half + square_width))) #encoder
wafer.shapes(layer2_index).insert(limit_region & wafer2_fill_region)
wafer.shapes(layer3_index).insert(pya.Box(-7500000, -6850000, 7500000, 6850000 - 1850000)) #printable area wafer 1
wafer.shapes(layer4_index).insert(pya.Box(-7500000, 6850000, 7500000, -1 * (6850000 - 1850000))) #printable area wafer 2
top.insert(pya.CellInstArray(wafer.cell_index(), pya.Trans(0, 0)))
layout.rename_cell(wafer.cell_index(), "Wafer_Border")
# def for circ grating
def gen_circ_grating(pitch, width, square_size, name):
#create grating archetype for circ grating
circ_grating = layout.create_cell("Circ_Grating")
circ_grating_inv = layout.create_cell("Circ_Grating_Inv")
i = 0
while (i * pitch) < (8000):
donut = layout.create_cell("DONUT", "Basic",
{ "actual_radius1": (i * pitch), "actual_radius2": (i * pitch + width), "npoints": 256, "layer": pya.LayerInfo(1, 0)} )
circ_grating.insert(pya.CellInstArray(donut.cell_index(), pya.Trans(0, 0)))
i = i + 1
i = 0
while (i * pitch) < (8000):
donut = layout.create_cell("DONUT", "Basic",
{ "actual_radius1": (i * pitch) + width, "actual_radius2": (i * pitch + width) + width, "npoints": 256, "layer": pya.LayerInfo(2, 0)} )
circ_grating_inv.insert(pya.CellInstArray(donut.cell_index(), pya.Trans(0, 0)))
i = i + 1
circ_grating_clip = layout.clip(circ_grating.cell_index(), pya.Box(-1 * square_size, -1 * square_size, square_size, square_size))
circ_grating_inv_clip = layout.clip(circ_grating_inv.cell_index(), pya.Box(-1 * square_size, -1 * square_size, square_size, square_size))
circ_grating.delete()
circ_grating_inv.delete()
layout.rename_cell(circ_grating_clip, name + "_Clip")
layout.rename_cell(circ_grating_inv_clip, name + "_Inv_Clip")
return [circ_grating_clip, circ_grating_inv_clip]
# verniers
linear_grating_vernier = layout.create_cell("Vernier")
base_period = image_size_half - 500000
revealing_period = image_dist
velocity_ratio = 1
pitch1 = (base_period * (revealing_period / velocity_ratio)) / (base_period - (revealing_period / velocity_ratio))
pitch2 = revealing_period / velocity_ratio
opening1 = 4000
#print(pitch1)
#print(pitch2)
frame_width = 300000
for i in range(-1 * int((image_size_half) / pitch1), int((image_size_half) / pitch1)):
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(opening1 / 2, -1 * frame_width, pitch1 - opening1 / 2, 0))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch1, 0)))
for i in range(-1 * int((image_size_half - image_dist) / pitch2), int((image_size_half - image_dist) / pitch2)):
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(opening1 / 2, -1 * frame_width, pitch2 - opening1 / 2, 0))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch2, 0)))
base_period = -1 * (image_size_half - 500000)
revealing_period = image_dist
velocity_ratio = 5
pitch3 = (base_period * (revealing_period / velocity_ratio)) / (base_period - (revealing_period / velocity_ratio))
pitch4 = revealing_period / velocity_ratio
opening2 = 800
for i in range(-1 * int(image_size_half / pitch3), int(image_size_half / pitch3)):
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(opening2 / 2, 0, pitch3 - opening2 / 2, frame_width))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch3, 0)))
for i in range(-1 * int((image_size_half - image_dist) / pitch4), int((image_size_half - image_dist) / pitch4)):
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(opening2 / 2, 0, pitch4 - opening2 / 2, frame_width))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch4, 0)))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(image_size_half - (2 * image_dist), -1 * frame_width, image_size_half, 0))
line.shapes(layer2_index).insert(pya.Box(-1 * (image_size_half - (2 * image_dist)), -1 * frame_width, -1 * (image_size_half), 0))
line.shapes(layer2_index).insert(pya.Box(image_size_half - (2 * image_dist), image_dist, image_size_half, image_dist + frame_width))
line.shapes(layer2_index).insert(pya.Box(-1 * (image_size_half - (2 * image_dist)), image_dist, -1 * (image_size_half), image_dist + frame_width))
#These four lines can be taken away to get rid of the bounding black out
line.shapes(layer2_index).insert(pya.Box(-1 * image_size_half, image_dist, image_size_half, 0 - image_dist))
line.shapes(layer2_index).insert(pya.Box(-1 * image_size_half, -1 * (frame_width - image_dist), image_size_half, -1 * (frame_width + image_dist)))
line.shapes(layer2_index).insert(pya.Box(-1 * image_size_half, 0, image_size_half, image_dist))
line.shapes(layer2_index).insert(pya.Box(-1 * image_size_half, frame_width + (1 * image_dist), image_size_half, frame_width - image_dist))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(image_size_half - image_dist, -1 * frame_width, image_size_half - (2 * image_dist), 0))
line.shapes(layer1_index).insert(pya.Box(-1 * (image_size_half - image_dist), -1 * frame_width, -1 * (image_size_half - (2 * image_dist)), 0))
line.shapes(layer1_index).insert(pya.Box(image_size_half - image_dist, 0, image_size_half - (2 * image_dist), frame_width))
line.shapes(layer1_index).insert(pya.Box(-1 * (image_size_half - image_dist), 0, -1 * (image_size_half - (2 * image_dist)), frame_width))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
vernier_extent = image_size_half + object_border + frame_width + image_dist
top.insert(pya.CellInstArray(linear_grating_vernier.cell_index(), pya.Trans(3, False, vernier_extent, 0)))
top.insert(pya.CellInstArray(linear_grating_vernier.cell_index(), pya.Trans(1, False, -1 * vernier_extent, 0)))
top.insert(pya.CellInstArray(linear_grating_vernier.cell_index(), pya.Trans(0, False, 0, vernier_extent)))
top.insert(pya.CellInstArray(linear_grating_vernier.cell_index(), pya.Trans(2, False, 0, -1 * vernier_extent)))
vernier_extent = vernier_extent + frame_width + image_dist
# linear grating unison for rotational alignment
linear_grating_uni = layout.create_cell("Linear_Grating_Uni")
pitch = 2000
line_width = 1000
frame_width = 300000 / 2
line_length = image_size_half - 500000
i = -1 * frame_width
while (i) < (frame_width):
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(0, -1 * line_length, line_width, line_length))
linear_grating_uni.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i, 0)))
i = i + pitch
i = -1 * frame_width
shift = line_width
while (i) < (frame_width):
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(0, -1 * line_length, line_width, line_length))
linear_grating_uni.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i + shift, 0)))
i = i + pitch
unison_rot_extent = vernier_extent + object_border + frame_width + image_dist
top.insert(pya.CellInstArray(linear_grating_uni.cell_index(), pya.Trans(2, False, unison_rot_extent, 0)))
top.insert(pya.CellInstArray(linear_grating_uni.cell_index(), pya.Trans(0, False, -1 * unison_rot_extent, 0)))
unison_rot_extent = unison_rot_extent + frame_width + image_dist
# 9 * 9 grid with larger squares
circ_grating_square_array_2 = layout.create_cell("Circ_Grating_Square_Array_2")
square_dist = 400000
pitch = 10
width = 5
square_size = (square_dist / 2) - 20000
[circ_grating_square_array_clip, circ_grating_square_array_inv_clip] = gen_circ_grating(pitch, width, square_size, "Circ_Grating_2")
for r in range(-1, 2):
for c in range(-1, 2):
circ_grating_square_array_2.insert(pya.CellInstArray(circ_grating_square_array_clip, pya.Trans(0, False, square_dist * r, square_dist * c)))
circ_grating_square_array_2.insert(pya.CellInstArray(circ_grating_square_array_inv_clip, pya.Trans(0, False, square_dist * r + (r * image_dist), square_dist * c + (c * image_dist))))
grid_extent = unison_rot_extent + square_size + square_dist + image_dist
y_offset = square_dist + image_dist + (square_size)
top.insert(pya.CellInstArray(circ_grating_square_array_2.cell_index(), pya.Trans(2, False, grid_extent, 0)))
top.insert(pya.CellInstArray(circ_grating_square_array_2.cell_index(), pya.Trans(0, False, -1 * grid_extent, 0)))
# verniers md course
linear_grating_vernier_md_course = layout.create_cell("Vernier_md_course")
square_size = 650000
fray = 0
line_length = square_size / 2 + fray
velocity_ratio = 2
pitch1 = ((square_size * 1) * (image_dist / velocity_ratio)) / ((square_size * 1) - (image_dist / velocity_ratio))
pitch2 = image_dist / velocity_ratio
opening = 8000
for i in range(-1 * int(square_size / 2 / pitch1) - 0, int(square_size / 2 / pitch1) + 0):
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(opening / 2, -1 * line_length, pitch1 - opening / 2, line_length))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch1, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, (i * pitch1))))
for i in range(-1 * int(square_size / 2 / pitch2) - 0, int(square_size / 2 / pitch2) + 0):
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(opening / 2, -1 * line_length, pitch2 - opening / 2, line_length))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch2, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, (i * pitch2))))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2 - image_dist, square_size / 2 + (1 * image_dist), square_size / 2 + (1 * image_dist)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2 - image_dist, square_size / 2 + (0 * image_dist), square_size / 2 + (1 * image_dist)))
#linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(2, False, 0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, True, 0, 0)))
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2, square_size / 2 + (1 * image_dist), square_size / 2 + (0 * image_dist)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(2, False, 0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(3, False, 0, 0)))
triangle = layout.create_cell("Triangle")
triangle.shapes(layer2_index).insert(pya.Polygon([pya.Point(-45000, -1 * image_dist), pya.Point(45000, -1 * image_dist), pya.Point(0, 0)]))
linear_grating_vernier_md_course.insert(pya.CellInstArray(triangle.cell_index(), pya.Trans(0, False, 0, -1 * (square_size / 2 + (image_dist * 1)))))
linear_grating_vernier_md_course.insert(pya.CellInstArray(triangle.cell_index(), pya.Trans(1, False, (square_size / 2 + (image_dist * 1)), 0)))
grid_extent = unison_rot_extent + (square_size / 2) + (image_dist * 1)
y_offset = y_offset + (square_size / 2) + (image_dist * 3)
top.insert(pya.CellInstArray(linear_grating_vernier_md_course.cell_index(), pya.Trans(0, False, (grid_extent + fray), (y_offset + fray))))
top.insert(pya.CellInstArray(linear_grating_vernier_md_course.cell_index(), pya.Trans(0, True, (grid_extent + fray), -1 * (y_offset + fray))))
top.insert(pya.CellInstArray(linear_grating_vernier_md_course.cell_index(), pya.Trans(2, False, -1 * (grid_extent + fray), -1 * (y_offset + fray))))
top.insert(pya.CellInstArray(linear_grating_vernier_md_course.cell_index(), pya.Trans(2, True, -1 * (grid_extent + fray), (y_offset + fray))))
# verniers md fine
linear_grating_vernier_md_fine = layout.create_cell("Vernier_md_fine")
square_size = 650000
fray = 0
line_length = square_size / 2 + fray
velocity_ratio = 3
pitch1 = ((square_size * -1) * (image_dist / velocity_ratio)) / ((square_size * -1) - (image_dist / velocity_ratio))
pitch2 = image_dist / velocity_ratio
opening = 8000 * 2/3
for i in range(-1 * int(square_size / 2 / pitch1) - 0, int(square_size / 2 / pitch1) + 0):
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(opening / 2, -1 * line_length, pitch1 - opening / 2, line_length))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch1, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, (i * pitch1))))
for i in range(-1 * int(square_size / 2 / pitch1) - 0, int(square_size / 2 / pitch1) + 0):
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(opening / 2, -1 * line_length, pitch2 - opening / 2, line_length))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch2, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, (i * pitch2))))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2 - image_dist, square_size / 2 + (1 * image_dist), square_size / 2 + (1 * image_dist)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2 - image_dist, square_size / 2 + (0 * image_dist), square_size / 2 + (1 * image_dist)))
#linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(2, False, 0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, True, 0, 0)))
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2, square_size / 2 + (1 * image_dist), square_size / 2 + (0 * image_dist)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(2, False, 0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(3, False, 0, 0)))
triangle = layout.create_cell("Triangle")
triangle.shapes(layer2_index).insert(pya.Polygon([pya.Point(-45000, -1 * image_dist), pya.Point(45000, -1 * image_dist), pya.Point(0, 0)]))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(triangle.cell_index(), pya.Trans(0, False, 0, -1 * (square_size / 2 + (image_dist * 1)))))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(triangle.cell_index(), pya.Trans(1, False, (square_size / 2 + (image_dist * 1)), 0)))
grid_extent = unison_rot_extent + (square_size / 2) + (image_dist * 1)
y_offset = y_offset + square_size + (image_dist * 1)
top.insert(pya.CellInstArray(linear_grating_vernier_md_course.cell_index(), pya.Trans(0, True, (grid_extent + fray), (y_offset + fray))))
top.insert(pya.CellInstArray(linear_grating_vernier_md_course.cell_index(), pya.Trans(0, False, (grid_extent + fray), -1 * (y_offset + fray))))
top.insert(pya.CellInstArray(linear_grating_vernier_md_course.cell_index(), pya.Trans(2, True, -1 * (grid_extent + fray), -1 * (y_offset + fray))))
top.insert(pya.CellInstArray(linear_grating_vernier_md_course.cell_index(), pya.Trans(2, False, -1 * (grid_extent + fray), (y_offset + fray))))
y_offset = y_offset + (square_size / 2) + (image_dist * 3)
# larger squares only in the unison position
circ_grating_uni = layout.create_cell("Circ_Grating_Uni")
pitch = 20
width = 10
square_size = 530000 / 2
[circ_grating_uni_clip, circ_grating_uni_inv_clip] = gen_circ_grating(pitch, width, square_size, "Circ_Grating_3")
circ_grating_uni.insert(pya.CellInstArray(circ_grating_uni_clip, pya.Trans(0, False, 0, 0)))
circ_grating_uni.insert(pya.CellInstArray(circ_grating_uni_inv_clip, pya.Trans(0, False, 0, 0)))
grid_extent = unison_rot_extent + square_size + image_dist
y_offset = y_offset + (square_size / 1)
top.insert(pya.CellInstArray(circ_grating_uni.cell_index(), pya.Trans(0, False, grid_extent, -1 * y_offset)))
top.insert(pya.CellInstArray(circ_grating_uni.cell_index(), pya.Trans(0, False, -1 * grid_extent, -1 * y_offset)))
top.insert(pya.CellInstArray(circ_grating_uni.cell_index(), pya.Trans(0, False, grid_extent, y_offset)))
top.insert(pya.CellInstArray(circ_grating_uni.cell_index(), pya.Trans(0, False, -1 * grid_extent, y_offset)))
#top.insert(pya.CellInstArray(linear_grating_encoder_clip, pya.Trans(0, False, image_size_half, image_size_half)))
# linear grating encoder for optional optosensor
def gen_encoder_grating(alg_layout, cell):
frame_width = 300000
linear_grating_encoder_1 = alg_layout.create_cell("Linear_Grating_Encoder_1")
linear_grating_encoder_2 = alg_layout.create_cell("Linear_Grating_Encoder_2")
pitch = 1000
line_width = 500
square_width = (frame_width * 2) + (image_dist * 2)
square_width = 2000000
line_length = square_width
i = -1 * square_width
while (i) < (square_width):
line = alg_layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(line_width, 0, -1 * square_width, line_width))
line.shapes(layer1_index).insert(pya.Box(0, 0, line_width, -1 * square_width))
linear_grating_encoder_1.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, False, i, i)))
line = alg_layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(line_width, 0, -1 * square_width, line_width))
line.shapes(layer2_index).insert(pya.Box(0, 0, line_width, -1 * square_width))
linear_grating_encoder_2.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, False, i, i)))
i = i + pitch
i = -1 * square_width
shift = line_width
while (i) < (frame_width + image_dist):
line = alg_layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(line_width, 0, -1 * square_width, line_width))
line.shapes(layer2_index).insert(pya.Box(0, 0, line_width, -1 * square_width))
linear_grating_encoder_1.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, False, i + shift, i + shift)))
line = alg_layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(line_width, 0, -1 * square_width, line_width))
line.shapes(layer1_index).insert(pya.Box(0, 0, line_width, -1 * square_width))
linear_grating_encoder_2.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, False, i + shift, i + shift)))
i = i + pitch
inner_clip_2 = alg_layout.clip(linear_grating_encoder_2.cell_index(), pya.Box(0, 0, frame_width + image_dist, frame_width + image_dist))
linear_grating_encoder_clip_2 = alg_layout.clip(linear_grating_encoder_2.cell_index(), pya.Box(0, 0, square_width, square_width))
cell.insert(pya.CellInstArray(linear_grating_encoder_clip_2, pya.Trans(0, False, image_size_half, image_size_half)))
cell.insert(pya.CellInstArray(inner_clip_2, pya.Trans(0, False, image_size_half + frame_width + image_dist, image_size_half + frame_width + image_dist)))
cell.insert(pya.CellInstArray(linear_grating_encoder_clip_2, pya.Trans(1, False, -1 * image_size_half, image_size_half)))
cell.insert(pya.CellInstArray(inner_clip_2, pya.Trans(1, False, -1 * (image_size_half + frame_width + image_dist), image_size_half + frame_width + image_dist)))
inner_clip_1 = alg_layout.clip(linear_grating_encoder_1.cell_index(), pya.Box(0, 0, frame_width + image_dist, frame_width + image_dist))
linear_grating_encoder_clip_1 = alg_layout.clip(linear_grating_encoder_1.cell_index(), pya.Box(0, 0, square_width, square_width))
cell.insert(pya.CellInstArray(linear_grating_encoder_clip_1, pya.Trans(2, False, -1 * image_size_half, -1 * image_size_half)))
cell.insert(pya.CellInstArray(inner_clip_1, pya.Trans(2, False, -1 * (image_size_half + frame_width + image_dist), -1 * (image_size_half + frame_width + image_dist))))
cell.insert(pya.CellInstArray(linear_grating_encoder_clip_1, pya.Trans(3, False, image_size_half, -1 * image_size_half)))
cell.insert(pya.CellInstArray(inner_clip_1, pya.Trans(3, False, image_size_half + frame_width + image_dist, -1 * (image_size_half + frame_width + image_dist))))
cell.flatten(1)
alg_layout.prune_cell(linear_grating_encoder_1.cell_index(), -1)
alg_layout.prune_cell(linear_grating_encoder_2.cell_index(), -1)
top.flatten(1)
wafer1_region1 = pya.Region(top.begin_shapes_rec(layer1_index))
wafer1_region2 = pya.Region(top.begin_shapes_rec(layer3_index))
wafer2_region1 = pya.Region(top.begin_shapes_rec(layer2_index))
wafer2_region2 = pya.Region(top.begin_shapes_rec(layer4_index))
alignment_layout = pya.Layout()
alignment = alignment_layout.create_cell("Alignment")
alignment_layout.dbu = 0.01
layer1_index = alignment_layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_index = alignment_layout.insert_layer(pya.LayerInfo.new(2, 0))
encode_region = pya.Region()
square_width = 2000000
encode_region.insert(pya.Box(image_size_half, image_size_half, image_size_half + square_width, image_size_half + square_width)) #encoder
encode_region.insert(pya.Box(image_size_half, -1 * image_size_half, image_size_half + square_width, -1 * (image_size_half + square_width))) #encoder
encode_region.insert(pya.Box(-1 * image_size_half, image_size_half, -1 * (image_size_half + square_width), image_size_half + square_width)) #encoder
encode_region.insert(pya.Box(-1 * image_size_half, -1 * image_size_half, -1 * (image_size_half + square_width), -1 * (image_size_half + square_width))) #encoder
alignment.shapes(layer1_index).insert((wafer1_region1 & wafer1_region2) - encode_region)
alignment.shapes(layer2_index).insert((wafer2_region1 & wafer2_region2) - encode_region)
gen_encoder_grating(alignment_layout, alignment)
#alignment_layout.transform(pya.Trans(2, False, 0, 0))
alignment_layout.write(os.path.join(base_dir, "..", "gds", "alignment_marks_overlapped.gds"))
alignment_inv_layout = pya.Layout()
alignment_inv = alignment_inv_layout.create_cell("Alignment_Inverse")
alignment_inv_layout.dbu = 0.01
layer1_index = alignment_inv_layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_index = alignment_inv_layout.insert_layer(pya.LayerInfo.new(2, 0))
alignment_inv.shapes(layer1_index).insert(wafer1_region2 - wafer1_region1)
alignment_inv.shapes(layer2_index).insert(wafer2_region2 - wafer2_region1)
gen_encoder_grating(alignment_inv_layout, alignment_inv)
#alignment_inv_layout.transform(pya.Trans(2, False, 0, 0))
alignment_inv_layout.write(os.path.join(base_dir, "..", "gds", "inverted_tonality", "alignment_marks_overlapped_inverse.gds"))

@ -0,0 +1,147 @@
import pya
import os
from PIL import Image
base_dir = os.path.dirname(os.path.abspath(__file__))
#for some reason pya is not getting the size so using PIL
im = Image.open(os.path.join(base_dir, "..", "visualizations", "11735", "shadow_img_0_final.png"))
#width, height = [100, 100]
width, height = im.size
im.close()
# create layout
layout = pya.Layout()
layout.dbu = 0.01
image = layout.create_cell("Image")
layer1_index = layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_index = layout.insert_layer(pya.LayerInfo.new(2, 0))
image1 = pya.Image(os.path.join(base_dir, "..", "visualizations", "11735", "shadow_img_0_final.png"))
# The dimension of one pixel
pixelSize = 2000
# image distance in pixels minus the 2 pixel offset
shift_mult = 5
image_dist = (shift_mult * 3 * 2)
image1_region = pya.Region()
image2_region = pya.Region()
image1_region_bb = pya.Region()
image2_region_bb = pya.Region()
final_region = pya.Region()
# Iterate over all rows in image1
for y in range(height):
# Iterate over all columns in image1
for x in range(width):
# Use each channel for a different layer
# d > 0.5 selects all pixels with a level > 50% in that channel
d = image1.get_pixel(x, y, 0)
if d < 0.5:
# Create a polygon corresponding to one pixel
p1 = pya.DPoint((x * pixelSize) - (0.5 * width * pixelSize), (y * pixelSize) - (0.5 * width * pixelSize))
p2 = pya.DPoint(((x + 1) * pixelSize) - (0.5 * width * pixelSize), ((y + 1) * pixelSize) - (0.5 * width * pixelSize))
dbox = pya.DBox(p1, p2)
box = pya.Box.from_dbox(dbox)
poly = pya.Polygon(box)
image1_region.insert(poly)
image1._destroy()
image2 = pya.Image(os.path.join(base_dir, "..", "visualizations", "11735", "shadow_img_1_final.png"))
# Iterate over all rows in image2
for y in range(image_dist, height - image_dist):
# Iterate over all columns in image2
for x in range(image_dist, width - image_dist):
# Use each channel for a different layer
# d > 0.5 selects all pixels with a level > 50% in that channel
d = image2.get_pixel(x, y, 0)
if d < 0.5:
# Create a polygon corresponding to one pixel
p1 = pya.DPoint((x * pixelSize) - (0.5 * width * pixelSize), (y * pixelSize) - (0.5 * width * pixelSize))
p2 = pya.DPoint(((x + 1) * pixelSize) - (0.5 * width * pixelSize), ((y + 1) * pixelSize) - (0.5 * width * pixelSize))
dbox = pya.DBox(p1, p2)
box = pya.Box.from_dbox(dbox)
poly = pya.Polygon(box)
image2_region.insert(poly)
print("pixel import finished")
image2._destroy()
image1_bb = pya.Box(-0.5 * width * pixelSize, -0.5 * height * pixelSize, 0.5 * width * pixelSize, 0.5 * width * pixelSize)
image2_bb = pya.Box(((-0.5 * width) + image_dist) * pixelSize, ((-0.5 * height) + image_dist) * pixelSize, ((0.5 * width) - image_dist) * pixelSize, ((0.5 * height) - image_dist) * pixelSize)
image1_region_bb.insert(image1_bb)
image2_region_bb.insert(image2_bb)
#if you resize image1, you must sent merged_semantics to True!!!!
#image1_region.merged_semantics = False
#image2_region.merged_semantics = False
#image1_region_inverse.merged_semantics = False
#image2_region_inverse.merged_semantics = False
#image1_region_bb.merged_semantics = False
#image2_region_bb.merged_semantics = False
#final_region.merged_semantics = False
#image1_region.strict_handling = True
#image2_region.strict_handling = True
#image1_region_inverse.strict_handling = True
#image2_region_inverse.strict_handling = True
#image2_region.strict_handling = True
#image1_region_bb.strict_handling = True
#image2_region_bb.strict_handling = True
#final_region.strict_handling = True
#image1_region.size(25) #opting not to resize image1
image2_region.size(150)
print("resize finished")
image_layout = pya.Layout()
image = image_layout.create_cell("Image")
image_layout.dbu = 0.01
layer1_image_index = image_layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_image_index = image_layout.insert_layer(pya.LayerInfo.new(2, 0))
print("finalizing layout for image_overlapped.gds")
#normal
image.shapes(layer1_index).insert(image1_region)
image_layout.clip(image.cell_index(), image1_bb)
processor = pya.ShapeProcessor()
processor.merge(image_layout, image, layer1_image_index, image.shapes(layer1_image_index), False, 0, False, True)
print("layer1 finished")
image.shapes(layer2_image_index).insert(image2_region_bb & image2_region)
print("layer2 finished")
print("layout for image_overlapped.gds finished")
image_layout.write(os.path.join(base_dir, "..", "gds", "image_overlapped.gds"))
print("image_overlapped.gds written")
image_inv_layout = pya.Layout()
image_inv = image_inv_layout.create_cell("Image_Inverse")
image_inv_layout.dbu = 0.01
layer1_image_inv_index = image_inv_layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_image_inv_index = image_inv_layout.insert_layer(pya.LayerInfo.new(2, 0))
print("finalizing layout for image_overlapped_inverse.gds")
#inverted
#image_inv.shapes(layer1_index).insert(pya.Box(-7500000, -6850000, 7500000, 6850000 - 1850000)) #printable area wafer 1
#image_inv.shapes(layer2_index).insert(pya.Box(-7500000, 6850000, 7500000, -1 * (6850000 - 1850000))) #printable area wafer 2
#the printable areas are rotated for the overlay with the alignment marks
image_inv.shapes(layer1_index).insert(pya.Box(-7500000, -6850000, 7500000, 6850000 - 1850000).transformed(pya.Trans(1, False, 0, 0))) #printable area wafer 1
image_inv.shapes(layer2_index).insert(pya.Box(-7500000, 6850000, 7500000, -1 * (6850000 - 1850000)).transformed(pya.Trans(1, False, 0, 0))) #printable area wafer 2
processor = pya.ShapeProcessor()
processor.boolean(image_layout, image, layer1_image_index, image_inv_layout, image_inv, layer1_image_inv_index, image_inv.shapes(layer1_image_inv_index), 3, False, False, True)
print("layer1 finished")
processor = pya.ShapeProcessor()
processor.boolean(image_layout, image, layer2_image_index, image_inv_layout, image_inv, layer2_image_inv_index, image_inv.shapes(layer2_image_inv_index), 3, False, False, True)
print("layer2 finished")
print("layout for image_overlapped_inverse.gds finished")
image_inv_layout.write(os.path.join(base_dir, "..", "gds", "inverted_tonality", "image_overlapped_inverse.gds"))
print("image_overlapped_inverse.gds written")

@ -0,0 +1,156 @@
import pya
import os
base_dir = os.path.dirname(os.path.abspath(__file__))
# init vars
velocity_ratio1 = 2
opening1 = 8000
velocity_ratio2 = 3
opening2 = opening1 * velocity_ratio1 / velocity_ratio2
pixel_size = 20
shift_mult = 5
image_size = 4266 * pixel_size * 100 #calculate this directly (4266 and 4242 for shift_mult 5 and 3, respectively)
image_size_half = image_size / 2
image_dist = (shift_mult * 3 * 2 + 2) * pixel_size * 100
object_border = 0
#print(image_dist)
# create layout
layout = pya.Layout()
layout.dbu = 0.01
top = layout.create_cell("Top")
layer1_index = layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_index = layout.insert_layer(pya.LayerInfo.new(2, 0))
layer3_index = layout.insert_layer(pya.LayerInfo.new(3, 0))
layer4_index = layout.insert_layer(pya.LayerInfo.new(4, 0))
layer5_index = layout.insert_layer(pya.LayerInfo.new(5, 0))
y_offset = 0
# verniers md course
linear_grating_vernier_md_course = layout.create_cell("Vernier_md_course")
square_size = 650000
fray = 0
line_length = square_size / 2 + fray
pitch11 = ((square_size * 1) * (image_dist / velocity_ratio1)) / ((square_size * 1) - (image_dist / velocity_ratio1))
pitch12 = image_dist / velocity_ratio1
for i in range(-1 * int(square_size / 2 / pitch11) - 0, int(square_size / 2 / pitch11) + 0):
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(opening1 / 2, -1 * line_length, pitch11 - opening1 / 2, line_length))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch11, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, (i * pitch11))))
for i in range(-1 * int(square_size / 2 / pitch12) - 0, int(square_size / 2 / pitch12) + 0):
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(opening1 / 2, -1 * line_length, pitch12 - opening1 / 2, line_length))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch12, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, (i * pitch12))))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2 - image_dist, square_size / 2 + (1 * image_dist), square_size / 2 + (1 * image_dist)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2 - image_dist, square_size / 2 + (0 * image_dist), square_size / 2 + (1 * image_dist)))
#linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(2, False, 0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, True, 0, 0)))
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2, square_size / 2 + (1 * image_dist), square_size / 2 + (0 * image_dist)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(2, False, 0, 0)))
linear_grating_vernier_md_course.insert(pya.CellInstArray(line.cell_index(), pya.Trans(3, False, 0, 0)))
triangle = layout.create_cell("Triangle")
triangle.shapes(layer2_index).insert(pya.Polygon([pya.Point(-45000, -1 * image_dist), pya.Point(45000, -1 * image_dist), pya.Point(0, 0)]))
linear_grating_vernier_md_course.insert(pya.CellInstArray(triangle.cell_index(), pya.Trans(0, False, 0, -1 * (square_size / 2 + (image_dist * 1)))))
linear_grating_vernier_md_course.insert(pya.CellInstArray(triangle.cell_index(), pya.Trans(1, False, (square_size / 2 + (image_dist * 1)), 0)))
y_offset = y_offset + (square_size / 2) + (image_dist * 3)
grid_extent = 0
top.insert(pya.CellInstArray(linear_grating_vernier_md_course.cell_index(), pya.Trans(0, False, (grid_extent + fray), (y_offset + fray))))
# verniers md fine
linear_grating_vernier_md_fine = layout.create_cell("Vernier_md_fine")
square_size = 650000
fray = 0
line_length = square_size / 2 + fray
pitch21 = ((square_size * -1) * (image_dist / velocity_ratio2)) / ((square_size * -1) - (image_dist / velocity_ratio2))
pitch22 = image_dist / velocity_ratio2
for i in range(-1 * int(square_size / 2 / pitch21) - 0, int(square_size / 2 / pitch21) + 0):
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(opening2 / 2, -1 * line_length, pitch21 - opening2 / 2, line_length))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch21, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, (i * pitch21))))
for i in range(-1 * int(square_size / 2 / pitch22) - 0, int(square_size / 2 / pitch22) + 0):
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(opening2 / 2, -1 * line_length, pitch22 - opening2 / 2, line_length))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch22, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, (i * pitch22))))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2 - image_dist, square_size / 2 + (1 * image_dist), square_size / 2 + (1 * image_dist)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2 - image_dist, square_size / 2 + (0 * image_dist), square_size / 2 + (1 * image_dist)))
#linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(2, False, 0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, True, 0, 0)))
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(-1 * (square_size / 2 + (1 * image_dist)), square_size / 2, square_size / 2 + (1 * image_dist), square_size / 2 + (0 * image_dist)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(1, False, 0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(2, False, 0, 0)))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(line.cell_index(), pya.Trans(3, False, 0, 0)))
triangle = layout.create_cell("Triangle")
triangle.shapes(layer2_index).insert(pya.Polygon([pya.Point(-45000, -1 * image_dist), pya.Point(45000, -1 * image_dist), pya.Point(0, 0)]))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(triangle.cell_index(), pya.Trans(0, False, 0, -1 * (square_size / 2 + (image_dist * 1)))))
linear_grating_vernier_md_fine.insert(pya.CellInstArray(triangle.cell_index(), pya.Trans(1, False, (square_size / 2 + (image_dist * 1)), 0)))
y_offset = y_offset + square_size + (image_dist * 1)
grid_extent = 0
top.insert(pya.CellInstArray(linear_grating_vernier_md_fine.cell_index(), pya.Trans(0, True, (grid_extent + fray), (y_offset + fray))))
top.flatten(1)
top.write(os.path.join(base_dir, "..", "gds", "md_vernier_test.gds"))
bb_region = pya.Region(pya.Box(-650000, -300000, 650000, 2000000))
wafer1 = pya.Region(top.begin_shapes_rec(layer1_index))
wafer2 = pya.Region(top.begin_shapes_rec(layer2_index))
alignment_inv_layout = pya.Layout()
alignment_inv = alignment_inv_layout.create_cell("Alignment_Inverse")
alignment_inv_layout.dbu = 0.01
layer1_index = alignment_inv_layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_index = alignment_inv_layout.insert_layer(pya.LayerInfo.new(2, 0))
alignment_inv.shapes(layer1_index).insert(bb_region - wafer1)
alignment_inv.shapes(layer2_index).insert(bb_region - wafer2)
alignment_inv_layout.write(os.path.join(base_dir, "..", "gds", "inverted_tonality", "md_vernier_test_inverse.gds"))

@ -0,0 +1,48 @@
import pya
import os
base_dir = os.path.dirname(os.path.abspath(__file__))
layout = pya.Layout()
layout.read(os.path.join(base_dir, "..", "gds", "image_with_alignment_marks_overlapped.gds"))
layout.delete_layer(1)
layer3_index = layout.insert_layer(pya.LayerInfo.new(3, 0))
layout.top_cell().shapes(0).insert(pya.Box(-7500000, 6850000 - 1850000 + 30000, 7500000, 6850000 - 1850000 + 30000 + 5000))
layout.top_cell().shapes(layer3_index).insert(pya.Box(-7500000, -7500000, 7500000, 7500000))
#layout.transform(pya.Trans(2, False, 0, 0))
layout.write(os.path.join(base_dir, "..", "gds", "wafer_1.gds"))
layout = pya.Layout()
layout.read(os.path.join(base_dir, "..", "gds", "image_with_alignment_marks_overlapped.gds"))
layout.delete_layer(0)
layer3_index = layout.insert_layer(pya.LayerInfo.new(3, 0))
#layout.transform(pya.Trans(2, True, 0, 0))
layout.transform(pya.Trans(0, True, 0, 0))
layout.top_cell().shapes(1).insert(pya.Box(-7500000, 6850000 - 1850000 + 30000, 7500000, 6850000 - 1850000 + 30000 + 5000))
layout.top_cell().shapes(layer3_index).insert(pya.Box(-7500000, -7500000, 7500000, 7500000))
layout.write(os.path.join(base_dir, "..", "gds", "wafer_2.gds"))
layout = pya.Layout()
layout.read(os.path.join(base_dir, "..", "gds", "inverted_tonality", "image_with_alignment_marks_overlapped_inverse.gds"))
layout.delete_layer(1)
#layout.transform(pya.Trans(2, False, 0, 0))
layout.write(os.path.join(base_dir, "..", "gds", "inverted_tonality", "wafer_1_inverse.gds"))
layout = pya.Layout()
layout.read(os.path.join(base_dir, "..", "gds", "inverted_tonality", "image_with_alignment_marks_overlapped_inverse.gds"))
layout.delete_layer(0)
#layout.transform(pya.Trans(2, True, 0, 0))
layout.transform(pya.Trans(0, True, 0, 0))
layout.write(os.path.join(base_dir, "..", "gds", "inverted_tonality", "wafer_2_inverse.gds"))

@ -0,0 +1,30 @@
import pya
#amount to shift in units of distance between images
shift_x = 0
shift_y = 0
#vars on current sizes
shift_mult = 5
pixel_size = 20
image_dist = (shift_mult * 3 * 2 + 2) * pixel_size * 100
print(image_dist)
#shift and take the overlap returning a 3rd layer
ly = pya.CellView.active().layout()
l10 = ly.layer(1, 0)
l20 = ly.layer(2, 0)
bbox = pya.Region()
bbox.insert(ly.top_cell().bbox())
#r10 = bbox - pya.Region(ly.top_cell().begin_shapes_rec(l10))
#r20 = bbox - pya.Region(ly.top_cell().begin_shapes_rec(l20))
r10 = pya.Region(ly.top_cell().begin_shapes_rec(l10))
r20 = pya.Region(ly.top_cell().begin_shapes_rec(l20))
r10.move(image_dist * shift_x, image_dist* shift_y)
ly.delete_layer(ly.layer(3, 0))
ly.top_cell().shapes(ly.layer(3, 0)).insert(bbox - (r10 | r20))
pya.LayoutView.current().add_missing_layers()

@ -0,0 +1,22 @@
import pya
#amount to shift in units of distance between images
shift_x = 0
shift_y = 0.1
#vars on current sizes
shift_mult = 5
pixel_size = 20
image_dist = (shift_mult * 3 * 2 + 2) * pixel_size * 100
print(image_dist)
#shift and take the overlap returning a 3rd layer
ly = pya.CellView.active().layout()
l10 = ly.layer(1, 0)
l20 = ly.layer(2, 0)
r10 = pya.Region(ly.top_cell().begin_shapes_rec(l10))
r20 = pya.Region(ly.top_cell().begin_shapes_rec(l20))
r10.move(image_dist * shift_x, image_dist* shift_y)
ly.delete_layer(ly.layer(3, 0))
ly.top_cell().shapes(ly.layer(3, 0)).insert(r10 & r20)
pya.LayoutView.current().add_missing_layers()

@ -0,0 +1,116 @@
import pya
import os
base_dir = os.path.dirname(os.path.abspath(__file__))
# init vars
velocity_ratio1 = 1
opening1 = 4000
velocity_ratio2 = 5
opening2 = opening1 * velocity_ratio1 / velocity_ratio2
pixel_size = 20
shift_mult = 5
image_size = 4266 * pixel_size * 100 #calculate this directly (4266 and 4242 for shift_mult 5 and 3, respectively)
image_size_half = image_size / 2
image_dist = (shift_mult * 3 * 2 + 2) * pixel_size * 100
object_border = 0
#print(image_dist)
# create layout
layout = pya.Layout()
layout.dbu = 0.01
top = layout.create_cell("Top")
layer1_index = layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_index = layout.insert_layer(pya.LayerInfo.new(2, 0))
layer3_index = layout.insert_layer(pya.LayerInfo.new(3, 0))
layer4_index = layout.insert_layer(pya.LayerInfo.new(4, 0))
layer5_index = layout.insert_layer(pya.LayerInfo.new(5, 0))
# verniers
linear_grating_vernier = layout.create_cell("Vernier")
base_period = image_size_half - 500000
revealing_period = image_dist
pitch11 = (base_period * (revealing_period / velocity_ratio1)) / (base_period - (revealing_period / velocity_ratio1))
pitch12 = revealing_period / velocity_ratio1
#print(pitch11)
#print(pitch12)
frame_width = 300000
for i in range(-1 * int((image_size_half) / pitch11), int((image_size_half) / pitch11)):
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(opening1 / 2, -1 * frame_width, pitch11 - opening1 / 2, 0))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch11, 0)))
for i in range(-1 * int((image_size_half - image_dist) / pitch12), int((image_size_half - image_dist) / pitch12)):
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(opening1 / 2, -1 * frame_width, pitch12 - opening1 / 2, 0))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch12, 0)))
base_period = -1 * (image_size_half - 500000)
revealing_period = image_dist
pitch21 = (base_period * (revealing_period / velocity_ratio2)) / (base_period - (revealing_period / velocity_ratio2))
pitch22 = revealing_period / velocity_ratio2
for i in range(-1 * int(image_size_half / pitch21), int(image_size_half / pitch21)):
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(opening2 / 2, 0, pitch21 - opening2 / 2, frame_width))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch21, 0)))
for i in range(-1 * int((image_size_half - image_dist) / pitch22), int((image_size_half - image_dist) / pitch22)):
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(opening2 / 2, 0, pitch22 - opening2 / 2, frame_width))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(i * pitch22, 0)))
line = layout.create_cell("Line")
line.shapes(layer2_index).insert(pya.Box(image_size_half - (2 * image_dist), -1 * frame_width, image_size_half, 0))
line.shapes(layer2_index).insert(pya.Box(-1 * (image_size_half - (2 * image_dist)), -1 * frame_width, -1 * (image_size_half), 0))
line.shapes(layer2_index).insert(pya.Box(image_size_half - (2 * image_dist), image_dist, image_size_half, image_dist + frame_width))
line.shapes(layer2_index).insert(pya.Box(-1 * (image_size_half - (2 * image_dist)), image_dist, -1 * (image_size_half), image_dist + frame_width))
#These four lines can be taken away to get rid of the bounding black out
line.shapes(layer2_index).insert(pya.Box(-1 * image_size_half, image_dist, image_size_half, 0 - image_dist))
line.shapes(layer2_index).insert(pya.Box(-1 * image_size_half, -1 * (frame_width - image_dist), image_size_half, -1 * (frame_width + image_dist)))
line.shapes(layer2_index).insert(pya.Box(-1 * image_size_half, 0, image_size_half, image_dist))
line.shapes(layer2_index).insert(pya.Box(-1 * image_size_half, frame_width + (2 * image_dist), image_size_half, frame_width - image_dist))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
line = layout.create_cell("Line")
line.shapes(layer1_index).insert(pya.Box(image_size_half - image_dist, -1 * frame_width, image_size_half - (2 * image_dist), 0))
line.shapes(layer1_index).insert(pya.Box(-1 * (image_size_half - image_dist), -1 * frame_width, -1 * (image_size_half - (2 * image_dist)), 0))
line.shapes(layer1_index).insert(pya.Box(image_size_half - image_dist, 0, image_size_half - (2 * image_dist), frame_width))
line.shapes(layer1_index).insert(pya.Box(-1 * (image_size_half - image_dist), 0, -1 * (image_size_half - (2 * image_dist)), frame_width))
linear_grating_vernier.insert(pya.CellInstArray(line.cell_index(), pya.Trans(0, 0)))
top.insert(pya.CellInstArray(linear_grating_vernier.cell_index(), pya.Trans(0,0 )))
top.flatten(1)
top.write(os.path.join(base_dir, "..", "gds", "ud_vernier_test.gds"))
bb_region = pya.Region(pya.Box(-5000000, -1 * (frame_width + image_dist), 5000000, frame_width + (2 * image_dist)))
wafer1 = pya.Region(top.begin_shapes_rec(layer1_index))
wafer2 = pya.Region(top.begin_shapes_rec(layer2_index))
alignment_inv_layout = pya.Layout()
alignment_inv = alignment_inv_layout.create_cell("Alignment_Inverse")
alignment_inv_layout.dbu = 0.01
layer1_index = alignment_inv_layout.insert_layer(pya.LayerInfo.new(1, 0))
layer2_index = alignment_inv_layout.insert_layer(pya.LayerInfo.new(2, 0))
alignment_inv.shapes(layer1_index).insert(bb_region - wafer1)
alignment_inv.shapes(layer2_index).insert(bb_region - wafer2)
alignment_inv_layout.write(os.path.join(base_dir, "..", "gds", "inverted_tonality", "ud_vernier_test_inverse.gds"))

5
latex/.gitignore vendored

@ -0,0 +1,5 @@
*.pdf
*.tiff
*.jpg
*.xcf

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\relax
\catcode 95\active
\citation{*}
\bibstyle{unsrt}
\bibdata{hdp}
\bibcite{doi:10.1002/j.1538-7305.1961.tb03975.x}{1}
\bibcite{berger1966undecidability}{2}
\bibcite{Robinson1971}{3}
\bibcite{Grunbaum:1986:TP:19304}{4}
\bibcite{Kari:1996:SAS:245761.245817}{5}
\bibcite{DBLP:journals/corr/JeandelR15}{6}

@ -0,0 +1,33 @@
\begin{thebibliography}{1}
\bibitem{doi:10.1002/j.1538-7305.1961.tb03975.x}
Hao Wang.
\newblock Proving theorems by pattern recognition — ii.
\newblock {\em Bell System Technical Journal}, 40(1):1--41, 1961.
\bibitem{berger1966undecidability}
R.~Berger.
\newblock {\em The Undecidability of the Domino Problem}.
\newblock Memoirs ; No 1/66. American Mathematical Society, 1966.
\bibitem{Robinson1971}
Raphael~M. Robinson.
\newblock Undecidability and nonperiodicity for tilings of the plane.
\newblock {\em Inventiones mathematicae}, 12(3):177--209, Sep 1971.
\bibitem{Grunbaum:1986:TP:19304}
Branko Gr\"{u}nbaum and G~C Shephard.
\newblock {\em Tilings and Patterns}.
\newblock W. H. Freeman \& Co., New York, NY, USA, 1986.
\bibitem{Kari:1996:SAS:245761.245817}
Jarkko Kari.
\newblock A small aperiodic set of wang tiles.
\newblock {\em Discrete Math.}, 160(1-3):259--264, November 1996.
\bibitem{DBLP:journals/corr/JeandelR15}
Emmanuel Jeandel and Micha{\"{e}}l Rao.
\newblock An aperiodic set of 11 wang tiles.
\newblock {\em CoRR}, abs/1506.06492, 2015.
\end{thebibliography}

@ -0,0 +1,46 @@
This is BibTeX, Version 0.99d (TeX Live 2019/Arch Linux)
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Database file #1: hdp.bib
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@ -0,0 +1,281 @@
\documentclass[10pt]{letter}
\usepackage[a4paper, top=0.7in, bottom=0.7in, left=0.7in, right=0.7in]{geometry}
\usepackage{mathtools}
\usepackage{wasysym}
\usepackage{multicol}
\usepackage{dirtree}
\usepackage{underscore}
\usepackage{pdfpages}
\usepackage[framed,numbered]{sclang-prettifier}
\usepackage{listings}
\usepackage[obeyspaces]{url}
\usepackage{datetime2}
%\usepackage{draftwatermark}
\renewcommand{\arraystretch}{1.3}
\usepackage{graphicx}
\usepackage{enumitem}
\DTMsetdatestyle{default}
\DTMsetup{datesep={.}}
%\SetWatermarkColor[rgb]{1, 0.6, 0.6}
%\SetWatermarkScale{2}
%\SetWatermarkHorCenter{1.25in}
%\SetWatermarkVerCenter{1.25in}
% Define Language
\lstdefinelanguage{Lilypond}
{
% list of keywords
morekeywords={
}
}
% Set Language
\lstset{
numbers=left,
numberstyle=\small,
numberstyle = \color{black!33},
numbersep=8pt,
frame = single,
language={Lilypond},
}
\newenvironment{note}{
\vspace{-3mm}
\small
\par
\leftskip=4em\rightskip=5em
\noindent\ignorespaces}{\par\smallskip}
\makeatletter
\newenvironment{thebibliography}[1]
{\list{\@biblabel{\@arabic\c@enumiv}}%
{\settowidth\labelwidth{\@biblabel{#1}}%
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\@clubpenalty \clubpenalty
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{\def\@noitemerr
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\endlist}
\newcommand\newblock{\hskip .11em\@plus.33em\@minus.07em}
\makeatother
\begin{document}
\textit{\textbf{a history of the domino problem}} \\
a performance-installation
\begin{flushright}
michael winter \\ schloss solitude and cdmx; 2018 - 2019 \\
\end{flushright}
\bigskip
\begin{center}
\begin{tabular}{cc}
\centering
\includegraphics[width=0.49\linewidth]{selects/maquina.png}
\centering
\includegraphics[width=0.49\linewidth]{selects/discos.png}
\end{tabular}
\end{center}
\bigskip
\textbf{Description / note}
The domino problem, first posed by Hao Wang in 1961, is an epistemological question that asks whether there exists an algorithm to determine if an arbitrary finite set of tiles with colored edges can cover the plane such that adjacent edges match color. He conjectured that if a set of such tiles covers the plane, it can only do so periodically. However, in 1966, his student, Robert Berger, proved that the problem is undecidable (that is, there is no general algorithm) by showing the existence of a set of tiles that can only cover the plane aperiodically. This initial set contained more than 20000 tiles. Over the past 60 years, there has been a continual reduction in the size of provably aperiodic sets to the most recent discovery of a set of 11 tiles along with a proof that no smaller sets exist. It is a beautiful narrative / history of a particular epistemological problem that challenged a group of people not only to solve it, but to understand it to the extent possible.
\textit{a history of the domino problem} is a performance-installation that visualizes and sonifies aperiodic tilings in order to trace the history of the domino problem. The tilings are visualized using a cryptographic scheme in which two `shadow images', each which look completely random independently, are combined / overlayed at various orientations to reveal the tilings in a form that replaces the colored edges of the original constructions with binary codes. The shadow images are printed on photomasks typically used to manufacture computer chips: quartz wafers with a chrome coating etched at a pixel size of approximately 20 microns. A high-precision, motorized multiaxis stage aligns the shadow images to reveal the tilings (along with 3 other images of poetic texts inspired by the history of the domino problem). The whole apparatus rests on a light source that illuminates the photomasks which are then magnified and projected. The visualizations are accompanied by musical compositions generated from the tilings that can be realized live by performers as intermittent augmentations within the installation or as singular pieces in concert.
The aim of the work is to create an artistic experience that demonstrates the aesthetic qualities of these found mathematical objects while also functioning as a sort of historical record.
This is ultimately a piece about how things fit together.
\bigskip
\textbf{Installation and performance setting}
As an installation, the apparatus that aligns the image should be centered in a dark room such that observers can view the photomasks up close. Ideally, this should be set up with a teleprompter mirror at a 45 degree angle above the apparatus so that the viewer can see the photomasks without having to bend over. On the other side of the mirror, a video camera is placed such that the resulting projected image aligns with what the viewer sees in the teleprompter mirror. The camera side of the mirror must be darkened out with a cover in order to allow the viewer to only see the reflection of the photomasks. The projection should be as large as possible and at as high a resolution as possible. Ideally, the camera should be able to zoom into the images of the tilings to show more detail.
In the installation, recordings of the musical pieces are played back; sometimes randomly and sometimes in sync with the respective tilings from which they were generated. The installation can be augmented (e.g. for an exhibition opening) by live performances of the musical pieces instead of the recordings. If so, direct access to the apparatus should be avoided in order for a situation where the observers can view the projected images and listen to the musical accompaniment in a tranquil and focused environment.
A demo of the apparatus is available at: \url{https://vimeo.com/375784136}.
\bigskip
\textbf{Photomask alignment}
Between the two photomasks, there are nine embedded images which can be seen at nine precise orientation organized in a 3 x 3 grid. The image area is surrounded by Moire pattern and Vernier markings to aid in the alignment. Provided below are a description of each of these markings.
\begin{center}
\includegraphics[width=0.7\linewidth]{selects/oraclesannotated.jpg}
\end{center}
\begin{description}[labelindent=0.5cm]
\item [unidimensional Verniers:] These are the most useful markings for image alignment. For each axis, there are a set of coarse Verniers (bordering the image) and a set of fine Verniers (further from the image) which move 5 times the speed of the coarse Veniers. Everytime an image is aligned the white blob will be centered in both the coarse and fine Verniers. These markings essentially amplify and scale the distance between the image (640 microns) and can be used by a motion tracker in a closed-loop alignment system.
\item [multidimenional Verniers:] These are Verniers that are centered in a two-dimenional space everytime an image is focused.
\item [linear Moire grating:] These gratings can be used to make sure that the plates are aligned rotationally (resulting in a completely monochrome bar without any patterns).
\item [circular Moire grating:] These gratings best represent the grid of the images. When an image is aligned the respective grating on the grid will be dark. The number of fringes denotes the accuracy of the alignment (none means perfectly aligned).
\end{description}
High precision optical stages are used for the alignment of the wafers. Ideally, the wafers are not touching (separated by a few microns). If the wafers touch, they will degrade over time as they move across each other. However, it is very difficult to achieve perfect alignment without the photomasks touching as the they need to be aligned in all 6 degrees of freedom ($x$, $y$, $z$, $\theta x$, $\theta y$, and $\theta z$) in order for the resulting image to be properly produced. Only the $x$ and $y$ axis need to be moved to find the images once all the other degrees of freedom are set accurately.
The original setup is as follows. Each of the photomasks are mounted onto tilt stages to be able to align the masks together rotationally (note that a more ideal setup would use goniometer stages). One of the tilt / goniometer stages is then affixed to a stage with 3 degrees of freedom: $x$, $y$, and $z$. The other is fixed directly to an optical breadboard.
To automate the alignment, high precision motors are used to move one of the photomasks on the $x$ and $y$ axes. In the original setup, the high precision motors are stepper motors. If the photomasks are not touching, an open-loop system can be used to automate alignment. That is, the accuracy of the step count of the motors should be sufficient for alignment. However, if the photomasks need to touch in order to produce the resulting images (as is the often the case with the original setup), the friction between the two photomasks will cause inaccuracies in an open-loop system. To compensate for this, the Vernier markings can be tracked optically (using motion-tracking software or opto-interrupts) in order to create a closed-loop system. The software used to automate the system and control the motors is detailed in the following section.
\begin{center}
\includegraphics[width=0.7\linewidth]{selects/maquinalit.jpg}
\end{center}
\bigskip
\textbf{Overview of computer code}
As the code is subject to change / improvements, the current state of the code is available through a git repository at the following address: \url{https://gitea.unboundedpress.org/mwinter/a_history_of_the_domino_problem}. The respository contains the computer code needed to run the installation along with all the code that generated the musical pieces and all the code / schematics / files to rebuild the installation. Further, this document along with each of the scores is marked with the date it was generated in order to verify it is the most recent version.
The repository is organized by the various languages / formats used to generate the musical pieces and visualizations as well as control the installation. To start, I will focus on the software needed to control the installation which includes four basic components:
\begin{itemize}[labelindent=0.5cm]
\item A SuperCollider program with the filename \url{installation_control.scd}.
\item A GUI interface written using Open Stage Control with the filename \url{installation_control_gui.json}
\item A motion tracker written in Python using OpenCV to track the Verniers for a closed-loop system with the filename \url{vernier_tracker.py}
\item Arduino code to communicate between Supercollider and the stepper-motor drivers with the filename\\ \url{multistepper.ino}
\end{itemize}
In the original setup, the Arduino code is loaded onto the Arduino and the three other programs are loaded and launched on a computer (e.g., a Raspberry Pi) connected to the Arduino to control the system. The SuperCollider program is the main control center. Both the GUI and the motion tracker (which takes in video input from the video camera) communicate to the SuperCollider program through OSC messages, which, in turn, sends serial messages to the Arduino to control the stepper motors via the stepper motor drivers. The Arduino code not only sends messages to the stepper motor drivers, but also takes input signals from the limit switches of the motors to ensure that the motors are not destroyed by running into a hard stop.
All the other code (primarily written in SuperCollider) was written to generate the musical pieces as well as the visualizations and is maintained in the repository for reference. For the musical pieces, the SuperCollider code generates electronic realizations of the compositions and Lilypond files for generation of the musical scores.
The photomasks were printed from the GDSII file format (\url{*.gds}). The workflow consisted of \url{*.png} generated by SuperCollider and then formatted into \url{*.gds} files using the Python KLayout API. However, all that is needed to reprint the photomasks are the files \url{wafer_1.gds} and \url{wafer_2.gds}. Note that the the \url{*.gds} files along with all larger files are archived in a code releases available at \url{https://gitea.unboundedpress.org/mwinter/a_history_of_the_domino_problem/releases}. Again, all the other files in the repository are maintained for reference.
\bigskip
\textbf{Appendix: partial historical timeline of the domino problem, selected bibliography, acknowledgments, and tiling images}
pre-history:\\
\begin{tabular}{p{0.8in}p{1.25in}p{4.25in}}
17th century & Leibniz & pioneer of binary arithmetic and the idea of computing machines \\
ca 1928 & Hilbert & posed the original "Entsheidungsproblem" \\
ca 1931 & Goedel & first showed that their exists truths that are undecidable with a finite set of axioms \\
ca 1936 & Turing & invented the concept of the modern day computer and showed its limits yet was unfortunately persecuted for his sexuality despite being a key figure in the triumph of the allied nations against the nazi regime
\end{tabular}
conjecture and first proof:\\
\begin{tabular}{p{0.8in}p{1.25in}p{4.25in}}
ca 1961 & Wang & conjectured that aperiodic tilings of the plane did not exist \\
ca 1966 & Berger & showed that an aperiodic set 20000+ tiles exist (using his method this was quickly reduced to 104 then 92 by Berger and Knuth, respectively)
\end{tabular}
first wave of reduction:\\
\begin{tabular}{p{0.8in}p{1.25in}p{4.25in}}
ca 1971 & Robinson \& Lauchli & 56 and 40 tiles, respectively; using a similar technique of tiling arbitrarily large squares discovered independently
\end{tabular}
second wave of reduction:\\
\begin{tabular}{p{0.8in}p{1.25in}p{4.25in}}
ca 1986 & Penrose \& Amman & 32 and 16 tiles, respectively; using a method that translates different, non-squared aperiodic tiles into Wang tiles
\end{tabular}
third wave of reduction:\\
\begin{tabular}{p{0.8in}p{1.25in}p{4.25in}}
ca 1996 & Kari \& Culik & 13 tiles using an new construction with aperiodic integer sequences
\end{tabular}
final reduction\\
\begin{tabular}{p{0.8in}p{1.25in}p{4.25in}}
ca 2015 & Jaendel \& Rao & 11 tiles with an incredible computer-assisted proof that no smaller aperiodic sets exist
\end{tabular}
\bigskip
\nocite{*}
\bibliographystyle{unsrt}
\bibliography{hdp}
\bigskip
A special thanks to: Alice Koegel, Ana Filipovic\textsuperscript{$*$}, Angela Butterstein\textsuperscript{}, Anita Carey-Yard\textsuperscript{}, Aykan Safoğlu\textsuperscript{$*$}, Bjoern Gottstein, Charis von Ristok\textsuperscript{}, Christof Pruss, Daniela Kern-Michler\textsuperscript{§}, David Frühauf\textsuperscript{$*$}, David Mathews\textsuperscript{$*$}, Deborah Walker, Denise Helene Sumi\textsuperscript{$*$}, Didier Aschour, Edith Lázár\textsuperscript{$*$}, Elena Morena Weber\textsuperscript{$*$}, Elke aus dem Moore\textsuperscript{}, Elmar Mellert, Florian Hoelscher, Gaetan Borot, Helmut Dietz\textsuperscript{}, Irasema Fernandez, Johanna Markert\textsuperscript{$*$}, Julian Hartbaum\textsuperscript{}, Konstantin Lom\textsuperscript{}, Leon Müllner\textsuperscript{$*$}, Luise Boege\textsuperscript{$*$}, Lukas Ludwig\textsuperscript{$*$}, Luke Wilkins\textsuperscript{$*$}, Marieanne Roth\textsuperscript{}, Mathias Irmsher\textsuperscript{}, Mitra Wakil\textsuperscript{$*$}, Patrizia Bach\textsuperscript{$*$}, Philip Mecke\textsuperscript{$*$}, Robert Blatt\textsuperscript{$*$}, Sander Wickersheim\textsuperscript{}, Savyon\textsuperscript{$*$}, Silke Pflüger\textsuperscript{}, Sílvia das Fadas\textsuperscript{$*$}, Simar Preet Kaur\textsuperscript{$*$}, Sonja Flury\textsuperscript{}, Sophia Guggenberger\textsuperscript{$*$}, Sophie-Charlotte Thieroff\textsuperscript{}, Stephan Martens\textsuperscript{}, Susanna Flock\textsuperscript{$*$}, Tom Rosenberg\textsuperscript{$*$}, Vincenzo Talluto\textsuperscript{§}, and Yuval Shenhar\textsuperscript{$*$}.
* denotes contemporary resident at Akademie Schloss Solitude\\
† denotes Akademie Schloss Solitude staff\\
‡ denotes Institut für Mikroelektronik Stuttgart staff\\
§ denotes Newport Optics staff\\
\vspace{\fill}
\begin{flushright}
version generated: \today
\end{flushright}
\newpage
\vspace*{\fill}
\centering
\includegraphics[width=1\linewidth]{selects/berger.jpg}
Berger
\vspace*{\fill}
\newpage
\vspace*{\fill}
\centering
\includegraphics[width=1\linewidth]{selects/robinson.jpg}
Robinson
\vspace*{\fill}
\newpage
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\centering
\includegraphics[width=1\linewidth]{selects/penrose.jpg}
Penrose
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\newpage
\vspace*{\fill}
\centering
\includegraphics[width=1\linewidth]{selects/ammann.jpg}
Ammann
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\newpage
\vspace*{\fill}
\centering
\includegraphics[width=1\linewidth]{selects/kari.jpg}
Kari
\vspace*{\fill}
\newpage
\vspace*{\fill}
\centering
\includegraphics[width=1\linewidth]{selects/jaendel.jpg}
Jaendel-Rao
\vspace*{\fill}
\includepdf[pages={-}]{../berger/berger\string_score.pdf}
\includepdf[pages={-}]{../robinson/robinson\string_score.pdf}
\includepdf[pages={-}]{../penrose/penrose\string_score.pdf}
\includepdf[pages={-}]{../ammann/ammann\string_score.pdf}
\includepdf[pages={-}]{../kari/kari\string_score.pdf}
\includepdf[pages={-}]{../jaendel/jaendel\string_rao\string_score.pdf}
\end{document}

@ -0,0 +1,78 @@
@article{doi:10.1002/j.1538-7305.1961.tb03975.x,
author = {Wang, Hao},
title = {Proving Theorems by Pattern Recognition — II},
journal = {Bell System Technical Journal},
volume = {40},
number = {1},
pages = {1-41},
year = {1961}
}
@book{berger1966undecidability,
title={The Undecidability of the Domino Problem},
author={Berger, R.},
isbn={9780821812662},
series={Memoirs ; No 1/66},
url={https://books.google.com/books?id=mLfTCQAAQBAJ},
year={1966},
publisher={American Mathematical Society}
}
@Article{Robinson1971,
author="Robinson, Raphael M.",
title="Undecidability and nonperiodicity for tilings of the plane",
journal="Inventiones mathematicae",
year="1971",
month="Sep",
day="01",
volume="12",
number="3",
pages="177--209",
issn="1432-1297",
doi="10.1007/BF01418780",
url="https://doi.org/10.1007/BF01418780"
}
@book{Grunbaum:1986:TP:19304,
author = {Gr\"{u}nbaum, Branko and Shephard, G C},
title = {Tilings and Patterns},
year = {1986},
isbn = {0-716-71193-1},
publisher = {W. H. Freeman \& Co.},
address = {New York, NY, USA},
}
@article{Kari:1996:SAS:245761.245817,
author = {Kari, Jarkko},
title = {A Small Aperiodic Set of Wang Tiles},
journal = {Discrete Math.},
issue_date = {Nov. 15, 1996},
volume = {160},
number = {1-3},
month = nov,
year = {1996},
issn = {0012-365X},
pages = {259--264},
numpages = {6},
url = {http://dx.doi.org/10.1016/0012-365X(95)00120-L},
doi = {10.1016/0012-365X(95)00120-L},
acmid = {245817},
publisher = {Elsevier Science Publishers B. V.},
address = {Amsterdam, The Netherlands, The Netherlands},
}
@article{DBLP:journals/corr/JeandelR15,
author = {Emmanuel Jeandel and
Micha{\"{e}}l Rao},
title = {An aperiodic set of 11 Wang tiles},
journal = {CoRR},
volume = {abs/1506.06492},
year = {2015},
url = {http://arxiv.org/abs/1506.06492},
archivePrefix = {arXiv},
eprint = {1506.06492},
timestamp = {Mon, 13 Aug 2018 16:48:45 +0200},
biburl = {https://dblp.org/rec/bib/journals/corr/JeandelR15},
bibsource = {dblp computer science bibliography, https://dblp.org}
}

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\textit{\textbf{ammann}} \\
\normalsize
from \textit{a history of the domino problem}\\
for 5 to 8 sustaining instruments
\bigskip
\bigskip
\normalsize
The ensemble can play any 5 or more parts (preferably as many as possible) and any 8 or more adjacent sections. If the ensemble starts after the first section (the 2nd through 13th sections), the performers should start on the first note that has an onset within the first measure of the section (replacing the tied note from the last measure of the previous section with a rest). If ending before the final section (the 8th through 19th sections), the last note of each part should be the note tied over from the penultimate measure of the section. Each part should be as distinct in timbre as possible.
All the parts are notated within one octave. Written above each note is an up or down arrow indicating whether the pitch be played high or low. That is, in each part, each pitch-class can occur in one of two ways: in either a higher register or a lower one (the up / down arrows should be interpreted in the same respective register throughout). Which registers are selected for each note in each part is open, but should be selected such that there is some overlap / pitch duplications among the parts and some separation. Limiting the overlap will naturally stratify the registers of the parts. The part number should generally correspond to its relative register (i.e. part 2 should be generally higher than part 1). The ensemble can explore replacing pitches of one to two of the parts with various non-pitched percussion instruments with relatively long decays. The up and down arrows would then be interpreted as two different types of the same instrument (e.g. two sizes of triangles).
The pitches of the piece are derived from a rational tuning systems based on the harmonic series. The notes in the score may be interpreted to the nearest quarter-tone (as written), or preferably with the following cent deviations given from the nearest pitch in 24-tone equal temperament.
\bigskip
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\bigskip
\footnotesize
*This piece is part of a large-scale performance-installation titled \textit{a history of the domino problem}. It may be played alone or alongside other pieces from \textit{a history of the domino problem}. Instructions are given in the score detailing the superordinate, large-scale work.
\normalsize
\vspace{\fill}
\begin{flushright}
michael winter\\
(schloss solitude, stuttgart and calle monclova 62, mexico city; 2018-19)\\
version generated: \today
\end{flushright}
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@ -0,0 +1,64 @@
\documentclass[10pt]{letter}
\usepackage[a4paper, top=0.7in, bottom=0.7in, left=0.70in, right=0.70in]{geometry}
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\begin{document}
\thispagestyle{empty}
\large
\textit{\textbf{berger-knuth}} \\
\normalsize
from \textit{a history of the domino problem}\\
for 3 or 6 sustaining instruments
\bigskip
\bigskip
\normalsize
The parts of the score are divided into two groups: `a' and `b'. Either group `a' or group `b' can be performed, but preferably both. Each part should be as distinct in timbre as possible, especially for the same part number between the two groups (e.g. 1a and 1b should be performed with different types of instruments). If only one group is interpreted, the tempo should be faster (more towards 90 beats per minute). If both groups are interpreted, the tempo should be slower (more towards 60 beats per minute). The tempo can also be slightly different for each section.
The ensemble can play any 2 or more adjacent sections. If the ensemble starts after the first section (the 2nd through 5th sections), the performers should start on the first note that has an onset within the first measure of the section (replacing the tied note from the last measure of the previous section with a rest). If ending before the final section (again, the 2nd through 5th sections), the last note of each part should be the note tied over from the penultimate measure of the section.
Generally soft and dynamically flat throughout with tones that decay over the duration of the note after the initial attack. Each part has three dynamic levels: \textit{p}, \textit{mp}, and \textit{mf}. However, part 1 should be softer than part 2 which should be softer than part 3. Performers may occasionally omit or cut short a note in order to breathe or give a sense of phrasing.
The pitches of the piece are derived from a rational tuning system. The notes in the score may be interpreted to the nearest quarter-tone (as written) or with the following cent deviations given from the nearest pitch in 24-tone equal temperament.
\bigskip
\includegraphics[scale=0.75]{berger\string_pitches.pdf}
\bigskip
\bigskip
\footnotesize
*This piece is part of a large-scale performance-installation titled \textit{a history of the domino problem}. It may be played alone or alongside other pieces from \textit{a history of the domino problem}. Instructions are given in the score detailing the superordinate, large-scale work.
\normalsize
\vspace{\fill}
\begin{flushright}
michael winter\\
(schloss solitude, stuttgart and calle monclova 62, mexico city; 2018-19)\\
version generated: \today
\end{flushright}
\includepdf[pages={-}]{../../score/lilypond/berger\string_knuth/berger\string_knuth.pdf}
\end{document}

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eeh'''4_\markup{23}^\markup{ \center-align{-22}}
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dih''4_\markup{11}^\markup{ \center-align{+1}}
s4
b'4_\markup{9}^\markup{ \center-align{+4}}
s4
geh'4_\markup{7}^\markup{ \center-align{+19}}
s4
cis'4_\markup{5}^\markup{ \center-align{-14}}
\clef bass
s4
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s4
a,,4_\markup{1}^\markup{ \center-align{+0}}
}
>>

@ -0,0 +1,8 @@
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\documentclass[10pt]{letter}
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\begin{document}
\thispagestyle{empty}
\large
\textit{\textbf{jaendel-rao}} \\
\normalsize
from \textit{a history of the domino problem}\\
for sustaining instruments
\bigskip
\bigskip
\normalsize
Provided are scores for two versions of this piece: reduced and full. The instructions for the pieces are essentially the same but the reduced version allows for fewer instrumental resources.
Each part is notated in two `voices': one below the center line and one above. Together, the various combinations indicate 4 ways of producing a pitched-tone which means that each pitch must be able to be played in one of the 4 following ways. 1) a rest written on the center line between the two voice indicates silence, 2) and 3) a rest in one voice with a note in the other indicates to produce the tone in one way or the other pending in which voice the note is given, and 4) a note above and below the center line indicates that both ways of producing the tone must be played together. As such, each part must be taken by an instrument that can play the same pitch in two ways at the same time; e.g. a double stop on a stringed instrument. Or, two instruments can be assigned to the same part; one playing the upper voice and the other playing the lower voice. For the latter, if the instruments are similar in timbre, they should be dislocated in space to give further distinction between the two voice. Another option is to use electronics and / or amplification to create the voice distinction; e.g. the performer sustains the tone throughout the piece and the 4 types of distinctions are as follows: 1) a rest written on the center line between the two voice indicates no amplification, 2) and 3) a rest in one voice with a note in the other indicates that the tone is amplified in either the left or right speaker pending in which voice the note is given, and 4) a note above and below the center line indicates that the tone is amplified through both speakers. The ensemble can explore other simple methods of distinction using one instrument per part (e.g. four dynamic levels or four tremolo speeds), but the previous options are preferred.
The ensemble can choose to perform any 4 or more sections (preferable more / all). Note that the sections are offset for each successively entering voice. The entrance and exit of each note should be rather abrupt / binary. However, the part as a whole should fade in at the beginning of a section and fade out at the end of a section. Crescendo and decrescendo markings indicate the start of the fade which should last 4 measures from the mark. If the (de)crescendo markings are given where there are rests on the center line, there may not be a fade at all if a centered rest is interpreted as silence. The peak amplitude should be quite present and equal for all parts.
As mentioned above, each part plays one pitch. The pitches are derived from adjacent odd harmonics of a harmonic series based on an arbitrary fundamental. These should be played as precisely as possible in the register they occur in the harmonic series. Given below is an example series based on an a fundamental of a low `a' with cent deviations given from the nearest pitch in 24-tone equal temperament. Note that each part enters from high to low and are labeled accordingly.
\bigskip
\includegraphics[scale=0.75]{jaendel\string_pitches.pdf}
\bigskip
\bigskip
\footnotesize
*This piece is part of a large-scale performance-installation titled \textit{a history of the domino problem}. It may be played alone or alongside other pieces from \textit{a history of the domino problem}. Instructions are given in the score detailing the superordinate, large-scale work.
\normalsize
\vspace{\fill}
\begin{flushright}
michael winter\\
(schloss solitude, stuttgart and calle monclova 62, mexico city; 2018-19)\\
version generated: \today
\end{flushright}
\includepdf[pages={-}]{../../score/lilypond/jaendel\string_rao/jaendel\string_rao\string_reduced.pdf}
\includepdf[pages={-}]{../../score/lilypond/jaendel\string_rao/jaendel\string_rao\string_full.pdf}
\end{document}

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\documentclass[10pt]{letter}
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\begin{document}
\thispagestyle{empty}
\large
\textit{\textbf{kari-culik}} \\
\normalsize
from \textit{a history of the domino problem}\\
for sustaining instruments and noise / percussion
\bigskip
\bigskip
\normalsize
The piece consists of a set of `ensemble' instruments notated in the top staff group along with a bass part and a noise / percussion part notated in the bottom staff group. At least 3 of the ensemble parts should be performed (but preferably all). Each of the the ensemble parts span several octaves. To the extent possible, each pitch should be played in the written register. If a single instrument cannot cover the entire range, the part may be played by two instruments. Another option is to transpose or omit notes that are out of range while maintaining a generally open registral spacing and ensuring that the piece does not feel too sparse / empty. Each ensemble part should be as distinct in timbre as possible.
The ensemble can play any 4 or more adjacent sections. If the ensemble starts after the first section (the 2nd through 7th sections), the performers should ignore that the note is tied from a note in the previous measure (the last measure of the previous section). If ending before the final section (the 4th through 9th sections), the performers should ignore that the note is tied to a note in the following measure (the first measure of the following section).
Each note of the ensemble parts should have a dynamic curve as shown in the plot below entering and exiting as softly as possible with a peak dynamic between mezzo-piano and mezzo-forte (as such, the piece should feel relatively soft and tranquil throughout).
\includegraphics[scale=0.25]{dynamic\string_curve.pdf}
Each tone of the bass part should have a more defined, consistent onset that then decays throughout the rest of the tone duration. That is, the duration of the onset is not defined by the length of the tone as with the dynamic curve of the ensemble parts.
Each line of the noise part should be interpreted as different registers of noise (e.g. a relatively lower noise, and a relatively high noise). The noise should crescendo throughout the duration of the written note to a peak dynamic still below the general peak dynamic of the ensemble. At the end of the written duration of the note, the tone can be allowed to decay naturally or decrescendo over a period of a few seconds. Therefore, each line will need to be played on a different instrument. A suitable example would be tremolos on two different symbols with different noise registers.
\bigskip
\bigskip
\footnotesize
*This piece is part of a large-scale performance-installation titled \textit{a history of the domino problem}. It may be played alone or alongside other pieces from \textit{a history of the domino problem}. Instructions are given in the score detailing the superordinate, large-scale work.
\normalsize
\vspace{\fill}
\begin{flushright}
michael winter\\
(schloss solitude, stuttgart and calle monclova 62, mexico city; 2018-19)\\
version generated: \today
\end{flushright}
\includepdf[pages={-}]{../../score/lilypond/kari\string_culik/kari\string_culik.pdf}
\end{document}

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@ -0,0 +1,62 @@
\documentclass[10pt]{letter}
\usepackage[a4paper, top=0.7in, bottom=0.7in, left=0.70in, right=0.70in]{geometry}
\usepackage{underscore}
\usepackage[obeyspaces]{url}
\usepackage{verbatim}
\usepackage{pdfpages}
\usepackage{datetime2}
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\begin{document}
\thispagestyle{empty}
\large
\textit{\textbf{penrose}} \\
\normalsize
from \textit{a history of the domino problem}\\
for 4 to 6 sustaining instruments
\bigskip
\bigskip
\normalsize
The ensemble can play any 4 or more parts (preferably as many as possible) and any 8 or more adjacent sections. The ensemble can explore replacing pitches of the one of the outer parts with various non-pitched percussion instruments with relatively long decays.
The piece should feel rather tranquil with a relatively constant dynamic throughout the piece. Parts with a higher temporal density at any given point should rise slightly above the rest of the ensemble. This sense of phrasing should come out naturally based on the temporal density alone, but can be further articulated by the performers applying a subtle swell over sequences of notes with relatively shorter durations. As a result, each section should be heard as a series of undulations / breaths. Performers may also occasionally omit or cut short a note in order to breathe or give a sense of phrasing.
Pitches can be transposed by an octave if necessary while maintaining relatively distinct registers among the parts to the extent possible. The pitches of the piece are derived from a rational tuning systems. The notes in the score may be interpreted to the nearest quarter-tone (as written), or preferably with the following cent deviations given from the nearest pitch in 24-tone equal temperament.
\bigskip
\includegraphics[scale=0.75]{penrose\string_pitches.pdf}
\bigskip
\bigskip
\footnotesize
*This piece is part of a large-scale performance-installation titled \textit{a history of the domino problem}. It may be played alone or alongside other pieces from \textit{a history of the domino problem}. Instructions are given in the score detailing the superordinate, large-scale work.
\normalsize
\vspace{\fill}
\begin{flushright}
michael winter\\
(schloss solitude, stuttgart and calle monclova 62, mexico city; 2018-19)\\
version generated: \today
\end{flushright}
\includepdf[pages={-}]{../../score/lilypond/penrose/penrose.pdf}
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\documentclass[10pt]{letter}
\usepackage[a4paper, top=0.7in, bottom=0.7in, left=0.70in, right=0.70in]{geometry}
\usepackage{underscore}
\usepackage[obeyspaces]{url}
\usepackage{verbatim}
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\begin{document}
\thispagestyle{empty}
\large
\textit{\textbf{robinson}} \\
\normalsize
from \textit{a history of the domino problem}\\
for 4 to 8 sustaining instruments
\bigskip
\bigskip
\normalsize
The ensemble can play any 4 or more adjacent parts (preferably as many as possible) and any 4 or more adjacent sections. The tempo (marked between 60 and 90 beats per second) can be derived from the number of players such that the more the performers, the slower the tempo. The tempo can also be slightly different for each section.
Each tone should be played as a swell that enters from and exits to as soft a dynamic as possible. The peak dynamic of the swell is given below the beginning of each note.
The pitches of the piece are derived from a rational tuning series based on the harmonic series. The notes in the score should be interpreted with the following cent deviations given from the nearest pitch in 24-tone equal temperament as accurately as possible.
\bigskip
\includegraphics[scale=0.75]{robinson\string_pitches.pdf}
\bigskip
\bigskip
\footnotesize
*This piece is part of a large-scale performance-installation titled \textit{a history of the domino problem}. It may be played alone or alongside other pieces from \textit{a history of the domino problem}. Instructions are given in the score detailing the superordinate, large-scale work.
\normalsize
\vspace{\fill}
\begin{flushright}
michael winter\\
(schloss solitude, stuttgart and calle monclova 62, mexico city; 2018-19)\\
version generated: \today
\end{flushright}
\includepdf[pages={-}]{../../score/lilypond/robinson/robinson.pdf}
\end{document}

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@ -0,0 +1,9 @@
<html>
<head>
<title>Video Streaming Demonstration</title>
</head>
<body>
<h1>Video Streaming Demonstration</h1>
<img src="{{ url_for('video_feed') }}">
</body>
</html>

@ -0,0 +1,162 @@
#This is a proof of concept for motion tracking of the vernier in very early stages
import cv2
import sys
from pythonosc.udp_client import SimpleUDPClient
from flask import Flask, render_template, Response
import threading
import argparse
outputFrame = None
lock = threading.Lock()
app = Flask(__name__)
ip = "127.0.0.1"
port = 57120
client = SimpleUDPClient(ip, port) # Create client
# Read video (eventually will be the live capture from the camera)
video = cv2.VideoCapture("/home/mwinter/Portfolio/a_history_of_the_domino_problem/a_history_of_the_domino_problem/recs/a_history_of_the_domino_problem_final_documentation_hq.mp4")
# Exit if video not opened.
if not video.isOpened():
print("Could not open video")
sys.exit()
# Read first frame.
video.set(cv2.CAP_PROP_POS_FRAMES, 5000)
ok, initFrame = video.read()
if not ok:
print('Cannot read video file')
sys.exit()
#frame = cv2.cvtColor(frame, cv2.COLOR_RGB2GRAY)
#frame = cv2.GaussianBlur(frame,(5,5),cv2.BORDER_DEFAULT)
# all this for selecting ROI
#xROI = cv2.selectROI('Tracking', initFrame)
#yROI = cv2.selectROI('Tracking', initFrame)
#print(xROI)
#print(yROI)
#xFine = (xROI[0], xROI[1], xROI[2], xROI[3] / 2)
#xCourse = (xROI[0], xROI[1] + (xROI[3] / 2), xROI[2], xROI[3] / 2)
#yFine = (yROI[0], yROI[1], yROI[2] / 2, yROI[3])
#yCourse = (yROI[0] + (yROI[2] / 2), yROI[1], yROI[2] / 2, yROI[3])
#print(xFine)
#print(yFine)
xFine = (848, 187, 225, 21.0)
yFine = (604, 402, 20.5, 276)
frameCountMod = 0
centroidX = [0, 0]
centroidY = [0, 0]
def track(frame, ROI, centroid, update):
if(update):
crop = frame[int(ROI[1]):int(ROI[1]+ROI[3]), int(ROI[0]):int(ROI[0]+ROI[2])]
crop = cv2.cvtColor(crop, cv2.COLOR_RGB2GRAY)
crop = cv2.GaussianBlur(crop,(7,7),cv2.BORDER_DEFAULT)
#ret, thresh = cv2.threshold(crop, 100, 255, cv2.THRESH_OTSU + cv2.THRESH_BINARY)
ret,thresh = cv2.threshold(crop, 50, 255, 0)
M = cv2.moments(thresh)
# calculate x,y coordinate of center
if M["m00"] != 0:
centroid[0] = int(M["m10"] / M["m00"])
centroid[1] = int(M["m01"] / M["m00"])
#else:
# cX, cY = 0, 0
#print(cY)
cv2.circle(frame, (int(ROI[0]) + centroid[0], int(ROI[1]) + centroid[1]), 5, (255, 255, 255), -1)
def detect_motion():
# grab global references to the video stream, output frame, and
# lock variables
global vs, outputFrame, lock
frameCountMod = 0
centroidX = [0, 0]
centroidY = [0, 0]
"""Video streaming generator function."""
while True:
# Read a new frame
ok, frame = video.read()
if not ok:
break
if(frameCountMod == 0):
track(frame, xFine, centroidX, True)
track(frame, yFine, centroidY, True)
xPos = (centroidX[0] / xFine[2]) * 2 - 1
yPos = (centroidY[1] / yFine[3]) * 2 - 1
client.send_message("/trackerpos", [xPos, yPos])
else:
track(frame, xFine, centroidX, False)
track(frame, yFine, centroidY, False)
frameCountMod = (frameCountMod + 1) % 10
cv2.rectangle(frame, (int(xFine[0]), int(xFine[1])), (int(xFine[0]+int(xFine[2])),int(xFine[1]+xFine[3])), (255, 255, 255), 5)
cv2.rectangle(frame, (int(yFine[0]), int(yFine[1])), (int(yFine[0]+int(yFine[2])),int(yFine[1]+yFine[3])), (255, 255, 255), 5)
# Display result
#cv2.imshow("Tracking", frame)
#cv2.imshow("Crop", crop)
with lock:
outputFrame = frame.copy()
# Exit if ESC pressed
#k = cv2.waitKey(1) & 0xff
#if k == 27 :
# cv2.destroyWindow('Tracking')
# break
@app.route('/')
def index():
"""Video streaming home page."""
return render_template('index.html')
def generate():
# grab global references to the output frame and lock variables
global outputFrame, lock
# loop over frames from the output stream
while True:
# wait until the lock is acquired
with lock:
# check if the output frame is available, otherwise skip
# the iteration of the loop
if outputFrame is None:
continue
# encode the frame in JPEG format
(flag, encodedImage) = cv2.imencode(".jpg", outputFrame)
# ensure the frame was successfully encoded
if not flag:
continue
# yield the output frame in the byte format
yield(b'--frame\r\n' b'Content-Type: image/jpeg\r\n\r\n' +
bytearray(encodedImage) + b'\r\n')
@app.route('/video_feed')
def video_feed():
"""Video streaming route. Put this in the src attribute of an img tag."""
return Response(generate(),mimetype='multipart/x-mixed-replace; boundary=frame')
if __name__ == '__main__':
t = threading.Thread(target=detect_motion)
t.daemon = True
t.start()
app.run(host='10.0.0.5', threaded=True)

2
recs/.gitignore vendored

@ -0,0 +1,2 @@
*.wav
*.mp4

@ -0,0 +1,212 @@
\version "2.19.81"
genStaff =
#(define-music-function (parser location part)
(string?)
(let * ((file (string-append "includes/ammann_part_" part ".ly")))
#{
\new Staff \with {
instrumentName = #part
shortInstrumentName = #part
}
<<
\include #file
>>
#}))
\paper {
#(set-paper-size "a4" 'portrait)
top-margin = 1 \cm
bottom-margin = 1 \cm
left-margin = 1.75 \cm
top-system-spacing =
#'((basic-distance . 15 )
(minimum-distance . 15 )
(padding . 0 )
(stretchability . 0))
last-bottom-spacing =
#'((basic-distance . 15 )
(minimum-distance . 15 )
(padding . 0 )
(stretchability . 0))
systems-per-page = 2
print-page-number = ##t
oddHeaderMarkup = \markup { \on-the-fly #not-first-page "(ammann)" }
evenHeaderMarkup = \markup { \on-the-fly #not-first-page "(ammann)" }
oddFooterMarkup = \markup { \fill-line {
\on-the-fly #not-first-page
\concat {
"-"
\fontsize #1.5
\on-the-fly #print-page-number-check-first
\fromproperty #'page:page-number-string
"-"}}}
evenFooterMarkup = \markup { \fill-line {
\on-the-fly #not-first-page
\concat {
"-"
\fontsize #1.5
\on-the-fly #print-page-number-check-first
\fromproperty #'page:page-number-string
"-"}}}
}
\header {
title = \markup { \italic {ammann}}
subtitle = \markup { \normal-text { from \italic{a history of the domino the problem}}}
composer = \markup \right-column {"michael winter" "(schloss solitude, stuttgart and calle monclova 62, mexico city; 2018-19)"}
tagline = ""
}
#(set-global-staff-size 11)
\layout {
indent = 0.0\cm
line-width = 17\cm
%ragged-last = ##t
\context {
\Score
\override BarNumber.extra-offset = #'(0 . 4)
\override BarNumber.stencil = #(make-stencil-circler 0.1 0.25 ly:text-interface::print)
\override RehearsalMark #'direction = #DOWN
}
\context {
\Staff
\override VerticalAxisGroup.staff-staff-spacing =
#'((basic-distance . 15 )
(minimum-distance . 15 )
(padding . 0 )
(stretchability . 0))
\override TimeSignature.font-size = #2
\override TimeSignature.break-align-symbol = #'clef
\override TimeSignature.X-offset =
#ly:self-alignment-interface::x-aligned-on-self
\override TimeSignature.self-alignment-X = #LEFT
%\override TimeSignature.after-line-breaking =
% #shift-right-at-line-begin
\override TimeSignature.Y-offset = #9
\override TimeSignature.extra-offset = #'(2 . 0)
}
\context {
\StaffGroup
\name "SemiStaffGroup"
\consists "Span_bar_engraver"
\override SpanBar.stencil =
#(lambda (grob)
(if (string=? (ly:grob-property grob 'glyph-name) "|")
(set! (ly:grob-property grob 'glyph-name) ""))
(ly:span-bar::print grob))
}
\context {
\Score
\accepts SemiStaffGroup
}
}
\score {
%showLastLength = R1*128
\new Score
%\with{ proportionalNotationDuration = #(ly:make-moment 1 16) }
<<
\new SemiStaffGroup {
<<
\new Staff \with {
instrumentName = #"8"
shortInstrumentName = #"8"
midiInstrument = #"clarinet"
}
<<
\include "includes/ammann_part_0.ly"
>>
\new Staff \with {
instrumentName = #"7"
shortInstrumentName = #"7"
midiInstrument = #"clarinet"
\remove "Time_signature_engraver"
}
<<
\include "includes/ammann_part_1.ly"
>>
\new Staff \with {
instrumentName = #"6"
shortInstrumentName = #"6"
midiInstrument = #"clarinet"
\remove "Time_signature_engraver"
}
<<
\include "includes/ammann_part_2.ly"
>>
\new Staff \with {
instrumentName = #"5"
shortInstrumentName = #"5"
midiInstrument = #"clarinet"
\remove "Time_signature_engraver"
}
<<
\include "includes/ammann_part_3.ly"
>>
\new Staff \with {
instrumentName = #"4"
shortInstrumentName = #"4"
midiInstrument = #"clarinet"
\remove "Time_signature_engraver"
}
<<
\include "includes/ammann_part_4.ly"
>>
\new Staff \with {
instrumentName = #"3"
shortInstrumentName = #"3"
midiInstrument = #"clarinet"
\remove "Time_signature_engraver"
}
<<
\include "includes/ammann_part_5.ly"
>>
\new Staff \with {
instrumentName = #"2"
shortInstrumentName = #"2"
midiInstrument = #"clarinet"
\remove "Time_signature_engraver"
}
<<
\include "includes/ammann_part_6.ly"
>>
\new Staff \with {
instrumentName = #"1"
shortInstrumentName = #"1"
midiInstrument = #"clarinet"
\remove "Time_signature_engraver"
}
<<
\include "includes/ammann_part_7.ly"
>>
%\genStaff #"0"
%\genStaff #"1"
%\genStaff #"2"
%\genStaff #"3"
%\genStaff #"4"
%\genStaff #"5"
>>
}
>>
\layout { }
\midi { }
}

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\version "2.19.81"
genStaff =
#(define-music-function (parser location part)
(string?)
(let * ((file (string-append "includes/berger_part_" part ".ly")))
#{
\new Staff \with {
instrumentName = #part
shortInstrumentName = #part
}
<<
\include #file
>>
#}))
\paper {
#(set-paper-size "a4" 'portrait)
top-margin = 1 \cm
bottom-margin = 1 \cm
left-margin = 1.75 \cm
top-system-spacing =
#'((basic-distance . 25 )
(minimum-distance . 25 )
(padding . 0 )
(stretchability . 0))
last-bottom-spacing =
#'((basic-distance . 15 )
(minimum-distance . 15 )
(padding . 0 )
(stretchability . 0))
systems-per-page = 3
print-page-number = ##t
oddHeaderMarkup = \markup { \on-the-fly #not-first-page "(berger-knuth)" }
evenHeaderMarkup = \markup { \on-the-fly #not-first-page "(berger-knuth)" }
oddFooterMarkup = \markup { \fill-line {
\on-the-fly #not-first-page
\concat {
"-"
\fontsize #1.5
\on-the-fly #print-page-number-check-first
\fromproperty #'page:page-number-string
"-"}}}
evenFooterMarkup = \markup { \fill-line {
\on-the-fly #not-first-page
\concat {
"-"
\fontsize #1.5
\on-the-fly #print-page-number-check-first
\fromproperty #'page:page-number-string
"-"}}}
}
\header {
title = \markup { \italic {berger-knuth}}
subtitle = \markup { \normal-text { from \italic{a history of the domino the problem}}}
composer = \markup \right-column {"michael winter" "(schloss solitude, stuttgart and calle monclova 62, mexico city; 2018-19)"}
tagline = ""
}
#(set-global-staff-size 11)
\layout {
indent = 0.0\cm
line-width = 17\cm
%ragged-last = ##t
\context {
\Score
\override BarNumber.extra-offset = #'(0 . 4)
\override BarNumber.stencil = #(make-stencil-circler 0.1 0.25 ly:text-interface::print)
\override RehearsalMark #'direction = #DOWN
}
\context {
\Staff
\override VerticalAxisGroup.staff-staff-spacing =
#'((basic-distance . 13 )
(minimum-distance . 13 )
(padding . 0 )
(stretchability . 0))
\override TimeSignature.font-size = #2
\override TimeSignature.break-align-symbol = #'clef
\override TimeSignature.X-offset =
#ly:self-alignment-interface::x-aligned-on-self
\override TimeSignature.self-alignment-X = #LEFT
%\override TimeSignature.after-line-breaking =
% #shift-right-at-line-begin
\override TimeSignature.Y-offset = #9
\override TimeSignature.extra-offset = #'(2 . 0)
}
\context {
\StaffGroup
\name "SemiStaffGroup"
\consists "Span_bar_engraver"
\override SpanBar.stencil =
#(lambda (grob)
(if (string=? (ly:grob-property grob 'glyph-name) "|")
(set! (ly:grob-property grob 'glyph-name) ""))
(ly:span-bar::print grob))
}
\context {
\Score
\accepts SemiStaffGroup
}
}
\score{
%showLastLength = R1*128
\new Score
%\with{ proportionalNotationDuration = #(ly:make-moment 1 16) }
<<
\new SemiStaffGroup {
<<
\new Staff \with {
instrumentName = #"1a"
shortInstrumentName = #"1a"
midiInstrument = #"flute"
}
<<
\include "includes/berger_part_3.ly"
>>
\new Staff \with {
instrumentName = #"2a"
shortInstrumentName = #"2a"
midiInstrument = #"clarinet"
\remove "Time_signature_engraver"
}
<<
\include "includes/berger_part_2.ly"
>>
\new Staff \with {
instrumentName = #"3a"
shortInstrumentName = #"3a"
midiInstrument = #"viola"
\remove "Time_signature_engraver"
}
<<
\include "includes/berger_part_1.ly"
>>
>>
}
\new SemiStaffGroup {
<<
\new Staff \with {
instrumentName = #"1b"
shortInstrumentName = #"1b"
midiInstrument = #"cello"
\remove "Time_signature_engraver"
}
<<
\include "includes/berger_part_7.ly"
>>
\new Staff \with {
instrumentName = #"2b"
shortInstrumentName = #"2b"
midiInstrument = #"saxophone"
\remove "Time_signature_engraver"
}
<<
\include "includes/berger_part_6.ly"
>>
\new Staff \with {
instrumentName = #"3b"
shortInstrumentName = #"3b"
midiInstrument = #"bassoon"
\remove "Time_signature_engraver"
}
<<
\include "includes/berger_part_5.ly"
>>
%\genStaff #"0"
%\genStaff #"1"
%\genStaff #"2"
%\genStaff #"3"
%\genStaff #"4"
%\genStaff #"5"
>>
}
>>
\midi{}
\layout{}
}

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<<
\numericTimeSignature
{
\override RehearsalMark.X-offset = #1 \override RehearsalMark.Y-offset = #4
\override Stem.details.beamed-lengths = #'(5)
\set Score.markFormatter = #format-mark-box-numbers
\tempo \markup {
\concat {
\smaller \general-align #Y #DOWN
\note #"4" #1 \normal-text " ≈ 90"
}}
s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default e''1 | s1 | r2 e''2 ~ | e''2 r2 | e''2 r2 | s1 | r2 e''2 ~ | e''2 r2 | s1 | s1 | r2 e''2 ~ | e''2 r2 | s1 | e''1 | r2 e''2 | s1 | s1 | e''1 | s1 | s1 | s1 | e''2 r2 | s1 | r2 e''2 ~ | e''2 r2 | e''2 r2 | s1 | r2 e''2 | s1 | s1 | s1 | s1 | \mark \default s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''2 r2 | s1 | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 | s1 | s1 | s1 | s1 | \mark \default e''1 ~ | e''2 r2 | e''1 | r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''1 ~ | e''1 | r2 e''2 ~ | e''2 r2 | e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 | r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''1 | s1 | s1 | s1 | s1 | \mark \default s1 | s1 | s1 | s1 | r2 e''2 | s1 | s1 | s1 | s1 | s1 | s1 | e''1 | s1 | s1 | s1 | e''2 r2 | s1 | s1 | s1 | s1 | s1 | r2 e''2 ~ | e''2 r2 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | r2 e''2 ~ | e''2 r2 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default e''1 | r2 e''2 ~ | e''1 ~ | e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''2 r2 | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 | s1 | s1 | s1 | s1 | \mark \default e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''1 ~ | e''1 | r2 e''2 ~ | e''2 r2 | e''2 r2 | e''1 | r2 e''2 ~ | e''2 r2 | e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''1 ~ | e''1 | r2 e''2 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 ] \bar "|." }
\\
{
\override RehearsalMark.direction = #DOWN \override RehearsalMark.X-offset = #2 \override RehearsalMark.Y-offset = #-8
\override Stem.details.beamed-lengths = #'(5)
\set Score.markFormatter = #format-mark-box-numbers
\tempo \markup {
\concat {
\smaller \general-align #Y #DOWN
\note #"4" #1 \normal-text " ≈ 90"
}}
s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } r2 f'2 ~ | f'1 ~ | f'2 r2 | f'1 | r2 f'2 ~ | f'1 ~ | f'2 r2 | f'1 ~ | f'1 ~ | f'1 ~ | f'2 r2 | f'1 ~ | f'1 | r2 f'2 ~ | f'2 r2 | f'1 ~ | f'1 | r2 f'2 ~ | f'1 ~ | f'1 ~ | f'1 | r2 f'2 ~ | f'1 ~ | f'2 r2 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'1 | r2 f'2 ~ | f'1 ~ | f'2 r2 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'1 | s1 | s1 | s1 | s1 | s1 | r2 f'2 ~ | f'1 | s1 | s1 | r2 f'2 ~ | f'2 r2 | s1 | f'1 ~ | f'2 r2 | s1 | s1 | f'1 ~ | f'2 r2 | s1 | s1 | s1 | s1 | r2 f'2 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'1 | s1 | s1 | r2 f'2 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'2 r2 | r2 f'2 | s1 | f'2 r2 | f'2 r2 | r2 f'2 | r2 f'2 ~ | f'2 r2 | f'2 r2 | r2 f'2 | r2 f'2 | s1 | f'2 r2 | f'1 | r2 f'2 | s1 | f'2 r2 | f'2 r2 | r2 f'2 | s1 | f'2 r2 | f'2 r2 | r2 f'2 | r2 f'2 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'2 r2 | f'2 r2 | r2 f'2 | r2 f'2 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'2 r2 | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 | r2 f'2 ~ | f'1 ~ | f'1 ~ | f'1 | r2 f'2 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'2 r2 | f'1 ~ | f'1 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'1 ~ | f'1 ~ | f'1 ~ | f'1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | f'2 r2 | s1 | s1 | s1 | f'2 r2 | s1 | r2 f'2 | s1 | s1 | s1 | r2 f'2 | s1 | s1 | s1 | s1 | s1 | s1 | f'2 r2 | s1 | s1 | s1 | f'2 r2 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } r2 f'2 ~ | f'2 r2 | f'2 r2 | f'1 | r2 f'2 ~ | f'2 r2 | f'2 r2 | f'1 | r2 f'2 | s1 | f'2 r2 | f'1 | r2 f'2 | r2 f'2 ~ | f'2 r2 | f'1 | r2 f'2 | r2 f'2 ~ | f'2 r2 | f'2 r2 | f'1 | r2 f'2 ~ | f'2 r2 | f'2 r2 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'1 | r2 f'2 | s1 | f'2 r2 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 ] \bar "|." }
\\
>>

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<<
\numericTimeSignature
{
\override RehearsalMark.X-offset = #1 \override RehearsalMark.Y-offset = #4
\override Stem.details.beamed-lengths = #'(5)
\set Score.markFormatter = #format-mark-box-numbers
\tempo \markup {
\concat {
\smaller \general-align #Y #DOWN
\note #"4" #1 \normal-text " ≈ 90"
}}
s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default e''1 ~ | e''4 r2. | r4 e''2. ~ | e''2. r4 | s1 | s1 | r4 e''2. ~ | e''2. r4 | s1 | r4 e''2. ~ | e''4 r2. | s1 | r2. e''4 ~ | e''1 ~ | e''4 r2. | r2. e''4 ~ | e''1 ~ | e''1 ~ | e''4 r2. | r2. e''4 ~ | e''2. r4 | s1 | s1 | r4 e''2. ~ | e''2. r4 | s1 | r4 e''2. ~ | e''1 | s1 | s1 | s1 | s1 | \mark \default e''4 r2 e''4 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''4 r2 e''4 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''4 r2 e''4 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''1 ~ | e''2. r4 | s1 | s1 | s1 | s1 | \mark \default s1 | r2. e''4 ~ | e''2. r4 | r4 e''2 r4 | s1 | r2. e''4 ~ | e''2. r4 | s1 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''4 r2. | s1 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''4 r2. | r2. e''4 ~ | e''2. r4 | r4 e''2 r4 | s1 | r2. e''4 ~ | e''2. r4 | s1 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''4 r2. | s1 | s1 | s1 | s1 | \mark \default s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default e''1 ~ | e''2. r4 | s1 | r4 e''2. ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''4 r2. | r4 e''2. ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''2. r4 | s1 | r4 e''2. ~ | e''1 ~ | e''2. r4 | r2. e''4 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 | s1 | s1 | s1 | s1 | \mark \default e''2. r4 | r4 e''2. ~ | e''1 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''4 r2 e''4 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''1 | s1 | s1 | s1 | s1 | \mark \default e''2. r4 | s1 | s1 | r2. e''4 ~ | e''4 r2. | s1 | r4 e''2. ~ | e''4 r2. | s1 | s1 | r4 e''2 r4 | s1 | s1 | s1 | s1 | s1 | r2. e''4 ~ | e''2. r4 | s1 | s1 | r2. e''4 ~ | e''4 r2. | s1 | r4 e''2. ~ | e''4 r2. | s1 | s1 | r4 e''2. | s1 | s1 | s1 | s1 | \mark \default s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 ] \bar "|." }
\\
{
\override RehearsalMark.direction = #DOWN \override RehearsalMark.X-offset = #2 \override RehearsalMark.Y-offset = #-8
\override Stem.details.beamed-lengths = #'(5)
\set Score.markFormatter = #format-mark-box-numbers
\tempo \markup {
\concat {
\smaller \general-align #Y #DOWN
\note #"4" #1 \normal-text " ≈ 90"
}}
s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } r4 f'2 r4 | s1 | r2. f'4 ~ | f'4 r2. | s1 | r4 f'2 r4 | r2. f'4 ~ | f'4 r2. | s1 | r4 f'2 r4 | r2. f'4 ~ | f'4 r2 f'4 ~ | f'4 r2. | r4 f'2 r4 | s1 | r2. f'4 ~ | f'4 r2. | r4 f'2 r4 | s1 | r2. f'4 ~ | f'4 r2. | s1 | r4 f'2 r4 | r2. f'4 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'4 r2. | s1 | r4 f'2 r4 | r2. f'4 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'1 ~ | f'2. r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'1 ~ | f'2. r4 | r4 f'2. ~ | f'1 ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2. ~ | f'1 ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2 r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'1 ~ | f'2. r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'1 ~ | f'2. r4 | r4 f'2. ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'1 ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2. | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'4 r2. | r2. f'4 ~ | f'1 ~ | f'4 r2. | s1 | r2. f'4 ~ | f'2. r4 | s1 | r4 f'2. ~ | f'1 ~ | f'2. r4 | s1 | r4 f'2. ~ | f'2. r4 | s1 | s1 | r4 f'2. ~ | f'4 r2. | r2. f'4 ~ | f'1 ~ | f'4 r2. | s1 | r2. f'4 ~ | f'1 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'4 r2. | r4 f'2. ~ | f'1 ~ | f'2. r4 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } r2. f'4 ~ | f'4 r2 f'4 ~ | f'4 r2. | r4 f'2 r4 | r2. f'4 ~ | f'4 r2 f'4 ~ | f'4 r2. | r4 f'2 r4 | r2. f'4 ~ | f'4 r2 f'4 ~ | f'4 r2. | r4 f'2 r4 | r4 f'2 r4 | r2. f'4 ~ | f'4 r2. | r4 f'2 r4 | r4 f'2 r4 | r2. f'4 ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2 r4 | r2. f'4 ~ | f'4 r2 f'4 ~ | f'4 r2. | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } r4 f'2 r4 | r2. f'4 ~ | f'4 r2 f'4 ~ | f'4 r2. | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } r4 f'2. ~ | f'1 ~ | f'1 ~ | f'2. r4 | r4 f'2. ~ | f'1 ~ | f'4 r2 f'4 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'4 r2 f'4 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'2. r4 | r4 f'2. ~ | f'1 ~ | f'1 ~ | f'2. r4 | r4 f'2. ~ | f'1 ~ | f'4 r2 f'4 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'1 ~ | f'1 ~ | f'1 ~ | f'4 r2 f'4 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'2. r4 | s1 | s1 | s1 | s1 | s1 | r4 f'2. ~ | f'2. r4 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | r2. f'4 ~ | f'1 ~ | f'4 r2. | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 ] \bar "|." }
\\
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<<
\numericTimeSignature
{
\override RehearsalMark.X-offset = #1 \override RehearsalMark.Y-offset = #4
\override Stem.details.beamed-lengths = #'(5)
\set Score.markFormatter = #format-mark-box-numbers
\tempo \markup {
\concat {
\smaller \general-align #Y #DOWN
\note #"4" #1 \normal-text " ≈ 90"
}}
\mark \default r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''2 r2 | e''1 | r2 e''2 ~ | e''2 r2 | e''2 r2 | e''1 | r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | s1 | s1 | s1 | s1 | \mark \default s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default s1 | r2 e''2 ~ | e''1 | s1 | r2 e''2 ~ | e''2 r2 | s1 | s1 | e''1 ~ | e''2 r2 | s1 | s1 | e''1 ~ | e''2 r2 | s1 | e''1 | s1 | s1 | r2 e''2 ~ | e''1 | s1 | s1 | s1 | s1 | s1 | r2 e''2 ~ | e''2 r2 | s1 | s1 | s1 | s1 | s1 | \mark \default e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 ~ | e''1 ~ | e''1 ~ | e''2 r2 | e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 ~ | e''1 | s1 | s1 | s1 | s1 | \mark \default e''2 r2 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''2 r2 | s1 | r2 e''2 ~ | e''2 r2 | e''2 r2 | e''1 | r2 e''2 ~ | e''2 r2 | s1 | e''1 | r2 e''2 | s1 | s1 | e''1 | r2 e''2 | r2 e''2 ~ | e''2 r2 | e''2 r2 | s1 | r2 e''2 ~ | e''2 r2 | e''2 r2 | e''1 | s1 | s1 | s1 | s1 | \mark \default s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default e''1 | s1 | e''1 ~ | e''2 r2 | s1 | e''1 ~ | e''1 ~ | e''2 r2 | s1 | e''1 ~ | e''1 ~ | e''2 r2 | r2 e''2 ~ | e''1 | s1 | r2 e''2 ~ | e''1 ~ | e''1 | s1 | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''2 r2 | s1 | e''1 ~ | e''1 | s1 | s1 | s1 | s1 | \mark \default r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 | r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 ~ | e''1 | r2 e''2 ~ | e''2 r2 | e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''1 ~ | e''1 | r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 | r2 e''2 ~ | e''1 ~ | e''2 r2 | e''1 ~ | e''1 ~ | e''1 ~ | e''2 r2 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 ] \bar "|." }
\\
{
\override RehearsalMark.direction = #DOWN \override RehearsalMark.X-offset = #2 \override RehearsalMark.Y-offset = #-8
\override Stem.details.beamed-lengths = #'(5)
\set Score.markFormatter = #format-mark-box-numbers
\tempo \markup {
\concat {
\smaller \general-align #Y #DOWN
\note #"4" #1 \normal-text " ≈ 90"
}}
\override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'2 r2 | f'2 r2 | r2 f'2 | r2 f'2 ~ | f'2 r2 | f'2 r2 | f'1 | r2 f'2 ~ | f'2 r2 | f'2 r2 | f'1 | r2 f'2 | s1 | f'2 r2 | f'1 | r2 f'2 | r2 f'2 ~ | f'2 r2 | f'2 r2 | r2 f'2 | r2 f'2 ~ | f'2 r2 | f'2 r2 | f'1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } r2 f'2 ~ | f'2 r2 | f'2 r2 | f'1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'1 ~ | f'2 r2 | s1 | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'2 r2 | s1 | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'1 ~ | f'1 ~ | f'1 ~ | f'1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } r2 f'2 | s1 | f'2 r2 | s1 | r2 f'2 | s1 | f'2 r2 | s1 | r2 f'2 | s1 | s1 | f'2 r2 | r2 f'2 | s1 | s1 | f'2 r2 | s1 | s1 | s1 | f'2 r2 | s1 | r2 f'2 | s1 | f'2 r2 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | r2 f'2 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'1 | r2 f'2 ~ | f'2 r2 | f'2 r2 | f'1 | r2 f'2 ~ | f'1 ~ | f'2 r2 | f'1 | r2 f'2 | r2 f'2 ~ | f'2 r2 | f'1 ~ | f'1 | r2 f'2 ~ | f'2 r2 | f'1 ~ | f'1 | r2 f'2 ~ | f'2 r2 | f'2 r2 | f'1 | r2 f'2 ~ | f'1 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'2 r2 | f'1 | r2 f'2 | r2 f'2 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | f'1 ~ | f'2 r2 | r2 f'2 ~ | f'1 ~ | f'1 | s1 | r2 f'2 ~ | f'1 | s1 | f'1 ~ | f'1 ~ | f'2 r2 | s1 | f'1 ~ | f'1 ~ | f'2 r2 | s1 | f'1 ~ | f'2 r2 | r2 f'2 ~ | f'1 ~ | f'1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } r2 f'2 ~ | f'1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'2 r2 | f'2 r2 | r2 f'2 | s1 | f'2 r2 | f'2 r2 | r2 f'2 | s1 | s1 | f'2 r2 | r2 f'2 | r2 f'2 | s1 | f'2 r2 | s1 | r2 f'2 | s1 | f'2 r2 | f'2 r2 | r2 f'2 | s1 | f'2 r2 | f'2 r2 | r2 f'2 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | f'2 r2 | r2 f'2 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 ] \bar "|." }
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\numericTimeSignature
{
\override RehearsalMark.X-offset = #1 \override RehearsalMark.Y-offset = #4
\override Stem.details.beamed-lengths = #'(5)
\set Score.markFormatter = #format-mark-box-numbers
\tempo \markup {
\concat {
\smaller \general-align #Y #DOWN
\note #"4" #1 \normal-text " ≈ 90"
}}
s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 | s1 | s1 | s1 | s1 | \mark \default r4 e''2. ~ | e''4 r2 e''4 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2 r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''4 r2 e''4 | s1 | s1 | s1 | s1 | \mark \default s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | r4 e''2 r4 | s1 | s1 | s1 | s1 | s1 | \mark \default e''4 r2. | s1 | s1 | s1 | s1 | r2. e''4 ~ | e''2. r4 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | r2. e''4 ~ | e''1 ~ | e''4 r2. | s1 | s1 | s1 | s1 | r2. e''4 ~ | e''2. r4 | s1 | s1 | r4 e''2. ~ | e''2. r4 | s1 | s1 | s1 | s1 | \mark \default e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''4 r2 e''4 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''1 ~ | e''2. r4 | r4 e''2. ~ | e''1 ~ | e''1 ~ | e''2. r4 | r4 e''2. | s1 | s1 | s1 | s1 | \mark \default e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''4 r2. | r2. e''4 ~ | e''2. r4 | r4 e''2 r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2 r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2 r4 | r4 e''2. ~ | e''4 r2 e''4 ~ | e''2. r4 | r4 e''2 r4 | s1 | s1 | s1 | s1 | \mark \default s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \mark \default e''2. r4 | s1 | s1 | r4 e''2. ~ | e''2. r4 | s1 | r4 e''2. ~ | e''1 ~ | e''2. r4 | r2. e''4 ~ | e''1 ~ | e''4 r2. | r2. e''4 ~ | e''1 ~ | e''1 ~ | e''4 r2. | r2. e''4 ~ | e''2. r4 | s1 | s1 | r4 e''2. ~ | e''2. r4 | s1 | r4 e''2. ~ | e''1 ~ | e''2. r4 | r2. e''4 ~ | e''1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 ] \bar "|." }
\\
{
\override RehearsalMark.direction = #DOWN \override RehearsalMark.X-offset = #2 \override RehearsalMark.Y-offset = #-8
\override Stem.details.beamed-lengths = #'(5)
\set Score.markFormatter = #format-mark-box-numbers
\tempo \markup {
\concat {
\smaller \general-align #Y #DOWN
\note #"4" #1 \normal-text " ≈ 90"
}}
s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | r4 f'2 r4 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | r2. f'4 ~ | f'4 r2. | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'4 r2 f'4 ~ | f'2. r4 | r4 f'2 r4 | r2. f'4 ~ | f'4 r2 f'4 ~ | f'4 r2. | r4 f'2 r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'4 r2. | r4 f'2 r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2 r4 | r2. f'4 ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2 r4 | r2. f'4 ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2 r4 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } r4 f'2. ~ | f'4 r2 f'4 ~ | f'4 r2. | r4 f'2 r4 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'1 ~ | f'1 ~ | f'4 r2 f'4 ~ | f'1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | r2. f'4 ~ | f'4 r2. | s1 | s1 | r2. f'4 ~ | f'4 r2. | s1 | s1 | r2. f'4 ~ | f'4 r2. | s1 | r4 f'2 r4 | s1 | s1 | s1 | r4 f'2 r4 | s1 | r2. f'4 ~ | f'4 r2. | s1 | s1 | r2. f'4 ~ | f'4 r2. | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | r2. f'4 ~ | f'4 r2. | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } r4 f'2 r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'1 ~ | f'2. r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2 r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2 r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | f'2. r4 | r4 f'2 r4 | r4 f'2. ~ | f'4 r2 f'4 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'4 r2 f'4 ~ | f'2. r4 | r4 f'2. ~ | f'4 r2 f'4 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } r2. f'4 ~ | f'1 ~ | f'1 ~ | f'4 r2. | r2. f'4 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'4 r2. | r4 f'2. ~ | f'1 ~ | f'2. r4 | s1 | r4 f'2. ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'1 ~ | f'4 r2. | r2. f'4 ~ | f'1 ~ | f'1 ~ | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } f'1 ~ | f'1 ~ | f'1 ~ | f'4 r2. | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic cresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | \override RehearsalMark.direction = #DOWN \mark \markup { \italic decresc. } s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 | s1 ] \bar "|." }
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