93 lines
2.6 KiB
Python
93 lines
2.6 KiB
Python
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#!/usr/bin/env python
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"""
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Pitch class - a point in harmonic space.
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Represented as an array of exponents on prime dimensions.
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Example: (0, 1, 0, 0) represents 3/2 (perfect fifth) in CHS_7
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"""
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from __future__ import annotations
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from fractions import Fraction
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from math import log
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from operator import add
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from typing import Iterator
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DIMS_8 = (2, 3, 5, 7, 11, 13, 17, 19)
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DIMS_7 = (2, 3, 5, 7, 11, 13, 17)
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DIMS_5 = (2, 3, 5, 7, 11)
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DIMS_4 = (2, 3, 5, 7)
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class Pitch:
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def __init__(self, hs_array: tuple[int, ...], dims: tuple[int, ...] | None = None):
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self.hs_array = hs_array
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self.dims = dims if dims is not None else DIMS_7
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def __hash__(self) -> int:
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return hash(self.hs_array)
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def __eq__(self, other: object) -> bool:
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if not isinstance(other, Pitch):
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return NotImplemented
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return self.hs_array == other.hs_array
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def __repr__(self) -> str:
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return f"Pitch({self.hs_array})"
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def __iter__(self):
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return iter(self.hs_array)
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def __len__(self) -> int:
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return len(self.hs_array)
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def __getitem__(self, index: int) -> int:
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return self.hs_array[index]
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def to_fraction(self) -> Fraction:
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"""Convert to frequency ratio (e.g., 3/2)."""
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from math import prod
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return Fraction(
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prod(pow(self.dims[d], self.hs_array[d]) for d in range(len(self.dims)))
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)
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def to_cents(self) -> float:
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"""Convert to cents (relative to 1/1 = 0 cents)."""
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fr = self.to_fraction()
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return 1200 * log(float(fr), 2)
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def collapse(self) -> Pitch:
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"""
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Collapse pitch so frequency ratio is in [1, 2).
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This removes octave information, useful for pitch classes.
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"""
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collapsed = list(self.hs_array)
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fr = self.to_fraction()
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if fr < 1:
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while fr < 1:
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fr *= 2
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collapsed[0] += 1
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elif fr >= 2:
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while fr >= 2:
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fr /= 2
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collapsed[0] -= 1
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return Pitch(tuple(collapsed), self.dims)
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def project(self) -> Pitch:
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"""Project pitch to [1, 2) range - same as collapse."""
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return self.collapse()
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def transpose(self, trans: Pitch) -> Pitch:
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"""Transpose by another pitch (add exponents element-wise)."""
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return Pitch(tuple(map(add, self.hs_array, trans.hs_array)), self.dims)
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def pitch_difference(self, other: Pitch) -> Pitch:
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"""Calculate the pitch difference (self - other)."""
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return Pitch(
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tuple(self.hs_array[d] - other.hs_array[d] for d in range(len(self.dims))),
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self.dims,
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)
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