\textbf{Description (which can optionally be used/adapted as a program note)}
\textit{seeds and ledgers 1--3} explore the reconciliation of distance in harmonic space, generally referred to as `consonance' or `dissonance', and melodic movement in pitch space, generally referred as a difference in `height'. Distance in harmonic space is measured as a complexity function on the frequency ratio between two tones: the higher the quantity and size of the prime factors needed to express the numbers in the frequency ratio, the more dissonant the relationship. Distance in pitch space is typically measured as the log of a frequency ratio and is often expressed in semitones or cents (100th of a tempered semitone). For example, the perfect 5th (a frequency ratio of 3/2) is one of the closest intervals in harmonic space but relatively far (7 semitones) in pitch space. On the contrary, tones that are distance in harmonic space often represent smaller melodic and chromatic differences/movements in pitch space.
The musical processes realized in \textit{seeds and ledgers} explore a reexamination of the traditional concept of `voice leading': how individual melodic lines create and maintain harmonies in aggregate while sometimes modulating. However, this musical question is recontextualized in a phenomenological framework called \textit{just-intonation} in \textit{harmonic space}. In just-intonation, whole number ratios express the frequency relationship between pitches. The resulting musical scales are untempered. They do not favor the purity of one interval over another such as with different well- and equal-temperaments, which prioritize and sacrifice the purity of different intervals for key cyclicness.
These pieces were generated using custom software that maintains `compact sets' (consonant groups of tones) in harmonic space among any simultaneously sounding tones, but favors smaller steps when one voice moves melodically. This is essentially a sort of `voice leading', which is a term often used in the tradition of western classical music.
Traditionally, distance between pitches is typically measured in terms of subjective height expressed in units of semitones or cents (100th of a tempered semitone). This particular concept of a musical space can be referred to as pitch (or melodic) space. However, in harmonic space, distance is measured as a complexity function on the frequency ratio between two tones: the smaller the quantity and size of the prime factors needed to express the numbers in the frequency ratio, the closer they are in harmonic space and relatively easier to tune. For example, the perfect 5th (a frequency ratio of 3/2) is one of the closest intervals in harmonic space but relatively far (7 semitones) in pitch space. On the contrary, smaller melodic and chromatic differences/movements in pitch space are often distant in harmonic space. This gives rise to several vexing musical questions. How is it possible to reconcile these two very different, well-defined measures of distance? How can one tune stepwise movement in pitch space when the relationship between two tones may actually be distant in harmonic space? How can one modulate in harmonic space since as the space is by definition acyclic?
A compact set is defined as a group of notes such that each note in the group is close in harmonic space to some other note in the group. But when one voice moves, the program will favor notes that move by a smaller step in pitch space from itself while transitioning to another compact set among all the tones.
In \textit{seeds and ledgers}, these problems are explored using a custom software program that maintains `compact sets' (consonant groups of tones) in harmonic space among any simultaneously sounding tones, but favors smaller steps in pitch space when one voice moves melodically. A compact set is defined as a group of notes such that each note in the group is close in harmonic space to some other note in the group, but not necessarily all of them. When one voice moves melodically, the program will favor notes that move by a smaller step in pitch space within a voice while modulating/transitioning to another compact set among all the voices.
Any individual part would be near impossible to play by itself. However, because compact sets are always maintained, each successive tone within a part can always be tuned via a relatively simple interval in harmonic space to a tone that is already sounding in one of the other instruments. As a result of this process, some of the passages have an almost baroque, contrapuntal feel; a chromatic drift in harmonic space constantly modulating.
@ -142,7 +141,7 @@ Given that the coda of piece 3 starting at measure 115 is exceedingly difficult,
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\textbf{Generating programs}
These pieces were generated using custom software written in SuperCollider with a front-end user interface written in Javascript called Open Stage Control. These programs can also be used to audition the pieces and each individual part. The most recent version of the code along with any utilities that are developed are downloadable from a git repository at: \url{https://unboundedpress.org/code/mwinter/seeds_and_ledgers}
These pieces were generated using custom software written in SuperCollider with a front-end user interface developed with Open Stage Control (Javascript). These programs can also be used to audition the pieces and each individual part. The most recent version of the code along with any utilities that are developed are downloadable from a git repository at: \url{https://unboundedpress.org/code/mwinter/seeds_and_ledgers}
The generation of this document (using LaTex) contains a version date at the bottom of this page in order to help track changes and the git repository will also detail commit changes. The piece was last generated using SuperCollider version 3.13 and Lilypond version 2.24.1.
