(c) 2005-2023 David A Grunberg

Thesis / Documentation

Welcome to CHIMPS! For personal and academic use.

by David A. Grunberg (c) 2005 – 2021

**Synopsis**

** Composition**
– the act of creating and codifying musical work

** Heuristically-Improved**
– Heuristic: “an approach to problem solving or
self-discovery that employs a practical method that is not guaranteed
to be optimal, perfect, or rational, but is nevertheless sufficient
for reaching an immediate, short-term goal or approximation.”
-Wikipedia

** Microtonal**
– Employing pitch frequencies that are outside the common
12-tone scale.

** Partitioned**
– Partitioning is a technique for dividing a musical line
across contrapuntal voices in a cyclical manner. (Described by
composer Charles Wourinen)

** Serialism**
- Musical compositional technique that employs a more-or-less
strict use of “tone rows” as the source material for
melodic content as well as other parameters such as note duration and
dynamics.

**Introduction**

[ **Intended Audience:**
This document and accompanying software is intended for an audience with familiarity with basic music theory
and some interest in 20th-century twelve-tone theory and serialism: Twelve-tone technique
]

Charles
Wourinen (1938-2020), in his book *Simple Composition*, wrote,
“What can be serialized? Everything.” Taking this
statement rather literally, we can extend Milton Babbitt’s
“Time Points” and Wourinen’s forms into the realms
of row-form selection, time (note and larger phrase durations),
phrase and section dynamics, and individual note dynamics.

Computer software is a perfect tool for executing the numeric manipulations needed for the serialization of “everything.” In addition, a web-based interface would allow the greatest number of people to experiment with the software. The first experimental version of this software was designed and coded by the author in early 2005.

**HORIZONTAL
(TIME) FRACTAL STRUCTURE**

With
this project, I extend Babbitt’s time-point concept to the time
domain of the large-scale form.
In Babbitt’s time-point concept, the start-time of each note event (relative to the previous event) is
proportional to the pitch interval from the previous pitch class in
the tone row.
In a “fractal” manner,
the length (time duration) of each full row statement of N notes
(called a phrase) will be ~~proportional~~ related to
the pitch intervals in the tone row. Likewise, N “sections”
of N phrases each make up the total composition. In other words, the
total composition is made up of N sections, each section having N
phrases, each phrase having N notes. Thus, the choice of intervals in the basic tone row will determine
the lengths of the entire work as well as the sections and phrases.

**A
Phrase is one full statement of a tone row, or several rows forms
played at the same time in counterpoint**.

**Meter**:
The composition has no “meter” in any real sense. The
music flows in time quite freely. For notational (or time-counting)
convenience only, I have metered all phrases in 2/4 time, with an
added odd-metered bar at phrase-end for any needed extra time. When
the resulting Midi files are imported into notation software, the
notation will have bar lines in 2/4 time, but these bar lines have no
musical significance.

**VERTICAL
STRUCTURE (PITCH AND VOICES)**

**Phrases, Choirs
and Partitions**

Each Phrase in time can be made up of one or more vertical “Choirs” in counterpoint. Each Choir may play a different row form (inversion / retrograde / retrograde-inversion / transposition).

Extending
contrapuntally, each Choir’s row statement can be further
“Partitioned” into multiple contrapuntal voices (a
technique described in Wourinen’s *Simple Composition*).
These contrapuntal voices share the statement pitches cyclically;
each voice taking its turn to play the next note of the row. For
example, a choir divided into three partitions would have the pitches
played thus: the first partition (voice) would play the first note of
the row, then the second voice would start the second note (while the
first note keeps sounding), then the third voice starts the third
note, then the first voice moves to the fourth note, and so on. After
the final note of the row is played, the next available voice takes
up the first pitch of the next row-form (phrase) to be played. If the
number of notes in the tone row is not divisible by the number of
partitions, then, as we can predict, the first note of succeeding
rows will not be played by the same partition voice every time. We
can predict that interesting, complex music will result if we employ
different instrument sounds for each partition (voice) in our band.

I have decided, for the moment, that the overall contrapuntal structures shall be selected by the user/composer, and not be serialized automatically. Why? Because, as a composer, I would like to choose the overall contrapuntal complexity and instrumental timbres; I still think in terms of human “players” or “singers” and instrumental timbres, and thus, I could choose an ensemble: for example, a bass, a piano, and a guitar, and the software could help me create music for this ensemble. While it’s certainly possible to serialize the vertical structure and timbral choices, I would find the results less “human,” although this attitude is subject to change!

TWELVE-TONE SERIALISM .. WHY TWELVE?

Composers naturally write for the instruments available in their time. In the early 20th-century, we had the piano keyboard that played twelve (relatively-) equal steps per octave (and of course the other acoustic instruments that approximated the same pitch set).

Without going into the history and acoustical reasons for how we arrived at 12 tones in the “Western” scale, it suffices to say that modern electronic synthesizers can dispense with that old restriction. We can employ any set of pitches that the human ear is capable of distinguishing. Somewhere along the way, the concept of the “cent” (one-hundreth of a semitone) became a convenient smallest-audible subdivision of the semitone, and modern synthesizers can be instructed to produce fundamental pitches at that scale – that is, 1200 different pitches per octave. Some synthesizers can utilize formulas of arbitrary frequency ratios. However, for our purposes, 1 cent is as small as we care to utilize.

RECENT UPDATES

2020
– Coded to allow “absolute value” measurement of
delta (change) from pitch to pitch, thus having just 6 different values instead
of 11. Background: In Babbitt’s Time Point system, we need to measure the melodic
interval from one note to the next. Is the pitch class “B”
*eleven* steps away from “C,” or *one *step
away from “C”? This
is an important question, the answer to which has consequences in the
musical output. In Babbitt, B is eleven steps up from C. If all pitch
classes are to be considered of equal importance, then there is
really no significance of *up* or *down* - at least when analyzing a tone row. That is, the
notes C3, C4, and C5 are the same pitch class. then we should only
use the “absolute value” of the distance from one pitch
class to another. That means that we only have six [or 599] possible
steps of distance, not eleven [or 1199].

2020. With the “absolute value” delta, it needs an “Exponential Time” option. (In Babbitt, the time scale is LINEAR with respect to the pitch delta.) With this new exponential time option, the durations of notes shall be exponential and the user can choose a “base” for the exponent. A base of 2.0 would result in our familiar note lengths 1/32, 1/16, 1/8, ¼, ½, whole, etc… but “dotted” durations would not occur. A base of less than 1.0 would result in the reverse result, larger intervals would result in shorter times. A base of exactly 1.0 would result in all notes having the same duration (try it for minimalist movie scores). Personally, I have been finding a base of 1.4 – 1.7 to be pleasing.

MICROTONAL SERIALISM

I propose a serial “matrix” based upon an N-tone row (not only 12) that is not chosen from the 12-tone equal-tempered scale, but any arbitrary pitches. Practically speaking, there are 1200 pitch classes available in a typical modern synthesizer based on MIDI note numbers and cents. Of course, in theory, there are an infinite number of frequencies within an octave, but how many are audibly distinct? 100 cents per semitone is a good guess at an upper limit.

If N arbitrary pitches (chosen from 1200) are assembled into an NxN serial matrix, this matrix will likely contain MORE than N different pitch classes. How does this happen? The interval C to C#+5 (C# in the equal-tempered scale plus 5 cents) is an interval of 105 cents, and when formally inverted, it becomes C to B-5 (B in the equal-tempered scale minus 5 cents). Thus, new pitch classes are introduced if we are doing what I call “formal inversion”.

If however, if the N tones are “equal-tempered” then there will only be N different resulting pitch classes, just as in traditional 12-tone composition. The 2021-03 release of this software provides an “easy-equal” command that will automatically calculate and create N equal-tempered pitch classes to choose from.

DIFFICULTIES: Notation and Live Performance.

Complex music
produced by this software will likely not be able to be performed "live" by human performers.
The first difficulty is the problem of notation: Our current system of music notation is based on twelve
notes per octave. This software can produce music made up of an arbitrary number of pitches per octave.
Likewise, our acoustic instruments are also based on a twelve-note-per-octave system -
regardless of tuning system employed ("well-temperament", e.g.). However, with careful pitch choices,
string and wind players may be able to perform the composition with some level of pitch accuracy.

TO DEVELOP IN THE FUTURE….

It
would be interesting to create a scale that repeats on a
cycle that spans a frequency ratio other than 2.0. It's fairly easy to code a version of this software
that produces notes in a scale pattern that spans any number of total cents, not only 1200. As a simple example,
our normal equal-tempered "major" scale is this, in cents:

0, 200, 400, 500, 700, 900, 1100, 1200 ...

An equal-tempered "major" scale stretched to 1400 cents would be simply:

0,233,467,583,1089,1245,1400 ... (each equal tempered step is about 116.7 cents)

WHAT IS THE POINT OF ALL THIS?

The 12-tone serial composition system, as it is taught in schools, is a system that attempts to remove the concepts of traditional harmony and counterpoint, and the concept of "key". Traditional harmony is also dependent on the musical "octave" being a frequency ratio of 2.0. The point of this software project is twofold: First, to demonstrate how software could generate 12-tone music of some complexity, referencing Wourinen as a basic model. Secondly, the power of computer music-playback allows us to challenge the tradition of *twelve* tones, and eventually to question the definition of a scalar "octave". Have some fun experimenting with this software, and I'll let the reader decide if I have been successful or not.

If you use this software to generate musical ideas that you use in a school project or published composition or film/video, I would appreciate you acknowleding this author and this CHIMPS system. Thanks!

HAPPY COMPOSING!

- D.G.

The sample score screenshot above is an excerpt from the composition "test-2 bass-fix-exponent". The image shows exactly how the resulting Midi file was imported into Sibelius v.7 notation software, without any modification.
You'll notice that one note in the tone row repeats (violating the "rules" of 12-tone composition).
That is by design; the tone row contains the note "C" twice.

RANDOM NOTES

Concept to improve the detailed notation when importing the MIDI files into Notation Software:

Produce an output file with information on dynamics, articulation, microtonal pitch, etc. Write a software plug-in to read this file, and apply to the score. But this is not possible in Sibelius - Plugins cannot read a file!

NOTES & RESOURCES

Midi Mapper and Virtual Midi Synth

__https://coolsoft.altervista.org/en/virtualmidisynth#soundfonts__