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Dear Friends


In my Doctoral Dissertation, I converted every FORTE number in a modulo 12 Rhythm via time-point-system.

There is a complete catalog included (see the link below). It's in portuguese.


After Janusz adjusted the Forte numbers to have the inversion, using "a" and "b" to differentiate the

 prime forms from the inversions, it was easy to convert using codes like this:

(setf ch0 (time-point-system (pcs '5-11b :pitch)'s :start 0))
(setf ch1 (time-point-system (pcs '6-33 :pitch)'s :start 1))
(setf ch2 (time-point-system (pcs '7-11b :pitch)'s :start 2))
(setf ch3 (time-point-system (pcs '3-11b :pitch)'s :start 3))
(setf ch4 (time-point-system (pcs '3-11b :pitch)'s :start 0))


The dissertation (in portuguese) can be downloaded HERE:

Das alturas ao ritmo : teoria dos conjuntos rítmicos como ferramenta composicional

From pitches to rhythm: rhythmic set theory as a compositional tool.


This doctoral dissertation is divided into two parts: the first deals a rhythmic set theory, and the second contains the portfolio of compositions developed during this period of studies. This dissertation presents a system of rhythmic organization parallel to the musical set theory pitch class organization FORTE (1973), as well as an adaptation of the time-point-system (BABBITT, 1962). From the standpoint of the traditional set theory, and also from the diatonic set theory, this unified approach allows to estabilish a connecting tissue of basic aspects: from the harmony and chords symbols to the rhythmic organization. At one time, in a complete catalog, the families of pitch class sets and chord symbols are related to their respective rhythmic counterparts. The musical motivation for this research came from my interest in the swinging and groovy repetitive rhythms called timelines (TOUSSAINT, 2013), commonly used in popular music. These dancing timelines have properties similar to those of the diatonic sets, and for this reason, this dissertation presents some properties of the diatonic pitch class sets, drawing a parallel with their rhythmic counterparts. These relationships also appear in the portfolio of compositions, characterizing some procedures used. The portfolio of compositions, which includes a composition for symphony orchestra, is presented form the standpoint of a duality between transparency and opacity. This duality address the essential differences in the audibility of the results from various composition techniques. This study of Rhythmic Set Theory will serve as an analytical approach of my compositional output in popular music, with a systematic way to understant and to extrapolate some aspects already used in my practice as composer and improviser.
Here is an analysis of a Wayne Krantz improvisation, using the rhythmic set theory system.
Hope you enjoy !!

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Thank you very much for taking the time to share ;-) Please feel free to continue to do so as I am most interested in this subject of Timepoint/Rhythm, especially as you apply your research to Opusmodus coding applications/implementations :)

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Thank You, Loopyc !

I' m trying to make this as practical as possible, applying the concepts in compositions and also for improvising. Best,


added 11 minutes later

Thank You, Janusz !!!

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Eight hours later! Spent all day reviewing related Opusumodus functions/documentation and researching your concepts and references...a very satisfying time in furtherance of my ongoing Opusmodus education ;-)


Thanks again Julio for the inspiration, and Janusz for ALREADY including/implementing so many useful tools related to these subjects :)

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