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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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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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Dear Julio, I just had this flash of an idea of converting the trichords (and then all forte numbers) into rhythms, and googled and of course some brilliant person has done it all and completely. Thank you! Will explore your dissertation (with help from google translate) May have to dip my toe into OM (i only use max/msp for programming) I really like your music idiomatic, embodied and expressive, when you could easily have created MIDI output. Great guitar playing. Question: have you/anyone explored forte numbers instead of 12 for say 5, 7, 8, 16, n units (for its use in meters, and - back to pitch - diatonic and microtonal use?

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Thanks a lot, MIlton !


I´m very happy to see your comment ! 

Actually, a lot of interesting rhythmic timelines are beyond the 12 units. In indian music there are very long cyclic rhythms and in popular music, the 16 n is very widespread, including the popular drum machines step sequencers.

But for the purpose of having a complete set of combinations, any number beyond 12 is too big, generating too much material to make a typology. Maybe in a larger cardinality we can talk about tendencies and not an specific typology. Opusmodus can deal with it, also.


Janusz programed a special function based in my dissertation, called pcs-rhythm. It´s well exemplified in the documentation. Here is the forum thread that give birth to the function.


All the best and thanks for your kind words !






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