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In my Dissertation, I worked a way to convert every chord and set in a modulo 12 rhythm, so the entire catalog of FORTE are converted to rhythms, following the steps of Babitt: As a hardcore serialist, Babbitt was interested in converting 12-tone rows to rhythms, in a kind of 12-tone rhythm theory. Below, Wuorinen show one example of a typical Babbitt idea: For the sake of explaining my idea of function, it's important to have in mind that for Babbitt, the order of the row is very important and lead to different results in the pitch to rhythm conversion. Take a look in the example below: In the preceeding figure, the order of the C major triad generate different rhythms. In the example (0 4 7) have a different result from (4 0 7) or (7 0 4). In the system I developed in my Dissertation, the order does NOT matter, since (0 4 7), (7 0 4) or (4 0 7) will result in exactly the same rhythm, as you can see below: In my system, the transposition equals rotation (as well as in Babbitt) And every chord symbol can be transformed in a rhythm: Even voicings can be converted in longer Rhythms (the more spread the voicing, the longer the rhythm): So I did every FORTE SET in the catalog, in this way: Below, you can see the example of the rhythm of the major triad (Forte number 3-11b). In the 1st bar there is the prime form (0 4 7). In each subsequent bar there is a rotation of the first set by 16th note increments. HERE IS THE POINT, for the sake of the new function ! The note C (that I call Rhythmic Fundamental, the "root" of the rhythm) is being displaced, as you can see in the circled notes. THE SET WRAP AROUND ITSELF, always forming 12 time-points (always twelve 16th notes), in a different way from Babbit, where the order of the sets generates longer rhythms. THIS WAY IS MORE INTERESTING For Popular and Minimalist Repetition Music, as well as 12 tone music. In the bottom staff, there are the complementary rhythm of the 3-11b set, i.e., the 9-11a set. In the catalog, every set is presented alongside its complementary set and every set is presented in 3/4 (16th notes) and in 12-8 (with the 8th note as the base value for the increments and rotations). So the function needed would be the one that mirror exacty this kind of conversion, not the tradicional time-point-system conversion, so I could use my catolog inside Opusmodus, connecting the diferent sets, like this: Or even using portions of the Rhythmic Sets, by truncating some of them, like this: In the preceeding example, only parts of the 2 sets are used (9 time points out of 12 in the first and 8 time points out of 12 in the second). So, I hope someone could help me to find a way of implementing this. Maybe Janusz or Stephane could find interesting to develop this kind of idea inside the software. All the best ! Julio Herrlein
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. http://hdl.handle.net/10183/179457 Abstract 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 !! Best, Julio