Looking for a Function to reorder a series of progressing ascending pitches?
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
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
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
All the best !
This caused a hanging (not responding) crash. I don´t know why...
(setf padrao '(7 -1 -5 4 -3 2 12 -16)) (setf pitches (gen-sieve '(c4 e6) padrao :type :pitch))
THIS DON´T CRASH
(setf padrao '(7 -1 -5 4 -3 2 12 -15)) (setf pitches (gen-sieve '(c4 e6) padrao :type :pitch))
One interesting thing that could be implemented as a function could be a form of generating Negative Harmony.
In the video below, there are some explanation of what it is and the origin in the Levy book.
It was a trendy topic due to the Jacob Collier interview. And there are a lot of fun videos making versions of pop tunes using negative harmony.
The way I understand it, it is simply a kind of mapping notes in relation to an axis, like in the figure below.
So we need a function that could map a note in any register to another note in the closest register to the first on.
So, any C note will be mapped to G, all Db to F#, all D to F, all, Eb to E, all B to Ab, all Bb to A.
It´s also possible to generate other mappings as well.
I think that replace map or substitute map can do the job, but I´m not sure (I will try), but I find interesting to post it here to explore the idea.
All the best,
It´s kind of funny to sse in this por versions how every is upside down and how you can generate an entirely new song from exactly the same material.
POP TUNES with negative harmony: