Generative 25: Porcupine (22edo)
Channel: duckapus
Date: 2023-04-25

This one was made for the Xenharmonic Alliance discord's April "tuning of the month", which is "Porcupine Temperament". It is also in 22/8 meter, or 11/8 in two bar groups. Made using the generative program I built in Max, but also manually edited and expanded quite a lot, so I'm calling it "semi-generative". The images in the video were made in midjourney. I could write an essay about each of these things: Porcupine temperament, 22/8 time, semi-generative stuff, and the images. Let's see if I can be terse.

As for 22/8 meter, or pairs of 11/8 measures, a fun thing is how 11/8 is almost 12/8 or 6/4, both pretty normal meters. Being one 8th note short of these normal meters can make 11/8 sound like it is continually rushing ahead, tripping over itself as if in a hurry, giving a sense of forward motion or restless eagerness—similar to how 7/8 can feel sometimes, being one 8th short of 4/4 time. I mostly subdivided the rhythm into groups of 2 and 3 over two bars of 11/8, often like this: 3-2-2-2-2 | 3-2-3-3. The 2s would be quarter notes, at 116 BPM.

Porcupine is a temperament, so there are multiple tunings one could use. In this case I used 22edo, or 22 equal divisions of the octave, instead of the 12 notes of "normal" 12edo. I decided to use 22/8 meter because it's in 22edo, might as well go all in on 22. An interesting thing about Porcupine is that it can be done in 14edo, 22edo, 29edo, and other tunings, but not in "normal" 12edo. I can't explain Porcupine very well, but one aspect is that it tempers out the two pitches of the "porcupine comma", which is the difference in pitch between three 6:5 minor 3rds (~315.6¢ * 3) and two 4:3 perfect 4ths (~498¢ * 2). In just intonation this makes a difference of about a quarter tone (49¢), pretty large for a comma, quite audible. 

Note that in "normal" 12edo the 3rd step is the min3 (300¢) and the 5th step is the P4 (500¢). Since 3*3 != 5*2, the porcupine comma is not tempered out. But in 22edo the 6th step is the min3 and the 9th step is the P4, and 6*3 == 9*2, so the porcupine comma *is* tempered out. All this results in interesting harmonic possibilities that simply cannot happen in 12edo. Like the P4 is divided into 3 equal parts, 2 of which make the min3. In 12edo you can't divide either the min3 (3 steps) or P4 (5 steps) in equal parts, since 3 and 5 are prime. While porcupine harmony can sound logical and decently concordant, it also sounds "xen" and "not normal", at least to all of us who have lived with 12edo and little else ever. So that's fun. 

Note that the oddness of Porcupine is a bit obscured in this piece due to the notes being pretty fast and staccato. At the end it slows down and notes are held longer, so the porcupine oddness becomes more obvious, and maybe one can get an idea of why they call it "porcupine". I mostly used 7-note modes of three porcupine scales, porcupine-7 MOS (4333333 in 22edo) and the MODMOS scales apparently called "lizard" (4324333), "horse" (4333342), and "lion" (4333423). The modes of these scales have animal names, like Chinchilla, Lizard, Iguana, Crocodile, Pig, Lion, Leopard, and Cheetah. The way my Max generative program works these mode changes act sort of like chord changes, or key changes, or perhaps something in between.