Dodecahedron (34 EDO Microtonal Contemporary Jazz)

This song uses the 34 EDO tuning system, which has nearly ideal major and minor thirds, as well as having a pretty good perfect fifth. The song also contains a substantial amount of polyrhythm. It uses a 4:5 polyrhythm as well as a 3:5 and 5:6 polyrhythm in other sections. This is the origin of the name. The dodecahedron is one of the Platonic solids. It has 12 faces, each of which is a regular pentagon. Thus, 3, 4, and 5 are all contained within the dodecahedron. The song uses a 12 note scale derived from an extremely extended major chord, beyond even a major 13th chord. Such an extension comes from alternatively stacking major and minor thirds which, in 34 EDO are 11 and 9 steps, respectively. The scale is a bit tempered beyond that, because otherwise, it would wind up with 2 different E's (11 and 12) and B's (31 and 32). Thus, I tempered it to get only one of each. (The scale is 0 6 9 11 15 17 20 23 26 29 31) The chord progression was CMaj7 G#Maj7 CMaj7 BMin7 CMaj7 G#Maj7 D#Min7 C#7 CMaj9. Near the end, the two solo instruments trade off on CMaj7 and G#Maj7. The "sax" sound plays in 5 (like the rhythm section), while the "trumpet" plays in 6. The "vibe" plays in 4 against the "sax" and 5 against the "trumpet." This beautiful picture is a 3-dimensional lattice spanned by dodecahedra created by DeviantArt user robolotion: https://www.deviantart.com/robolotion... LMMS was used to create the song.