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Hi everyone! After a few pieces in 31edo, I'm really excited to share some of my work in just intonation. This was a mostly improvised piece for 12 notes tuned to frequency ratios: 38:40:43:46:48:51:54:57:61:64:68:72:76. I call this my novemdecimal 12-chromatic tuning. It uses all ratios with a common numerary nexus of 19 or 19*2 to generate the pitch content. A prime is only factorable by one and itself meaning that within the space between the 1:2:3:4 factors of a prime number, you essentially generate a digital harmonic series with a different resolution between the harmonic factors. I call this a lineal segment. 19:38:57:76 is then perceived as 1:2:3:4 and the gaps between generate the harmonic content. This is a reduction of the lineal segment between 38:76 (2:4) which provides a perfect 2:3 in addition to tons of intervals unique to /19 (novemdecimal). Here is the tuning used in the piece: note: ratio: cents: 0: 1/1 0.0 1: 20/19 88 2: 43/38 214 3: 23/19 330 4: 24/19 404 5: 51/38 509 6: 27/19 608 7: 3/2 701.9 8: 61/38 819.3 9: 32/19 902.4 10: 34/19 1007.4 11: 36/19 1106.3 12: 2/1 1200.0 This system of just intonation works opposite to many traditional and longstanding views on just intonation. Namely, invertible symmetry (the idea the 16:19 is equivalent to 19:32) and prime limits. In this primodal system, prime limit is never considered.
