Orgone

Orgone

Subgroups	2.7.11
Reduced mapping	⟨1; 3 -2]
ET join	11 & 15
Generators (CWE)	~77/64 = 323.3¢
MOS scales	4L 3s, 4L 7s, 11L 4s
Ploidacot	trimech
Comma basis	65536/65219 (2.7.11)
Minimax error	-odd-limit: ¢
Target scale size	-odd-limit: notes

Orgone, 11 & 15, is a highly efficient temperament of the 2.7.11 subgroup, tempering out 65536/65219, such that three intervals of 11/8 reach the same point as two intervals of 8/7; the generator is therefore (11/8)/(8/7) = 77/64, two of which stack to 16/11 and three of which stack to 7/4.

26edo is a good tuning of Orgone; 41edo is on the flatter end of the generator spectrum and 37edo is on the sharper end.

Extensions

Superkleismic is the primary extension of Orgone to the full 11-limit. The generator is interpreted as 6/5, which stacks twice to make 16/11 and three times to make 7/4 (keemic tempering, which is also supported by porcupine and flattone); the 7/4 itself stacks three times (octave-reduced) to reach 4/3 (slendric tempering). Superkleismic is an important temperament in 15edo and 26edo. It may also be valuable to consider the 2.(5/3).7.11 version, which is supported by 11edo (and thus 22edo).

Interval chain

In the following table, odd harmonics and subharmonics 1–11 are in bold.

#	Cents	Approximate ratios	Superkleismic (2.3.5.7.11)
0	0	1/1
1	322	77/64	6/5
2	644	16/11
3	966	7/4
4	88	128/121	21/20, 22/21
5	410	14/11
6	732	49/32	32/21
7	1054	224/121	11/6
8	176	...	10/9
9	498		4/3
10	820		8/5
11	1142		48/25, 36/35, 33/32
12	264		7/6
13	586		7/5

List of patent vals

Main article: Orgone/Patent vals