Orgone: Difference between revisions
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'''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. | '''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. | ||
[[File:Orgone7.png|thumb|Orgone heptatonic MOS]] | |||
[[26edo]] is a good tuning of Orgone; [[41edo]] is on the flatter end of the generator spectrum and [[37edo]] is on the sharper end. | [[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 == | == 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 | '''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, 26edo, and 41edo. It may also be valuable to consider the 2.(5/3).7.11 version, which is supported by 11edo (and thus 22edo). | ||
== Interval chain == | == Interval chain == | ||
Latest revision as of 02:12, 2 June 2026
| Orgone |
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, 26edo, and 41edo. 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
