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== 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 26edo.
'''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).


== List of patent vals ==
== List of patent vals ==

Revision as of 06:12, 28 March 2026

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.

Interval chain

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

# Cents* Approximate ratios
0 0.0 1/1
1 323.3 77/64
2 646.7 16/11
3 970.0 7/4
4 93.4 128/121
5 416.7 14/11
6 740.1 49/32
7 1063.4 224/121

* in 2.7.11-subgroup CWE tuning, octave reduced

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).

List of patent vals

Main article: Orgone/Patent vals


ViewTalkEditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot MeantoneSchismicLeapdayArchy
Complexity 2 Diaschismic (diploid monocot) • Pajara (diploid monocot) • Injera (diploid monocot) • Rastmatic (dicot) • Mohajira (dicot) • Intertridecimal (dicot) • Interseptimal (alpha-dicot)
Complexity 3 Augmented (triploid) • Misty (triploid) • Slendric (tricot) • Porcupine (omega-tricot)
Complexity 4 Diminished (tetraploid) • Tetracot (tetracot) • Buzzard (alpha-tetracot) • Squares (beta-tetracot) • Negri (omega-tetracot)
Complexity 5-6 Magic (alpha-pentacot) • Amity (gamma-pentacot) • Kleismic (alpha-hexacot) • Miracle (hexacot)
Higher complexity Orwell (alpha-heptacot) • Sensi (beta-heptacot) • Octacot (octacot) • Wurschmidt (beta-octacot) • Valentine (enneacot) • Ammonite (epsilon-enneacot) • Myna (beta-decacot) • Ennealimmal (enneaploid dicot)
Straddle-3 A-Team (alter-tricot) • Machine (alter-monocot)
No-3 Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperament DicotMavilaFather
Higher-rank
Rank-3 HemifamityMarvelParapyth