Orgone

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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


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