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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 ==
'''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 ==
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|-
|-
! #
! #
! Cents*
! Cents
! Approximate ratios
! Approximate ratios
!Superkleismic (2.3.5.7.11)
|-
|-
| 0
| 0
| 0.0
| 0
| '''1/1'''
| '''1/1'''
|
|-
|-
| 1
| 1
| 323.3
| 322
| 77/64
| 77/64
|6/5
|-
|-
| 2
| 2
| 646.7
| 644
| '''16/11'''
| '''16/11'''
|
|-
|-
| 3
| 3
| 970.0
| 966
| '''7/4'''
| '''7/4'''
|
|-
|-
| 4
| 4
| 93.4
| 88
| 128/121
| 128/121
|21/20, 22/21
|-
|-
| 5
| 5
| 416.7
| 410
| 14/11
| 14/11
|
|-
|-
| 6
| 6
| 740.1
| 732
| 49/32
| 49/32
|32/21
|-
|-
| 7
| 7
| 1063.4
| 1054
| 224/121
| 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
|}
|}
<nowiki/>* in 2.7.11-subgroup [[CWE]] tuning, octave reduced
 
 
== List of patent vals ==
:''Main article: [[Orgone/Patent vals]]''
{{navbox regtemp}}
{{navbox regtemp}}
{{cat|temperaments}}
{{cat|temperaments}}

Latest revision as of 02:12, 2 June 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.

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.

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


View • Talk • EditRegular temperaments
Rank-2
Acot Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave)
Monocot Meantone • Schismic • Gentle-fifth temperaments • Archy
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 Mabilic (alpha-triseph) • Orgone (trimech) • Didacus (diseph)
No-octaves Sensamagic (monogem)
Exotemperaments Dicot • Mavila • Father
Higher-rank
Rank-3 Hemifamity • Marvel • Parapyth
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