Orgone: Difference between revisions
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[[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 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 == | == Interval chain == | ||
| Line 18: | Line 21: | ||
|- | |- | ||
! # | ! # | ||
! Cents | ! Cents | ||
! Approximate ratios | ! Approximate ratios | ||
!Superkleismic (2.3.5.7.11) | |||
|- | |- | ||
| 0 | | 0 | ||
| | | 0 | ||
| '''1/1''' | | '''1/1''' | ||
| | |||
|- | |- | ||
| 1 | | 1 | ||
| | | 322 | ||
| 77/64 | | 77/64 | ||
|6/5 | |||
|- | |- | ||
| 2 | | 2 | ||
| | | 644 | ||
| '''16/11''' | | '''16/11''' | ||
| | |||
|- | |- | ||
| 3 | | 3 | ||
| | | 966 | ||
| '''7/4''' | | '''7/4''' | ||
| | |||
|- | |- | ||
| 4 | | 4 | ||
| | | 88 | ||
| 128/121 | | 128/121 | ||
|21/20, 22/21 | |||
|- | |- | ||
| 5 | | 5 | ||
| | | 410 | ||
| 14/11 | | 14/11 | ||
| | |||
|- | |- | ||
| 6 | | 6 | ||
| | | 732 | ||
| 49/32 | | 49/32 | ||
|32/21 | |||
|- | |- | ||
| 7 | | 7 | ||
| | | 1054 | ||
| 224/121 | | 224/121 | ||
| | |11/6 | ||
|- | |- | ||
| | |8 | ||
|176 | |||
|... | |||
|10/9 | |||
|- | |- | ||
| | |9 | ||
|498 | |||
| | |||
|4/3 | |||
|- | |- | ||
| | |10 | ||
|820 | |||
| | |||
|8/5 | |||
|- | |- | ||
|11|| | |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]]'' | |||
{{navbox regtemp}} | {{navbox regtemp}} | ||
{{cat|temperaments}} | {{cat|temperaments}} | ||
Latest revision as of 01:05, 29 March 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 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
| View • Talk • EditRegular temperaments | |
|---|---|
| Rank-2 | |
| Acot | Blackwood (1/5-octave) • Whitewood (1/7-octave) • Compton (1/12-octave) |
| Monocot | Meantone • Schismic • Leapday • 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 | Trismegistus (alpha-triseph) • Orgone (trimech) • Didacus (diseph) |
| No-octaves | Sensamagic (monogem) |
| Exotemperament | Dicot • Mavila • Father |
| Higher-rank | |
| Rank-3 | Hemifamity • Marvel • Parapyth |
