Gamelismic and portent: Difference between revisions
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{{Infobox regtemp | |||
| Title = Gamelismic; portent | |||
| Subgroups = 2.3.5.7, 2.3.5.7.11 | |||
| Comma basis = [[1029/1024]] (7-limit); <br>[[385/384]], [[441/440]] (11-limit) | |||
| Edo join 1 = 15 | Edo join 2 = 26 | Edo join 3 = 31 | |||
| Mapping = 1; 3 0 -1 4; 0 1 0 -1 | |||
| Generators = 8/7, 5/4 | |||
| Generators tuning = 233.8, 385.3 | |||
| Optimization method = CWE | |||
| Odd limit 1 = 9 | Mistuning 1 = 2.41 | Complexity 1 = ? | |||
| Odd limit 2 = 11-limit 21 | Mistuning 2 = 2.81 | Complexity 2 = ? | |||
}} | |||
'''Gamelismic''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] [[generator|generated]] by a supermajor second of [[~]][[8/7]], three of them stacking to ~[[3/2]], and an independent dimension for [[prime interval|prime]] [[5/1|5]]. Thus it [[tempering out|tempers out]] [[1029/1024]], the gamelisma, in the [[7-limit]], which means it is an [[expansion]] of [[slendric]], the [[rank-2 temperament|rank-2]] [[2.3.7 subgroup|2.3.7-subgroup]] temperament that tempers out the same comma. It has an obvious [[extension]] to the [[11-limit]] tempering out [[385/384]] and [[441/440]], called '''portent''', as {{nowrap| 1029/1024 {{=}} (385/384)(441/440) }}. | '''Gamelismic''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] [[generator|generated]] by a supermajor second of [[~]][[8/7]], three of them stacking to ~[[3/2]], and an independent dimension for [[prime interval|prime]] [[5/1|5]]. Thus it [[tempering out|tempers out]] [[1029/1024]], the gamelisma, in the [[7-limit]], which means it is an [[expansion]] of [[slendric]], the [[rank-2 temperament|rank-2]] [[2.3.7 subgroup|2.3.7-subgroup]] temperament that tempers out the same comma. It has an obvious [[extension]] to the [[11-limit]] tempering out [[385/384]] and [[441/440]], called '''portent''', as {{nowrap| 1029/1024 {{=}} (385/384)(441/440) }}. | ||
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* [[Portent11tri]] – 11-tone [[trivalent scale]] in 190edo tuning | * [[Portent11tri]] – 11-tone [[trivalent scale]] in 190edo tuning | ||
* [[Portent26]] – 26-tone [[hobbit scale]] in 11-odd-limit minimax tuning | * [[Portent26]] – 26-tone [[hobbit scale]] in 11-odd-limit minimax tuning | ||
* [[Penslen]] | |||
== Tunings == | == Tunings == | ||
Latest revision as of 18:35, 19 March 2026
| Gamelismic; portent |
385/384, 441/440 (11-limit)
11-limit 21-odd-limit: 2.81 ¢
11-limit 21-odd-limit: ? notes
Gamelismic is a rank-3 temperament generated by a supermajor second of ~8/7, three of them stacking to ~3/2, and an independent dimension for prime 5. Thus it tempers out 1029/1024, the gamelisma, in the 7-limit, which means it is an expansion of slendric, the rank-2 2.3.7-subgroup temperament that tempers out the same comma. It has an obvious extension to the 11-limit tempering out 385/384 and 441/440, called portent, as 1029/1024 = (385/384)(441/440).
See Gamelismic family #Gamelismic and Gamelismic family #Portent for technical data.
Interval lattice
-
11-limit portent
Chords
Portent enables essentially tempered chords of gamelismic, keenanismic, and werckismic.
Scales
- Portent11tri – 11-tone trivalent scale in 190edo tuning
- Portent26 – 26-tone hobbit scale in 11-odd-limit minimax tuning
- Penslen
Tunings
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~8/7 = 233.8889 ¢, ~5/4 = 385.3137 ¢ | CWE: ~8/7 = 233.7474 ¢, ~5/4 = 385.5205 ¢ | POTE: ~8/7 = 233.6875 ¢, ~5/4 = 385.1853 ¢ |
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~8/7 = 233.9922 ¢, ~5/4 = 385.7972 ¢ | CWE: ~8/7 = 233.7616 ¢, ~5/4 = 385.3149 ¢ | POTE: ~8/7 = 233.6884 ¢, ~5/4 = 385.1618 ¢ |