Schismic: Difference between revisions
Restore some deletions. Distinguish strong and weak extensions. Don't add "maqamschismic" until it's proven notable. - mysterious extra steps in the interval chain |
→Scales: idiosyncratic terms |
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{{About|the regular temperament sometimes known as "helmholtz"|the music theorist|Hermann von Helmholtz}} | |||
{{Infobox regtemp | {{Infobox regtemp | ||
| Title = Schismic | | Title = Schismic | ||
| Subgroups = 2.3.5 | | Subgroups = 2.3.5 | ||
| Comma basis = [[32805/32768]] | | Comma basis = [[32805/32768]] | ||
| | | Edo join 1 = 12 | Edo join 2 = 53 | ||
| Mapping = 1; 1 -8 | | Mapping = 1; 1 -8 | ||
| Generators = 3/2 | |||
| Generators tuning = 701.731 | |||
| Optimization method = CWE | |||
| MOS scales = [[2L 3s]], [[5L 2s]], [[5L 7s]], [[12L 5s]] | |||
| Pergen = (P8, P5) | | Pergen = (P8, P5) | ||
| Color name = Layoti | | Color name = Layoti | ||
| Odd limit 1 = 5 | Mistuning 1 = 0.217 | Complexity 1 = 12 | | Odd limit 1 = 5 | Mistuning 1 = 0.217 | Complexity 1 = 12 | ||
| Odd limit 2 = | | Odd limit 2 = 5-limit 125 | Mistuning 2 = 0.837 | Complexity 2 = 29 | ||
}} | }} | ||
'''Schismic''', '''schismatic''', or '''helmholtz''' is a [[5-limit]] [[regular temperament|temperament]] which takes an almost just [[3/2|perfect fifth]] and stacks it eightfold to reach [[8/5]], mapping [[5/4]] to the diminished fourth (e.g. C–F♭) and [[tempering out]] the schisma, [[32805/32768]]. | '''Schismic''', '''schismatic''', or '''helmholtz''' is a [[5-limit]] [[regular temperament|temperament]] which takes an almost just [[3/2|perfect fifth]] and stacks it eightfold to reach [[8/5]], mapping [[5/4]] to the diminished fourth (e.g. C–F♭) and [[tempering out]] the schisma, [[32805/32768]]. | ||
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== Scales == | == Scales == | ||
{{Idiosyncratic terms|The later mos names are proposals that can be found on the page [[TAMNAMS Extension]].}} | |||
* [[5L 7s]] (p-chromatic) | * [[5L 7s]] (p-chromatic) | ||
* [[12L 5s]] (p-enharmonic) | * [[12L 5s]] (p-enharmonic) | ||
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| 69\118 || || 701.6949 || | | 69\118 || || 701.6949 || | ||
|- | |- | ||
| || 5/4 || 701.7108 || 1/8-comma | | || 5/4 || 701.7108 || 1/8-comma, lower bound of 5-odd-limit diamond tradeoff | ||
|- | |- | ||
| || 25/24 || 701.7252 || 2/17-comma | | || 25/24 || 701.7252 || 2/17-comma | ||
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| 31\53 || || 701.8868 || | | 31\53 || || 701.8868 || | ||
|- | |- | ||
| || 3/2 || 701.9550 || Pythagorean tuning | | || 3/2 || 701.9550 || Pythagorean tuning, upper bound of 5-odd-limit diamond tradeoff | ||
|- | |- | ||
| 24\41 || || 702.4390 || | | 24\41 || || 702.4390 || | ||
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[[Category:Schismic| ]] <!-- main article --> | [[Category:Schismic| ]] <!-- main article --> | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Microtemperaments]] | |||
[[Category:Schismatic family]] | [[Category:Schismatic family]] | ||