Diaschismic: Difference between revisions
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{{Infobox | {{Infobox regtemp | ||
| Title = Diaschismic | | Title = Diaschismic | ||
| Subgroups = 2.3.5, 2.3.5.7, 2.3.5.7.11.13.17 | | Subgroups = 2.3.5, 2.3.5.7, 2.3.5.7.11.13.17 | ||
| Comma basis = [[2048/2025]] (5-limit);<br>[[126/125]], [[2048/2025]] (7-limit); <br>[[126/125]], [[136/135]], [[176/175]], <br>[[196/195]], [[256/255]] (17-limit) | | Comma basis = [[2048/2025]] (5-limit); <br>[[126/125]], [[2048/2025]] (7-limit); <br>[[126/125]], [[136/135]], [[176/175]], <br>[[196/195]], [[256/255]] (17-limit) | ||
| Edo join 1 = 46 | Edo join 2 = 58 | | Edo join 1 = 46 | Edo join 2 = 58 | ||
| | | Mapping = 2; 1 -2 -8 -12 -15 1 | ||
| Generators = 3/2 | Generators tuning = 703.9 | Optimization method = CWE | |||
| MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]] | | MOS scales = [[2L 8s]], [[10L 2s]], [[12L 10s]] | ||
| Pergen = (P8/2, P5) | | Pergen = (P8/2, P5) | ||
| Color name = Saguguti | | Color name = Saguguti | ||
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| Odd limit 2 = 17-limit 21 | Mistuning 2 = ??? | Complexity 2 = 46 | | Odd limit 2 = 17-limit 21 | Mistuning 2 = ??? | Complexity 2 = 46 | ||
}} | }} | ||
'''Diaschismic''', sometimes known as ''srutal'' in the [[5-limit]], is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a [[3/2|perfect fifth]] or that minus a half-octave [[period]], which is a semitone representing [[16/15]]. Two of these semitones give a whole tone of [[9/8]], so the diaschisma, [[2048/2025]], is [[tempering out|tempered out]], and we also have a whole tone plus a period represent [[8/5]]. | '''Diaschismic''', sometimes known as ''srutal'' in the [[5-limit]], is a half-octave [[regular temperament|temperament]] [[generator|generated]] by a [[3/2|perfect fifth]] or that minus a half-octave [[period]], which is a semitone representing [[16/15]]. Two of these semitones give a whole tone of [[9/8]], so the diaschisma, [[2048/2025]], is [[tempering out|tempered out]], and we also have a whole tone plus a period represent [[8/5]]. | ||
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Notice also the little interval between the largest of a category and the smallest of the next. This interval spans 46 generator steps, so it vanishes in 46edo, but is tuned to the same size as the comma step in 58edo. 104edo tunes it to one half the size of the comma step, which may be seen as a good compromise. | Notice also the little interval between the largest of a category and the smallest of the next. This interval spans 46 generator steps, so it vanishes in 46edo, but is tuned to the same size as the comma step in 58edo. 104edo tunes it to one half the size of the comma step, which may be seen as a good compromise. | ||
{{Clear}} | |||
== Chords and harmony == | == Chords and harmony == | ||
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|- | |- | ||
| | | | ||
| | | 7/6 | ||
| 703.681 | | 703.681 | ||
| | | | ||
|- | |||
| [[162edo|95\162]] | |||
| | |||
| 703.704 | |||
| 162cef val | |||
|- | |- | ||
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| 703.965 | | 703.965 | ||
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|- | |||
| [[150edo|88\150]] | |||
| | |||
| 704.000 | |||
| 150c val | |||
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[[Category:Diaschismic family]] | [[Category:Diaschismic family]] | ||
[[Category:Starling temperaments]] | [[Category:Starling temperaments]] | ||
[[Category: | [[Category:Aberschismic temperaments]] | ||