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| {{Infobox MOS}} | | {{Infobox MOS}} |
| '''7L 3s<4/1>''' (sometimes called '''diaquadic''') refers to a non-octave [[MOS scale]] family with a period of a [[4/1]] and which has 7 large and 3 small steps. These scales are in some ways a double octave clone of [[5L 2s|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685-cent flat fifth and [[5edo]]/10ed4's 720-cent sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720-cent fifth and collapsed is 685-cent fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale.
| | {{MOS intro}} |
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| == Modes ==
| | These scales are in some ways a double octave clone of [[5L 2s|diatonic scale]]s because they are generated from perfect fifths and have the [[7edo]]/[[7ed4]] 685{{c}} flat fifth and [[5edo]]/10ed4's 720{{c}} sharp fifth at the ends of the tuning spectrum. However, ~3/2 is now the chroma-negative rather than chroma-positive generator, equalized and collapsed tunings are now swapped (equalized is 720{{c}} fifth and collapsed is 685{{c}} fifth), and the basic tuning is now the 705-cent gentle fifth from [[17edo]]/[[17ed4]] instead of 12edo's fifth. Diaquadic scales are also more widely spaced than diatonic scales, closer melodically to an octave-period pentatonic scale. |
| The darker modes contain both major triads and augmented triads on the root, and the brighter modes contain both minor and diminished triads on the root.
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| * LLLsLLsLLs 9|0
| | == Scale properties == |
| * LLsLLLsLLs 8|1
| | {{TAMNAMS use}} |
| * LLsLLsLLLs 7|2
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| * LLsLLsLLsL 6|3
| | === Intervals === |
| * LsLLLsLLsL 5|4
| | {{MOS intervals}} |
| * LsLLsLLLsL 4|5
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| * LsLLsLLsLL 3|6
| | === Generator chain === |
| * sLLLsLLsLL 2|7
| | {{MOS genchain}} |
| * sLLsLLLsLL 1|8
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| * sLLsLLsLLL 0|9
| | === Modes === |
| | {{MOS mode degrees}} |
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| | == Scale tree == |
| | {{MOS tuning spectrum |
| | | 5/3 = [[Quarchy]] is around here |
| | | 3/1 = [[Tetrominant]] is around here |
| | | 4/1 = [[Meanquad]] is around here |
| | }} |
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| == Temperaments == | | == Temperaments == |
| There are two major rank-2 temperament interpretations of diaquadic, corresponding to double octave clones of [[meantone]] and [[archy]]. | | There are two major rank-2 temperament interpretations of diaquadic, [[meanquad]] and [[quarchy]], corresponding to double-octave clones of [[meantone]] and [[archy]]. |
| === Meanquad ===
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| ''Main article: [[Meanquad]]''
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| * [[Subgroup]]: 4.5.6
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| * [[Comma list]]: [[81/80]]
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| * [[Val]]s: 7, 31, 38, 24, 17, 10, 69, 45, 55, 11[-5], 52, 41, 13[+5], 27[+5]
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| * [[CTE tuning]]: ~[[3/2]] = 697.214
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| === Quarchy ===
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| * [[Subgroup]]: 4.6.7
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| * [[Comma list]]: [[64/63]]
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| * [[Val]]s: 10, 17, 7, 27, 37, 44, 13, 24, 47, 11[+7], 23, 57, 16, 41
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| * [[CTE tuning]]: ~[[3/2]] = 709.595
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| === Supertetryth ===
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