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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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| == Intervals ==
| | 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. |
| {|class="wikitable"
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| |-
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| !Dark generators
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| !colspan="2"|Notation
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| ![[17ed4]] cents
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| !
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| !Bright generators
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| !colspan="2"|Notation
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| ![[17ed4]] cents
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| |-
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| |0
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| |J
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| |perfect 0-step
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| |1694.16
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| |0
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| |J
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| |perfect 10-step
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| |282.36
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| |-
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| |1
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| |M
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| |perfect 3-step
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| |705.90
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| |1
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| |Q
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| |perfect 7-step
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| |1694.16
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| |-
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| |2
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| |Pb
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| |minor 6-step
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| |1411.80
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| |2
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| |N
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| |major 4-step
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| |988.26
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| |-
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| |3
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| |Sb
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| |minor 9-step
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| |2117.70
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| |3
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| |K
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| |major 1-step
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| |282.36
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| |-
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| |4
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| |Lb
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| |minor 2-step
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| |423.54
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| |4
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| |R
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| |major 8-step
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| |1976.52
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| |-
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| |5
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| |Ob
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| |minor 5-step
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| |1129.44
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| |5
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| |O
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| |major 5-step
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| |1270.62
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| |-
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| |6
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| |Rb
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| |minor 8-step
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| |1835.34
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| |6
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| |L
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| |major 2-step
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| |564.72
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| |-
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| |7
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| |Kb
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| |minor 1-step
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| |141.18
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| |7
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| |S
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| |major 9-step
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| |2258.88
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| |-
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| |8
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| |Nb
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| |minor 4-step
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| |847.08
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| |8
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| |P
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| |major 6-step
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| |1552.98
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| |}
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| == Modes == | | == Scale properties == |
| 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.
| | {{TAMNAMS use}} |
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| * LLLsLLsLLs 9|0
| | === Intervals === |
| * LLsLLLsLLs 8|1
| | {{MOS intervals}} |
| * LLsLLsLLLs 7|2
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| * LLsLLsLLsL 6|3
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| * LsLLLsLLsL 5|4
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| * LsLLsLLLsL 4|5
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| * LsLLsLLsLL 3|6
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| * sLLLsLLsLL 2|7
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| * sLLsLLLsLL 1|8
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| * sLLsLLsLLL 0|9
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| | === Generator chain === |
| | {{MOS genchain}} |
| | |
| | === Modes === |
| | {{MOS mode degrees}} |
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| == Scale tree == | | == Scale tree == |
| {{Scale tree|Comments=5/3:Quarchy is around here;3/1:Tetrominant is around here;4/1:Meanquad is around here}} | | {{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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| * {{Mapping|legend=1|1 0 1|0 4 1}}
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| * [[Support]]ing ETs: 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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| ==== Tetrominant ====
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| * [[Subgroup]]: 4.5.6.7
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| * [[Comma list]]: [[36/35]], [[64/63]]
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| * {{Mapping|legend=1|1 0 1 2|0 4 1 -2}}
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| * [[Support]]ing ETs: 7, 17, 24, 10, 31, 41, 27[+5], 38[+7], 55[+7], 58[+5, +7], 65[+5, +7], 44[+5], 75[+5, +7]
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| * [[CTE tuning]]: ~[[3/2]] = 699.622
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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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| * {{Mapping|legend=1|1 2 0|0 1 -2}}
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| * [[Support]]ing ETs: 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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