Augmented family: Difference between revisions
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The 5-limit parent comma for the '''augmented family''' is 128/125, the [[128/125|diesis]]. Its [[monzo]] is {{Monzo| 7 0 -3 }}, and flipping that yields <<3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for [[5-limit]] augmented, though a sharper fifth might be preferred to go with the sharp third. | The 5-limit parent comma for the '''augmented family''' is 128/125, the [[128/125|diesis]]. Its [[monzo]] is {{Monzo| 7 0 -3 }}, and flipping that yields <<3 0 -7|| for the [[wedgie]]. Hence the period is 1/3 octave, and this is what is used for a major third. The [[generator]] can be taken as a fifth or a semitone, and [[12edo]], with its excellent fifth, is an obvious tuning for [[5-limit]] augmented, though a sharper fifth might be preferred to go with the sharp third. | ||
Comma: 128/125 | = Augmented = | ||
[[Comma]]: 128/125 | |||
POTE generator: ~3/2 = | [[POTE tuning|POTE generator]]: ~3/2 = 706.638 | ||
Map: [<3 0 7|, <0 1 0|] | [[Map]]: [<3 0 7|, <0 1 0|] | ||
{{Vals|legend=1| 3, 12, 27, 39, 51c, 90cc }} | |||
Badness: 0.022315 | [[Badness]]: 0.022315 | ||
== Seven-limit children == | == Seven-limit children == | ||
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[[Comma list]]: 36/35, 128/125 | [[Comma list]]: 36/35, 128/125 | ||
[[POTE tuning|POTE generator]]: 696.011 | [[POTE tuning|POTE generator]]: ~3/2 = 696.011 | ||
[[Map]]: [<3 0 7 -1|, <0 1 0 2|] | [[Map]]: [<3 0 7 -1|, <0 1 0 2|] | ||
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[[Comma list]]: 64/63, 126/125 | [[Comma list]]: 64/63, 126/125 | ||
[[POTE_tuning|POTE generator]]: 709.257 | [[POTE_tuning|POTE generator]]: ~3/2 = 709.257 | ||
Map: [<3 0 7 18|, <0 1 0 -2|] | Map: [<3 0 7 18|, <0 1 0 -2|] | ||
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Comma list: 50/49, 128/125 | Comma list: 50/49, 128/125 | ||
[[POTE_tuning|POTE generator]]: 710.963 | [[POTE_tuning|POTE generator]]: ~3/2 = 710.963 | ||
Map: [<6 0 14 17|, <0 1 0 0|] | Map: [<6 0 14 17|, <0 1 0 0|] | ||