Augmented family: Difference between revisions
corrected structure; simplified some links; introduces Template:Monzo; moved interwiki link down |
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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. | ||
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Wedgie: <<6 0 0 -14 -17 0|| | Wedgie: <<6 0 0 -14 -17 0|| | ||
EDOs: [[6edo|6]], [[12edo|12]], [[30edo|30d]], | EDOs: [[6edo|6]], [[12edo|12]], [[30edo|30d]], [[42edo|42d]], [[54edo|54cd]] | ||
Badness: 0.0577 | Badness: 0.0577 | ||