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.

== Seven limit children ==

= Seven-limit children =

The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and ~~hemis~~ 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving ~~quarter-tones~~ instead of semitones.

The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and triforce 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quartertones instead of semitones.

== August ==

@@ Line 3: / Line 3: @@
 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 &lt;&lt;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.
-== Seven limit children ==
+= Seven-limit children =
-The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and hemis 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quarter-tones instead of semitones.
+The second comma of the [[Normal lists|normal comma list]] defines which [[7-limit]] family member we are looking at. August adds 36/35, augene 64/63, hexe 256/245, hemiaug 245/243, and triforce 49/48. Hexe splits the period to 1/6 octave, and hemiaug the generator, giving quartertones instead of semitones.
 == August ==