Diminished seventh chord: Difference between revisions
introduce temperaments by building up (rather than removing) tempered commas; give chords for each mentioned temperament; include a description of the conventional 5-limit meantone chord; clarify historical connection between quarter-comma meantone and starling |
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== In just intonation == | == In just intonation == | ||
* [[ | In the [[7-limit]]: | ||
* [[125:150:180:216]] | * [[15:18:21:25]] is a [[preimage]] of the chord found in diminished temperament, found in [[genus]] 3<sup>2</sup>⋅5<sup>2</sup>⋅7. | ||
* [[225:270:320:384]] < | * [[35:42:50:60]] is a preimage of the chord found in starling temperament, also found in genus 3<sup>2</sup>⋅5<sup>2</sup>⋅7. | ||
In the [[5-limit]]: | |||
* [[125:150:180:216]] is the 125-odd chord produced by stacking three [[6/5]] minor thirds. | |||
* [[225:270:320:384]] is a 75-odd chord found on vii<sup>o7</sup> ({{Frac|15|8}}) in the duodene, and is closely related to the [[36:45:54:64]] dominant seventh chord, stacking on an additional minor third (to make a “dominant ninth”) and dropping the root. | |||
* [[75:90:108:128]] is another 75-odd [[preimage]] of the meantone chord. | |||
* [[75:90:108:125]] is another 125-odd preimage of the dimipent chord. | |||
* [[90:108:125:150]] is another 125-odd preimage of the dimipent chord. | |||
In higher limits: | |||
* [[10:12:14:17]] is a 17-limit interpretation of the chord associated with François-Joseph Fétis. | |||
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