Diminished triad: Difference between revisions
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Mention 25:30:36 before 135:160:192 in the JI section. Of the two diminished chords in the duodene but not found in Zarlino, 25:30:36 is simpler. |
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| Line 10: | Line 10: | ||
In the 5-limit: | In the 5-limit: | ||
* [[45:54:64]] is found on vii<sup>o</sup> ({{Frac|45|32}}) in Ptolemy's intense diatonic scale ([[Zarlino]]), perhaps the most common [[5-limit]] diatonic. | * [[45:54:64]] is found on vii<sup>o</sup> ({{Frac|45|32}}) in Ptolemy's intense diatonic scale ([[Zarlino]]), perhaps the most common [[5-limit]] diatonic. | ||
* [[25:30:36]] is obtained by stacking two [[6/5]] minor thirds, and found on iii<sup>o</sup> ({{Frac|5|4}}) and vi<sup>o</sup> ({{Frac|5|3}}) in the [[duodene]]. | |||
* [[135:160:192]] is found on ii<sup>o</sup> ({{Frac|9|8}}) and ♯vi<sup>o</sup> ({{Frac|45|32}}) in the [[duodene]]. | * [[135:160:192]] is found on ii<sup>o</sup> ({{Frac|9|8}}) and ♯vi<sup>o</sup> ({{Frac|45|32}}) in the [[duodene]]. | ||
In the 3-limit: | In the 3-limit: | ||
Revision as of 20:15, 19 August 2024
A diminished triad is a triad comprising a root, minor third, and diminished fifth.
In just intonation
In the 7-limit:
In the 5-limit:
- 45:54:64 is found on viio (45⁄32) in Ptolemy's intense diatonic scale (Zarlino), perhaps the most common 5-limit diatonic.
- 25:30:36 is obtained by stacking two 6/5 minor thirds, and found on iiio (5⁄4) and vio (5⁄3) in the duodene.
- 135:160:192 is found on iio (9⁄8) and ♯vio (45⁄32) in the duodene.
In the 3-limit:
- 729:864:1024 is found on the viio of the Pythagorean diatonic scale.