Diminished triad: Difference between revisions
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In the 7-limit: | In the 7-limit: | ||
* [[5:6:7]] is an upper structure of [[4:5:6:7]], the ''harmonic seventh chord''. | * [[5:6:7]] is an upper structure of [[4:5:6:7]], the ''harmonic seventh chord''. | ||
* [[30:35:42]] (1/1 - 7/6 - 7/5) is a subharmonic chord. | |||
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: | ||
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[[Category:Diminished triads| ]] <!-- main article --> | [[Category:Diminished triads| ]] <!-- main article --> | ||
[[Category:Just intonation chords]] | [[Category:Just intonation chords]] | ||
{{todo|inline=1|expand|add examples|comment=needs information about temperaments}} | |||
Latest revision as of 02:13, 15 December 2024
A diminished triad is a triad comprising a root, minor third, and diminished fifth.
In just intonation
In the 7-limit:
- 5:6:7 is an upper structure of 4:5:6:7, the harmonic seventh chord.
- 30:35:42 (1/1 - 7/6 - 7/5) is a subharmonic chord.
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.
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Todo: expand, add examples
needs information about temperaments |