54:64:81: Difference between revisions

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{{Infobox Chord|ColorName=wa or w}}
{{Infobox Chord|ColorName=wa or w}}
'''54:64:81''', is a [[minor triad]] found on the ii, iii, and vi of the [[3-limit]] [[5L 2s|diatonic scale]].
'''54:64:81''', is a [[minor triad]] found on the ii, iii, and vi of the [[3-limit]] [[5L 2s|diatonic scale]].  It is easily referred to as the '''Pythagorean minor triad''', and, unlike [[10:12:15]], 54:64:81 is [[ambitonal]].


In [[meantone]] this chord is [[tempered together]] with both [[10:12:15]] and [[27:32:40]], so it may be considered a 3-limit approximation of those chords, or a chord in its own right with a less-stable third. Unlike 10:12:15, 54:64:81 is [[ambitonal]].
In [[meantone]] this chord is [[tempered together]] with both 10:12:15 and [[27:32:40]], so it may be considered a 3-limit approximation of those chords, or a chord in its own right with a less-stable third. Accordingly, [[User:Aura|Aura]] takes advantage of these properties in his non-meantone [[5-limit]] music where it shows up as the triad built on the ii degree in Ionian mode in place of 27:32:40, thus allowing it to be more reliably used in the major scale's [[Wikipedia: Circle progression|circle progression]], while also cutting back on tonal ambiguity.


[[Category:Minor triads|##]] <!-- 2-digit first number -->
[[Category:Minor triads|##]] <!-- 2-digit first number -->

Revision as of 17:08, 25 October 2025

Chord information
Harmonics 54:64:81
Subharmonics 1/(96:81:64)
Intervals from root 1/132/273/2
Cents from root 294¢702¢
Step intervals 32/27, 81/64
Step cents 294¢, 408¢
Color name wa or w
Prime limit 3
Genus 34 (81)
Intervallic odd limit 81
Otonal odd limit 81
Utonal odd limit 81
Consistent edos (d ≥ 2) 12edo**, 17edo*, 24edo*, 29edo*, …

54:64:81, is a minor triad found on the ii, iii, and vi of the 3-limit diatonic scale. It is easily referred to as the Pythagorean minor triad, and, unlike 10:12:15, 54:64:81 is ambitonal.

In meantone this chord is tempered together with both 10:12:15 and 27:32:40, so it may be considered a 3-limit approximation of those chords, or a chord in its own right with a less-stable third. Accordingly, Aura takes advantage of these properties in his non-meantone 5-limit music where it shows up as the triad built on the ii degree in Ionian mode in place of 27:32:40, thus allowing it to be more reliably used in the major scale's circle progression, while also cutting back on tonal ambiguity.