54:64:81: Difference between revisions

Chord information
Harmonics	54:64:81
Subharmonics	1/(96:81:64)
Intervals from root	1/1–32/27–3/2
Cents from root	0¢–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, …
	* 2 ≤ d < 4; 4 ≤ d < 8; * 8 ≤ d < 16; …

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VisualWikitext

Latest revision as of 01:28, 30 October 2025

54:64:81, also known as the Pythagorean minor triad, is a just 3-limit minor triad. Its third differs from the third of the much simpler 5-limit minor triad 10:12:15 by only the 81/80 comma.

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 {{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]].  It is easily referred to as the '''Pythagorean minor triad''', and, unlike [[10:12:15]], 54:64:81 is [[ambitonal]].
+'''54:64:81''', also known as the '''Pythagorean minor triad''', is a just 3-limit [[minor triad]]. Its third differs from the third of the much simpler 5-limit minor triad [[10:12:15]] by only the [[81/80]] comma.
-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 -->

54:64:81: Difference between revisions

Latest revision as of 01:28, 30 October 2025

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