64:81:96: Difference between revisions

Chord information
Harmonics	64:81:96
Subharmonics	1/(81:64:54)
Intervals from root	1/1–81/64–3/2
Cents from root	0¢–408¢–702¢
Step intervals	81/64, 32/27
Step cents	408¢, 294¢
Color name	lawa or Lw
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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Revision as of 01:23, 30 October 2025

64:81:96 is a just 3-limit major triad, also known as the Pythagorean major triad. Its third differs from the third of the 5-limit major triad 4:5:6 by only the 81/80 comma. Assuming a harmonic timbre, the 5-limit triad is considerably more consonant.

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 {{Infobox Chord|ColorName=lawa or Lw}}
-'''64:81:96''' is a [[major triad]] found on the I, IV, and V of the [[3-limit]] [[5L 2s|diatonic scale]].  It is easily referred to as the '''Pythagorean major triad''', and, unlike [[4:5:6]], 54:64:81 is [[ambitonal]].
+'''64:81:96''' is a just 3-limit [[major triad]], also known as the '''Pythagorean major triad'''. Its third differs from the third of the 5-limit major triad [[4:5:6]] by only the [[81/80]] comma. Assuming a harmonic timbre, the 5-limit triad is considerably more consonant.
-In [[meantone]] this chord is tempered together with 4:5:6; it may be considered a 3-limit approximation of that chord, or used in its own right as a chord 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 IV degree in Ionian mode, thus preventing that scale degree from being tonicized by accident and lessening tonal ambiguity in plagal and semiplagal cadences, as well as other chord progressions that use both I and IV.
 [[Category:Major triads|##]] <!-- 2-digit first number -->

64:81:96: Difference between revisions

Revision as of 01:23, 30 October 2025

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