175/144: Difference between revisions

Interval information
Ratio	175/144
Factorization	2-4 × 3-2 × 52 × 7
Monzo	[-4 -2 2 1⟩
Size in cents	337.5433 ¢
Name	avicennmic minor third
Color name	zyy3, zoyoyo 3rd
FJS name	[math]\displaystyle{ \text{M3}^{5,5,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	14.6211
Weil norm (log2 max(n, d))	14.9024
Wilson norm (sopfr(nd))	31
	Open this interval in xen-calc

Latest revision as of 13:04, 19 October 2026

175/144, the avicennmic minor third, is a 7-limit interval that exceeds the Pythagorean minor third by an avicennma. It is more likely to function as a major third in just intonation, being a Pythagorean major third flattened by two syntonic commas and a septimal comma. This function is further evidenced by the fact that it equals a stack of a 7/6 septimal minor third and a 25/24 classical chromatic semitone.

This interval has also been called the keemic minor third, viewed as fudged from 6/5 instead.

This interval is a near-optimal generator for the sixix temperament.

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-'''175/144''', the '''avicennmic minor third''', is a [[7-limit]] interval that exceeds the [[32/27|Pythagorean minor third]] by an [[525/512|avicennma]]. It functions as a ''major'' third, being a [[81/64|Pythagorean major third]] flattened by two [[syntonic comma]]s and a [[septimal comma]], which is further evidenced by the fact that it equals a stack of a [[7/6]] septimal minor third and a [[25/24]] classical chromatic semitone.
+'''175/144''', the '''avicennmic minor third''', is a [[7-limit]] interval that exceeds the [[32/27|Pythagorean minor third]] by an [[525/512|avicennma]]. It is more likely to function as a ''major'' third in [[just intonation]], being a [[81/64|Pythagorean major third]] flattened by two [[syntonic comma]]s and a [[septimal comma]]. This function is further evidenced by the fact that it equals a stack of a [[7/6]] septimal minor third and a [[25/24]] classical chromatic semitone.
 == Terminology ==