65536/59049: Difference between revisions

Interval information
Ratio	65536/59049
Factorization	216 × 3-10
Monzo	[16 -10⟩
Size in cents	180.45¢
Name	Pythagorean diminished third
Color name	sawa 3rd, sw3
FJS name	[math]\displaystyle{ \text{d3} }[/math]
Special properties	reduced,; reduced subharmonic
Tenney norm (log2 nd)	31.8496
Weil norm (log2 max(n, d))	32
Wilson norm (sopfr(nd))	62
	Open this interval in xen-calc

Revision as of 05:12, 4 February 2026

65536/59049, the Pythagorean diminished third, is an interval in 3-limit just intonation. It is equal to a pythagorean minor third minus an apotome, hence the name.

Despite being classified as a third, it is only a schisma sharp of 10/9, and is thus equated with 10/9 in the schismic temperament. It is also equated to 11/10 in pele, as well as its rank-2 subtemperaments diaschismic, mystery, leapday, and andromeda.

Revision as of 05:12, 4 February 2026 view source Overthink (talk \| contribs) autopatrolled 2,726 edits note mystery ← Older edit		Revision as of 05:12, 4 February 2026 view source Overthink (talk \| contribs) autopatrolled 2,726 edits add name in infobox Newer edit →
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	{{Infobox Interval\|Color name=sawa 3rd, sw3}}		{{Infobox Interval\|Name=Pythagorean diminished third\|Color name=sawa 3rd, sw3}}
	'''65536/59049''', the '''Pythagorean diminished third''', is an interval in [[3-limit]] [[just intonation]]. It is equal to a [[32/27\|pythagorean minor third]] minus an [[2187/2048\|apotome]], hence the name.		'''65536/59049''', the '''Pythagorean diminished third''', is an interval in [[3-limit]] [[just intonation]]. It is equal to a [[32/27\|pythagorean minor third]] minus an [[2187/2048\|apotome]], hence the name.