6561/5120 - Revision history

CompactStar at 08:06, 2 May 2026

2026-05-02T08:06:04Z

← Older revision		Revision as of 08:06, 2 May 2026
Line 3:		Line 3:
	\| Color name = lagu 3rd, Lg3		\| Color name = lagu 3rd, Lg3
	}}		}}
	'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. A weird consequence is that this interval is equated to [[5/4]] in [[meantone]] temperament, so it is tuned grossly inaccurately in most "normal" tunings of meantone (if you wanted to for some reason, you could have a meantone tuning with a sharp fifth that would make this interval accurate ~~but~~ 5/4 inaccurate). It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]]. It also differs from [[9/7]], the Pythagorean major third, by [[5120/5103]], giving [[hemifamity]] temperaments a more intuitive interpretation of this interval.		'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. A weird consequence is that this interval is equated to [[5/4]] in [[meantone]] temperament, so it is tuned grossly inaccurately in most "normal" tunings of meantone (if you wanted to for some reason, you could have a meantone tuning with a sharp fifth that would make this interval the accurate one and 5/4 inaccurate). It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]]. It also differs from [[9/7]], the Pythagorean major third, by [[5120/5103]], giving [[hemifamity]] temperaments a more intuitive interpretation of this interval.

	[[Category:Major third]]		[[Category:Major third]]
	[[Category:Supermajor third]]		[[Category:Supermajor third]]

CompactStar at 08:05, 2 May 2026

2026-05-02T08:05:53Z

← Older revision		Revision as of 08:05, 2 May 2026
Line 3:		Line 3:
	\| Color name = lagu 3rd, Lg3		\| Color name = lagu 3rd, Lg3
	}}		}}
	'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]].		'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. A weird consequence is that this interval is equated to [[5/4]] in [[meantone]] temperament, so it is tuned grossly inaccurately in most "normal" tunings of meantone (if you wanted to for some reason, you could have a meantone tuning with a sharp fifth that would make this interval accurate but 5/4 inaccurate). It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]]. It also differs from [[9/7]], the Pythagorean major third, by [[5120/5103]], giving [[hemifamity]] temperaments a more intuitive interpretation of this interval.

	[[Category:Major third]]		[[Category:Major third]]
	[[Category:Supermajor third]]		[[Category:Supermajor third]]

Jerdle: ly3 does not exist, and Ly3 would be large yo. This is large gu.

2025-03-25T20:06:40Z

ly3 does not exist, and Ly3 would be large yo. This is large gu.

← Older revision		Revision as of 20:06, 25 March 2025
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	\| Name = retroptolemaic major third		\| Name = retroptolemaic major third
	\| Color name = lagu 3rd, ~~ly3~~		\| Color name = lagu 3rd, Lg3
	}}		}}
	'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]].		'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]].

CompactStar at 00:22, 15 August 2024

2024-08-15T00:22:12Z

← Older revision		Revision as of 00:22, 15 August 2024
Line 4:		Line 4:
	}}		}}
	'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]].		'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]].

			[[Category:Major third]]
			[[Category:Supermajor third]]

Lériendil: Created page with "{{Infobox Interval | Name = retroptolemaic major third | Color name = lagu 3rd, ly3 }} '''6561/5120''', the '''retroptolemaic major third''', is a 5-limit interval mea..."

2024-08-14T08:21:53Z

Created page with "{{Infobox Interval | Name = retroptolemaic major third | Color name = lagu 3rd, ly3 }} '''6561/5120''', the '''retroptolemaic major third''', is a 5-limit interval mea..."

New page

{{Infobox Interval
| Name = retroptolemaic major third
| Color name = lagu 3rd, ly3
}}
'''6561/5120''', the '''retroptolemaic major third''', is a [[5-limit]] [[interval]] measuring about 429.32{{cent}}. It is equal to the Pythagorean major third of [[81/64]] ''raised'' by a syntonic comma ([[81/80]]), compared to the just major third [[5/4]] which is the Pythagorean interval ''lowered'' by the syntonic comma. It differs from [[41/32]], the 41st harmonic, by the unnoticeable comma [[6561/6560]].