Augmented (temperament) - Revision history

Vector at 20:00, 25 May 2026

2026-05-25T20:00:40Z

← Older revision		Revision as of 20:00, 25 May 2026
Line 2:		Line 2:

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' (2.3.5.7[12 & 15]), which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[15edo]] and [[27edo]] are notable tunings of Augene. Augene is generally the preferred extension due to consistent sharpness on the third and fifth bringing the 4:5:6 chord closer to DR and making 6/5 better tuned (which is best supported by 15edo).		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' (2.3.5.7[12 & 15]), which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[15edo]] and [[27edo]] are notable tunings of Augene. Augene is generally the preferred extension due to consistent sharpness on the third and fifth bringing the 4:5:6 chord closer to DR and making 6/5 better tuned (which is best supported by 15edo).

			The other extension is 12 & 21, which tempers together 16/15 and 15/14 and makes it so 5/4 + 6/5 + 6/5 = 7/4, and therefore suggests a flat tuning of the fifth, as in 33edo.

	== List of patent vals ==		== List of patent vals ==

Vector at 19:57, 25 May 2026

2026-05-25T19:57:36Z

← Older revision		Revision as of 19:57, 25 May 2026
Line 1:		Line 1:
	'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament generated by a 1\3 period (representing 5/4) and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]). It tempers out 128/125, the difference between a stack of three 5/4s and the octave.		'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament generated by a 1\3 period (representing 5/4) and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]). It tempers out 128/125, the difference between a stack of three 5/4s and the octave.

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' (2.3.5.7[12 & 15]), which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[15edo]] and [[27edo]] are notable tunings of Augene.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' (2.3.5.7[12 & 15]), which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[15edo]] and [[27edo]] are notable tunings of Augene. Augene is generally the preferred extension due to consistent sharpness on the third and fifth bringing the 4:5:6 chord closer to DR and making 6/5 better tuned (which is best supported by 15edo).

	== List of patent vals ==		== List of patent vals ==

Inthar: /* List of patent vals */

2026-04-14T14:40:09Z

List of patent vals

← Older revision		Revision as of 14:40, 14 April 2026
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	\|\|33\|\|12 & 21\|\|690.909\|\|981.818		\|\|33\|\|12 & 21\|\|690.909\|\|981.818
	\|-		\|-
	\|\|12\|\|~~12 & 15~~, 12 & 21\|\|700.000\|\|1000.000		\|\|12\|\|Augene, 12 & 21\|\|700.000\|\|1000.000
	\|-		\|-
	\|\|39\|\|\|\|707.692\|\|953.846		\|\|39\|\|\|\|707.692\|\|953.846
	\|-		\|-
	\|\|27\|\|~~12 & 15~~\|\|711.111\|\|977.778		\|\|27\|\|Augene\|\|711.111\|\|977.778
	\|-		\|-
	\|\|42\|\|~~12 & 15~~\|\|714.286\|\|971.429		\|\|42\|\|Augene\|\|714.286\|\|971.429
	\|-		\|-
	\|\|15\|\|~~12 & 15\|\|720.000\|\|960.000~~		\|\|15\|\|Augene\|\|720.000\|\|960.000
	\|-
	~~\|\|30\|\|12 & 15~~\|\|720.000\|\|960.000
	\|-		\|-
	\|\|18\|\|\|\|733.333\|\|1000.000		\|\|18\|\|\|\|733.333\|\|1000.000
	\|-		\|-
	\|\|3\|\|~~12 & 15~~\|\|800.000\|\|800.000		\|\|3\|\|Augene\|\|800.000\|\|800.000
	\|}		\|}
	{{Navbox regtemp}}		{{Navbox regtemp}}
	{{Cat\|Temperaments}}		{{Cat\|Temperaments}}

Inthar at 14:25, 14 April 2026

2026-04-14T14:25:52Z

← Older revision		Revision as of 14:25, 14 April 2026
Line 1:		Line 1:
	'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament generated by a 1\3 period (representing 5/4) and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]). It tempers out 128/125, the difference between a stack of three 5/4s and the octave.		'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament generated by a 1\3 period (representing 5/4) and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]). It tempers out 128/125, the difference between a stack of three 5/4s and the octave.

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[15edo]] and [[27edo]] are notable tunings of Augene.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' (2.3.5.7[12 & 15]), which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[15edo]] and [[27edo]] are notable tunings of Augene.

	== List of patent vals ==		== List of patent vals ==

Inthar at 14:15, 14 April 2026

2026-04-14T14:15:22Z

@@ Line 3: / Line 3: @@
 Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[15edo]] and [[27edo]] are notable tunings of Augene.
 {{Navbox regtemp}}
 {{Cat|Temperaments}}

Inthar at 04:48, 13 April 2026

2026-04-13T04:48:30Z

← Older revision		Revision as of 04:48, 13 April 2026
Line 1:		Line 1:
	'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament generated by a 1\3 period (representing 5/4) and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]). It tempers out 128/125, the difference between a stack of three 5/4s and the octave.		'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament generated by a 1\3 period (representing 5/4) and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]). It tempers out 128/125, the difference between a stack of three 5/4s and the octave.

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] ~~is a~~ notable ~~tuning~~ of Augene.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[15edo]] and [[27edo]] are notable tunings of Augene.

	{{Navbox regtemp}}		{{Navbox regtemp}}
	{{Cat\|Temperaments}}		{{Cat\|Temperaments}}

Inthar at 01:02, 9 April 2026

2026-04-09T01:02:07Z

← Older revision		Revision as of 01:02, 9 April 2026
Line 1:		Line 1:
	'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament ~~tempering out 128/125, the difference between a stack of three 5/4s and the octave. It is~~ generated by a 1\3 period and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]).		'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament generated by a 1\3 period (representing 5/4) and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]). It tempers out 128/125, the difference between a stack of three 5/4s and the octave.

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] is a notable tuning of Augene.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] is a notable tuning of Augene.

Inthar at 00:49, 9 April 2026

2026-04-09T00:49:02Z

← Older revision		Revision as of 00:49, 9 April 2026
Line 1:		Line 1:
	'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament tempering out 128/125, the difference between a stack of three 5/4s and the octave. It is generated by a 1\3 period and a 3/2 generator.		'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament tempering out 128/125, the difference between a stack of three 5/4s and the octave. It is generated by a 1\3 period and a 3/2 generator; it has MOS scales triwood ([[3L 3s]]) and tcherepnin ([[3L 6s]]).

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] is a notable tuning of Augene.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] is a notable tuning of Augene.

Inthar at 00:46, 9 April 2026

2026-04-09T00:46:58Z

← Older revision		Revision as of 00:46, 9 April 2026
Line 1:		Line 1:
	'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament tempering out [[128/125]], the difference between a stack of three 5/4s and the octave. It is generated by a 1\3 period and a 3/2 generator.		'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament tempering out 128/125, the difference between a stack of three 5/4s and the octave. It is generated by a 1\3 period and a 3/2 generator.

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] is a notable tuning of Augene.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] is a notable tuning of Augene.

Inthar at 00:46, 9 April 2026

2026-04-09T00:46:32Z

← Older revision		Revision as of 00:46, 9 April 2026
Line 1:		Line 1:
	'''Augmented''', 12 & 15, is a 5-limit temperament tempering out [[128/125]], the difference between a stack of three 5/4s and the octave. It is generated by a 1\3 period and a 3/2 generator.		'''Augmented''', [[12edo\|12]] & [[15edo\|15]], is a 5-limit temperament tempering out [[128/125]], the difference between a stack of three 5/4s and the octave. It is generated by a 1\3 period and a 3/2 generator.

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth and provides sharp tunings for primes 3, 5, and 7. [[27edo]] is a notable tuning of Augene.

	{{Navbox regtemp}}		{{Navbox regtemp}}
	{{Cat\|Temperaments}}		{{Cat\|Temperaments}}