Augmented (temperament) - Revision history

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}}

Inthar at 00:45, 9 April 2026

2026-04-09T00:45:01Z

← Older revision		Revision as of 00:45, 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''', 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.

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' ~~(''AW-jeen'')~~, 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.

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

Inthar at 00:44, 9 April 2026

2026-04-09T00:44:45Z

← Older revision		Revision as of 00:44, 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''', 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.

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

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

Inthar at 00:43, 9 April 2026

2026-04-09T00:43:52Z

← Older revision		Revision as of 00:43, 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''', 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.

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' (AW-jeen), which adds [[Archy]] tempering to the fifth.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' (''AW-jeen''), which adds [[Archy]] tempering to the fifth.

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

Inthar at 00:43, 9 April 2026

2026-04-09T00:43:41Z

← Older revision		Revision as of 00:43, 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''', 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.

	Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''' (AW-jeen), which adds [[Archy]] tempering to the fifth.

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

Inthar at 00:43, 9 April 2026

2026-04-09T00:43:18Z

← Older revision		Revision as of 00:43, 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''', 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 admits a [[structurally induced]] 7-limit extension ~~(because 128/125 = 126/125 * 64/63)~~, called '''Augene''', which adds [[Archy]] tempering to the fifth.		Because 128/125 = 126/125 * 64/63, Augmented admits a [[structurally induced]] 7-limit extension, called '''Augene''', which adds [[Archy]] tempering to the fifth.

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

Inthar: Created page with "'''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 admits a structurally induced 7-limit extension (because 128/125 = 126/125 * 64/63), called '''Augene''', which adds Archy tempering to the fifth. {{Navbox regtemp}} {{Cat|Temperaments}}"

2026-04-09T00:42:30Z

Created page with "'''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 admits a structurally induced 7-limit extension (because 128/125 = 126/125 * 64/63), called '''Augene''', which adds Archy tempering to the fifth. {{Navbox regtemp}} {{Cat|Temperaments}}"

New page

'''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 admits a [[structurally induced]] 7-limit extension (because 128/125 = 126/125 * 64/63), called '''Augene''', which adds [[Archy]] tempering to the fifth.

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