Augmented (temperament): Difference between revisions
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'''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''' | 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}} | ||
Revision as of 00:45, 9 April 2026
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 and provides sharp tunings for primes 3, 5, and 7.
