Carlos Alpha: Difference between revisions
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== Theory == | == Theory == | ||
Carlos optimized the tuning on 3/2, 5/4 and 6/5, such that the tuning divides the octave in <math>\frac{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)}</math> ≃ 15.391524 equal steps and the fifth in 9.003464 equal steps of 77.964990 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ed3/2), corresponding to 15.3856[[edo]]. | Carlos optimized the tuning on 3/2, 5/4 and 6/5, such that the tuning divides the octave in <math>\frac{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)}</math> ≃ 15.391524 equal steps and the fifth in 9.003464 equal steps of 77.964990 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each ([[9ed3/2|9edf]]), corresponding to 15.3856[[edo]]. | ||
Carlos Alpha is very closely related to [[Starling temperaments #Valentine temperament|valentine temperament]]. For a list of 11-limit [[dyadic chord]]s of Carlos Alpha, see [[Chords of valentine]]. | Carlos Alpha is very closely related to [[Starling temperaments #Valentine temperament|valentine temperament]]. For a list of 11-limit [[dyadic chord]]s of Carlos Alpha, see [[Chords of valentine]]. | ||