Hecate hexad: Difference between revisions
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The hecate hexad an [[ | The '''hecate hexad''', an [[Dyadic chord|essentially tempered chord]], is the 1-[[9/8]]-[[5/4]]-[[7/5]]-[[14/9]]-[[7/4]] chord, tempered in the [[Marvel family #Hecate|hecate]] ({[[225/224]], [[385/384]], [[325/324]]}) temperament, which makes the steps of the scale 9/8-[[10/9]]-9/8-10/9-9/8-[[8/7]]. Another way of viewing the hecate hexad is that it is the hecate tempering of two [[marvel triad]]s separated by an interval of 9/8. This can be filled in with a third augmented triad at the fifth, leading to the hecate tempering of the nine-note [[Euler genus]] consisting of divisors of 225, reduced to an octave. Extending this to the marveldene, the hecate-tempered Ellis duodene which is the hecate tempering of the divisors of 675 [[octave reduction|reduced to an octave]], gives a scale with two hecate hexads a fifth apart. | ||
See [[hecatehex]] for the chord in Scala file. | |||
[[Category:Essentially tempered chords]] | |||
[[Category:Marvel]] | |||
[[Category:Hecate]] | |||
[[Category:Hexads]] | |||
Latest revision as of 12:15, 23 May 2023
The hecate hexad, an essentially tempered chord, is the 1-9/8-5/4-7/5-14/9-7/4 chord, tempered in the hecate ({225/224, 385/384, 325/324}) temperament, which makes the steps of the scale 9/8-10/9-9/8-10/9-9/8-8/7. Another way of viewing the hecate hexad is that it is the hecate tempering of two marvel triads separated by an interval of 9/8. This can be filled in with a third augmented triad at the fifth, leading to the hecate tempering of the nine-note Euler genus consisting of divisors of 225, reduced to an octave. Extending this to the marveldene, the hecate-tempered Ellis duodene which is the hecate tempering of the divisors of 675 reduced to an octave, gives a scale with two hecate hexads a fifth apart.
See hecatehex for the chord in Scala file.