Hecate hexad: Difference between revisions

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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|~~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.

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.

[[Category:~~Chord~~]]

[[Category:Chords]]

[[Category:Dyadic]]

[[Category:Marvel]]

[[Category:Hexad]]

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-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|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.
+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.
-[[Category:Chord]]
+[[Category:Chords]]
 [[Category:Dyadic]]
 [[Category:Marvel]]
 [[Category:Hexad]]