Hecate hexad

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.