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7-limit Haluska commas

🔗Gene Ward Smith <gwsmith@svpal.org>

3/29/2004 2:36:29 PM

If we start the list from 225/224, the 7-limit Haluska commas begin

225/224
[-5, 2, 2, -1]

2401/2400
[-5, -1, -2, 4]

4375/4374
[-1, -7, 4, 1]

250047/250000
[-4, 6, -6, 3]

78125000/78121827
[3, -13, 10, -2]

205891132094649/205885750000000
[-7, 30, -9, -7]

Taking the commas in pairs gives us miracle, ennealimmal, ennealimmal,
ennealimmal and finally something which breaks out of the ennealimmal
gravitational field:

|88 151 183 35 43 1>

[<1 -19 -33 -40|, <0 88 151 183|]

Generator: 731/3125, representing an interval of 147/125.

Even for me, this is getting over the top, but it does have a rather
low badness rating, comparable to meantone or miracle if you believe
in log-flatness.