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Pelogic and "hexidecimal"

🔗Herman Miller <hmiller@IO.COM>

2/12/2004 9:51:50 PM

From the big 7-limit temperament list:

Number 19 Pelogic

[1, -3, -4, -7, -9, -1] [[1, 2, 1, 1], [0, -1, 3, 4]]
TOP tuning [1209.734056, 1886.526887, 2808.557731, 3341.498957]
TOP generators [1209.734056, 532.9412251]
bad: 39.824125 comp: 2.022675 err: 9.734056

Number 94 Hexidecimal

[1, -3, 5, -7, 5, 20] [[1, 2, 1, 5], [0, -1, 3, -5]]
TOP tuning [1208.959294, 1887.754858, 2799.450479, 3393.977822]
TOP generators [1208.959293, 530.1637287]
bad: 84.341555 comp: 3.068202 err: 8.959294

The 5-limit Pelogic has this TOP tuning:
[1206.548265, 1891.576247, 2771.109114]

The 7-limit temperament labeled "Pelogic" has a better 7:1 approximation
at -5 generators (3383.96 cents in the TOP tuning). Worse, the 7:4 with
the +4 mapping is way too flat. In short, the mapping [0, -1, 3, -5] is
better even with the TOP tuning given for "Number 19 Pelogic". It also
works better with the traditional pelogic ET's 16 and 23. The TOP tuning
for "Hexidecimal" is closer to the 5-limit Pelogic TOP tuning than
Number 19's TOP tuning is. I suggest that the name "Pelogic" would be
more appropriately applied to Number 94 than Number 19.