[tuning-math] Re: Compton/Erlich temperament



On Thu, 18 Jul 2002 01:22:19 -0700 Carl Lumma <carl@xxxxxxxxx> writes:

> How do we classify the Compton/Erlich scheme of tuning multiple
> 12-et keyboards 15 cents apart?  Some sort of planar temperament
> with the following commas?
> 
> 531441/524288 (pythagorean comma)
> 5120/5103 (difference between syntonic comma and 64/63)
> 
> Is this right?

I think it's another system, discussed below. The wedgie you find from
the pyth comma and 5120/5103 gives what we are calling a linear
temperament. It is [0,12,12,-6,-19,19], and has a TM reduced basis
<50/49, 3645/3584>. The mapping is

[[12, 19,       28, 34], [0, 0, -1, -1]]

However, the rms optimum is 23.4 cents apart, not 15.

I think what you want is the linear temperament with wedgie
[0,12,12,-6,-19,19], TM reduced basis 
<225/224, 250047/250000> and mapping [[12,19,28,34],[0,0,-1,-1]]. You can
use the 72 or 84 ets for this.

By the way, is 250047/250000 not deserving of a little recognition?

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