RE: tuning synths

Paul Erlich writes:

> >-3986.313713865*LOG(C2/B2) [. . .]
>
> Well, this last number converts from base ten to base two, and then
> multiplies by 1200 to convert from octaves to cents.

Oh yeah. Guess I combined factors for brevity's sake and forgot what I'd
done.

Thanks, Paul!

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David,

I agree that JI makes for the best harmonies in most cases. There are
exceptions, such as a pentatonic scale played as a chord, where a meantone
tuning changes the three thirds from Pythagorean to near-just, without
giving up much consonance in the fifths. But yes, melody and harmony often
have contradictory implications for tuning.

>> Finally, consider the geometric series
>>
>> . .x^-9, x^-8, x^-7, x^-6, x^-5, x^-4, x^-3, x^-2, x^-1, x, x^2, x^3,
>> x^4, x^5, x^6, x^7, x^8, x^9, . . .
>>
>> where x>0 and x does not equal 1. Whether the units of measurement are
>> string length or wavelength or time period, as above, or frequency, as
in
>> the 800:900:1000 Hz example, the result is the same: equal temperament!

>Alright. I figured out how to use the geometric series shown above to
>acheive octave-repeating ET by supplying x with the nth root of two, where
n
>is the number of divisions/octave. But I don't understand what you mean
by
>putting a series of integrally-related frequencies such as 800:900:1000 Hz
>into the equation. If you apply the geometric series to a _single_
frequency
>you get ET. But I can't seem to get the 800:900:1000 Hz _series_ to make
ET,
>no matter what I do to it.

All I was saying is that if you use frequency units as your units of
measurement, the geometric series gives you equal temperament.

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