Wendy Carlos scales

Someone please give me the tuning data
on Wendy Carlos's "alpha", "beta", and
"gamma" scales. All I need is the cent
values of the "steps".

The info is in Scott Wilkinson's "Tuning In" -
my copy is packed away at the moment.
I need this for the Dictionary update.

- Monzo
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On Fri, 19 Mar 1999, Joseph L Monzo wrote:
> Someone please give me the tuning data
> on Wendy Carlos's "alpha", "beta", and
> "gamma" scales. All I need is the cent
> values of the "steps".

According to the Spring 1987 _Computer Music Journal_ article by Wendy:

Alpha 78.0 cents (15.385 steps/octave)
Beta 63.8 cents (18.809 steps/octave)
Gamma 35.1 cents (34.188 steps/octave, purt-near
the sum of the above two)

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "How about that? The guy can't run six balls,
-\-\-- o and they make him president."

NOTE: dehyphenate node to remove spamblock. <*>

> Beta 63.8 cents (18.809 steps/octave)

Interesting... All this time I thought it was 64.

>>Beta 63.8 cents (18.809 steps/octave)
>
>Interesting... All this time I thought it was 64.

Actually, I believe it is defined as the 11th root of 1.5.

C.

On Sun, 21 Mar 1999, Carl Lumma wrote:
>>> Beta 63.8 cents (18.809 steps/octave)
>>
>> Interesting... All this time I thought it was 64.

Well, that's pretty close.

> Actually, I believe it is defined as the 11th root of 1.5.

Nope, it's defined strictly as a local minimum of the root-mean-square
error function that Wendy set up with 3/2, 5/4, 6/5, 7/4, and 11/8 as
target intervals.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "How about that? The guy can't run six balls,
-\-\-- o and they make him president."

NOTE: dehyphenate node to remove spamblock. <*>

> >>> Beta 63.8 cents (18.809 steps/octave)
> >> Interesting... All this time I thought it was 64.
>
> Well, that's pretty close.

Basically that's certainly true, but it's definitely important to
consider how much a seemingly innocent 0.2-cent can add up to. Consider,
for example, a more or less typical instrumental range of 3 octaves. If I
calculated correctly, you'll accumulate over 11 cents in that range.