Topic: The Ellis duodene in 101-equal

1 scales

Thread (2 messages)

From: Gene Ward Smith (2004-07-29)
Subject: The Ellis duodene in 101-equal

It occurred to me that yet another method of producing circulating
temperaments would be to take a Fokker block and then temper it so
that the commas of the block shink without actually vanishing; this is
a sort of intermediate hypothesis situation, where instead of
tempering to an equal temperament, we temper to a circulating temperament.

Suppose for instance that we want to temper the Ellis duodene. In
101-et, 81/80 shrinks to 55% of its value, 128/125 shrinks to 58% of
its value, and 2048/2025 shrinks to 61% of its value. A fifth flat by
81/80 becomes less flat, and the wolf sharp by 2048/2025 less sharp;
likewise major thirds sharp by 128/125 become less sharp. The result
is closer to 12-et than the original duodene, but still with some of
the tuning properties of the duodene. 

Here's the Ellis duodene in 101-et for your consideration:

! duo101.scl
Ellis duodene tempered in 101-et
12
!
106.930693
201.980198
308.910891
392.079208
499.009901
594.059406
700.990099
807.920792
891.089109
1009.900990
1093.069307
1200.000000

From: Carl Lumma (2004-07-29)
Subject: Re: The Ellis duodene in 101-equal

All;

Sorry I've been so distant lately.  I'm still reading everything
with much delight!  Just swamped with extra-list matters at the
moment.  Now, on to Gene's message....

>It occurred to me that yet another method of producing circulating
>temperaments would be to take a Fokker block and then temper it so
>that the commas of the block shink without actually vanishing; this
>is a sort of intermediate hypothesis situation, where instead of
>tempering to an equal temperament, we temper to a circulating
>temperament.

There we go!  Definitely part of the "middle path".

>Suppose for instance that we want to temper the Ellis duodene. In
>101-et, 81/80 shrinks to 55% of its value, 128/125 shrinks to 58% of
>its value, and 2048/2025 shrinks to 61% of its value. A fifth flat by
>81/80 becomes less flat, and the wolf sharp by 2048/2025 less sharp;
>likewise major thirds sharp by 128/125 become less sharp. The result
>is closer to 12-et than the original duodene, but still with some of
>the tuning properties of the duodene. 
>
>Here's the Ellis duodene in 101-et for your consideration:
>
>! duo101.scl
>Ellis duodene tempered in 101-et
>12
>!
>106.930693
>201.980198
>308.910891
>392.079208
>499.009901
>594.059406
>700.990099
>807.920792
>891.089109
>1009.900990
>1093.069307
>1200.000000

I bet Kurt would be interested in this.

-Carl