Re: Buddhi's question

Hi Paul,

Yes, 25/24 fits, sorry.

5/4 above 5/3. While 16/15 is 5/4 below 4/3.

Sorry again about carelessness in including entire digest - will take care
about that.

I think my quarter comma meantone is okay - it has fifths of 696.578 cents
everywhere except between f sharp and d flat where it's 737.6373 for the
wolf, and quarter comma is a quarter of 81/80 = 21.5063 cents / 4 =
5.37657
cents.

Then 701.955 - 5.37657 cents = 696.578 cents - okay.

Please correct me if there is something wrong in this derivation.

I'm going to have a go at adding an option to choose resolution for
factorisation in the Tune Smithy number options dialog, so that you can look
for closest small ratio within 0.5 cents (say) of the value in cents. Could
be useful at times, and would have prevented that mistake about the j.i.
ratios - sorry again,

Robert

Robert,

I apologize -- I did not see that you wrote "with the comma between F# and
Db". The default for 12-tone meantone, though, puts the comma between G# and
Eb, and Buddhi's synth's scales do it this way -- thus the difference.

-Paul

Hi Paul,

(I posted this last night, but accidentally sent it to myself, and just
found it in my inbox)

>I apologize -- I did not see that you wrote "with the comma between F# and
>Db". The default for 12-tone meantone, though, puts the comma between G#
and
>Eb, and Buddhi's synth's scales do it this way -- thus the difference.

That's all right.

Not sure why I did it F# and Db; the TS default is G# to Eb as well (what
you get when you choose that option when you first run the prog).

Then TS makes it:

0 cents 100-23.95 cents 200-6.843 cents 300+10.26 cents 400-13.69 cents
500+3.422 cents 600-20.53 cents 700-3.422 cents 800-27.37 cents 900-10.26
cents 1000+6.843 cents 1100-17.11 cents 1200 cents

which does indeed put the wolf fifth between G# and Eb, and all the others
are a quarter comma flat.

Fits most of the numbers. However has 14 instead of -27.37 instead for the
G#, and -18 instead
of -10 for the A.

Result of those changes is:
wolf fifth between C# and Ab
700-11 cents between d and A
700+4 between A and E.
Rest all quarter comma.
(checked it in TS as it has option to show the interval between notes in a
chord when you play them).

TS makes C# to Ab quarter comma as
0 cents 100-23.95 cents 200-6.843 cents 300+10.26 cents 400-13.69 cents
500+3.422 cents 600-20.53 cents 700-3.422 cents 800+13.69 cents 900-10.26
cents 1000+6.843 cents 1100-17.11 cents 1200 cents

So fits that except for the 900-18, which would need to be 900-10.

Should have thought of trying out the numbers and working backwards like
this!

I see there are some tempered quarter comma mean-tone scales in the SCALA
archive.

Over to the experts!
....

Robert