TOP

I've added TOP tempering to Scala, Gene's webpage was very helpful
in getting it right in one try.
The command is PROJECT/TEMPER/TOP and the dialog Modify:Temper.

http://www.xs4all.nl/~huygensf/software/Scala_Setup.exe

Manuel

Manuel Op de Coul wrote:

> I've added TOP tempering to Scala, Gene's webpage was very helpful
> in getting it right in one try.
> The command is PROJECT/TEMPER/TOP and the dialog Modify:Temper.
> > http://www.xs4all.nl/~huygensf/software/Scala_Setup.exe

Cool! I tried it out on this 7-limit JI scale, one of my favorites from a few years back, which I've been playing with recently....

0: 1/1 0.000 unison, perfect prime
1: 21/20 84.467 minor semitone
2: 9/8 203.910 major whole tone
3: 6/5 315.641 minor third
4: 63/50 400.108 quasi-equal major third
5: 27/20 519.551 acute fourth
6: 7/5 582.512 septimal or Huygens' tritone, BP fourth
7: 3/2 701.955 perfect fifth
8: 63/40 786.422 narrow minor sixth
9: 42/25 898.153 quasi-tempered major sixth
10: 9/5 1017.596 just minor seventh, BP seventh
11: 189/100 1102.063
12: 2/1 1200.000 octave

If you do a "show intervals" on this scale, it's got a 75/56 and a 112/75, which would benefit from tempering out the 225/224 (as someone suggested on the tuning list when I first mentioned this scale).

0: 1/1 0.000 unison, perfect prime
1: 85.230 cents 85.230
2: 200.864 cents 200.864
3: 316.499 cents 316.499
4: 401.728 cents 401.728
5: 517.363 cents 517.363
6: 585.044 cents 585.044
7: 700.679 cents 700.679
8: 785.908 cents 785.908
9: 901.543 cents 901.543
10: 1017.178 cents 1017.178
11: 1102.407 cents 1102.407
12: 1200.494 cents 1200.494

This is actually a pretty nice scale, even with music that isn't especially designed for it (because it has a roughly similar pattern to meantone), but it does have a couple of fairly mild "wolf" intervals in addition to the meantone ones. Of course, if you stick to the near-JI intervals and avoid the misspelled ones, it all sounds nice and smooth.

Herman wrote:
0: 1/1 0.000 unison, perfect prime
1: 85.230 cents 85.230
2: 200.864 cents 200.864
3: 316.499 cents 316.499
4: 401.728 cents 401.728
5: 517.363 cents 517.363
6: 585.044 cents 585.044
7: 700.679 cents 700.679
8: 785.908 cents 785.908
9: 901.543 cents 901.543
10: 1017.178 cents 1017.178
11: 1102.407 cents 1102.407
12: 1200.494 cents 1200.494

I forgot to take care of the case where an interval not to be
tempered is not prime. That's easily fixed. So you could
specify to keep the 6/5 just for example to get this instead:

0: 1/1 0.000 unison, perfect prime
1: 84.345 cents 84.345
2: 199.993 cents 199.993
3: 6/5 315.641 minor third
4: 399.986 cents 399.986
5: 515.634 cents 515.634
6: 584.666 cents 584.666
7: 700.314 cents 700.314
8: 784.659 cents 784.659
9: 900.307 cents 900.307
10: 1015.955 cents 1015.955
11: 1100.300 cents 1100.300
12: 1200.635 cents 1200.635

Manuel

In a small update I fixed the TOP tempering in Scala.
Also added another variant with command PROJECT/TEMPER/MINIMAX
and dialog Modify:Temper.
This is equivalent to Dave Keenan's algorithm with only
the primes as consonant intervals.
I could make an option to let the user add more consonant
intervals if there's interest.

http://www.xs4all.nl/~huygensf/software/Scala_Setup.exe

Manuel

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:

> In a small update I fixed the TOP tempering in Scala.

Do you think you could add a feature which makes only a single MTS
tuning dump if possible?

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> Do you think you could add a feature which makes only a single MTS
> tuning dump if possible?

That's been a feature for as long as I can remember.
SET SYNTH 107
SEND/FILE dump.mid

Manuel

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:

> That's been a feature for as long as I can remember.
> SET SYNTH 107
> SEND/FILE dump.mid

Thanks, Manuel. This does illustrate how badly Scala needs a user's
manual. Document.html is awfully thin for such a complex program. Of
course a 100 page pdf file is a hell of a lot of work to write. :)