Yahoo Tuning Groups Ultimate Backup makemicromusic Carlos Scales

What's really cool is that 1200 TET, 200 TET, Alpha, Beta, Gamma,
12TET etc. all fit into and equally divided octave of 1,200,200 TET.
Imagine the possibilities of loading this into keyboards and using it
to play `Dancing Queen!!'

Ok, all sarcastic comments aside, I think it goes something like this:

There is nothing sacred about any scale, and yes, the original
reaction was a bit sharp if you will but the point of discussion
here about the Carlos scales was that instead of creating a tonal
structure based on the octave as a dividing point (as is traditional)
Ms. Carlos used a series of intervals that are of interest to her (in
this case perfect fifths) and used them as a division point to get
the musical result that she wanted and composed around the resultant
strengths and deviations of said product.

Mathematically we could go around and around and around dividing
things into ever smaller focal points, but not really get anywhere.
My personal sound generation preference is Csound, which allows me to
program in decimal values of cycles per second so technically I
could use a TET to any miniscule division that my heart desireswhich
could be very interesting from an abstract point of view to see what
happens but this particular list appears to be more devoted to
actually debating and sharing the musical side of the issue rather
than dancing around the mathematical onanism that sometimes can
become involved in this endeavors

Maybe if some of the lists of cent divisions were accompanied by
explanations as to the resultant strengths and weakness of the
resultant intervalsthe differences from 12 TET, etc. That would be
musically interesting otherwise they are just infinitely delete-able
sets of random digits clogging up my email box. I think all here can
make Excel divide.

I really enjoy 9ths, 11ths, 7ths, etc. Could I use a similar method
to Ms. Carlos' to create a scale that would provide me with good dies
(con)cordant values in these sets, much to the sacrifice of my non-
favoured 3rds, 5ths, Octaves? Or a division of a western octave
that would provide me with the most discord possible when run through
various modulations? What intervals would I base this on?

That would be interesting maybe

</rant off>

🔗Herman Miller <hmiller@...>

T. Mark Turner wrote:

> I really enjoy 9ths, 11ths, 7ths, etc. Could I use a similar method > to Ms. Carlos' to create a scale that would provide me with good dies
> (con)cordant values in these sets, much to the sacrifice of my non-
> favoured 3rds, 5ths, Octaves? Or a division of a western octave > that would provide me with the most discord possible when run through > various modulations? What intervals would I base this on? > > That would be interestingï¿½ maybeï¿½ Scala makes it easy with the "Fit to mode of nonoctave ET" command. Say you're interested in 6/5, 5/4, 3/2. Create a scale with these intervals, select "Fit to mode of nonoctave ET" from the Approximate menu, and there you go. After three crude approximations, three scales that approach the Carlos Alpha, Beta, and Gamma scales show up, followed by four scales with really tiny steps.

So let's say you really like 7/4, 9/4, and 11/4. Here's a couple of possibilities.

1: 11 2: 16 3: 20
LS 87.70399 cents, 13.68239/oct. RMS diff: 2.8699 cents
MM 87.74658 cents, 13.67575/oct. Max. dev: 3.6136 cents
1: 25 2: 36 3: 45
LS 38.91807 cents, 30.83400/oct. RMS diff: 2.8982 cents
MM 38.89731 cents, 30.85046/oct. Max. dev: 3.6068 cents

🔗Graham Breed <gbreed@...>

T. Mark Turner wrote:

You can go to

http://x31eq.com/temper/regular.html

and set the prime limit as, for example, 7.9.11 and see what comes out. The top row of the results are some equal divisions of the first number in the limit (7 here). With the other parameters at their defaults I get:

8 9 30 31 38 39 47 48 69 77 86 107 108 116 124 125 146 147 155 163

Graham

Carlos Scales

🔗T. Mark Turner <tmarc_turner@...>

🔗Herman Miller <hmiller@...>

🔗Graham Breed <gbreed@...>