Using the G. Breed Temperament Finder

Perhaps in this phase of my quest, I'd be disappointed if I could find another Grail.

But, I was playing around with my scale, and I said to myself,

"Self, wouldn't it be nice if you could have one key that takes care of both 8/7 and 15/13--the comma of 104:105."

"... and, S., wouldn't it be nice to keep getting rid of 32/27 vs. 13/11 difference--the comma of 352:351..."

"and, S., wouldn't it be nice to get rid of the difference between 11/8 and 18/13--the comma of 143:144."

I typed these into the box:

http://x31eq.com/temper/

in the unison vector search.

Supposing for some reason I still want 43 pitches or around that, with a whole lot of detail between 1/1 and 6/5...

what other commas should I type in that I've already forgotten about?

What other parameter values might I try?

This* caught my eye, do I generate it by simply using 409.88 as a generator and throw in 400 and 800 cents for the "3" bit, or will this give me nothing useful?

*This:

3 & 41

Equal Temperament Mappings
2 3 5 7 11 13
[< 41 65 95 115 142 152 ]
< 3 5 7 8 11 11 ]>

Reduced Mapping
2 3 5 7 11 13
[< 1 5 3 -3 12 2 ]
< 0 -10 -2 17 -25 5 ]>

Generator Tunings (cents)
[1200.060, 409.880>

Step Tunings (cents)
[29.580, -4.239>

Tuning Map (cents)
<1200.060, 1901.501, 2780.421, 3367.781, 4153.722, 4449.521]

Complexity 4.529736
Adjusted Error 5.458426 cents
TOP-RMS Error 1.475075 cents/octave

I might never decide to live with whatever scale I find, but on the other hand, I *might*...

caleb

--- In tuning@yahoogroups.com, "calebmrgn" <calebmrgn@...> wrote:

> This* caught my eye, do I generate it by simply using 409.88 as a generator and throw in 400 and 800 cents for the "3" bit, or will this give me nothing useful?

There's no "3 bit" to worry about. It's a linear temperament, with generator half of a minor sixth. A basis for the commas is {105/104, 144/143, 352/351, 625/616}, where the 625/616 strikes me as a little cheesy, so playing the game of replacing it with something else or using the rank 3 temperament without it might be interesting.

There doesn't seem to be much reason to use this rather than simply using 41edo, as that's how many notes you are looking at, but you can use a MOS instead. One possible tuning would be 249edo, using the val <249 395 577 698 863 923| to map to primes. A closely related tuning is the minimax tuning in the 13 and 15 limits; in terms of fractional monzos that would be

[|1 0 0 0 0 0>, |5/3 0 0 0 1/3 -1/3>,
|7/3 0 0 0 1/15 -1/15>, |8/3 0 0 0 -17/30 17/30>,
|11/3 0 0 0 5/6 -5/6>, |11/3 0 0 0 -1/6 1/6>]

These can be converted to cents values in the same way as ordinary monzos with integer coefficients.

The generator 85/249 lies between 15/44 and 14/41, in a range where there are 44 note MOS with 41 large steps and 3 small ones, which might be advantageous.

> *This:
>
> 3 & 41
>
> Equal Temperament Mappings
> 2 3 5 7 11 13
> [< 41 65 95 115 142 152 ]
> < 3 5 7 8 11 11 ]>
>
> Reduced Mapping
> 2 3 5 7 11 13
> [< 1 5 3 -3 12 2 ]
> < 0 -10 -2 17 -25 5 ]>
>
> Generator Tunings (cents)
> [1200.060, 409.880>
>
> Step Tunings (cents)
> [29.580, -4.239>
>
> Tuning Map (cents)
> <1200.060, 1901.501, 2780.421, 3367.781, 4153.722, 4449.521]

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> There's no "3 bit" to worry about. It's a linear temperament, with generator half of a minor sixth. A basis for the commas is {105/104, 144/143, 352/351, 625/616}, where the 625/616 strikes me as a little cheesy, so playing the game of replacing it with something else or using the rank 3 temperament without it might be interesting.

Miracle (in its 13-limit incarnation) is one of these, which once again suggests studloco.

I don't understand what you wrote yet, but I intend to figure it out without you explaining further.

For un-nubile newbs who like newtral thirds like me, I'd recommend this page explaining the names of linear temperaments.

I hadn't seen before just now. This page makes the deeply mysterious names less mysterious, and his links to other pages that are helpful.

http://webcache.googleusercontent.com/search?q=cache:88rxtAMFRtAJ:x31eq.com/catalog.htm+microtonal+minimax+tuning+13-limit&cd=2&hl=en&ct=clnk&gl=us

-c

On Sep 15, 2010, at 2:27 PM, genewardsmith wrote:

>
>
> --- In tuning@yahoogroups.com, "calebmrgn" <calebmrgn@...> wrote:
>
> > This* caught my eye, do I generate it by simply using 409.88 as a generator and throw in 400 and 800 cents for the "3" bit, or will this give me nothing useful?
>
> There's no "3 bit" to worry about. It's a linear temperament, with generator half of a minor sixth. A basis for the commas is {105/104, 144/143, 352/351, 625/616}, where the 625/616 strikes me as a little cheesy, so playing the game of replacing it with something else or using the rank 3 temperament without it might be interesting.
>
> There doesn't seem to be much reason to use this rather than simply using 41edo, as that's how many notes you are looking at, but you can use a MOS instead. One possible tuning would be 249edo, using the val <249 395 577 698 863 923| to map to primes. A closely related tuning is the minimax tuning in the 13 and 15 limits; in terms of fractional monzos that would be
>
> [|1 0 0 0 0 0>, |5/3 0 0 0 1/3 -1/3>,
> |7/3 0 0 0 1/15 -1/15>, |8/3 0 0 0 -17/30 17/30>,
> |11/3 0 0 0 5/6 -5/6>, |11/3 0 0 0 -1/6 1/6>]
>
> These can be converted to cents values in the same way as ordinary monzos with integer coefficients.
>
> The generator 85/249 lies between 15/44 and 14/41, in a range where there are 44 note MOS with 41 large steps and 3 small ones, which might be advantageous.
>
> > *This:
> >
> > 3 & 41
> >
> > Equal Temperament Mappings
> > 2 3 5 7 11 13
> > [< 41 65 95 115 142 152 ]
> > < 3 5 7 8 11 11 ]>
> >
> > Reduced Mapping
> > 2 3 5 7 11 13
> > [< 1 5 3 -3 12 2 ]
> > < 0 -10 -2 17 -25 5 ]>
> >
> > Generator Tunings (cents)
> > [1200.060, 409.880>
> >
> > Step Tunings (cents)
> > [29.580, -4.239>
> >
> > Tuning Map (cents)
> > <1200.060, 1901.501, 2780.421, 3367.781, 4153.722, 4449.521]
>
>