Fwd: the ultimate proportional beating well-temperament

Attached for this ultimate well-temperament is the brat data in PNG
format.

Oz.

✩ ✩ ✩
www.ozanyarman.com

Begin forwarded message:

> From: Ozan Yarman <ozanyarman@...>
> Date: May 11, 2010 7:18:54 AM GMT+03:00
> To: Tuning List <tuning@yahoogroups.com>
> Subject: the ultimate proportional beating well-temperament
>
> Inspired by George Secor's pursuit for synchronous beating 12-tone
> Temperaments, here is my "Ultimate Well-Temperament" that is
> synchronous in all major and minor triads:
>
> 12-tone Ultimate Well Temperament by Oz.
> |
> 1/1
> 277/262
> 147/131
> 156/131
> 329/262
> 175/131
> 185/131
> 196/131
> 208/131
> 220/131
> 234/131
> 247/131
> 2/1
>
> Cents:
>
> 1/1
> 96.383 cents
> 199.499 cents
> 302.375 cents
> 394.225 cents
> 501.346 cents
> 597.550 cents
> 697.544 cents
> 800.420 cents
> 897.524 cents
> 1004.330 cents
> 1097.933 cents
> 2/1
>
> Cycle of fifths:
>
> 0.000 cents 0.000 0 0 commas
> 697.544 cents -4.411 -135
> 701.955 cents -4.411 -135
> 698.025 cents -8.341 -256
> 696.701 cents -13.595 -417
> 703.708 cents -11.842 -363
> 699.617 cents -14.180 -435
> 698.833 cents -17.302 -531
> 704.037 cents -15.220 -467
> 701.955 cents -15.220 -467
> 701.955 cents -15.220 -467
> 697.016 cents -20.159 -619
> 698.654 cents -23.460 -720 -Pythagorean comma, ditonic
> comma
> Average absolute difference: 13.6134 cents
> Root mean square difference: 15.3317 cents
> Maximum absolute difference: 23.4600 cents
> Maximum formal fifth difference: 5.2541 cents
> |
>
> The scale also yields simple integer beats at 440 Hz standard
> diapason.
>
> Cordially,
> Dr. Oz.
>
> ✩ ✩ ✩
> www.ozanyarman.com
>