Mailing list post
From: Gene Ward Smith (2004-07-30)
Subject: Well-tuning the syndie scales
The syndies are the four Fokker blocks arising from 81/80 and 128/125.
I tried the well-tuning I mention on tuning-math on them, which has
the fifth approximated by (7168/11)^(1/16) and major thirds by
sqrt(11/7); in three cases this did not give a circulating temperament
but rather (three versions of) something similar to 1/5-comma
meantone; in particular, the meantone with fifth (176/7)^(1/8), which
has 14/11-sized dimished fourths.
The really interesting case is the well-tuning of syndie3, which is
more familiar as the Ellis duodene. This gives us a circulating
temperament, with 9 nearly pure fifths, two fifths flat by 13.99 cents
and one sharp by 12.27 cents. It has eight major thirds of good
quality, sharp by 4.93 cents, and four diminished fourth-style major
thirds which are exact 14/11s. All in all rather similar to bifrost,
but hardly the same.
! syndwell3.scl
Syndie #3 in 3~(469762048/11)^(1/16) 5~(176/7)^(1/2) well tuning
12
!
81.397788
189.057522
296.717257
391.246018
498.905752
580.303540
687.963275
782.492036
890.151770
997.811504
1079.209293
1200.000000
Full thread (3 messages)
From: Gene Ward Smith (2004-07-30)
Subject: Well-tuning the syndie scales
The syndies are the four Fokker blocks arising from 81/80 and 128/125.
I tried the well-tuning I mention on tuning-math on them, which has
the fifth approximated by (7168/11)^(1/16) and major thirds by
sqrt(11/7); in three cases this did not give a circulating temperament
but rather (three versions of) something similar to 1/5-comma
meantone; in particular, the meantone with fifth (176/7)^(1/8), which
has 14/11-sized dimished fourths.
The really interesting case is the well-tuning of syndie3, which is
more familiar as the Ellis duodene. This gives us a circulating
temperament, with 9 nearly pure fifths, two fifths flat by 13.99 cents
and one sharp by 12.27 cents. It has eight major thirds of good
quality, sharp by 4.93 cents, and four diminished fourth-style major
thirds which are exact 14/11s. All in all rather similar to bifrost,
but hardly the same.
! syndwell3.scl
Syndie #3 in 3~(469762048/11)^(1/16) 5~(176/7)^(1/2) well tuning
12
!
81.397788
189.057522
296.717257
391.246018
498.905752
580.303540
687.963275
782.492036
890.151770
997.811504
1079.209293
1200.000000
From: Gene Ward Smith (2004-07-30)
Subject: Re: Well-tuning the syndie scales
--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
The well-tuning of the Ellis duodene was in a rather perverse key;
here is the classic duodene well-tuned. It has flat fifths in D and
Bb, and a sharp one in F#; the rest are less than a cent flat. It has
pure 14/11 major thirds in A, E, B, and F#, with the rest being
sqrt(11/7) major thirds, 4.93 cents sharp. And it circulates!
! duowell.scl
Ellis duodene well-tuned to fifth=(7168/11)^(1/16) third=(11/7)^(1/2)
12
!
107.659734
202.188496
309.848230
391.246018
498.905752
593.434513
701.094248
808.753982
890.151770
1010.942478
1092.340266
1200.000000
From: Carl Lumma (2004-07-30)
Subject: Re: [tuning-math] Well-tuning the syndie scales
>I tried the well-tuning I mention on tuning-math on them,
I mentiod this is tuning-math.
-Carl