Topic: A circulating 31 tone temperament with 22 pure major thirds

1 scales

Thread (2 messages)

From: Gene Ward Smith (2005-09-08)
Subject: A circulating 31 tone temperament with 22 pure major thirds

Not everyone is a fan of 1/4 comma meantone, but for those who are,
here is an RI scale with 22 pure thirds and eight triads with brats of
4. The pure thirds in this mode extend from Ebb to E# major, and the
anomalous brat of 4.61 is located at 1/2 mod 31 fifths, which is to
say, -15 (+16) fifths. In no sense is it a wolf, of course.

! cbrat31.scl
A circulating scale with 22 pure major thirds and eight +4 brats
31
!
22347754324000/21855094139237
22853429062500/21855094139237
23401911360000/21855094139237
381997181640625/349681506227792
24447819625000/21855094139237
25034567296000/21855094139237
204342701675325/174840753113896
130779329072208/109275470696185
53442914344625/43710188278474
5/4
32/25
28566786328125/21855094139237
29252389200000/21855094139237
29895406250000/21855094139237
30559774531250/21855094139237
31293209120000/21855094139237
1021713508376625/699363012455584
32694832268052/21855094139237
836049407488832/546377353480925
25/16
8/5
142833931640625/87420376556948
36565486500000/21855094139237
37443058176000/21855094139237
76399436328125/43710188278474
39116511400000/21855094139237
39982270421000/21855094139237
40868540335065/21855094139237
1046234632577664/546377353480925
125/64
2

From: Ozan Yarman (2005-09-10)
Subject: Re: [tuning] A circulating 31 tone temperament with 22 pure major thirds

That is an ingenious proposition! Probably the best 31-note meantone tuning ever.
  ----- Original Message ----- 
  From: Gene Ward Smith 
  To: tuning@yahoogroups.com 
  Sent: 09 Eylül 2005 Cuma 2:39 
  Subject: [tuning] A circulating 31 tone temperament with 22 pure major thirds


  Not everyone is a fan of 1/4 comma meantone, but for those who are,
  here is an RI scale with 22 pure thirds and eight triads with brats of
  4. The pure thirds in this mode extend from Ebb to E# major, and the
  anomalous brat of 4.61 is located at 1/2 mod 31 fifths, which is to
  say, -15 (+16) fifths. In no sense is it a wolf, of course.

  ! cbrat31.scl
  A circulating scale with 22 pure major thirds and eight +4 brats
  31
  !
  22347754324000/21855094139237
  22853429062500/21855094139237
  23401911360000/21855094139237
  381997181640625/349681506227792
  24447819625000/21855094139237
  25034567296000/21855094139237
  204342701675325/174840753113896
  130779329072208/109275470696185
  53442914344625/43710188278474
  5/4
  32/25
  28566786328125/21855094139237
  29252389200000/21855094139237
  29895406250000/21855094139237
  30559774531250/21855094139237
  31293209120000/21855094139237
  1021713508376625/699363012455584
  32694832268052/21855094139237
  836049407488832/546377353480925
  25/16
  8/5
  142833931640625/87420376556948
  36565486500000/21855094139237
  37443058176000/21855094139237
  76399436328125/43710188278474
  39116511400000/21855094139237
  39982270421000/21855094139237
  40868540335065/21855094139237
  1046234632577664/546377353480925
  125/64
  2