circle31
Approximate 31edo with 18 5^(1/4) fifths, 12 (56/5)^(1/6) fifths, and a (4096/6125)*sqrt(5)
Properties
| Notes | 31 |
|---|
| Period | 1200.0 ¢ |
|---|
| Just | No |
|---|
| Source |
Mailing lists
|
|---|
| Reference | https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105320.html#105320 |
|---|
| Thread | 1 scale |
|---|
| Tone (¢) |
Step (¢) |
| 39 |
39 |
| 76 |
37 |
| 117 |
41 |
| 154 |
37 |
| 193 |
40 |
| 233 |
40 |
| 269 |
36 |
| 310 |
41 |
| 348 |
38 |
| 386 |
39 |
| 427 |
41 |
| 462 |
35 |
| 503 |
41 |
| 542 |
39 |
| 579 |
38 |
| 621 |
41 |
| 657 |
36 |
| 697 |
40 |
| 736 |
40 |
| 773 |
36 |
| 814 |
41 |
| 851 |
37 |
| 890 |
39 |
| 930 |
41 |
| 966 |
35 |
| 1007 |
41 |
| 1045 |
38 |
| 1083 |
38 |
| 1124 |
41 |
| 1159 |
35 |
| 1200 |
41 |
Similar scales
Parent scales
Child scales
Mailing list post
From: genewardsmith (2012-11-08)
Subject: A 31edo approximation with some pure 5/4 and 7/5 intervals
This has a gamut of 12 meantone (56/5)^(1/6) fifths, and so 6 = 12-6 pure 7/5s, and 18 1/4-comma 5^(1/4) fifths, and so 14 = 18-4 pure 5/4s. The difference between this and 31edo is subtle, but you can bring it out, eg by using two-part harmony. What Vicentino would have made of it I don't know.
! circle31.scl
!
Approximate 31edo with 18 5^(1/4) fifths, 12 (56/5)^(1/6) fifths, and a (4096/6125)*sqrt(5)
31
!
39.04564
76.04900
117.10786
153.61881
193.15686
233.21637
269.20586
310.26471
347.78954
386.31371
427.38710
462.36271
503.42157
541.96027
579.47057
620.52943
656.53344
696.57843
736.13100
772.62743
813.68629
850.70417
889.73529
930.30173
965.78428
1006.84314
1044.87491
1082.89214
1123.95100
1159.44808
1200.00000
Full thread (1 messages)
From: genewardsmith (2012-11-08)
Subject: A 31edo approximation with some pure 5/4 and 7/5 intervals
This has a gamut of 12 meantone (56/5)^(1/6) fifths, and so 6 = 12-6 pure 7/5s, and 18 1/4-comma 5^(1/4) fifths, and so 14 = 18-4 pure 5/4s. The difference between this and 31edo is subtle, but you can bring it out, eg by using two-part harmony. What Vicentino would have made of it I don't know.
! circle31.scl
!
Approximate 31edo with 18 5^(1/4) fifths, 12 (56/5)^(1/6) fifths, and a (4096/6125)*sqrt(5)
31
!
39.04564
76.04900
117.10786
153.61881
193.15686
233.21637
269.20586
310.26471
347.78954
386.31371
427.38710
462.36271
503.42157
541.96027
579.47057
620.52943
656.53344
696.57843
736.13100
772.62743
813.68629
850.70417
889.73529
930.30173
965.78428
1006.84314
1044.87491
1082.89214
1123.95100
1159.44808
1200.00000
Raw file
! circle31.scl
!
Approximate 31edo with 18 5^(1/4) fifths, 12 (56/5)^(1/6) fifths, and a (4096/6125)*sqrt(5)
31
!
39.04564
76.04900
117.10786
153.61881
193.15686
233.21637
269.20586
310.26471
347.78954
386.31371
427.38710
462.36271
503.42157
541.96027
579.47057
620.52943
656.53344
696.57843
736.13100
772.62743
813.68629
850.70417
889.73529
930.30173
965.78428
1006.84314
1044.87491
1082.89214
1123.95100
1159.44808
1200.00000
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105320.html#105320
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_90000-106393.json
! topic_id = 105320
! msg_id = 105320