cbrat31
A circulating scale with 22 pure major thirds and eight +4 brats
Properties
| Notes | 31 |
|---|---|
| Period | 1200.0 ¢ |
| Just | 39982270421-limit |
| Source | Mailing lists |
| Reference | https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_60277.html#60277 |
| Thread | 1 scale |
| Tone | Tone (¢) | Step | Step (¢) |
|---|---|---|---|
| 22347754324000/21855094139237 | 39 | 22347754324000/21855094139237 | 39 |
| 22853429062500/21855094139237 | 77 | 45706858125/44695508648 | 39 |
| 23401911360000/21855094139237 | 118 | 128/125 | 41 |
| 381997181640625/349681506227792 | 153 | 611195490625/599088930816 | 35 |
| 24447819625000/21855094139237 | 194 | 128/125 | 41 |
| 25034567296000/21855094139237 | 235 | 128/125 | 41 |
| 204342701675325/174840753113896 | 270 | 8173708067013/8011061534720 | 35 |
| 130779329072208/109275470696185 | 311 | 128/125 | 41 |
| 53442914344625/43710188278474 | 348 | 267214571723125/261558658144416 | 37 |
| 5/4 | 386 | 21855094139237/21377165737850 | 38 |
| 32/25 | 427 | 128/125 | 41 |
| 28566786328125/21855094139237 | 464 | 714169658203125/699363012455584 | 36 |
| 29252389200000/21855094139237 | 505 | 128/125 | 41 |
| 29895406250000/21855094139237 | 542 | 597908125/585047784 | 38 |
| 30559774531250/21855094139237 | 580 | 195582557/191330600 | 38 |
| 31293209120000/21855094139237 | 621 | 128/125 | 41 |
| 1021713508376625/699363012455584 | 656 | 8173708067013/8011061534720 | 35 |
| 32694832268052/21855094139237 | 697 | 128/125 | 41 |
| 836049407488832/546377353480925 | 736 | 209012351872208/204342701675325 | 39 |
| 25/16 | 773 | 13659433837023125/13376790519821312 | 36 |
| 8/5 | 814 | 128/125 | 41 |
| 142833931640625/87420376556948 | 850 | 714169658203125/699363012455584 | 36 |
| 36565486500000/21855094139237 | 891 | 128/125 | 41 |
| 37443058176000/21855094139237 | 932 | 128/125 | 41 |
| 76399436328125/43710188278474 | 967 | 611195490625/599088930816 | 35 |
| 39116511400000/21855094139237 | 1008 | 128/125 | 41 |
| 39982270421000/21855094139237 | 1046 | 39982270421/39116511400 | 38 |
| 40868540335065/21855094139237 | 1084 | 8173708067013/7996454084200 | 38 |
| 1046234632577664/546377353480925 | 1125 | 128/125 | 41 |
| 125/64 | 1159 | 68297169185115625/66959016484970496 | 34 |
| 2 | 1200 | 128/125 | 41 |
Similar scales
| File | Notes | Rotation | Max diff (¢) |
|---|---|---|---|
| circle31 | 31 | 18 | 1.4 |
| xen18-erlich-meantone-31 | 31 | 26 | 2.8 |
| edo-31 | 31 | 13 | 3.0 |
| xen18-erlich-cynder-31 | 31 | 0 | 3.7 |
| 31edo-top | 31 | 1 | 3.8 |
| xen18-erlich-luna-31 | 31 | 25 | 4.9 |
| vala | 31 | 0 | 6.7 |
| xen18-erlich-myna-31 | 31 | 0 | 7.3 |
| xen18-erlich-miracle-31 | 31 | 0 | 8.3 |
| rational_canasta_tuning_22793_23190 | 31 | 0 | 8.4 |
Parent scales
| File | Notes | Max diff (¢) |
|---|---|---|
| irregular | 46 | 3.0 |
| xen18-erlich-meantone-50 | 50 | 2.8 |
| miracle41 | 41 | 6.8 |
| xen18-erlich-wurschmidt-34 | 34 | 9.7 |
| studwacko | 41 | 7.9 |
| hemw | 41 | 7.9 |
| miracle3 | 41 | 8.0 |
| xen18-erlich-miracle-41 | 41 | 8.3 |
| miracle41s | 41 | 8.6 |
| edo-62 | 62 | 3.0 |
Child scales
| File | Notes | Max diff (¢) |
|---|---|---|
| regular | 7 | 0.6 |
| xen18-erlich-luna-05 | 5 | 1.0 |
| xen18-erlich-luna-07 | 7 | 1.1 |
| xen18-erlich-luna-06 | 6 | 1.1 |
| appalachian | 12 | 1.3 |
| xen18-schulter-didymic-1-4-17 | 17 | 1.3 |
| xen18-schulter-didymic-1-4-12 | 12 | 1.3 |
| meanquar | 12 | 1.3 |
| meanquar_19 | 19 | 1.3 |
| meanqratapprox | 12 | 1.3 |
Mailing list post
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
Full 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: [email protected] 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
Raw file
! 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 ! ! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_60277.html#60277 ! ! [info] ! source = Mailing lists ! file = tuning/messages/yahoo_tuning_messages_api_raw_55190-71650.json ! topic_id = 60277 ! msg_id = 60277