User:BudjarnLambeth/Table of n-comma meantone generators: Difference between revisions
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|[[5/12-comma meantone]]||692.994||Close to [[71edo]] | |[[5/12-comma meantone]]||692.994||Close to [[71edo]] | ||
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|[[7/17-comma meantone]]||693.099|| | |||
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|[[2/5-comma meantone]]||693.352||Close to [[45edo]] | |[[2/5-comma meantone]]||693.352||Close to [[45edo]] | ||
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|[[7/18-comma meantone]]||693.591|| | |||
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|[[5/13-comma meantone]]||693.683||Close to [[64edo]] | |[[5/13-comma meantone]]||693.683||Close to [[64edo]] | ||
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|[[5/14-comma meantone]]||694.274|| | |[[5/14-comma meantone]]||694.274|| | ||
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|[[6/17-comma meantone]]||694.365|| | |||
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|[[1/3-comma meantone]]||694.786||Close to [[19edo]]. Historically significant (see [[historical temperaments]]). | |[[1/3-comma meantone]]||694.786||Close to [[19edo]]. Historically significant (see [[historical temperaments]]). | ||
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|[[3/10-comma meantone]]||695.503||Close to [[88edo]] | |[[3/10-comma meantone]]||695.503||Close to [[88edo]] | ||
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|[[5/17-comma meantone]]||695.630|| | |||
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|[[2/7-comma meantone]]||695.810||Close to [[69edo]]. Historically significant (see [[historical temperaments]]). | |[[2/7-comma meantone]]||695.810||Close to [[69edo]]. Historically significant (see [[historical temperaments]]). | ||
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|[[5/18-comma meantone]]||695.981||Close to [[50edo]]. Historically significant (see [[historical temperaments]]). | |[[5/18-comma meantone]]||695.981||Close to [[50edo]]. Historically significant (see [[historical temperaments]]). | ||
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|[[3/11-comma meantone]]||696. | |[[3/11-comma meantone]]||696.090||Close to [[50edo]] | ||
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|[[7/26-comma meantone]]||696.165||Close to [[golden meantone]]. Historically significant (see [[historical temperaments]]). | |[[7/26-comma meantone]]||696.165||Close to [[golden meantone]]. Historically significant (see [[historical temperaments]]). | ||
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|[[Quarter-comma meantone|1/4-comma meantone]]||696.578||Close to [[31edo]]. Historically significant (see [[historical temperaments]]). | |[[Quarter-comma meantone|1/4-comma meantone]]||696.578||Close to [[31edo]]. Historically significant (see [[historical temperaments]]). | ||
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|[[4/17-comma meantone]]||696.895|| | |||
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|[[3/13-comma meantone]]||696.992||Close to septimal & tridecimal CTE tunings. | |[[3/13-comma meantone]]||696.992||Close to septimal & tridecimal CTE tunings. | ||
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|[[2/11-comma meantone]]||698.045||Close to [[55edo]]. | |[[2/11-comma meantone]]||698.045||Close to [[55edo]]. | ||
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|[[3/17-comma meantone]]||699.425|| | |||
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|[[1/6-comma meantone]]||698.371||Close to [[67edo]]. Historically significant (see [[historical temperaments]]). | |[[1/6-comma meantone]]||698.371||Close to [[67edo]]. Historically significant (see [[historical temperaments]]). | ||
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|[[1/8-comma meantone]]||699.267|| | |[[1/8-comma meantone]]||699.267|| | ||
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|[[2/17-comma meantone]]||699.425|| | |||
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|[[1/9-comma meantone]]||699.565|| | |[[1/9-comma meantone]]||699.565|| | ||
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|[[1/16-comma meantone]]||700.611||No 19-tone MOS | |[[1/16-comma meantone]]||700.611||No 19-tone MOS | ||
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|[[1/17-comma meantone]]||700.690||No 19-tone MOS | |||
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|[[1/18-comma meantone]]||700.760||No 19-tone MOS | |||
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|0/1-comma “meantone” ([[Pythagorean tuning]])||701.955||Not meantone but included for reference. 9/8 is exact. Anything sharper will have whole tones not between 10/9 and 9/8, along with continuing to lack a 19-tone MOS. | |0/1-comma “meantone” ([[Pythagorean tuning]])||701.955||Not meantone but included for reference. 9/8 is exact. Anything sharper will have whole tones not between 10/9 and 9/8, along with continuing to lack a 19-tone MOS. | ||
|} | |} | ||
[[Category:Tables]][[Category:Meantone]] | [[Category:Tables]][[Category:Meantone]] | ||
Revision as of 12:24, 1 March 2024
| Temperament | Generator (cents) | Comments |
|---|---|---|
| 1/1-comma “meantone” (actually mavila) | 680.449 | Not meantone but included for reference |
| 7edo | 685.714 | Not meantone. It and anything flatter than it cannot generate a 12-tone MOS. |
| 3/4-comma meantone | 685.825 | Whole tone is not between 10/9 and 9/8, so whether it counts as meantone is very questionable. |
| 11/15-comma meantone | 686.184 | Whole tone not between 10/9 and 9/8 |
| 8/11-comma meantone | 686.314 | Whole tone not between 10/9 and 9/8 |
| 5/7-comma meantone | 686.593 | Whole tone not between 10/9 and 9/8 |
| 7/10-comma meantone | 686.901 | Whole tone not between 10/9 and 9/8 |
| 9/13-comma meantone | 687.066 | Whole tone not between 10/9 and 9/8 |
| 11/16-comma meantone | 687.169 | Whole tone not between 10/9 and 9/8 |
| 2/3-comma meantone | 687.617 | Whole tone not between 10/9 and 9/8 |
| 9/14-comma meantone | 688.129 | Whole tone not between 10/9 and 9/8 |
| 7/11-comma meantone | 688.269 | Whole tone not between 10/9 and 9/8 |
| 5/8-comma meantone | 688.514 | Whole tone not between 10/9 and 9/8 |
| 8/13-comma meantone | 688.72 | Whole tone not between 10/9 and 9/8 |
| 3/5-comma meantone | 689.051 | Whole tone not between 10/9 and 9/8 |
| 7/12-comma meantone | 689.41 | Whole tone not between 10/9 and 9/8 |
| 4/7-comma meantone | 689.666 | Whole tone not between 10/9 and 9/8 |
| 9/16-comma meantone | 689.858 | Whole tone not between 10/9 and 9/8 |
| 5/9-comma meantone | 690.007 | Whole tone not between 10/9 and 9/8 |
| 6/11-comma meantone | 690.224 | Whole tone not between 10/9 and 9/8 |
| 7/13-comma meantone | 690.375 | Whole tone not between 10/9 and 9/8 |
| 8/15-comma meantone | 690.485 | Close to 33edo. Whole tone not between 10/9 and 9/8 |
| 1/2-comma meantone | 691.202 | Close to 92edo, 59edo. Historically significant (see historical temperaments. Whole tone not between 10/9 and 9/8 (it’s exactly 10/9) |
| 7/15-comma meantone | 691.919 | Close to 85edo. This is the first tuning on this list which is unambiguously meantone, since the whole tone is between 10/9 and 9/8. |
| 6/13-comma meantone | 692.029 | |
| 5/11-comma meantone | 692.179 | |
| 4/9-comma meantone | 692.397 | Close to 26edo |
| 7/16-comma meantone | 692.546 | |
| 3/7-comma meantone | 692.738 | |
| 5/12-comma meantone | 692.994 | Close to 71edo |
| 7/17-comma meantone | 693.099 | |
| 2/5-comma meantone | 693.352 | Close to 45edo |
| 7/18-comma meantone | 693.591 | |
| 5/13-comma meantone | 693.683 | Close to 64edo |
| 3/8-comma meantone | 693.890 | Close to 83edo |
| 4/11-comma meantone | 694.134 | Almost exactly 1/3 Pythagorean comma meantone |
| 5/14-comma meantone | 694.274 | |
| 6/17-comma meantone | 694.365 | |
| 1/3-comma meantone | 694.786 | Close to 19edo. Historically significant (see historical temperaments). |
| 5/16-comma meantone | 695.234 | |
| 4/13-comma meantone | 695.338 | |
| 3/10-comma meantone | 695.503 | Close to 88edo |
| 5/17-comma meantone | 695.630 | |
| 2/7-comma meantone | 695.810 | Close to 69edo. Historically significant (see historical temperaments). |
| 5/18-comma meantone | 695.981 | Close to 50edo. Historically significant (see historical temperaments). |
| 3/11-comma meantone | 696.090 | Close to 50edo |
| 7/26-comma meantone | 696.165 | Close to golden meantone. Historically significant (see historical temperaments). |
| 4/15-comma meantone | 696.22 | Close to 81edo, close to golden meantone |
| 1/4-comma meantone | 696.578 | Close to 31edo. Historically significant (see historical temperaments). |
| 4/17-comma meantone | 696.895 | |
| 3/13-comma meantone | 696.992 | Close to septimal & tridecimal CTE tunings. |
| 2/9-comma meantone | 697.176 | Close to 5-limit and undecimal CTE tunings. Historically significant (see historical temperaments). |
| 3/14-comma meantone | 697.346 | Close to 74edo. Historically significant (see historical temperaments). |
| 1/5-comma meantone | 697.654 | Close tp 43edo. Historically significant (see historical temperaments). |
| 3/16-comma meantone | 697.923 | |
| 2/11-comma meantone | 698.045 | Close to 55edo. |
| 3/17-comma meantone | 699.425 | |
| 1/6-comma meantone | 698.371 | Close to 67edo. Historically significant (see historical temperaments). |
| 4/25-comma meantone | 698.514 | Close to 67edo. Historically significant (see historical temperaments). |
| 2/13-comma meantone | 698.646 | |
| 1/7-comma meantone | 698.883 | Close to 79edo, 91edo. Historically significant (see historical temperaments). |
| 2/15-comma meantone | 699.088 | |
| 1/8-comma meantone | 699.267 | |
| 2/17-comma meantone | 699.425 | |
| 1/9-comma meantone | 699.565 | |
| 1/10-comma meantone | 699.804 | |
| 1/11-comma meantone | 700.000 | Effectively indistinguishable from 12edo. Does not generate a 19-tone MOS scale, so whether it counts as meantone is very questionable. |
| 1/12-comma meantone | 700.163 | No 19-tone MOS |
| 1/13-comma meantone | 700.301 | No 19-tone MOS |
| 1/14-comma meantone | 700.419 | No 19-tone MOS |
| 1/15-comma meantone | 700.521 | No 19-tone MOS |
| 1/16-comma meantone | 700.611 | No 19-tone MOS |
| 1/17-comma meantone | 700.690 | No 19-tone MOS |
| 1/18-comma meantone | 700.760 | No 19-tone MOS |
| 0/1-comma “meantone” (Pythagorean tuning) | 701.955 | Not meantone but included for reference. 9/8 is exact. Anything sharper will have whole tones not between 10/9 and 9/8, along with continuing to lack a 19-tone MOS. |