55edo: Difference between revisions
+subsets and supersets |
Correct many entries in the interval table |
||
| Line 34: | Line 34: | ||
| 1 | | 1 | ||
| 21.8 | | 21.8 | ||
| | | 65/64, 78/77, 99/98, ''128/125'' | ||
| ^1 | | ^1 | ||
| up 1sn | | up 1sn | ||
| Line 41: | Line 41: | ||
| 2 | | 2 | ||
| 43.6 | | 43.6 | ||
| 36/35 | | 36/35, ''64/63'' | ||
| ^^1 | | ^^1 | ||
| dup 1sn | | dup 1sn | ||
| Line 48: | Line 48: | ||
| 3 | | 3 | ||
| 65.5 | | 65.5 | ||
| 28/27 | | 28/27 | ||
| vvm2 | | vvm2 | ||
| dudminor 2nd | | dudminor 2nd | ||
| Line 55: | Line 55: | ||
| 4 | | 4 | ||
| 87.3 | | 87.3 | ||
| 25/24 | | 21/20, ''18/17'', ''25/24'' | ||
| vm2 | | vm2 | ||
| downminor 2nd | | downminor 2nd | ||
| Line 62: | Line 62: | ||
| 5 | | 5 | ||
| 109.1 | | 109.1 | ||
| 16/15 | | 16/15, 17/16 | ||
| m2 | | m2 | ||
| minor 2nd | | minor 2nd | ||
| Line 69: | Line 69: | ||
| 6 | | 6 | ||
| 130.9 | | 130.9 | ||
| 14/13 | | 13/12, 14/13 | ||
| ^m2 | | ^m2 | ||
| upminor 2nd | | upminor 2nd | ||
| Line 76: | Line 76: | ||
| 7 | | 7 | ||
| 152.7 | | 152.7 | ||
| | | 12/11, ''11/10'' | ||
| ~2 | | ~2 | ||
| mid 2nd | | mid 2nd | ||
| Line 83: | Line 83: | ||
| 8 | | 8 | ||
| 174.5 | | 174.5 | ||
| | | | ||
| vM2 | | vM2 | ||
| downmajor 2nd | | downmajor 2nd | ||
| Line 90: | Line 90: | ||
| 9 | | 9 | ||
| 196.4 | | 196.4 | ||
| 9/8, 10/9 | | 9/8, ''10/9'' | ||
| M2 | | M2 | ||
| major 2nd | | major 2nd | ||
| Line 104: | Line 104: | ||
| 11 | | 11 | ||
| 240.0 | | 240.0 | ||
| 8/7 | | 8/7 | ||
| ^^M2 | | ^^M2 | ||
| dupmajor 2nd | | dupmajor 2nd | ||
| Line 125: | Line 125: | ||
| 14 | | 14 | ||
| 305.5 | | 305.5 | ||
| 6/5 | | 6/5 | ||
| m3 | | m3 | ||
| minor 3rd | | minor 3rd | ||
| Line 132: | Line 132: | ||
| 15 | | 15 | ||
| 327.3 | | 327.3 | ||
| | | | ||
| ^m3 | | ^m3 | ||
| upminor 3rd | | upminor 3rd | ||
| Line 146: | Line 146: | ||
| 17 | | 17 | ||
| 370.9 | | 370.9 | ||
| 16/13 | | 26/21, ''16/13'' | ||
| vM3 | | vM3 | ||
| downmajor 3rd | | downmajor 3rd | ||
| Line 174: | Line 174: | ||
| 21 | | 21 | ||
| 458.2 | | 458.2 | ||
| | | ''21/16'' | ||
| vv4 | | vv4 | ||
| dud 4th | | dud 4th | ||
| Line 181: | Line 181: | ||
| 22 | | 22 | ||
| 480.0 | | 480.0 | ||
| | | | ||
| v4 | | v4 | ||
| down 4th | | down 4th | ||
| Line 188: | Line 188: | ||
| 23 | | 23 | ||
| 501.8 | | 501.8 | ||
| 4/3, 27/20 | | 4/3, ''27/20'' | ||
| P4 | | P4 | ||
| perfect 4th | | perfect 4th | ||
| Line 195: | Line 195: | ||
| 24 | | 24 | ||
| 523.6 | | 523.6 | ||
| | | | ||
| ^4 | | ^4 | ||
| up 4th | | up 4th | ||
| Line 202: | Line 202: | ||
| 25 | | 25 | ||
| 545.5 | | 545.5 | ||
| 11/8 | | 11/8, 15/11 | ||
| ~4 | | ~4 | ||
| mid 4th | | mid 4th | ||
| Line 209: | Line 209: | ||
| 26 | | 26 | ||
| 567.3 | | 567.3 | ||
| 18/13 | | 18/13 | ||
| vA4 | | vA4 | ||
| downaug 4th | | downaug 4th | ||
| Line 216: | Line 216: | ||
| 27 | | 27 | ||
| 589.1 | | 589.1 | ||
| 7/5 | | 7/5, 24/17 | ||
| A4, vd5 | | A4, vd5 | ||
| aug 4th, downdim 5th | | aug 4th, downdim 5th | ||
| Line 223: | Line 223: | ||
| 28 | | 28 | ||
| 610.9 | | 610.9 | ||
| 10/7 | | 10/7, 17/12 | ||
| ^A4, d5 | | ^A4, d5 | ||
| upaug 4th, dim 5th | | upaug 4th, dim 5th | ||
| Line 230: | Line 230: | ||
| 29 | | 29 | ||
| 632.7 | | 632.7 | ||
| 13/9 | | 13/9 | ||
| ^d5 | | ^d5 | ||
| updim 5th | | updim 5th | ||
| Line 237: | Line 237: | ||
| 30 | | 30 | ||
| 654.5 | | 654.5 | ||
| 16/11 | | 16/11, 22/15 | ||
| ~5 | | ~5 | ||
| mid 5th | | mid 5th | ||
| Line 244: | Line 244: | ||
| 31 | | 31 | ||
| 676.4 | | 676.4 | ||
| | | | ||
| v5 | | v5 | ||
| down 5th | | down 5th | ||
| Line 251: | Line 251: | ||
| 32 | | 32 | ||
| 698.2 | | 698.2 | ||
| 3/2, 40/27 | | 3/2, ''40/27'' | ||
| P5 | | P5 | ||
| perfect 5th | | perfect 5th | ||
| Line 258: | Line 258: | ||
| 33 | | 33 | ||
| 720.0 | | 720.0 | ||
| | | | ||
| ^5 | | ^5 | ||
| up 5th | | up 5th | ||
| Line 265: | Line 265: | ||
| 34 | | 34 | ||
| 741.8 | | 741.8 | ||
| | | ''32/21'' | ||
| ^^5 | | ^^5 | ||
| dup 5th | | dup 5th | ||
| Line 293: | Line 293: | ||
| 38 | | 38 | ||
| 829.1 | | 829.1 | ||
| 13/8 | | 21/13, ''13/8'' | ||
| ^m6 | | ^m6 | ||
| upminor 6th | | upminor 6th | ||
| Line 307: | Line 307: | ||
| 40 | | 40 | ||
| 872.7 | | 872.7 | ||
| | | | ||
| vM6 | | vM6 | ||
| downmajor 6th | | downmajor 6th | ||
| Line 314: | Line 314: | ||
| 41 | | 41 | ||
| 894.5 | | 894.5 | ||
| 5/3 | | 5/3 | ||
| M6 | | M6 | ||
| major 6th | | major 6th | ||
| Line 335: | Line 335: | ||
| 44 | | 44 | ||
| 960.0 | | 960.0 | ||
| 7/4 | | 7/4 | ||
| vvm7 | | vvm7 | ||
| dudminor 7th | | dudminor 7th | ||
| Line 349: | Line 349: | ||
| 46 | | 46 | ||
| 1003.6 | | 1003.6 | ||
| 16/9, 9/5 | | 16/9, ''9/5'' | ||
| m7 | | m7 | ||
| minor 7th | | minor 7th | ||
| Line 356: | Line 356: | ||
| 47 | | 47 | ||
| 1025.5 | | 1025.5 | ||
| | | | ||
| ^m7 | | ^m7 | ||
| upminor 7th | | upminor 7th | ||
| Line 363: | Line 363: | ||
| 48 | | 48 | ||
| 1047.3 | | 1047.3 | ||
| ''20/11'' | | 11/6, ''20/11'' | ||
| ~7 | | ~7 | ||
| mid 7th | | mid 7th | ||
| Line 370: | Line 370: | ||
| 49 | | 49 | ||
| 1069.1 | | 1069.1 | ||
| | | 13/7, 24/13 | ||
| vM7 | | vM7 | ||
| downmajor 7th | | downmajor 7th | ||
| Line 377: | Line 377: | ||
| 50 | | 50 | ||
| 1090.9 | | 1090.9 | ||
| 15/8 | | 15/8, ''32/17'' | ||
| M7 | | M7 | ||
| major 7th | | major 7th | ||
| Line 384: | Line 384: | ||
| 51 | | 51 | ||
| 1112.7 | | 1112.7 | ||
| 40/21, 48/25 | | 40/21, ''17/9'', ''48/25'' | ||
| ^M7 | | ^M7 | ||
| upmajor 7th | | upmajor 7th | ||
| Line 391: | Line 391: | ||
| 52 | | 52 | ||
| 1134.5 | | 1134.5 | ||
| 56/27 | | 56/27 | ||
| ^^M7 | | ^^M7 | ||
| dupmajor 7th | | dupmajor 7th | ||
| Line 398: | Line 398: | ||
| 53 | | 53 | ||
| 1156.4 | | 1156.4 | ||
| 35/18 | | 35/18, ''63/32'' | ||
| vv8 | | vv8 | ||
| dud 8ve | | dud 8ve | ||
| Line 405: | Line 405: | ||
| 54 | | 54 | ||
| 1178.2 | | 1178.2 | ||
| | | 128/65, 77/39, 196/99, ''125/64'' | ||
| v8 | | v8 | ||
| down 8ve | | down 8ve | ||
| Line 417: | Line 417: | ||
| D | | D | ||
|} | |} | ||
<nowiki>*</nowiki> 55f val (tending flat), inconsistent intervals labeled in ''italic'' | |||
== Selected just intervals by error == | == Approximation to JI == | ||
=== Selected just intervals by error === | |||
The following table shows how [[15-odd-limit]] just intervals are represented in 55edo (ordered by absolute error). | The following table shows how [[15-odd-limit]] just intervals are represented in 55edo (ordered by absolute error). | ||
{{15-odd-limit|55}} | {{15-odd-limit|55}} | ||
| Line 424: | Line 426: | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" |[[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" |[[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" |[[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" |Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" |Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|-87 55}} | | {{monzo| -87 55 }} | ||
|{{mapping|55 87}} | | {{mapping| 55 87 }} | ||
| +1.1903 | | +1.1903 | ||
| 1.1915 | | 1.1915 | ||
| 5.46 | | 5.46 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|81/80, 6442450944/6103515625 | | 81/80, 6442450944/6103515625 | ||
|{{mapping|55 87 128}} | | {{mapping| 55 87 128 }} | ||
| -0.1309 | | -0.1309 | ||
| 2.1012 | | 2.1012 | ||
Revision as of 07:42, 8 March 2024
| ← 54edo | 55edo | 56edo → |
Theory
55edo can be used for a meantone tuning, and is close to 1/6-comma meantone (and is almost exactly 10/57-comma meantone.) Telemann suggested it as a theoretical basis for analyzing the intervals of meantone, in which he was followed by Leopold and Wolfgang Mozart. It can also be used for mohajira and liese temperaments.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.77 | +6.41 | -8.83 | -7.55 | -5.86 | +10.38 | +2.64 | +4.14 | +7.94 | +9.22 | +4.45 |
| Relative (%) | -17.3 | +29.4 | -40.5 | -34.6 | -26.9 | +47.6 | +12.1 | +19.0 | +36.4 | +42.3 | +20.4 | |
| Steps (reduced) |
87 (32) |
128 (18) |
154 (44) |
174 (9) |
190 (25) |
204 (39) |
215 (50) |
225 (5) |
234 (14) |
242 (22) |
249 (29) | |
Subsets and supersets
Since 55 factors into 5 × 11, 55edo contains 5edo and 11edo as its subsets.
Intervals
| # | Cents | Approximate Ratios | Ups and Downs Notation | ||
|---|---|---|---|---|---|
| 0 | 0.0 | 1/1 | P1 | perfect 1sn | D |
| 1 | 21.8 | 65/64, 78/77, 99/98, 128/125 | ^1 | up 1sn | ^D |
| 2 | 43.6 | 36/35, 64/63 | ^^1 | dup 1sn | ^^D |
| 3 | 65.5 | 28/27 | vvm2 | dudminor 2nd | vvEb |
| 4 | 87.3 | 21/20, 18/17, 25/24 | vm2 | downminor 2nd | vEb |
| 5 | 109.1 | 16/15, 17/16 | m2 | minor 2nd | Eb |
| 6 | 130.9 | 13/12, 14/13 | ^m2 | upminor 2nd | ^Eb |
| 7 | 152.7 | 12/11, 11/10 | ~2 | mid 2nd | vvE |
| 8 | 174.5 | vM2 | downmajor 2nd | vE | |
| 9 | 196.4 | 9/8, 10/9 | M2 | major 2nd | E |
| 10 | 218.2 | 17/15 | ^M2 | upmajor 2nd | ^E |
| 11 | 240.0 | 8/7 | ^^M2 | dupmajor 2nd | ^^E |
| 12 | 261.8 | 7/6 | vvm3 | dudminor 3rd | vvF |
| 13 | 283.6 | 13/11 | vm3 | downminor 3rd | vF |
| 14 | 305.5 | 6/5 | m3 | minor 3rd | F |
| 15 | 327.3 | ^m3 | upminor 3rd | ^F | |
| 16 | 349.1 | 11/9, 27/22 | ~3 | mid 3rd | ^^F |
| 17 | 370.9 | 26/21, 16/13 | vM3 | downmajor 3rd | vF# |
| 18 | 392.7 | 5/4 | M3 | major 3rd | F# |
| 19 | 414.5 | 14/11 | ^M3 | upmajor 3rd | ^F# |
| 20 | 436.4 | 9/7 | ^^M3 | dupmajor 3rd | ^^F# |
| 21 | 458.2 | 21/16 | vv4 | dud 4th | vvG |
| 22 | 480.0 | v4 | down 4th | vG | |
| 23 | 501.8 | 4/3, 27/20 | P4 | perfect 4th | G |
| 24 | 523.6 | ^4 | up 4th | ^G | |
| 25 | 545.5 | 11/8, 15/11 | ~4 | mid 4th | ^^G |
| 26 | 567.3 | 18/13 | vA4 | downaug 4th | vG# |
| 27 | 589.1 | 7/5, 24/17 | A4, vd5 | aug 4th, downdim 5th | G#, vAb |
| 28 | 610.9 | 10/7, 17/12 | ^A4, d5 | upaug 4th, dim 5th | ^G#, Ab |
| 29 | 632.7 | 13/9 | ^d5 | updim 5th | ^Ab |
| 30 | 654.5 | 16/11, 22/15 | ~5 | mid 5th | vvA |
| 31 | 676.4 | v5 | down 5th | vA | |
| 32 | 698.2 | 3/2, 40/27 | P5 | perfect 5th | A |
| 33 | 720.0 | ^5 | up 5th | ^A | |
| 34 | 741.8 | 32/21 | ^^5 | dup 5th | ^^A |
| 35 | 763.6 | 14/9 | vvm6 | dudminor 6th | vvBb |
| 36 | 785.5 | 11/7 | vm6 | downminor 6th | vBb |
| 37 | 807.3 | 8/5 | m6 | minor 6th | Bb |
| 38 | 829.1 | 21/13, 13/8 | ^m6 | upminor 6th | ^Bb |
| 39 | 850.9 | 18/11, 44/27 | ~6 | mid 6th | vvB |
| 40 | 872.7 | vM6 | downmajor 6th | vB | |
| 41 | 894.5 | 5/3 | M6 | major 6th | B |
| 42 | 916.4 | 22/13 | ^M6 | upmajor 6th | ^B |
| 43 | 938.2 | 12/7 | ^^M6 | dupmajor 6th | ^^B |
| 44 | 960.0 | 7/4 | vvm7 | dudminor 7th | vvC |
| 45 | 981.8 | 30/17 | vm7 | downminor 7th | vC |
| 46 | 1003.6 | 16/9, 9/5 | m7 | minor 7th | C |
| 47 | 1025.5 | ^m7 | upminor 7th | ^C | |
| 48 | 1047.3 | 11/6, 20/11 | ~7 | mid 7th | ^^C |
| 49 | 1069.1 | 13/7, 24/13 | vM7 | downmajor 7th | vC# |
| 50 | 1090.9 | 15/8, 32/17 | M7 | major 7th | C# |
| 51 | 1112.7 | 40/21, 17/9, 48/25 | ^M7 | upmajor 7th | ^C# |
| 52 | 1134.5 | 56/27 | ^^M7 | dupmajor 7th | ^^C# |
| 53 | 1156.4 | 35/18, 63/32 | vv8 | dud 8ve | vvD |
| 54 | 1178.2 | 128/65, 77/39, 196/99, 125/64 | v8 | down 8ve | vD |
| 55 | 1200.0 | 2/1 | P8 | perfect 8ve | D |
* 55f val (tending flat), inconsistent intervals labeled in italic
Approximation to JI
Selected just intervals by error
The following table shows how 15-odd-limit just intervals are represented in 55edo (ordered by absolute error). The following tables show how 15-odd-limit intervals are represented in 55edo. Prime harmonics are in bold; inconsistent intervals are in italics.
| Interval and complement | Error (abs, ¢) | Error (rel, %) |
|---|---|---|
| 1/1, 2/1 | 0.000 | 0.0 |
| 9/7, 14/9 | 1.280 | 5.9 |
| 11/9, 18/11 | 1.683 | 7.7 |
| 11/6, 12/11 | 2.090 | 9.6 |
| 13/7, 14/13 | 2.611 | 12.0 |
| 15/8, 16/15 | 2.640 | 12.1 |
| 11/7, 14/11 | 2.963 | 13.6 |
| 3/2, 4/3 | 3.773 | 17.3 |
| 13/9, 18/13 | 3.890 | 17.8 |
| 13/10, 20/13 | 3.968 | 18.2 |
| 7/6, 12/7 | 5.053 | 23.2 |
| 13/11, 22/13 | 5.573 | 25.5 |
| 11/8, 16/11 | 5.863 | 26.9 |
| 5/4, 8/5 | 6.414 | 29.4 |
| 7/5, 10/7 | 6.579 | 30.2 |
| 9/8, 16/9 | 7.546 | 34.6 |
| 13/12, 24/13 | 7.664 | 35.1 |
| 15/13, 26/15 | 7.741 | 35.5 |
| 9/5, 10/9 | 7.858 | 36.0 |
| 15/11, 22/15 | 8.504 | 39.0 |
| 7/4, 8/7 | 8.826 | 40.5 |
| 11/10, 20/11 | 9.541 | 43.7 |
| 5/3, 6/5 | 10.187 | 46.7 |
| 15/14, 28/15 | 10.352 | 47.4 |
| 13/8, 16/13 | 10.381 | 47.6 |
| Interval and complement | Error (abs, ¢) | Error (rel, %) |
|---|---|---|
| 1/1, 2/1 | 0.000 | 0.0 |
| 9/7, 14/9 | 1.280 | 5.9 |
| 11/9, 18/11 | 1.683 | 7.7 |
| 11/6, 12/11 | 2.090 | 9.6 |
| 15/8, 16/15 | 2.640 | 12.1 |
| 11/7, 14/11 | 2.963 | 13.6 |
| 3/2, 4/3 | 3.773 | 17.3 |
| 13/10, 20/13 | 3.968 | 18.2 |
| 7/6, 12/7 | 5.053 | 23.2 |
| 11/8, 16/11 | 5.863 | 26.9 |
| 5/4, 8/5 | 6.414 | 29.4 |
| 9/8, 16/9 | 7.546 | 34.6 |
| 15/13, 26/15 | 7.741 | 35.5 |
| 15/11, 22/15 | 8.504 | 39.0 |
| 7/4, 8/7 | 8.826 | 40.5 |
| 5/3, 6/5 | 10.187 | 46.7 |
| 13/8, 16/13 | 10.381 | 47.6 |
| 15/14, 28/15 | 11.466 | 52.6 |
| 11/10, 20/11 | 12.277 | 56.3 |
| 9/5, 10/9 | 13.960 | 64.0 |
| 13/12, 24/13 | 14.155 | 64.9 |
| 7/5, 10/7 | 15.239 | 69.8 |
| 13/11, 22/13 | 16.245 | 74.5 |
| 13/9, 18/13 | 17.928 | 82.2 |
| 13/7, 14/13 | 19.207 | 88.0 |
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-87 55⟩ | [⟨55 87]] | +1.1903 | 1.1915 | 5.46 |
| 2.3.5 | 81/80, 6442450944/6103515625 | [⟨55 87 128]] | -0.1309 | 2.1012 | 9.63 |
Commas
5-limit commas: 81/80, [31 1 -14⟩, [27 5 -15⟩
7-limit commas: 31104/30625, 6144/6125, 81648/78125, 16128/15625, 28672/28125, 33075/32768, 83349/80000, 1029/1000, 686/675, 10976/10935, 16807/16384, 84035/82944
11-limit commas: 59049/58564, 74088/73205, 46656/46585, 21609/21296, 12005/11979, 19683/19360, 243/242, 3087/3025, 5488/5445, 19683/19250, 1944/1925, 45927/45056, 2835/2816, 35721/34375, 7056/6875, 12544/12375, 7203/7040, 2401/2376, 24057/24010, 72171/70000, 891/875, 176/175, 2079/2048, 385/384, 3234/3125, 17248/16875, 26411/25600, 26411/2592, 26411/262404, 88209/87808, 30976/30625, 3267/3200, 121/120, 81312/78125, 41503/40000, 41503/40500, 35937/35000, 2662/2625, 42592/42525, 83853/81920, 9317/9216, 65219/62500, 43923/43904, 14641/14400, 14641/14580
13-limit commas: 59535/57122, 29400/28561, 29568/28561, 29645/28561, 24576/24167, 99225/96668, 24500/24167, 50421/48334, 45927/43940, 2268/2197, 2240/2197, 57624/54925, 61875/61516, 57024/54925, 11264/10985, 72765/70304, 13475/13182, 22869/21970, 6776/6591, 20736/20449, 20480/20449, 84035/81796, 91125/91091, 65536/65065, 15309/14872, 1890/1859, 5600/5577, 9604/9295, 59049/57967, 58320/57967, 4374/4225, 864/845, 512/507, 11025/10816, 6125/6084, 21952/21125, 16807/16224, 84035/82134, 66825/66248, 90112/88725, 56133/54080, 693/676, 1540/1521, 26411/25350, 58806/57967, 58080/57967, 88209/84500, 4356/4225, 7744/7605, 88935/86528, 33275/33124, 27951/27040, 9317/9126, 58564/57967, 43923/42250, 17496/17303, 87808/86515, 55296/55055, 25515/25168, 1575/1573, 64827/62920, 4802/4719, 98415/98098, 59049/57200, 729/715, 144/143, 18375/18304, 18522/17875, 10976/10725, 84035/82368, 59049/56875, 11664/11375, 2304/2275, 4096/4095, 1701/1664, 105/104, 42336/40625, 25088/24375, 21609/20800, 2401/2340, 9604/9477, 72171/71344, 2673/2600, 66/65, 352/351, 13475/13312, 33957/32500, 15092/14625, 81675/81536, 58806/56875, 11616/11375, 61952/61425, 68607/66560, 847/832, 4235/4212, 35937/35672, 1331/1300, 5324/5265, 58564/56875, 85293/85184, 13377/13310, 85293/84700, 15288/15125, 31213/30976, 67392/67375, 28431/28160, 34944/34375, 4459/4400, 4459/4455, 28431/28000, 351/350, 79872/78125, 66339/65536, 51597/50000, 637/625, 10192/10125, 31213/30720, 31213/31104, 30888/30625, 1287/1280, 81081/78125, 16016/15625, 49049/48000, 49049/48600, 14157/14000, 33033/32768, 77077/75000, 51909/51200, 17303/17280, 75712/75625, 8281/8250, 41067/40960, 31941/31250, 9464/9375, 57967/57600, 91091/90000, 61347/61250, 79092/78125
Rank-2 temperaments
| Periods per 8ve |
Generator | Temperaments |
|---|---|---|
| 1 | 6\55 | Twothirdtonic |
| 1 | 16\55 | Vicentino / mohajira |
| 1 | 23\55 | Meantone |
| 1 | 26\55 | Liese |
| 1 | 27\55 | Untriton / aufo |
| 5 | 6\55 | Qintosec |
| 11 | 3\55 | Hendecatonic |
Instruments
Music
Modern renderings
- "Jesus bleibet meine Freude" from Herz und Mund und Tat und Leben, BWV 147 (1723) – arranged for two organs, rendered by Claudi Meneghin (2021)
- "Contrapunctus 4" from The Art of Fugue, BWV 1080 (1742–1749) – rendered by Claudi Meneghin (2024)
- Prelude in E Minor "The Great" – rendered by Claudi Meneghin (2023)
- Rondo alla Turca from the Piano Sonata No. 11, KV 331 (1778) – rendered by Francium (2023)
- Fugue in G minor, KV 401 (1782) – rendered by Francium (2023)
- Adagio in B minor, KV 540 (1788) – rendered by Carlo Serafini (2011) (blog entry)
- Allegro from the Piano Sonata No. 16, KV 545 (1788) – rendered by Francium (2023)
21st century
- Double Fugue on "We Wish You a Merry Christmas" for String Quartet (2020)
- Canon at the Diatonic Semitone on an Ancient Lombard Theme (2021)
- Chacony "Lament & Deception" for Two Violins and Cello (2021), for Baroque Wind Ensemble (2023)
- Fantasy "Almost a Fugue" on a Theme by Giuliani, for String Quartet (2021)
External links
- "Mozart's tuning: 55edo" (containing another listening example) in the Tonalsoft Encyclopedia