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{{Infobox ET}} | |||
'''24EDT''' is the [[Edt|equal division of the third harmonic]] into 24 parts of 79.2481 [[cent|cents]] each, corresponding to 15.1423 [[edo]] (similar to every seventh step of [[106edo]]). It is related to the rank-three temperament which tempers out 325/324, 625/624, and 468512/468195 in the 13-limit, which is supported by [[15edo|15]], [[106edo|106]], [[121edo|121]], [[212edo|212]], and [[227edo|227]] EDOs. | '''24EDT''' is the [[Edt|equal division of the third harmonic]] into 24 parts of 79.2481 [[cent|cents]] each, corresponding to 15.1423 [[edo]] (similar to every seventh step of [[106edo]]). It is related to the rank-three temperament which tempers out 325/324, 625/624, and 468512/468195 in the 13-limit, which is supported by [[15edo|15]], [[106edo|106]], [[121edo|121]], [[212edo|212]], and [[227edo|227]] EDOs. | ||
== Theory == | |||
{{Harmonics in equal|24|3|1|prec=2|columns=15}} | |||
== Interval table == | |||
{| class="wikitable" | {| class="wikitable" | ||
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! | comments | ! | comments | ||
|- | |- | ||
! colspan="3" | 0 | |||
| | '''exact [[1/1]]''' | | | '''exact [[1/1]]''' | ||
| | | | | | ||
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==Related | ==Related regular temperaments== | ||
===11-limit 15&106&212=== | ===11-limit 15&106&212=== | ||
Commas: 15625/15552, 585640/583443 | Commas: 15625/15552, 585640/583443 | ||
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POTE generators: ~7/4 = 968.8778, ~22/21 = 79.2597 | POTE generators: ~7/4 = 968.8778, ~22/21 = 79.2597 | ||
Mapping: [<1 0 1 0 -1|, <0 24 20 0 25|, <0 0 0 1 1|] | |||
EDOs: 15, 106, 121, 212, 227 | EDOs: 15, 106, 121, 212, 227 | ||
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POTE generators: ~7/4 = 968.8187, ~22/21 = 79.2727 | POTE generators: ~7/4 = 968.8187, ~22/21 = 79.2727 | ||
Mapping: [<1 0 1 0 -1 0|, <0 24 20 0 25 56|, <0 0 0 1 1 0|] | |||
EDOs: 15, 106, 121, 212, 227 | EDOs: 15, 106, 121, 212, 227 | ||
{{todo|expand}} | |||
Latest revision as of 19:21, 1 August 2025
| ← 23edt | 24edt | 25edt → |
24EDT is the equal division of the third harmonic into 24 parts of 79.2481 cents each, corresponding to 15.1423 edo (similar to every seventh step of 106edo). It is related to the rank-three temperament which tempers out 325/324, 625/624, and 468512/468195 in the 13-limit, which is supported by 15, 106, 121, 212, and 227 EDOs.
Theory
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.28 | +0.00 | -22.56 | -12.63 | -11.28 | +38.84 | -33.83 | +0.00 | -23.91 | -30.42 | -22.56 | -2.63 | +27.57 | -12.63 | +34.14 |
| Relative (%) | -14.2 | +0.0 | -28.5 | -15.9 | -14.2 | +49.0 | -42.7 | +0.0 | -30.2 | -38.4 | -28.5 | -3.3 | +34.8 | -15.9 | +43.1 | |
| Steps (reduced) |
15 (15) |
24 (0) |
30 (6) |
35 (11) |
39 (15) |
43 (19) |
45 (21) |
48 (0) |
50 (2) |
52 (4) |
54 (6) |
56 (8) |
58 (10) |
59 (11) |
61 (13) | |
Interval table
| degree | cents value | hekts | corresponding JI intervals |
comments |
|---|---|---|---|---|
| 0 | exact 1/1 | |||
| 1 | 79.2481 | 54.167 | 22/21 | |
| 2 | 158.4963 | 108.333 | pseudo-12/11 | |
| 3 | 237.7444 | 162.5 | 39/34, 8/7 | |
| 4 | 316.9925 | 216.667 | 6/5 | |
| 5 | 396.2406 | 270.833 | 44/35 | pseudo-5/4 |
| 6 | 475.4888 | 325 | 21/16 | pseudo-4/3 |
| 7 | 554.7369 | 379.167 | 11/8 | |
| 8 | 633.985 | 433.333 | 75/52, 13/9 | |
| 9 | 713.2331 | 487.5 | pseudo-3/2 | |
| 10 | 792.4813 | 541.667 | 30/19, 19/12 | |
| 11 | 871.7294 | 595.833 | pseudo-5/3 | |
| 12 | 950.9775 | 650 | 45/26, 26/15 | |
| 13 | 1030.2256 | 704.167 | pseudo-9/5 | |
| 14 | 1109.4738 | 758.333 | 36/19, 19/10 | |
| 15 | 1188.7219 | 812.5 | pseudooctave | |
| 16 | 1267.97 | 866.667 | 52/25, 27/13 | |
| 17 | 1347.2181 | 920.833 | 24/11 | |
| 18 | 1426.4663 | 975 | 16/7 | pseudo-9/4 |
| 19 | 1505.7144 | 1029.167 | 105/44 | pseudo-12/5 (6/5 plus pseudooctave) |
| 20 | 1584.9625 | 1083.333 | 5/2 | |
| 21 | 1664.2106 | 1137.5 | 34/13, 21/8 | φ2 |
| 22 | 1743.4588 | 1191.667 | pseudo-11/4 (11/8 plus pseudooctave) | |
| 23 | 1822.7069 | 1245.833. | 63/22 | |
| 24 | 1901.955 | 1300 | exact 3/1 | just perfect fifth plus an octave |
Related regular temperaments
11-limit 15&106&212
Commas: 15625/15552, 585640/583443
POTE generators: ~7/4 = 968.8778, ~22/21 = 79.2597
Mapping: [<1 0 1 0 -1|, <0 24 20 0 25|, <0 0 0 1 1|]
EDOs: 15, 106, 121, 212, 227
13-limit 15&106&212
Commas: 325/324, 625/624, 468512/468195
POTE generators: ~7/4 = 968.8187, ~22/21 = 79.2727
Mapping: [<1 0 1 0 -1 0|, <0 24 20 0 25 56|, <0 0 0 1 1 0|]
EDOs: 15, 106, 121, 212, 227