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{{Infobox ET}} | {{Infobox ET}} | ||
The 56 equal division of 3, the tritave, divides it into 56 equal parts of 33.963 cents each, corresponding to 35.332 edo. It tempers out 245/243 in the 7-limit, 1331/1323 in the 11-limit and 275/273 in the 13-limit. It [[support]]s the 3.5.7.11.13 temperament with mapping [<1 5 0 1 10|, <0 -6 3 2 -13|]. | The 56 equal division of 3, the tritave, divides it into 56 equal parts of 33.963 cents each, corresponding to 35.332 edo. It tempers out 245/243 in the 7-limit, 1331/1323 in the 11-limit and 275/273 in the 13-limit. It [[support]]s the 3.5.7.11.13 temperament with mapping [<1 5 0 1 10|, <0 -6 3 2 -13|]. It is the twelfth [[the Riemann zeta function and tuning#Removing primes|no-twos zeta peak edt]]. | ||
{{Harmonics in equal|56|3|1|intervals= | == Harmonics == | ||
{{Harmonics in equal|56|3|1|intervals = prime|columns = 9}} | |||
{{Harmonics in equal|56|3|1|start = 12|collapsed = 1|intervals = odd}} | |||
== Intervals == | |||
{{Interval table}} | |||
Latest revision as of 13:06, 10 April 2025
| ← 55edt | 56edt | 57edt → |
The 56 equal division of 3, the tritave, divides it into 56 equal parts of 33.963 cents each, corresponding to 35.332 edo. It tempers out 245/243 in the 7-limit, 1331/1323 in the 11-limit and 275/273 in the 13-limit. It supports the 3.5.7.11.13 temperament with mapping [<1 5 0 1 10|, <0 -6 3 2 -13|]. It is the twelfth no-twos zeta peak edt.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -11.3 | +0.0 | -1.3 | -6.4 | -7.8 | +8.7 | -14.2 | -3.0 | +5.9 |
| Relative (%) | -33.2 | +0.0 | -3.9 | -19.0 | -22.9 | +25.6 | -41.9 | -8.8 | +17.3 | |
| Steps (reduced) |
35 (35) |
56 (0) |
82 (26) |
99 (43) |
122 (10) |
131 (19) |
144 (32) |
150 (38) |
160 (48) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | +0.0 | +12.1 | -1.4 | -7.8 | -7.7 | -2.1 | +8.7 | -10.0 | +9.5 | -1.3 |
| Relative (%) | -7.7 | +0.0 | +35.7 | -4.2 | -22.9 | -22.8 | -6.1 | +25.6 | -29.3 | +27.9 | -3.9 | |
| Steps (reduced) |
164 (52) |
168 (0) |
172 (4) |
175 (7) |
178 (10) |
181 (13) |
184 (16) |
187 (19) |
189 (21) |
192 (24) |
194 (26) | |
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 34 | 23.2 | |
| 2 | 67.9 | 46.4 | 26/25, 27/26 |
| 3 | 101.9 | 69.6 | 18/17 |
| 4 | 135.9 | 92.9 | 27/25 |
| 5 | 169.8 | 116.1 | 11/10, 21/19 |
| 6 | 203.8 | 139.3 | |
| 7 | 237.7 | 162.5 | 31/27 |
| 8 | 271.7 | 185.7 | 7/6 |
| 9 | 305.7 | 208.9 | 25/21, 31/26 |
| 10 | 339.6 | 232.1 | 17/14 |
| 11 | 373.6 | 255.4 | 26/21, 31/25 |
| 12 | 407.6 | 278.6 | 19/15 |
| 13 | 441.5 | 301.8 | 22/17 |
| 14 | 475.5 | 325 | 25/19 |
| 15 | 509.5 | 348.2 | |
| 16 | 543.4 | 371.4 | 26/19 |
| 17 | 577.4 | 394.6 | |
| 18 | 611.3 | 417.9 | 27/19 |
| 19 | 645.3 | 441.1 | |
| 20 | 679.3 | 464.3 | |
| 21 | 713.2 | 487.5 | |
| 22 | 747.2 | 510.7 | |
| 23 | 781.2 | 533.9 | 11/7 |
| 24 | 815.1 | 557.1 | |
| 25 | 849.1 | 580.4 | 18/11, 31/19 |
| 26 | 883.1 | 603.6 | 5/3 |
| 27 | 917 | 626.8 | 17/10 |
| 28 | 951 | 650 | 19/11, 26/15, 33/19 |
| 29 | 984.9 | 673.2 | 23/13, 30/17 |
| 30 | 1018.9 | 696.4 | 9/5 |
| 31 | 1052.9 | 719.6 | 11/6 |
| 32 | 1086.8 | 742.9 | |
| 33 | 1120.8 | 766.1 | 21/11 |
| 34 | 1154.8 | 789.3 | |
| 35 | 1188.7 | 812.5 | |
| 36 | 1222.7 | 835.7 | |
| 37 | 1256.6 | 858.9 | 31/15 |
| 38 | 1290.6 | 882.1 | 19/9 |
| 39 | 1324.6 | 905.4 | |
| 40 | 1358.5 | 928.6 | |
| 41 | 1392.5 | 951.8 | 29/13 |
| 42 | 1426.5 | 975 | |
| 43 | 1460.4 | 998.2 | |
| 44 | 1494.4 | 1021.4 | |
| 45 | 1528.4 | 1044.6 | |
| 46 | 1562.3 | 1067.9 | |
| 47 | 1596.3 | 1091.1 | |
| 48 | 1630.2 | 1114.3 | 18/7 |
| 49 | 1664.2 | 1137.5 | |
| 50 | 1698.2 | 1160.7 | |
| 51 | 1732.1 | 1183.9 | 19/7, 30/11 |
| 52 | 1766.1 | 1207.1 | 25/9 |
| 53 | 1800.1 | 1230.4 | 17/6 |
| 54 | 1834 | 1253.6 | 26/9 |
| 55 | 1868 | 1276.8 | |
| 56 | 1902 | 1300 | 3/1 |