56edt: Difference between revisions
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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|]. 56edt is the twelfth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak edt]]. | 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|]. 56edt is the twelfth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|no-twos zeta peak edt]]. | ||
{{Harmonics in equal| | {{Harmonics in equal|56|3|1|intervals=odd|columns=18}} | ||
[[Category:Edt]] | [[Category:Edt]] | ||
Revision as of 10:18, 22 August 2024
| ← 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|]. 56edt is the twelfth no-twos zeta peak edt.
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | 33 | 35 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0 | -1.3 | -6.4 | +0.0 | -7.8 | +8.7 | -1.3 | -14.2 | -3.0 | -6.4 | +5.9 | -2.6 | +0.0 | +12.1 | -1.4 | -7.8 | -7.7 | -2.1 |
| Relative (%) | +0.0 | -3.9 | -19.0 | +0.0 | -22.9 | +25.6 | -3.9 | -41.9 | -8.8 | -19.0 | +17.3 | -7.7 | +0.0 | +35.7 | -4.2 | -22.9 | -22.8 | -6.1 | |
| Steps (reduced) |
56 (0) |
82 (26) |
99 (43) |
112 (0) |
122 (10) |
131 (19) |
138 (26) |
144 (32) |
150 (38) |
155 (43) |
160 (48) |
164 (52) |
168 (0) |
172 (4) |
175 (7) |
178 (10) |
181 (13) |
184 (16) | |