262edt: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
'''262EDT''' is the [[EDT|equal division of the third harmonic]] into 262 parts of 7. | '''262EDT''' is the [[EDT|equal division of the third harmonic]] into 262 parts of 7.2594 [[cent|cents]] each, corresponding to 165.3036 [[edo]] (similar to every third step of [[496edo]]). It doubles [[131edt]], which is consistent to the no-evens 25-[[odd limit#Nonoctave equaves|throdd limit]], and improves the representation of a number of higher primes so that 262edt is consistent to the no-evens 43-throdd limit with the sole exception of intervals of 19, and 41/37, all of which are still within 60% of a step of their [[patent val]] approximations. | ||
== Harmonics == | == Harmonics == | ||
{{Harmonics in equal|262|3|1|intervals=odd|columns=21}} | {{Harmonics in equal|262|3|1|intervals=odd|columns=21}} | ||
Revision as of 04:36, 21 September 2024
| ← 261edt | 262edt | 263edt → |
262EDT is the equal division of the third harmonic into 262 parts of 7.2594 cents each, corresponding to 165.3036 edo (similar to every third step of 496edo). It doubles 131edt, which is consistent to the no-evens 25-throdd limit, and improves the representation of a number of higher primes so that 262edt is consistent to the no-evens 43-throdd limit with the sole exception of intervals of 19, and 41/37, all of which are still within 60% of a step of their patent val approximations.
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | +1.28 | -0.48 | +0.00 | +1.04 | +2.21 | +1.28 | +2.38 | -1.44 | -0.48 | +1.73 | +2.57 | +0.00 | -0.30 | +0.39 | +1.04 | +0.81 | -1.03 | +2.21 | +2.74 | +0.14 |
| Relative (%) | +0.0 | +17.7 | -6.6 | +0.0 | +14.4 | +30.4 | +17.7 | +32.8 | -19.8 | -6.6 | +23.9 | +35.4 | +0.0 | -4.2 | +5.4 | +14.4 | +11.1 | -14.1 | +30.4 | +37.7 | +1.9 | |
| Steps (reduced) |
262 (0) |
384 (122) |
464 (202) |
524 (0) |
572 (48) |
612 (88) |
646 (122) |
676 (152) |
702 (178) |
726 (202) |
748 (224) |
768 (244) |
786 (0) |
803 (17) |
819 (33) |
834 (48) |
848 (62) |
861 (75) |
874 (88) |
886 (100) |
897 (111) | |