298edo: Difference between revisions
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{{primes in edo|298|columns=17}} | {{primes in edo|298|columns=17}} | ||
298edo has excellent representation of the 2.5.11.17.23.43.53.59 subgroup, with all the harmonics having errors of less than 10 rc. It is a double of [[149edo]], which is the smallest edo that is uniquely consistent within the [[17-odd-limit]]. It | 298edo has excellent representation of the 2.5.11.17.23.43.53.59 subgroup, with all the harmonics having errors of less than 10 rc. It is a double of [[149edo]], which is the smallest edo that is uniquely consistent within the [[17-odd-limit]]. It [[support]]s a 17-limit extension of [[Sensi]], 111 & 103 & 298. However, compared to 149edo, 298edo's patent val differs on the mapping of 7, 11, and 13th harmonics. | ||
In the patent val, 298edo tempers out 351/350, 561/560, 936/935, and 1156/1155 in the full 17-limit. In the 2.5.11.13.17 subgroup, it tempers out [[2200/2197]] and [[6656/6655]]. | In the patent val, 298edo tempers out 351/350, 561/560, 936/935, and 1156/1155 in the full 17-limit. In the 2.5.11.13.17 subgroup, it tempers out [[2200/2197]] and [[6656/6655]]. | ||
Revision as of 18:16, 25 January 2022
298 equal division divides the octave into steps of 4.027 cents each.
Theory
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298edo has excellent representation of the 2.5.11.17.23.43.53.59 subgroup, with all the harmonics having errors of less than 10 rc. It is a double of 149edo, which is the smallest edo that is uniquely consistent within the 17-odd-limit. It supports a 17-limit extension of Sensi, 111 & 103 & 298. However, compared to 149edo, 298edo's patent val differs on the mapping of 7, 11, and 13th harmonics.
In the patent val, 298edo tempers out 351/350, 561/560, 936/935, and 1156/1155 in the full 17-limit. In the 2.5.11.13.17 subgroup, it tempers out 2200/2197 and 6656/6655.
In the 2.5.11.17.23.43.53.59, 298edo tempers out 3176/3175, 3128/3125, 3128/3127, 32906/32065 and 76585/76582.
The concoctic scale for 298edo is a generator of 105 steps (paraconcoctic).