298edo: Difference between revisions
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{{EDO prologue|298}} | {{Infobox ET|Fifth=174\298 ([[149edo|87\149]])|Prime factorization=2 * 149}}{{EDO prologue|298}} | ||
== Theory == | == Theory == | ||
{{ | {{Harmonics in equal|298}} | ||
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. | |||
It can be viewed as a "spicy 149edo" as a result, and different temperaments can be extracted from 298edo by simply viewing its prime harmonics as variations from 149edo by its own half-step. | |||
In the 7-limit in the patent val, it supports [[bison]] temperament and the rank 3 temperament hemiwuermity. In the 298cd val, it supports [[miracle]]. | |||
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]]. | ||
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In the 2.5.11.17.23.43.53.59, 298edo tempers out 3176/3175, 3128/3125, 3128/3127, 32906/32065 and 76585/76582. | 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). | The [[concoctic]] scale for 298edo is a scale produced by a generator of 105 steps (paraconcoctic), and the associated rank two temperament is 105 & 298. | ||
== Rank two temperaments by generator == | |||
Note: Temperaments represented by 149edo are not included. | |||
{| class="wikitable center-all left-5" | |||
!Periods | |||
per octave | |||
!Generator | |||
(reduced) | |||
!Cents | |||
(reduced) | |||
!Associated | |||
ratio | |||
!Temperaments | |||
|- | |||
|1 | |||
|39\298 | |||
|157.04 | |||
|35/32 | |||
|[[Bison]] | |||
|} | |||
Revision as of 10:07, 29 May 2022
| ← 297edo | 298edo | 299edo → |
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.28 | +0.26 | +1.64 | +1.46 | +0.36 | +1.08 | -1.02 | -0.26 | +0.47 | +0.36 | -0.09 |
| Relative (%) | -31.9 | +6.5 | +40.8 | +36.2 | +8.9 | +26.9 | -25.3 | -6.4 | +11.8 | +8.9 | -2.1 | |
| Steps (reduced) |
472 (174) |
692 (96) |
837 (241) |
945 (51) |
1031 (137) |
1103 (209) |
1164 (270) |
1218 (26) |
1266 (74) |
1309 (117) |
1348 (156) | |
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.
It can be viewed as a "spicy 149edo" as a result, and different temperaments can be extracted from 298edo by simply viewing its prime harmonics as variations from 149edo by its own half-step.
In the 7-limit in the patent val, it supports bison temperament and the rank 3 temperament hemiwuermity. In the 298cd val, it supports miracle.
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 scale produced by a generator of 105 steps (paraconcoctic), and the associated rank two temperament is 105 & 298.
Rank two temperaments by generator
Note: Temperaments represented by 149edo are not included.
| Periods
per octave |
Generator
(reduced) |
Cents
(reduced) |
Associated
ratio |
Temperaments |
|---|---|---|---|---|
| 1 | 39\298 | 157.04 | 35/32 | Bison |