298edo: Difference between revisions
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| Prime factorization = 2 × 149 | | Prime factorization = 2 × 149 | ||
| Fifth = 174\298 ([[149edo|87\149]]) | | Fifth = 174\298 ([[149edo|87\149]]) | ||
}} | |Semitones=26:24 (104.70c:96.64c)|Step size=4.0268c}} | ||
{{EDO intro|298}} | {{EDO intro|298}} | ||
== Theory == | == Theory == | ||
{{Harmonics in equal|298}} | {{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]]. | 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]].. However, the patent vals differ on the mapping of 7, 11, and 13th harmonics. Thus 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. | ||
298edo supports unconventional extensions of [[Sensi]] to higher dimensions. The 298d val in 11-limit (149-edo with 298-edo 11/8) supports [[hagrid]], in addition to 118 & 31 & 298d variant of [[hemithirds]]. In the 298cd val, it supports [[miracle]]. | |||
The patent val in 298edo is desolate for temperaments, but it supports [[bison]] temperament and the rank 3 temperament hemiwuermity. In the 2.5.11.13 subgroup, 298edo supports [[emka]]. In the full 13-limit, 298edo supports an unnamed 77 & 298 temperament with [[13/8]] as its generator. | |||
In | |||
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. | ||
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ratio | ratio | ||
!Temperaments | !Temperaments | ||
|- | |||
|1 | |||
|137\298 | |||
|551.67 | |||
|11/8 | |||
|[[Emka]] | |||
|- | |- | ||
|2 | |2 | ||
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[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Bison]] | [[Category:Bison]] | ||
[[Category: | [[Category:Emka family]] | ||
Revision as of 21:40, 9 August 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.. However, the patent vals differ on the mapping of 7, 11, and 13th harmonics. Thus 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.
298edo supports unconventional extensions of Sensi to higher dimensions. The 298d val in 11-limit (149-edo with 298-edo 11/8) supports hagrid, in addition to 118 & 31 & 298d variant of hemithirds. In the 298cd val, it supports miracle.
The patent val in 298edo is desolate for temperaments, but it supports bison temperament and the rank 3 temperament hemiwuermity. In the 2.5.11.13 subgroup, 298edo supports emka. In the full 13-limit, 298edo supports an unnamed 77 & 298 temperament with 13/8 as its generator.
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 | 137\298 | 551.67 | 11/8 | Emka |
| 2 | 39\298 | 157.04 | 35/32 | Bison |