298edo: Difference between revisions

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| Prime factorization = 2 × 149

| Fifth = 174\298 ([[149edo|87\149]])

}}

|Semitones=26:24 (104.70c:96.64c)|Step size=4.0268c}}

== Theory ==

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.

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.

~~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]].

~~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~~]].

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 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.

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ratio

!Temperaments

|-

|1

|137\298

|551.67

|11/8

|[[Emka]]

|-

|2

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[[Category:Equal divisions of the octave|###]]

[[Category:Bison]]

[[Category:~~Sensi~~]]

[[Category:Emka family]]

@@ Line 2: / Line 2: @@
 | Prime factorization = 2 × 149
 | Fifth = 174\298 ([[149edo|87\149]])
-}}
+|Semitones=26:24 (104.70c:96.64c)|Step size=4.0268c}}
 {{EDO intro|298}}
 == Theory ==
 {{Harmonics in equal|298}}
-edo 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.
+edo 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.
-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.
+edo 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]].
-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]].
+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 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.
@@ Line 31: / Line 29: @@
 ratio
 !Temperaments
+|-
+|1
+|137\298
+|551.67
+|11/8
+|[[Emka]]
 |-
 |2
@@ Line 41: / Line 45: @@
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Bison]]
-[[Category:Sensi]]
+[[Category:Emka family]]