298edo: Difference between revisions

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{{Infobox ET|Fifth=174\298 ([[149edo|87\149]])|Prime factorization=2 * 149}}{{EDO prologue|298}}

== 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~~]]. ~~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]].

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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.

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]]

|}

@@ Line 1: / Line 1: @@
-{{EDO prologue|298}}
+{{Infobox ET|Fifth=174\298 ([[149edo|87\149]])|Prime factorization=2 * 149}}{{EDO prologue|298}}
 == Theory ==
-{{primes in edo|298|columns=17}}
+{{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]]. 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]].
@@ Line 10: / Line 13: @@
 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]]
+|}