298edo: Difference between revisions

Line 1:

{{Infobox ET

| Prime factorization = 2 × 149

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

| Step size = 4.0268¢

|Semitones=26:24 (104.~~70c~~:96.~~64c~~)~~|Step size=4.0268c~~}}

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

| Semitones = 26:24 (104.70¢:96.64¢)

}}

== 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 r¢. It is a double of [[149edo]], but the patent vals differ on the mapping of the 7th, 11th, 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 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]].

298edo supports unconventional extensions of [[sensi]] to higher dimensions. The 298d val in 11-limit (149edo with 298edo 11/8) supports [[hagrid]], in addition to the 31 & 298d variant and the 118 & 298d variant of [[hemithirds]]. The 298cd val 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.

The patent val in 298edo supports the [[bison]] temperament and the rank-3 temperament [[hemimage]]. 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.

=== Prime harmonics ===

== Rank ~~two~~ temperaments ~~by generator~~ ==

== Rank-2 temperaments ==

Note: ~~Temperaments~~ represented by 149edo are not included.

Note: 5-limit temperaments represented by 149edo are not included.

{| class="wikitable center-all left-5"

!Periods

! Periods<br>per Octave

per ~~octave~~

! Generator<br>(Reduced)

!Generator

! Cents<br>(Reduced)

(~~reduced~~)

! Associated<br>Ratio

!Cents

! Temperaments

(~~reduced~~)

!Associated

~~ratio~~

!Temperaments

|-

|1

| 1

|137\298

| 137\298

|551.67

| 551.67

|11/8

| 11/8

|[[Emka]]

| [[Emka]]

|-

|2

| 2

|39\298

| 39\298

|157.04

| 157.04

|35/32

| 35/32

|[[Bison]]

| [[Bison]]

|}

== Scales ==

The [[concoctic]] scale for 298edo is a scale produced by a generator of 105 steps (paraconcoctic), and the associated rank-2 temperament is 105 & 298.

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

[[Category:Bison]]

[[Category:Emka family]]

@@ Line 1: / Line 1: @@
 {{Infobox ET
 | Prime factorization = 2 × 149
-| Fifth = 174\298 ([[149edo|87\149]])
+| Step size = 4.0268¢
-|Semitones=26:24 (104.70c:96.64c)|Step size=4.0268c}}
+| Fifth = 174\298 (→ [[149edo|87\149]])
+| Semitones = 26:24 (104.70¢:96.64¢)
+}}
 {{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 r¢. It is a double of [[149edo]], but the patent vals differ on the mapping of the 7th, 11th, 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.
-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.
-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]].
+edo supports unconventional extensions of [[sensi]] to higher dimensions. The 298d val in 11-limit (149edo with 298edo 11/8) supports [[hagrid]], in addition to the 31 & 298d variant and the 118 & 298d variant of [[hemithirds]]. The 298cd val 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.
+The patent val in 298edo supports the [[bison]] temperament and the rank-3 temperament [[hemimage]]. 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.
+=== Prime harmonics ===
+{{Harmonics in equal|298}}
-== Rank two temperaments by generator ==
+== Rank-2 temperaments ==
-Note: Temperaments represented by 149edo are not included.
+Note: 5-limit temperaments represented by 149edo are not included.
 {| class="wikitable center-all left-5"
-!Periods
+! Periods<br>per Octave
-per octave
+! Generator<br>(Reduced)
-!Generator
+! Cents<br>(Reduced)
-(reduced)
+! Associated<br>Ratio
-!Cents
+! Temperaments
-(reduced)
-!Associated
-ratio
-!Temperaments
 |-
-|1
+| 1
-|137\298
+| 137\298
-|551.67
+| 551.67
-|11/8
+| 11/8
-|[[Emka]]
+| [[Emka]]
 |-
-|2
+| 2
-|39\298
+| 39\298
-|157.04
+| 157.04
-|35/32
+| 35/32
-|[[Bison]]
+| [[Bison]]
 |}
+== Scales ==
+The [[concoctic]] scale for 298edo is a scale produced by a generator of 105 steps (paraconcoctic), and the associated rank-2 temperament is 105 & 298.
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Bison]]
 [[Category:Emka family]]