94edo: Difference between revisions

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=== Subsets and supersets ===

Since 94 factors into primes as {{nowrap| 2 × 47 }}, 94edo contains [[2edo]] and [[47edo]] as subset edos. It can be thought of as two sets of 47edo offset by one step of 94edo. It inherits from 47edo's good approximations of primes 5, 7, 13, and 17, while dramatically improving on prime 3, as well as primes 11, 19, and 23 to a lesser degree.

Since 94 factors into primes as {{nowrap| 2 × 47 }}, 94edo contains [[2edo]] and [[47edo]] as subset edos. It can be thought of as two sets of 47edo offset by one step of 94edo. It inherits from 47edo's good approximations of primes 5, 7, 13, and 17, while dramatically improving on prime 3, as well as primes 11, 19, and 23 to a lesser degree. Tripling 94edo yields [[282edo]], which converts flat-tending harmonics to sharp, so as to achieve distinct consistency through the 23-limit and consistency through the 29-limit.

== Intervals ==

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=== Sagittal ===

94edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal_notation#~~Athenian_extension_single-shaft~~|Athenian ~~extension~~]], with the apotome equal to 9 edosteps and the limma to 7 edosteps.

94edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal_notation#Athenian|Athenian set]], with the apotome equal to 9 edosteps and the limma to 7 edosteps.

{| class="wikitable" style="text-align: center;"

! colspan="2" |Steps

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| rowspan="2" |<big>{{sagittal|(|(}}</big>

| rowspan="2" |<big>{{sagittal|/|\}}</big>

|<~~small~~>{{sagittal|~~#}}{{sagittal~~|~~\!/~~}}</~~small~~>

| rowspan="2" |<big>{{sagittal|(|)}}</big>

|~~~~{{sagittal|#}}{{sagittal|~~(!(~~}}~~~~

|{{sagittal|(!(}}{{sagittal|#}}

|~~~~{{sagittal|#}}{{sagittal|\!}}~~~~

|{{sagittal|\!}}{{sagittal|#}}

|~~~~{{sagittal|#}}{{sagittal|~~~!(~~}}~~~~

|{{sagittal|~!(}}{{sagittal|#}}

|~~~~{{sagittal|#}}~~~~

|{{sagittal|#}}

|-

!Revo

~~|<big>{{sagittal|(|)}}</big>~~

|<big>{{sagittal|~||(}}</big>

|<big>{{sagittal|||\}}</big>

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{| class="commatable wikitable center-1 center-2 right-3 center-6"

! [[Harmonic limit|Prime limit]]

! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>

! [[Ratio]]<ref group="note">Ratios with more than 8 digits are presented by placeholders with informative hints</ref>

! [[Cents]]

! [[Monzo]]

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| Pittsburghisma

|}

== Scales ==

@@ Line 20: / Line 20: @@
 === Subsets and supersets ===
-Since 94 factors into primes as {{nowrap| 2 × 47 }}, 94edo contains [[2edo]] and [[47edo]] as subset edos. It can be thought of as two sets of 47edo offset by one step of 94edo. It inherits from 47edo's good approximations of primes 5, 7, 13, and 17, while dramatically improving on prime 3, as well as primes 11, 19, and 23 to a lesser degree.
+Since 94 factors into primes as {{nowrap| 2 × 47 }}, 94edo contains [[2edo]] and [[47edo]] as subset edos. It can be thought of as two sets of 47edo offset by one step of 94edo. It inherits from 47edo's good approximations of primes 5, 7, 13, and 17, while dramatically improving on prime 3, as well as primes 11, 19, and 23 to a lesser degree. Tripling 94edo yields [[282edo]], which converts flat-tending harmonics to sharp, so as to achieve distinct consistency through the 23-limit and consistency through the 29-limit.
 == Intervals ==
@@ Line 910: / Line 910: @@
 === Sagittal ===
-edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal_notation#Athenian_extension_single-shaft|Athenian extension]], with the apotome equal to 9 edosteps and the limma to 7 edosteps.
+edo can be notated in [[Sagittal notation|Sagittal]] using the [[Sagittal_notation#Athenian|Athenian set]], with the apotome equal to 9 edosteps and the limma to 7 edosteps.
 {| class="wikitable" style="text-align: center;"
 ! colspan="2" |Steps
@@ Line 931: / Line 931: @@
 | rowspan="2" |<big>{{sagittal|(|(}}</big>
 | rowspan="2" |<big>{{sagittal|/|\}}</big>
-|<small>{{sagittal|#}}{{sagittal|\!/}}</small>
+| rowspan="2" |<big>{{sagittal|(|)}}</big>
-|<small>{{sagittal|#}}{{sagittal|(!(}}</small>
+|{{sagittal|(!(}}{{sagittal|#}}
-|<small>{{sagittal|#}}{{sagittal|\!}}</small>
+|{{sagittal|\!}}{{sagittal|#}}
-|<small>{{sagittal|#}}{{sagittal|~!(}}</small>
+|{{sagittal|~!(}}{{sagittal|#}}
-|<small>{{sagittal|#}}</small>
+|{{sagittal|#}}
 |-
 !Revo
-|<big>{{sagittal|(|)}}</big>
 |<big>{{sagittal|~||(}}</big>
 |<big>{{sagittal|||\}}</big>
@@ Line 1,126: / Line 1,125: @@
 {| class="commatable wikitable center-1 center-2 right-3 center-6"
 ! [[Harmonic limit|Prime<br>limit]]
-! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
+! [[Ratio]]<ref group="note">Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
 ! [[Cents]]
 ! [[Monzo]]
@@ Line 1,388: / Line 1,387: @@
 | Pittsburghisma
 |}
+<references group="note"/>
 == Scales ==