1789edo: Difference between revisions

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The '''1789 equal divisions of the octave''' ('''1789edo'''), or the '''1789-tone equal temperament''' ('''1789tet'''), '''1789 equal temperament''' ('''1789et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 1789 [[equal]] parts of about 0.671 [[cent]]s each. It is the 278th [[prime edo]].

== Theory ==

1789edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it is excellent in approximating harmonics [[5/1|5]], [[9/1|9]], [[11/1|11]], [[13/1|13]] and [[21/1|21]], making it suitable for a 2.9.5.21.11.13 [[subgroup]] interpretation.

1789edo can be adapted for use with the 2.5.11.13.29.31.47.59.61 [[subgroup]]. Perhaps the most notable fact about 1789edo, is ~~the fact~~ that it tempers out the jacobin comma ([[6656/6655]]), and it is also consistent on the subgroup 2.5.11.13 of the comma, which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic.

For higher harmonics, 1789edo can be adapted for use with the 2.9.5.21.11.13.29.31.47.59.61 subgroup. Perhaps the most notable fact about 1789edo is that it [[tempering out|tempers out]] the jacobin comma ([[6656/6655]]), and it is also consistent on the subgroup 2.5.11.13 of the comma, which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic.

1789edo is consistent in the no-threes 13-odd-limit. Since its double, [[3578edo]], is consistent in the 21-odd-limit, it can be thought of as a [[K*N subgroups|2*1789]] 2.9.5.7.11.13.225.289.361.21 subgroup temperament, on which it shares mapping with 3578edo and tempers out the same commas.

=== Odd harmonics ===

=== Jacobin temperaments ===

''Main ~~article: [[~~The Jacobins~~]]''~~

Since 1789edo tempers out the jacobin comma and it is defined by stacking three 11/8s to reach 13/10, one can use that as a generator. The resulting temperament is 37 & 1789, called onzonic. Name "onzonic" comes from the French word for eleven, ''onze''.

Since 1789edo tempers out the jacobin comma and it is defined by stacking three 11/8s to reach 13/10, one can use that as a generator. The resulting temperament is {{nowrap|37 & 1789}}, called onzonic. Name "onzonic" comes from the French word for eleven, ''onze''.

1789edo supports the 2.5.11.13.19 subgroup temperament called ''estates general'' defined as 1789 & 3125. This is referencing the fact that Estates General were called by Louis XVI on 5th May 1789, written as 05/05, and 3125 is 5 to the 5th power and also provides an optimal patent val for tempering out the jacobin comma, contuing the lore.

1789edo supports the 2.5.11.13.19 subgroup temperament called ''estates general'' defined as {{nowrap|1789 & 3125}}. This is referencing the fact that Estates General were called by Louis XVI on 5th May 1789, written as 05/05, and 3125 is 5 to the 5th power and also provides an optimal patent val for tempering out the jacobin comma, contuing the lore.

=== Other ===

1789edo can be used for the finite "French decimal" ~~temperament - that~~ is, where all the interval targets in just intonation are expressed as terminating decimals. For example, [[5/4]], [[25/16]], [[128/125]], [[32/25]], 625/512, etc.

1789edo can be used for the finite "French decimal" temperament—that is, where all the interval targets in just intonation are expressed as terminating decimals. For example, [[5/4]], [[25/16]], [[128/125]], [[32/25]], 625/512, etc.

Since the 5/4 of 1789edo is on the 576th step, a highly divisible number, 1789edo can replicate a lot of [[~~Ed5~~/4]] ~~temperaments - more~~ exactly those which are divisors of 576, and that includes all from [[2ed5/4]] to [[9ed5/4]], skipping [[7ed5/4]]. One such scale which stands for [[4ed5/4]], is a tuning for the [[hemiluna]] temperament in the 1789bd val in the 13-limit. It is also worth noting that 1789bd val is better tuned than the patent val.

Since the 5/4 of 1789edo is on the 576th step, a highly divisible number, 1789edo can replicate a lot of [[ed5/4]] temperaments—more exactly those which are divisors of 576, and that includes all from [[2ed5/4]] to [[9ed5/4]], skipping [[7ed5/4]]. One such scale which stands for [[4ed5/4]], is a tuning for the [[hemiluna]] temperament in the 1789bd val in the 13-limit. It is also worth noting that 1789bd val is better tuned than the patent val.

1789edo has an essentially perfect [[9/8]], a very common interval. 1789edo supports the 2.9.5.11.13 subgroup temperament called ''commatose'' which uses the Pythagorean comma as a generator, which is excess of six 9/8s over the octave in this case. It is defined as a 460 & 1789 temperament.

1789edo has an essentially perfect [[9/8]], a very common interval. 1789edo supports the 2.9.5.11.13 subgroup temperament called ''commatose'' which uses the Pythagorean comma as a generator, which is excess of six 9/8s over the octave in this case. It is defined as a {{nowrap|460 & 1789}} temperament.

Since 1789edo has a very precise 31/29, it supports tricesimoprimal ~~miracloid - a~~ version of secor with 31/29 as the generator and a flat, meantone-esque fifth of about 692.23 cents. Using the maximal evenness method, we find a 52 & 1789 temperament. Best subgroup for it is 2.5.7.11.19.29.31, since both 52edo and 1789edo support it well, and the comma basis is 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688.

Since 1789edo has a very precise 31/29, it supports tricesimoprimal miracloid—a version of secor with 31/29 as the generator and a flat, meantone-esque fifth of about 692.23 cents. Using the maximal evenness method, we find a {{nowrap|52 & 1789}} temperament. Best subgroup for it is 2.5.7.11.19.29.31, since both 52edo and 1789edo support it well, and the comma basis is 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688.

On the patent val in the 7-limit, 1789edo supports 99 & 373 temperament called maviloid. In addition, it also tempers out [[2401/2400]].

On the patent val in the 7-limit, 1789edo supports {{nowrap|99 & 373}} temperament called maviloid. In addition, it also tempers out [[2401/2400]].

=== Subsets and supersets ===

1789edo is the 278th [[prime edo]]. [[3578edo]], which doubles it, is consistent in the [[21-odd-limit]].

== Table of selected intervals ==

{| class="wikitable mw-collapsible mw-collapsed"

|+ style=white-space:nowrap | Selected intervals in 1789edo

|+ style="font-size: 105%; white-space: nowrap;" | Selected intervals in 1789edo

|-

! Step

! Eliora's ~~Naming System~~

! Eliora's naming system

! JI ~~Approximation~~ or ~~Other Interpretations~~*

! JI approximation or other interpretations*

|-

| 0

Line 64:

Line 67:

| 65/62

|-

|125

| 125

|Sextilimeans generator

| Sextilimeans generator

|16807/16000

| 16807/16000

|-

| 172

Line 104:

Line 107:

| [[13/10]]

|-

|750

| 750

|Sextilimeans fourth

| Sextilimeans fourth

|

|-

| 777

| Maviloid generator

|875/648

| 875/648

|-

| 822

Line 120:

Line 123:

| (31/29)6

|-

|1039

| 1039

|Sextilimeans fifth

| Sextilimeans fifth

|

|-

| 1046

| Minor fifth

| [[3/2]]†

| [[3/2]]**

|-

| 1047

| Major fifth

| [[3/2]]†

| [[3/2]]**

|-

| 1213

Line 156:

Line 159:

| 2/1

|}

<nowiki>*~~</nowiki> based~~ on the 2.5.11.13.29.31 subgroup where applicable

<nowiki />* Based on the 2.5.11.13.29.31 subgroup where applicable

† 1046\1789 as 3/2 is the patent val, 1047\1789 as 3/2 is the 1789b val

<nowiki />** 1046\1789 as 3/2 is the patent val, 1047\1789 as 3/2 is the 1789b val

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list~~|Comma List~~]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal 8ve ~~Stretch~~ (¢)

! rowspan="2" | Optimal 8ve stretch (¢)

! colspan="2" | Tuning ~~Error~~

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

Line 173:

Line 177:

| 2.9

| {{monzo| -5671 1789 }}

| [{{~~val~~| 1789 5671 }}]

| {{mapping| 1789 5671 }}

| -0.00044

| −0.00044

| 0.00044

| 0.06

Line 180:

Line 184:

| 2.9.5

| {{monzo| -70 36 -19 }}, {{monzo| 129 -7 -46 }}

| [{{~~val~~| 1789 5671 4154 }}]

| {{mapping| 1789 5671 4154 }}

| -0.00710

| −0.00710

| 0.00942

| 1.40

Line 187:

Line 191:

| 2.9.5.7

| 420175/419904, {{monzo| 34 2 -21 3 }}, {{monzo| -55 15 2 1 }}

| [{{~~val~~| 1789 5671 4154 5022 }}]

| {{mapping| 1789 5671 4154 5022 }}

| +0.01606

| 0.04093

| 6.10

|- style="border-top: double;"

| 2.5.11.13

| 6656/6655, {{monzo| 43 -18 5 -5 }}, {{monzo| -38 -32 10 21 }}

| {{mapping| 1789 4154 6189 6620}}

| −0.00490

| 0.01405

| 2.09

|-

~~|style="border-top: double;" |2.5.11.13~~

| 2.5.11.13.29

~~|style="border-top: double;" |6656/6655, {{monzo|43 -18 5 -5}}, {{monzo|-38 -32 10 21}}~~

| 6656/6655, 371293/371200, {{monzo| -18 -6 -1 3 5 }}, {{monzo| 34 -20 5 0 -1 }}

~~|style="border-top: double;" |[{{val| 1789 4154 6189 6620}}]~~

| {{mapping| 1789 4154 6189 6620 8691 }}

~~|style="border-top: double;" | -0.00490~~

| −0.00591

~~|style="border-top: double;" |0.01405~~

| 0.01272

~~|style="border-top: double;" |2.09~~

| 1.90

|-

|2.5.11.13.29

|6656/6655, 371293/371200, {{monzo|-18 -6 -1 3 5}}, {{monzo|34 -20 5 0 -1}}

|[{{~~val~~| 1789 4154 6189 6620 8691}}]

| -0.00591

|0.01272

|1.90

|-

| 2.5.11.13.29.31

| 6656/6655, 387283/387200, 2640704/2640625, 3455881/3455756, 594880000/594823321

| [{{~~val~~| 1789 4154 6189 6620 8691 8863 }}]

| {{mapping| 1789 4154 6189 6620 8691 8863 }}

| -0.00363

| −0.00363

| 0.01268

| 1.89

Line 215:

Line 219:

=== Rank-2 temperaments ===

{| class="wikitable center-all left-4"

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

! ~~Generator~~ ~~(Reduced)~~

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

! Cents~~ (Reduced)~~

|-

! Associated ~~Ratio~~

! Periods per 8ve

! Generator*

! Cents*

! Associated ratio*

! Temperament

|-

| 1

| 35\1789

| 23.48

| 531441/524288

|[[Commatose]]

| [[Commatose]]

|-

|125\1789

| "

|83.85

| 125\1789

|16807/16000

| 83.85

|[[Sextilimeans]]

| 16807/16000

| [[Sextilimeans]]

|-

|144\1789

| "

|96.59

| 144\1789

|200/189

| 96.59

|[[Hemiluna]] (1789bd)

| 200/189

| [[Hemiluna]] (1789bd)

|-

| "

| 172\1789

| 115.37

Line 241:

Line 252:

| [[Tricesimoprimal miracloid]]

|-

|377\1789

| "

|252.88

| 377\1789

|53094899/45875200

| 252.88

|[[Double ~~Bastille~~]]

| 53094899/45875200

| [[Double bastille]]

|-

| "

| 576\1789

| 386.36

Line 251:

Line 264:

| [[French decimal]]

|-

| "

| 754\1789

| 505.76

| {{monzo| 104 0 57 0 -14 5 }}

| [[Pure bastille]]

|-

| "

| 777\1789

| 521.18

| 875/648

|[[Maviloid]]

| [[Maviloid]]

|-

| "

| 778\1789

| 521.86

| 80275/59392

|[[Estates general]]

| [[Estates general]]

|-

|822\1789

| "

|551.37

| 822\1789

|11/8

| 551.37

|[[Onzonic]]

| 11/8

| [[Onzonic]]

|-

|865\1789

| "

|580.21

| 865\1789

|~~{{Monzo|294 -46 7 -57}}~~

| 580.21

|Eternal ~~Revolutionary~~

| 6875/4914

| [[Eternal revolutionary]] (1789bd)

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

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

== Music ==

; [[Eliora]]

* [https://www.youtube.com/watch?v=1zrnsGODQSg ''Etude la (R)evolution''] (2022)

* [https://www.youtube.com/watch?v=1zrnsGODQSg Etude la (R)evolution, Op. 1, No. 2]by [[Eliora]]

~~~~

~~[[Category:Prime EDO]]~~

[[Category:Jacobin]]

[[Category:Listen]]

~~[[Category:Listen]]~~

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''1789 equal divisions of the octave''' ('''1789edo'''), or the '''1789-tone equal temperament''' ('''1789tet'''), '''1789 equal temperament''' ('''1789et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 1789 [[equal]] parts of about 0.671 [[cent]]s each. It is the 278th [[prime edo]].
+{{ED intro}}
 == Theory ==
+edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it is excellent in approximating harmonics [[5/1|5]], [[9/1|9]], [[11/1|11]], [[13/1|13]] and [[21/1|21]], making it suitable for a 2.9.5.21.11.13 [[subgroup]] interpretation.
-edo can be adapted for use with the 2.5.11.13.29.31.47.59.61 [[subgroup]]. Perhaps the most notable fact about 1789edo, is the fact that it tempers out the jacobin comma ([[6656/6655]]), and it is also consistent on the subgroup 2.5.11.13 of the comma, which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic.
+For higher harmonics, 1789edo can be adapted for use with the 2.9.5.21.11.13.29.31.47.59.61 subgroup. Perhaps the most notable fact about 1789edo is that it [[tempering out|tempers out]] the jacobin comma ([[6656/6655]]), and it is also consistent on the subgroup 2.5.11.13 of the comma, which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic.
-edo is consistent in the no-threes 13-odd-limit. Since its double, [[3578edo]], is consistent in the 21-odd-limit, it can be thought of as a [[K*N subgroups|2*1789]] 2.9.5.7.11.13.225.289.361.21 subgroup temperament, on which it shares mapping with 3578edo and tempers out the same commas.
 === Odd harmonics ===
-{{Harmonics in equal|1789|columns = 10}}
+{{Harmonics in equal|1789}}
 === Jacobin temperaments ===
-''Main article: [[The Jacobins]]''
+{{Main| The Jacobins }}
-Since 1789edo tempers out the jacobin comma and it is defined by stacking three 11/8s to reach 13/10, one can use that as a generator. The resulting temperament is 37 & 1789, called onzonic. Name "onzonic" comes from the French word for eleven, ''onze''.
+Since 1789edo tempers out the jacobin comma and it is defined by stacking three 11/8s to reach 13/10, one can use that as a generator. The resulting temperament is {{nowrap|37 &amp; 1789}}, called onzonic. Name "onzonic" comes from the French word for eleven, ''onze''.
-edo supports the 2.5.11.13.19 subgroup temperament called ''estates general'' defined as 1789 & 3125. This is referencing the fact that Estates General were called by Louis XVI on 5th May 1789, written as 05/05, and 3125 is 5 to the 5th power and also provides an optimal patent val for tempering out the jacobin comma, contuing the lore.
+edo supports the 2.5.11.13.19 subgroup temperament called ''estates general'' defined as {{nowrap|1789 & 3125}}. This is referencing the fact that Estates General were called by Louis XVI on 5th May 1789, written as 05/05, and 3125 is 5 to the 5th power and also provides an optimal patent val for tempering out the jacobin comma, contuing the lore.
 === Other ===
-edo can be used for the finite "French decimal" temperament - that is, where all the interval targets in just intonation are expressed as terminating decimals. For example, [[5/4]], [[25/16]], [[128/125]], [[32/25]], 625/512, etc.
+edo can be used for the finite "French decimal" temperament—that is, where all the interval targets in just intonation are expressed as terminating decimals. For example, [[5/4]], [[25/16]], [[128/125]], [[32/25]], 625/512, etc.
-Since the 5/4 of 1789edo is on the 576th step, a highly divisible number, 1789edo can replicate a lot of [[Ed5/4]] temperaments - more exactly those which are divisors of 576, and that includes all from [[2ed5/4]] to [[9ed5/4]], skipping [[7ed5/4]]. One such scale which stands for [[4ed5/4]], is a tuning for the [[hemiluna]] temperament in the 1789bd val in the 13-limit. It is also worth noting that 1789bd val is better tuned than the patent val.
+Since the 5/4 of 1789edo is on the 576th step, a highly divisible number, 1789edo can replicate a lot of [[ed5/4]] temperaments—more exactly those which are divisors of 576, and that includes all from [[2ed5/4]] to [[9ed5/4]], skipping [[7ed5/4]]. One such scale which stands for [[4ed5/4]], is a tuning for the [[hemiluna]] temperament in the 1789bd val in the 13-limit. It is also worth noting that 1789bd val is better tuned than the patent val.
-edo has an essentially perfect [[9/8]], a very common interval. 1789edo supports the 2.9.5.11.13 subgroup temperament called ''commatose'' which uses the Pythagorean comma as a generator, which is excess of six 9/8s over the octave in this case. It is defined as a 460 & 1789 temperament.
+edo has an essentially perfect [[9/8]], a very common interval. 1789edo supports the 2.9.5.11.13 subgroup temperament called ''commatose'' which uses the Pythagorean comma as a generator, which is excess of six 9/8s over the octave in this case. It is defined as a {{nowrap|460 & 1789}} temperament.
-Since 1789edo has a very precise 31/29, it supports tricesimoprimal miracloid - a version of secor with 31/29 as the generator and a flat, meantone-esque fifth of about 692.23 cents. Using the maximal evenness method, we find a 52 & 1789 temperament. Best subgroup for it is 2.5.7.11.19.29.31, since both 52edo and 1789edo support it well, and the comma basis is 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688.
+Since 1789edo has a very precise 31/29, it supports tricesimoprimal miracloid—a version of secor with 31/29 as the generator and a flat, meantone-esque fifth of about 692.23 cents. Using the maximal evenness method, we find a {{nowrap|52 & 1789}} temperament. Best subgroup for it is 2.5.7.11.19.29.31, since both 52edo and 1789edo support it well, and the comma basis is 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688.
-On the patent val in the 7-limit, 1789edo supports 99 & 373 temperament called maviloid. In addition, it also tempers out [[2401/2400]].
+On the patent val in the 7-limit, 1789edo supports {{nowrap|99 & 373}} temperament called maviloid. In addition, it also tempers out [[2401/2400]].
+=== Subsets and supersets ===
+edo is the 278th [[prime edo]]. [[3578edo]], which doubles it, is consistent in the [[21-odd-limit]].
 == Table of selected intervals ==
 {| class="wikitable mw-collapsible mw-collapsed"
-|+ style=white-space:nowrap | Selected intervals in 1789edo
+|+ style="font-size: 105%; white-space: nowrap;" | Selected intervals in 1789edo
+|-
 ! Step
-! Eliora's Naming System
+! Eliora's naming system
-! JI Approximation or Other Interpretations*
+! JI approximation or other interpretations*
 |-
 | 0
@@ Line 64: / Line 67: @@
 | 65/62
 |-
-|125
+| 125
-|Sextilimeans generator
+| Sextilimeans generator
-|16807/16000
+| 16807/16000
 |-
 | 172
@@ Line 104: / Line 107: @@
 | [[13/10]]
 |-
-|750
+| 750
-|Sextilimeans fourth
+| Sextilimeans fourth
 |
 |-
 | 777
 | Maviloid generator
-|875/648
+| 875/648
 |-
 | 822
@@ Line 120: / Line 123: @@
 | (31/29)<sup>6</sup>
 |-
-|1039
+| 1039
-|Sextilimeans fifth
+| Sextilimeans fifth
 |
 |-
 | 1046
 | Minor fifth
-| [[3/2]]†
+| [[3/2]]**
 |-
 | 1047
 | Major fifth
-| [[3/2]]†
+| [[3/2]]**
 |-
 | 1213
@@ Line 156: / Line 159: @@
 | 2/1
 |}
-<nowiki>*</nowiki> based on the 2.5.11.13.29.31 subgroup where applicable
+<nowiki />* Based on the 2.5.11.13.29.31 subgroup where applicable
-† 1046\1789 as 3/2 is the patent val, 1047\1789 as 3/2 is the 1789b val
+<nowiki />** 1046\1789 as 3/2 is the patent val, 1047\1789 as 3/2 is the 1789b val
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br>8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 173: / Line 177: @@
 | 2.9
 | {{monzo| -5671 1789 }}
-| [{{val| 1789 5671 }}]
+| {{mapping| 1789 5671 }}
-| -0.00044
+| −0.00044
 | 0.00044
 | 0.06
@@ Line 180: / Line 184: @@
 | 2.9.5
 | {{monzo| -70 36 -19 }}, {{monzo| 129 -7 -46 }}
-| [{{val| 1789 5671 4154 }}]
+| {{mapping| 1789 5671 4154 }}
-| -0.00710
+| −0.00710
 | 0.00942
 | 1.40
@@ Line 187: / Line 191: @@
 | 2.9.5.7
 | 420175/419904, {{monzo| 34 2 -21 3 }}, {{monzo| -55 15 2 1 }}
-| [{{val| 1789 5671 4154 5022 }}]
+| {{mapping| 1789 5671 4154 5022 }}
 | +0.01606
 | 0.04093
 | 6.10
+|- style="border-top: double;"
+| 2.5.11.13
+| 6656/6655, {{monzo| 43 -18  5 -5 }},  {{monzo| -38 -32 10 21 }}
+| {{mapping| 1789 4154 6189 6620}}
+| −0.00490
+| 0.01405
+| 2.09
 |-
-|style="border-top: double;" |2.5.11.13
+| 2.5.11.13.29
-|style="border-top: double;" |6656/6655, {{monzo|43 -18  5 -5}},  {{monzo|-38 -32 10 21}}
+| 6656/6655, 371293/371200, {{monzo| -18 -6 -1 3 5 }}, {{monzo| 34 -20 5 0 -1 }}
-|style="border-top: double;" |[{{val| 1789 4154 6189 6620}}]
+| {{mapping| 1789 4154 6189 6620 8691 }}
-|style="border-top: double;" | -0.00490
+| −0.00591
-|style="border-top: double;" |0.01405
+| 0.01272
-|style="border-top: double;" |2.09
+| 1.90
-|-
-|2.5.11.13.29
-|6656/6655, 371293/371200, {{monzo|-18 -6 -1 3 5}}, {{monzo|34 -20 5 0 -1}}
-|[{{val| 1789 4154 6189 6620 8691}}]
-| -0.00591
-|0.01272
-|1.90
 |-
 | 2.5.11.13.29.31
 | 6656/6655, 387283/387200, 2640704/2640625, 3455881/3455756, 594880000/594823321
-| [{{val| 1789 4154 6189 6620 8691 8863 }}]
+| {{mapping| 1789 4154 6189 6620 8691 8863 }}
-| -0.00363
+| −0.00363
 | 0.01268
 | 1.89
@@ Line 215: / Line 219: @@
 === Rank-2 temperaments ===
-{| class="wikitable center-all left-4"
+{| class="wikitable center-all left-5"
-! Generator<br>(Reduced)
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Cents<br>(Reduced)
+|-
-! Associated<br>Ratio
+! Periods<br>per 8ve
+! Generator*
+! Cents*
+! Associated<br>ratio*
 ! Temperament
 |-
+| 1
 | 35\1789
 | 23.48
 | 531441/524288
-|[[Commatose]]
+| [[Commatose]]
 |-
-|125\1789
+| "
-|83.85
+| 125\1789
-|16807/16000
+| 83.85
-|[[Sextilimeans]]
+| 16807/16000
+| [[Sextilimeans]]
 |-
-|144\1789
+| "
-|96.59
+| 144\1789
-|200/189
+| 96.59
-|[[Hemiluna]] (1789bd)
+| 200/189
+| [[Hemiluna]] (1789bd)
 |-
+| "
 | 172\1789
 | 115.37
@@ Line 241: / Line 252: @@
 | [[Tricesimoprimal miracloid]]
 |-
-|377\1789
+| "
-|252.88
+| 377\1789
-|53094899/45875200
+| 252.88
-|[[Double Bastille]]
+| 53094899/45875200
+| [[Double bastille]]
 |-
+| "
 | 576\1789
 | 386.36
@@ Line 251: / Line 264: @@
 | [[French decimal]]
 |-
+| "
+| 754\1789
+| 505.76
+| {{monzo| 104 0 57 0 -14 5 }}
+| [[Pure bastille]]
+|-
+| "
 | 777\1789
 | 521.18
 | 875/648
-|[[Maviloid]]
+| [[Maviloid]]
 |-
+| "
 | 778\1789
 | 521.86
 | 80275/59392
-|[[Estates general]]
+| [[Estates general]]
 |-
-|822\1789
+| "
-|551.37
+| 822\1789
-|11/8
+| 551.37
-|[[Onzonic]]
+| 11/8
+| [[Onzonic]]
 |-
-|865\1789
+| "
-|580.21
+| 865\1789
-|{{Monzo|294 -46 7 -57}}
+| 580.21
-|Eternal Revolutionary
+| 6875/4914
+| [[Eternal revolutionary]] (1789bd)
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
-[[Category:Equal divisions of the octave|####]]
 == Music ==
+; [[Eliora]]
+* [https://www.youtube.com/watch?v=1zrnsGODQSg ''Etude la (R)evolution''] (2022)
-* [https://www.youtube.com/watch?v=1zrnsGODQSg Etude la (R)evolution, Op. 1, No. 2]by [[Eliora]]
-<!-- 4-digit number -->
-[[Category:Prime EDO]]
 [[Category:Jacobin]]
+[[Category:Listen]]
 {{Todo| review | clarify }}
-[[Category:Listen]]