The Jacobins: Difference between revisions

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=== Pure onzonic ===

Pure onzonic is the temperament that was initially ~~defined~~ as "jacobin" before ~~[[Flora Canou]]~~ pointed out that the name ~~"jacobin temperament"~~ would ~~refer to a~~ rank-5 temperamnet tempering out 6656/6655. Since ~~jacobin comma~~ is the difference between a stack of three 11/8s and 13/10, it ~~was~~ natural to choose 11/8 as the generator ~~for~~ the ~~rank 2 "jacobin temperament". Name "pure onzonic" is thus reserved for the pure 2.5.11.13 subgroup~~.

Pure onzonic is the temperament that was initially referred to as "jacobin" before it was pointed out that the same name would be reserved for the rank-5 temperamnet tempering out 6656/6655 alone. Since 6656/6655 is the difference between a stack of three 11/8's and 13/10, it is natural to choose a rank-2 temperament that uses 11/8 as the generator to exploit the comma.

Subgroup: 2.5.11.13

[[Subgroup]]: 2.5.11.13

Comma list: 6656/6655, {{monzo|-119 -46 15 47}}

[[Comma list]]: 6656/6655, {{monzo| -119 -46 15 47 }}

Mapping: [{{val|1 74 3 74}}, {{val|0 -156 1 -153}}]

[[Mapping]]: [{{val| 1 74 3 74 }}, {{val| 0 -156 1 -153 }}]

Optimal tuning (CTE): ~11/8 = 551.370

[[Optimal tuning]] ([[CTE]]): ~11/8 = 551.370

Vals: {{EDOs|37, 1789}}

Vals: {{EDOs| 37, 1789 }}

== Estates general ==

Named so because it is ~~defined~~ as the 1789 & 3125 temperament due to 3125 providing optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined starting with the 2.5.11.13.19 subgroup, upwards to the 2.5.11.13.19.23.29.31 subgroup.

Named so because it is described as the 1789 & 3125 temperament due to 3125 providing the optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined starting with the 2.5.11.13.19 subgroup, upwards to the 2.5.11.13.19.23.29.31 subgroup.

Subgroup: 2.5.11.13.19

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== Sextilimeans ==

~~It's~~ like sextilififths, but the fourth that is divided into 6 is tuned ~~meantone, corresponding~~ to a ~~fifth of 1039\1789~~, or about 1/4.26-commma meantone.

Sextilimeans is like sextilififths, but the fourth that is divided into 6 in sextilififths is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is mapped to -482 generator steps. It is described as the 229 & 1789 temperament.

~~Defined~~ as the 229 & 1789 temperament.

Subgroup: 2.5.7.11.13

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== Double Bastille ==

~~Defined~~ as the 1789 & 2814 temperament, and named because 2814 divided in two is 1407, and Bastille storming happened on 14 July 1789. Unfortunately 1407 & 1789 temperament does not temper out the jacobin comma ~~(at least in the patent val)~~, so it's not ~~possible to include it~~ here.

Described as the 1789 & 2814 temperament, and named because 2814 divided in two is 1407, and Bastille storming happened on 14 July 1789. Unfortunately the 1407 & 1789 temperament in the patent val does not temper out the jacobin comma, so it is not included here.

Subgroup: 2.5.7.11.13

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Vals: 1789, 2814, ...

[[Category:Commatic realms]]

[[Category:Jacobin]]

@@ Line 9: / Line 9: @@
 === Pure onzonic ===
-Pure onzonic is the temperament that was initially defined as "jacobin" before [[Flora Canou]] pointed out that the name "jacobin temperament" would refer to a rank-5 temperamnet tempering out 6656/6655. Since jacobin comma is the difference between a stack of three 11/8s and 13/10, it was natural to choose 11/8 as the generator for the rank 2 "jacobin temperament". Name "pure onzonic" is thus reserved for the pure 2.5.11.13 subgroup.
+Pure onzonic is the temperament that was initially referred to as "jacobin" before it was pointed out that the same name would be reserved for the rank-5 temperamnet tempering out 6656/6655 alone. Since 6656/6655 is the difference between a stack of three 11/8's and 13/10, it is natural to choose a rank-2 temperament that uses 11/8 as the generator to exploit the comma.
-Subgroup: 2.5.11.13
+[[Subgroup]]: 2.5.11.13
-Comma list: 6656/6655, {{monzo|-119 -46 15 47}}
+[[Comma list]]: 6656/6655, {{monzo| -119 -46 15 47 }}
-Mapping: [{{val|1 74 3 74}}, {{val|0 -156 1 -153}}]
+[[Mapping]]: [{{val| 1 74 3 74 }}, {{val| 0 -156 1 -153 }}]
-Optimal tuning (CTE): ~11/8 = 551.370
+[[Optimal tuning]] ([[CTE]]): ~11/8 = 551.370
-Vals: {{EDOs|37, 1789}}
+Vals: {{EDOs| 37, 1789 }}
 == Estates general ==
-Named so because it is defined as the 1789 & 3125 temperament due to 3125 providing optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined starting with the 2.5.11.13.19 subgroup, upwards to the 2.5.11.13.19.23.29.31 subgroup.
+Named so because it is described as the 1789 & 3125 temperament due to 3125 providing the optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined starting with the 2.5.11.13.19 subgroup, upwards to the 2.5.11.13.19.23.29.31 subgroup.
 Subgroup: 2.5.11.13.19
@@ Line 60: / Line 60: @@
 == Sextilimeans ==
-It's like sextilififths, but the fourth that is divided into 6 is tuned meantone, corresponding to a fifth of 1039\1789, or about 1/4.26-commma meantone.
+Sextilimeans is like sextilififths, but the fourth that is divided into 6 in sextilififths is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is mapped to -482 generator steps. It is described as the 229 & 1789 temperament.
-Defined as the 229 & 1789 temperament.
 Subgroup: 2.5.7.11.13
@@ Line 74: / Line 73: @@
 == Double Bastille ==
-Defined as the 1789 & 2814 temperament, and named because 2814 divided in two is 1407, and Bastille storming happened on 14 July 1789. Unfortunately 1407 & 1789 temperament does not temper out the jacobin comma (at least in the patent val), so it's not possible to include it here.
+Described as the 1789 & 2814 temperament, and named because 2814 divided in two is 1407, and Bastille storming happened on 14 July 1789. Unfortunately the 1407 & 1789 temperament in the patent val does not temper out the jacobin comma, so it is not included here.
 Subgroup: 2.5.7.11.13
@@ Line 85: / Line 84: @@
 Vals: 1789, 2814, ...
 [[Category:Commatic realms]]
 [[Category:Jacobin]]