6656/6655: Difference between revisions

(2 intermediate revisions by 2 users not shown)

Line 7:

== Temperaments ==

By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament. You may find a list of good JI-approximating edos that support this temperament below. Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament.

By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament. You may find a list of good JI-approximating edos that support this temperament below. Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].

The 17-limit factorization shows us a natural path of extension, also given below.

Line 17:

[[Mapping]]:

[~~{{val~~| 1 0 0 0 0 -9 }}, ~~ ~~

{| class="right-all"

~~{{val~~| 0 1 0 0 0 0 }}, ~~ ~~

|-

~~{{val~~| 0 0 1 0 0 1 }}, ~~ ~~

| [⟨ || 1 || 0 || 0 || 0 || 0 || -9 || ],

~~{{val~~| 0 0 0 1 0 0 }}, ~~ ~~

|-

~~{{val~~| 0 0 0 0 1 3 }}]

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || ],

|-

| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || ],

|-

| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 1 || 3 || ]]

|}

: mapping generators: ~2, ~3, ~5, ~7, ~11

Line 33:

Line 40:

Mapping:

[~~{{val~~| 1 0 0 0 0 -9 6 }}, ~~ ~~

{| class="right-all"

~~{{val~~| 0 1 0 0 0 0 2 }}, ~~ ~~

|-

~~{{val~~| 0 0 1 0 0 1 2 }}, ~~ ~~

| [⟨ || 1 || 0 || 0 || 0 || 0 || -9 || 6 || ],

~~{{val~~| 0 0 0 1 0 0 -1 }}, ~~ ~~

|-

~~{{val~~| 0 0 0 0 1 3 -2 }}]

| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 2 || ],

|-

| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || 2 || ],

|-

| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -1 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 1 || 3 || -2 || ]]

|}

Optimal ET sequence: {{Optimal ET sequence| 15g, 22, 37g, 39dfg, 41g, 50, 63g, 72, 111, 152f, 159, 183, 239f, 248, 270, 311, 422, 494, 581, 742, 764, 814, 1075, 1236, 1395, 1506, 2000, 2581, 2814, 2901, 3323, 3395, 8296e, 11691e, 16322ee, 17086cdeeg, 21223cdeefg }}

Line 46:

Line 60:

[[Category:Jacobin]]

[[Category:Commas with unknown etymology]]

{{todo|add etymology|comment=I know it’s something to do with the French Revolution, but what, exactly? Spell it all out please, why exactly does the name “jacobin” uniquely fit this particular comma?}}

@@ Line 7: / Line 7: @@
 == Temperaments ==
-By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament. You may find a list of good JI-approximating edos that support this temperament below. Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament.
+By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament. You may find a list of good JI-approximating edos that support this temperament below. Although 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]].
 The 17-limit factorization shows us a natural path of extension, also given below.
@@ Line 17: / Line 17: @@
 [[Mapping]]: <br>
-[{{val| 1 0 0 0 0 -9 }}, <br>
+{| class="right-all"
-{{val| 0 1 0 0 0 0 }}, <br>
+|-
-{{val| 0 0 1 0 0 1 }}, <br>
+| [⟨ || 1 || 0 || 0 || 0 || 0 || -9 || ],
-{{val| 0 0 0 1 0 0 }}, <br>
+|-
-{{val| 0 0 0 0 1 3 }}]
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 3 || ]]
+|}
 : mapping generators: ~2, ~3, ~5, ~7, ~11
@@ Line 33: / Line 40: @@
 Mapping: <br>
-[{{val| 1 0 0 0 0 -9 6 }}, <br>
+{| class="right-all"
-{{val| 0 1 0 0 0 0 2 }}, <br>
+|-
-{{val| 0 0 1 0 0 1 2 }}, <br>
+| [⟨ || 1 || 0 || 0 || 0 || 0 || -9 || 6 || ],
-{{val| 0 0 0 1 0 0 -1 }}, <br>
+|-
-{{val| 0 0 0 0 1 3 -2 }}]
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 2 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || 2 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 3 || -2 || ]]
+|}
 Optimal ET sequence: {{Optimal ET sequence| 15g, 22, 37g, 39dfg, 41g, 50, 63g, 72, 111, 152f, 159, 183, 239f, 248, 270, 311, 422, 494, 581, 742, 764, 814, 1075, 1236, 1395, 1506, 2000, 2581, 2814, 2901, 3323, 3395, 8296e, 11691e, 16322ee, 17086cdeeg, 21223cdeefg }}
@@ Line 46: / Line 60: @@
 [[Category:Jacobin]]
+[[Category:Commas with unknown etymology]]
+{{todo|add etymology|comment=I know it’s something to do with the French Revolution, but what, exactly? Spell it all out please, why exactly does the name “jacobin” uniquely fit this particular comma?}}