6656/6655: Difference between revisions

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{{Infobox Interval

~~| Ratio = 6656/6655~~

~~| Monzo = 9 0 -1 0 -3 1~~

~~| Cents = 0.26012~~

| Name = jacobin comma

| Color name = ~~thotrilu~~-agu comma

| Color name = Thotrilu-agu comma

| Comma = yes

}}

'''6656/6655''', the '''jacobin comma''', is a [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] ~~interval~~ of about 0.~~26012 [[~~cent~~]]s~~. It is the difference between a stack of three [[11/8]] superfourths and one [[13/10]] [[naiadic]] plus an [[octave]].

'''6656/6655''', the '''jacobin comma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] [[comma]] of about 0.26{{cent}}. It is the difference between a stack of three [[11/8]] superfourths and one [[13/10]] [[naiadic]] plus an [[octave]] ([[13/5]]).

In terms of commas, it is the difference between [[364/363]] and [[385/384]], between [[2080/2079]] and [[3025/3024]] as well as between [[4096/4095]] and [[10648/10647]]. In the [[17-limit]], it factors neatly into ([[12376/12375]])⋅([[14400/14399]]).

== Temperaments ==

By tempering it out, the '''jacobin temperament''' is defined. ~~Perhaps most remarkably~~, ~~'''~~[[1789edo]]~~'''~~ is an edo that ~~supports~~ the jacobin temperament. ~~Simpler edos that support this temperament include {{EDOs| 37~~, ~~72, 135, 159, 183, 194, 320 }}~~. ~~On the larger end,~~ the ~~list includes edos like~~ {{~~EDOs~~| ~~3395 and 3125~~ }}~~. Although~~ it is more rational to use ~~JI-approximating~~ edos ~~like the above mentioned~~ for this temperament, ~~1789edo has~~ a ~~unique position due to its number of steps~~ being a ~~hallmark year~~ of the French Revolution.

By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistent to distance 2 on the subgroup 2.5.11.13, the subgroup of the comma. Although 1789edo has a unique position due to its number of steps being a hallmark year of the {{W|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 by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.

See [[The Jacobins#Jacobin]] for technical data.

== Etymology ==

This comma was apparently named by [[Gene Ward Smith]] in 2014 for reasons unknown<ref>[https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 Xenharmonic Wiki | ''List of superparticular intervals (Revision as of 23:46, 13 June 2014 by Wikispaces>genewardsmith)'']</ref>. An hypothesis is that "jacobin" refers to the {{w|Jacobins}}, a political group founded in 1789 during the French Revolution, since this comma is tempered out by [[1789edo]], a tuning which, furthermore, is [[consistent]] to distance 2 in the 2.5.11.13-subgroup-limited [[13-odd-limit]], reinforcing the importance of this comma in this tuning.

== See also ==

* [[13-limit]]

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

~~[[Category:13-limit]]~~

== References ==

~~[[Category:Ratio]]~~

[[Category:~~Unnoticeable comma~~]]

[[Category:Jacobin]]

[[Category:~~Superparticular~~]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 6656/6655
-| Monzo = 9 0 -1 0 -3 1
-| Cents = 0.26012
 | Name = jacobin comma
-| Color name = thotrilu-agu comma
+| Color name = Thotrilu-agu comma
+| Comma = yes
 }}
-'''6656/6655''', the '''jacobin comma''', is a [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] interval of about 0.26012 [[cent]]s. It is the difference between a stack of three [[11/8]] superfourths and one [[13/10]] [[naiadic]] plus an [[octave]].
+'''6656/6655''', the '''jacobin comma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] (also 2.5.11.13 [[subgroup]]) [[superparticular]] [[comma]] of about 0.26{{cent}}. It is the difference between a stack of three [[11/8]] superfourths and one [[13/10]] [[naiadic]] plus an [[octave]] ([[13/5]]).
+In terms of commas, it is the difference between [[364/363]] and [[385/384]], between [[2080/2079]] and [[3025/3024]] as well as between [[4096/4095]] and [[10648/10647]]. In the [[17-limit]], it factors neatly into ([[12376/12375]])⋅([[14400/14399]]).
 == Temperaments ==
-By tempering it out, the '''jacobin temperament''' is defined. Perhaps most remarkably, '''[[1789edo]]''' is an edo that supports the jacobin temperament. Simpler edos that support this temperament include {{EDOs| 37, 72, 135, 159, 183, 194, 320 }}. On the larger end, the list includes edos like {{EDOs| 3395 and 3125 }}. Although it is more rational to use JI-approximating edos like the above mentioned for this temperament, 1789edo has a unique position due to its number of steps being a hallmark year of the French Revolution.
+By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistent to distance 2 on the subgroup 2.5.11.13, the subgroup of the comma. Although 1789edo has a unique position due to its number of steps being a hallmark year of the {{W|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 by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class.
+See [[The Jacobins#Jacobin]] for technical data.
+== Etymology ==
+This comma was apparently named by [[Gene Ward Smith]] in 2014 for reasons unknown<ref>[https://en.xen.wiki/index.php?title=List_of_superparticular_intervals&diff=next&oldid=18864 Xenharmonic Wiki | ''List of superparticular intervals (Revision as of 23:46, 13 June 2014 by Wikispaces>genewardsmith)'']</ref>. An hypothesis is that "jacobin" refers to the {{w|Jacobins}}, a political group founded in 1789 during the French Revolution, since this comma is tempered out by [[1789edo]], a tuning which, furthermore, is [[consistent]] to distance 2 in the 2.5.11.13-subgroup-limited [[13-odd-limit]], reinforcing the importance of this comma in this tuning.
 == See also ==
-* [[13-limit]]
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
-[[Category:13-limit]]
+== References ==
-[[Category:Ratio]]
-[[Category:Unnoticeable comma]]
+[[Category:Jacobin]]
-[[Category:Superparticular]]
+[[Category:Commas with unknown etymology]]