Septischisma: Difference between revisions

(12 intermediate revisions by 4 users not shown)

Line 1:

{{Infobox Interval

| Ratio = 33554432/33480783

| Name = ~~garischisma~~, ~~septimal schisma~~

| Name = septischisma, gary comma

| Color name = ssr2, sasaru 2nd,<br>~~Sasaru comma~~

| Color name = ssr2, sasaru 2nd,<br>ssrM, sasaruma

| Comma = yes

}}

The '''septischisma''', a.k.a. '''gary comma''', is a very [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It can be considered the septimal counterpart of the [[schisma]]: whereas the schisma is the difference between the [[Pythagorean comma]] and the [[syntonic comma]], the septischisma is the difference between the [[septimal comma]] and the Pythagorean comma. Equivalently, it can be described as the amount by which a stack of two [[Pythagorean apotome]]s falls short of a [[8/7|septimal whole tone]]. It is also the difference between the [[aberschisma]] and the schisma in the full 7-limit.

~~The '''garischisma''' or '''septimal schisma''' is a~~ [[7-limit]] [[~~comma~~]] ~~measuring about 3.80 cents. While the [[schisma]] is the difference between the~~ [[~~Pythagorean comma]] and the [[81~~/80|~~syntonic~~ comma]]~~, the garischisma, in contrast, is the difference between the Pythagorean comma~~ and ~~the~~ [[64/63|~~septimal comma~~]]~~. It can also be described as the difference between the~~ [[~~8/7|septimal whole tone~~]] and ~~two~~ [[~~2187/2048|apotomes~~]].

It factors into the following [[11-limit|11-]] and [[13-limit]] commas:

* The [[19712/19683|symbiotic comma]] and [[131072/130977|olympia]];

* The [[wilschisma]] and the [[minisma]].

== Temperaments ==

Tempering it out in the full 7-limit leads to the rank-3 ~~'''garischismic~~ temperament~~'''~~.

[[Tempering out]] this comma in the full 7-limit leads to the rank-3 [[septischismic]] temperament, or in the [[2.3.7 subgroup]], the rank-2 [[gary]] temperament.

~~=== Garischismic (41 & 53 & 270) ===~~

See [[Septischismic family]] for the [[temperament families and clans|family]] of rank-3 temperaments where it is tempered out. See [[Septischismic clan]] for the [[temperament families and clans|clan]] of rank-2 temperaments where it is tempered out.

~~Subgroup: 2.~~3.5.7

[[~~Comma list~~]]~~: 33554432/33480783~~

== Etymology ==

The name of this comma used to be ''garischisma'', from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi. This name partly lingers in the subgroup temperament ''gary'' and a number of other rank-2 temperaments.

~~[[Mapping]]: [{{val| 1 0 0 25 }}, {{val| 0 1 0 -14 }}, {{val| 0 0 1 0 }}]~~

The current name is a trivial contraction of ''septimal schisma'' into one word.

[[~~POTE generator]]s~~: ~~~3/2 = 702.2079, ~5/4 = 386.5100~~

[[Category:Septischismic]]

[[Category:Commas named for their regular temperament properties]]

~~{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}~~

~~[[Badness~~]]~~: 1.313 × 10<sup>-3</sup>~~

~~== See also ==~~

* [[Garischismic clan]], the rank-2 clan where it is tempered out

* [[Small comma]]

[[Category:~~Garischismic~~]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Ratio = 33554432/33480783
-| Name = garischisma, septimal schisma
+| Name = septischisma, gary comma
-| Color name = ssr2, sasaru 2nd,<br>Sasaru comma
+| Color name = ssr2, sasaru 2nd,<br>ssrM, sasaruma
 | Comma = yes
 }}
+The '''septischisma''', a.k.a. '''gary comma''', is a very [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It can be considered the septimal counterpart of the [[schisma]]: whereas the schisma is the difference between the [[Pythagorean comma]] and the [[syntonic comma]], the septischisma is the difference between the [[septimal comma]] and the Pythagorean comma. Equivalently, it can be described as the amount by which a stack of two [[Pythagorean apotome]]s falls short of a [[8/7|septimal whole tone]]. It is also the difference between the [[aberschisma]] and the schisma in the full 7-limit.
-The '''garischisma''' or '''septimal schisma''' is a [[7-limit]] [[comma]] measuring about 3.80 cents. While the [[schisma]] is the difference between the [[Pythagorean comma]] and the [[81/80|syntonic comma]], the garischisma, in contrast, is the difference between the Pythagorean comma and the [[64/63|septimal comma]]. It can also be described as the difference between the [[8/7|septimal whole tone]] and two [[2187/2048|apotomes]].
+It factors into the following [[11-limit|11-]] and [[13-limit]] commas:
+* The [[19712/19683|symbiotic comma]] and [[131072/130977|olympia]];
+* The [[wilschisma]] and the [[minisma]].
 == Temperaments ==
-Tempering it out in the full 7-limit leads to the rank-3 '''garischismic temperament'''.
+[[Tempering out]] this comma in the full 7-limit leads to the rank-3 [[septischismic]] temperament, or in the [[2.3.7 subgroup]], the rank-2 [[gary]] temperament.
-=== Garischismic (41 & 53 & 270) ===
+See [[Septischismic family]] for the [[temperament families and clans|family]] of rank-3 temperaments where it is tempered out. See [[Septischismic clan]] for the [[temperament families and clans|clan]] of rank-2 temperaments where it is tempered out.
-Subgroup: 2.3.5.7
-[[Comma list]]: 33554432/33480783
+== Etymology ==
+The name of this comma used to be ''garischisma'', from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi. This name partly lingers in the subgroup temperament ''gary'' and a number of other rank-2 temperaments.
-[[Mapping]]: [{{val| 1 0 0 25 }}, {{val| 0 1 0 -14 }}, {{val| 0 0 1 0 }}]
+The current name is a trivial contraction of ''septimal schisma'' into one word.
-[[POTE generator]]s: ~3/2 = 702.2079, ~5/4 = 386.5100
+[[Category:Septischismic]]
+[[Category:Commas named for their regular temperament properties]]
-{{Optimal ET sequence|legend=1| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}
-[[Badness]]: 1.313 × 10<sup>-3</sup>
-== See also ==
-* [[Garischismic clan]], the rank-2 clan where it is tempered out
-* [[Small comma]]
-[[Category:Garischismic]]