2080/2079: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = ibnsinma, sinaisma

~~| Ratio = 2080/2079~~

| Color name = 3o1ury1, tholuruyo 1sn, <br>Tholuruyo comma

~~| Monzo = 5 -3 1 -1 -1 1~~

| Comma = yes

~~| Cents = 0.83252~~

| Name = ibnsinma

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

'''2080/2079''', the '''ibnsinma''', is a [[13-limit]] [[unnoticeable comma]] measuring about 0.8 [[cent]]s. It is ~~such~~ a ~~significant comma in the 13-limit being the difference between the following commas:~~

'''2080/2079''', the '''ibnsinma''', otherwise known as the '''sinaisma''', is a [[13-limit]] [[unnoticeable comma]] measuring about 0.83 [[cent]]s. It is the amount by which a stack consisting of [[11/10]] and [[14/13]] falls short of Pythagorean minor third, [[32/27]].

* [[65/63]] and [[33/32]]

== Commatic relations ==

This comma identifies itself as the difference between eight pairs of 13-limit superparticular ratios:

* [[64/63]] and [[66/65]]

* [[78/77]] and [[81/80]]

* [[100/99]] and [[105/104]]

* [[5120/5103]] and [[352/351]]

* [[352/351]] and [[847/845]]

* [[325/324]] and [[385/384]]

* [[364/363]] and [[441/440]]

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* [[676/675]] and [[1001/1000]]

* [[1716/1715]] and [[9801/9800]]

Not to mention some nonsuperparticular but useful ratios:

* [[896/891]] and [[196/195]]

* [[5120/5103]] and [[352/351]]

* [[352/351]] and [[847/845]]

Or as a relation in the four formal commas defined by [[Functional Just System]]:

* ((64/63)([[1053/1024]])) / ((81/80)([[33/32]])).

It factors into the following superparticular intervals:

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* [[3025/3024]] and [[6656/6655]]

By tempering it out is defined the '''ibnsinmic temperament''', which enables the ~~'''~~ibnsinmic chords~~'''~~, the essentially tempered ~~chords~~ in the 21-odd-limit.

In [[Sagittal notation]], it is the default comma represented by two [[mina]]s or six [[tina]]s.

== Temperaments ==

By tempering it out is defined the '''ibnsinmic''' or '''sinaismic temperament''', which enables the [[ibnsinmic chords|ibnsinmic a.k.a. sinaismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. Another consequence is that it makes [[fifth complement]]s of [[13/11]] and [[80/63]], and of [[40/33]] and [[26/21]]. You may find a list of good equal temperaments that support this temperament below.

[[Subgroup]]: 2.3.5.7.11.13

[[Mapping]]: <br>

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || -5 || ],

|-

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

|-

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

|-

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

|-

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

|}

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

{{Optimal ET sequence|legend=1| 12f, 14cf, 15, 17c, 19, 22f, 26, 29, 31f, 39df, 41, 46, 53, 58, 72, 87, 111, 130, 183, 198, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e, 3326de, 3596de, 3907bdee, 4401bdee, 4671bde }} *

<nowiki>*</nowiki> [[optimal patent val]]: [[3044edo|3044]]

In [[~~Sagittal notation~~]], it ~~is the default~~ comma ~~represented~~ by ~~two~~ [[~~mina~~]]s ~~or six~~ [[~~tina~~]]s.

== Etymology ==

This comma was named by [[Margo Schulter]] in 2012, when it went by ''ibn Sina's comma''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105620.html Yahoo! Tuning List | ''123201/123200 chalmersia, 194481/194480 scintillisma'']</ref>. It was contracted to ''avicennma'' and later changed to ''ibnsinma'' by [[Gene Ward Smith]], all essentially meaning the same. Note that ''avicennma'' refers to Avicenna's enharmonic diesis ([[525/512]]) today. In 2023, [[Flora Canou]] proposed ''sinaisma'' as another spelling, reflecting the fact that the [[interval region]] arising from the same source is called ''[[sinaic]]''.

== See also ==

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* [[List of superparticular intervals]]

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

== Notes ==

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

[[Category:Ibnsinmic]]

[[Category:~~Superparticular~~]]

[[Category:Commas named after polymaths]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = ibnsinma, sinaisma
-| Ratio = 2080/2079
+| Color name = 3o1ury1, tholuruyo 1sn, <br>Tholuruyo comma
-| Monzo = 5 -3 1 -1 -1 1
+| Comma = yes
-| Cents = 0.83252
-| Name = ibnsinma
-| Color name =
-| FJS name =
-| Sound =
 }}
-'''2080/2079''', the '''ibnsinma''', is a [[13-limit]] [[unnoticeable comma]] measuring about 0.8 [[cent]]s. It is such a significant comma in the 13-limit being the difference between the following commas:
+'''2080/2079''', the '''ibnsinma''', otherwise known as the '''sinaisma''', is a [[13-limit]] [[unnoticeable comma]] measuring about 0.83 [[cent]]s. It is the amount by which a stack consisting of [[11/10]] and [[14/13]] falls short of Pythagorean minor third, [[32/27]].
-* [[65/63]] and [[33/32]]
+== Commatic relations ==
+This comma identifies itself as the difference between eight pairs of 13-limit superparticular ratios:
 * [[64/63]] and [[66/65]]
 * [[78/77]] and [[81/80]]
 * [[100/99]] and [[105/104]]
-* [[5120/5103]] and [[352/351]]
-* [[352/351]] and [[847/845]]
 * [[325/324]] and [[385/384]]
 * [[364/363]] and [[441/440]]
@@ Line 21: / Line 16: @@
 * [[676/675]] and [[1001/1000]]
 * [[1716/1715]] and [[9801/9800]]
+Not to mention some nonsuperparticular but useful ratios:
+* [[896/891]] and [[196/195]]
+* [[5120/5103]] and [[352/351]]
+* [[352/351]] and [[847/845]]
+Or as a relation in the four formal commas defined by [[Functional Just System]]:
+* ((64/63)([[1053/1024]])) / ((81/80)([[33/32]])).
 It factors into the following superparticular intervals:
@@ Line 26: / Line 29: @@
 * [[3025/3024]] and [[6656/6655]]
-By tempering it out is defined the '''ibnsinmic temperament''', which enables the '''ibnsinmic chords''', the essentially tempered chords in the 21-odd-limit.
+In [[Sagittal notation]], it is the default comma represented by two [[mina]]s or six [[tina]]s.
+== Temperaments ==
+By tempering it out is defined the '''ibnsinmic''' or '''sinaismic temperament''', which enables the [[ibnsinmic chords|ibnsinmic a.k.a. sinaismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. Another consequence is that it makes [[fifth complement]]s of [[13/11]] and [[80/63]], and of [[40/33]] and [[26/21]]. You may find a list of good equal temperaments that support this temperament below.
+[[Subgroup]]: 2.3.5.7.11.13
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || -5 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 3 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~11
+{{Optimal ET sequence|legend=1| 12f, 14cf, 15, 17c, 19, 22f, 26, 29, 31f, 39df, 41, 46, 53, 58, 72, 87, 111, 130, 183, 198, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e, 3326de, 3596de, 3907bdee, 4401bdee, 4671bde }} *
+<nowiki>*</nowiki> [[optimal patent val]]: [[3044edo|3044]]
-In [[Sagittal notation]], it is the default comma represented by two [[mina]]s or six [[tina]]s.
+== Etymology ==
+This comma was named by [[Margo Schulter]] in 2012, when it went by ''ibn Sina's comma''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105620.html Yahoo! Tuning List | ''123201/123200 chalmersia, 194481/194480 scintillisma'']</ref>. It was contracted to ''avicennma'' and later changed to ''ibnsinma'' by [[Gene Ward Smith]], all essentially meaning the same. Note that ''avicennma'' refers to Avicenna's enharmonic diesis ([[525/512]]) today. In 2023, [[Flora Canou]] proposed ''sinaisma'' as another spelling, reflecting the fact that the [[interval region]] arising from the same source is called ''[[sinaic]]''.
 == See also ==
@@ Line 34: / Line 63: @@
 * [[List of superparticular intervals]]
-[[Category:13-limit]]
+== Notes ==
-[[Category:Unnoticeable comma]]
 [[Category:Ibnsinmic]]
-[[Category:Superparticular]]
+[[Category:Commas named after polymaths]]