2080/2079: Difference between revisions

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{{Infobox Interval
{{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 an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[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]]
* [[64/63]] and [[66/65]]
* [[78/77]] and [[81/80]]
* [[78/77]] and [[81/80]]
* [[100/99]] and [[105/104]]
* [[100/99]] and [[105/104]]
* [[896/891]] and [[196/195]]
* [[5120/5103]] and [[352/351]]
* [[352/351]] and [[847/845]]
* [[325/324]] and [[385/384]]
* [[325/324]] and [[385/384]]
* [[364/363]] and [[441/440]]
* [[364/363]] and [[441/440]]
Line 22: Line 16:
* [[676/675]] and [[1001/1000]]
* [[676/675]] and [[1001/1000]]
* [[1716/1715]] and [[9801/9800]]
* [[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:  
It factors into the following superparticular intervals:  
Line 30: Line 32:


== Temperaments ==
== Temperaments ==
By tempering it out is defined the '''ibnsinmic temperament''', which enables the '''ibnsinmic chords''', the essentially tempered chords 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.  
[[Tempering out]] this comma in the 13-limit defines the rank-5 '''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 [[13/11]] and [[80/63]] [[fifth complement]]s of each other, as well as [[40/33]] and [[26/21]]. You may find a list of good [[equal temperament]]s that [[support]] this temperament below.  


Subgroup: 2.3.5.7.11.13
[[Subgroup]]: 2.3.5.7.11.13


[[Mapping]]: <br>
[[Mapping]]: <br>
[{{val| 1 0 0 0 0 -5 }}, <br>
{| class="right-all"
{{val| 0 1 0 0 0 3 }}, <br>
|-
{{val| 0 0 1 0 0 -1 }}, <br>
| [⟨ || 1 || 0 || 0 || 0 || 0 || -5 || ],
{{val| 0 0 0 1 0 1 }}, <br>
|-
{{val| 0 0 0 0 1 1 }}]
| ⟨ || 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


Mapping generators: ~2, ~3, ~5, ~7, ~11
[[Optimal tuning]]s:
: [[WE]]: ~2 = 1199.9519{{c}}, ~3/2 = 702.0756{{c}}, ~5/4 = 386.3580{{c}}, ~7/4 = 968.9979{{c}}, ~11/8 = 551.5774{{c}}
: [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0843{{c}}, ~5/4 = 386.3184{{c}}, ~7/4 = 968.9934{{c}}, ~11/8 = 551.5497{{c}}


{{Val list|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 }} *
{{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]]
<nowiki>*</nowiki> [[optimal patent val]]: [[3044edo|3044]]
[[Badness]] (Sintel): 0.149
== 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 ==
== See also ==
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]


[[Category:13-limit]]
== References ==
[[Category:Unnoticeable comma]]
 
[[Category:Ibnsinmic]]
[[Category:Ibnsinmic]]
[[Category:Superparticular]]
[[Category:Commas named after polymaths]]

Latest revision as of 08:00, 4 March 2026

Interval information
Ratio 2080/2079
Factorization 25 × 3-3 × 5 × 7-1 × 11-1 × 13
Monzo [5 -3 1 -1 -1 1⟩
Size in cents 0.8325242¢
Names ibnsinma,
sinaisma
Color name 3o1ury1, tholuruyo 1sn,
Tholuruyo comma
FJS name [math]\displaystyle{ \text{P1}^{5,13}_{7,11} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 22.044
Weil norm (log2 max(n, d)) 22.0447
Wilson norm (sopfr(nd)) 55
Comma size unnoticeable
S-expressions S64⋅S65,
S78⋅S79⋅S80
Open this interval in xen-calc

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

Commatic relations

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

Not to mention some nonsuperparticular but useful ratios:

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

It factors into the following superparticular intervals:

In Sagittal notation, it is the default comma represented by two minas or six tinas.

Temperaments

Tempering out this comma in the 13-limit defines the rank-5 ibnsinmic or sinaismic temperament, which enables the ibnsinmic a.k.a. sinaismic chords, the essentially tempered chords in the 21-odd-limit. Another consequence is that it makes 13/11 and 80/63 fifth complements of each other, as well as 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:

[⟨ 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 tunings:

WE: ~2 = 1199.9519 ¢, ~3/2 = 702.0756 ¢, ~5/4 = 386.3580 ¢, ~7/4 = 968.9979 ¢, ~11/8 = 551.5774 ¢
CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.0843 ¢, ~5/4 = 386.3184 ¢, ~7/4 = 968.9934 ¢, ~11/8 = 551.5497 ¢

Optimal ET sequence: 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 *

* optimal patent val: 3044

Badness (Sintel): 0.149

Etymology

This comma was named by Margo Schulter in 2012, when it went by ibn Sina's comma[1]. 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

References

  1. ↑ Yahoo! Tuning List | 123201/123200 chalmersia, 194481/194480 scintillisma
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