5832/5831: Difference between revisions

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'''5832/5831''', the '''chlorisma''', is an exceptionally small [[17-limit]] [[unnoticeable comma]] of less than 0.3 cents. It is the difference between [[18/17]] and [[343/324]]. Tempering it out equates a stack of three [[7/6]] subminor thirds with a stack consisting of an [[18/17]] lesser septendecimal semitone and a [[3/2]] perfect fifth, that is, a [[27/17]] quasi-tempered minor sixth.
'''5832/5831''', the '''chlorisma''', is an exceptionally small [[17-limit]] (also 2.3.7.17 [[subgroup]]) [[unnoticeable comma]] of less than 0.3 cents. It is the difference between [[18/17]] and [[343/324]], and the difference between a stack of three [[9/7]]s and [[17/8]].


In terms of commas, it is the difference between the palingenetic comma ([[1701/1700]]) and the breedsma ([[2401/2400]]), as well as the difference between the squbema ([[729/728]]) and the horizon comma ([[833/832]]).
In [[Sagittal notation]], this is the default comma represented by two [[tina]]s.


In [[Sagittal notation]], this is the default comma represented by two [[Tina|tinas]].
== Commatic relations ==
In terms of commas, it is the difference between the following superparticular pairs:
 
* [[540/539]] and [[595/594]]
* [[729/728]] and [[833/832]]
* [[1701/1700]] and [[2401/2400]]
* [[1716/1715]] and [[2431/2430]]
* [[4914/4913]] and [[31213/31212]]
 
It factors into the following superparticular pair:
 
* [[9801/9800]] and [[14400/14399]]
 
== Temperaments ==
Tempering out this comma in the 17-limit results in the rank-6 '''chlorismic temperament''', or in the 2.3.7.17 subgroup, the rank-3 '''chloric temperament'''. In either case it equates a stack of three [[9/7]] supermajor thirds with [[17/8]], the 17th harmonic minus three octaves.
 
== Etymology ==
The chlorisma was named by [[User:Jerdle|Jerdle]] in 2021. Despite the similar name, it has no relation to the previously-named [[chlorine]] temperament.  


== See also ==
== See also ==
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[[Category:Chlorismic]]
[[Category:Chlorismic]]
[[Category:Commas with unknown etymology]]

Latest revision as of 18:32, 17 January 2025

Interval information
Ratio 5832/5831
Factorization 23 × 36 × 7-3 × 17-1
Monzo [3 6 0 -3 0 0 -1⟩
Size in cents 0.2968763¢
Name chlorisma
Color name 17r3-3, sutriru negative
3rd, Sutriru comma
FJS name [math]\displaystyle{ \text{dd}{-3}_{7,7,7,17} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 25.0193
Weil height (log2 max(n, d)) 25.0196
Wilson height (sopfr(nd)) 62
Comma size unnoticeable
Open this interval in xen-calc

5832/5831, the chlorisma, is an exceptionally small 17-limit (also 2.3.7.17 subgroup) unnoticeable comma of less than 0.3 cents. It is the difference between 18/17 and 343/324, and the difference between a stack of three 9/7s and 17/8.

In Sagittal notation, this is the default comma represented by two tinas.

Commatic relations

In terms of commas, it is the difference between the following superparticular pairs:

It factors into the following superparticular pair:

Temperaments

Tempering out this comma in the 17-limit results in the rank-6 chlorismic temperament, or in the 2.3.7.17 subgroup, the rank-3 chloric temperament. In either case it equates a stack of three 9/7 supermajor thirds with 17/8, the 17th harmonic minus three octaves.

Etymology

The chlorisma was named by Jerdle in 2021. Despite the similar name, it has no relation to the previously-named chlorine temperament.

See also

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