5832/5831: Difference between revisions

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'''5832/5831''', the '''chlorisma''', is an [[unnoticeable comma|exceptionally small]] [[17-limit]] (also 2.3.7.17-[[subgroup]]) [[unnoticeable comma]] of about 0.297 [[cent]]s. It is the difference between [[18/17]] and [[343/324]], and the difference between a stack of three [[9/7]]'s and [[17/8]].
'''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 [[Sagittal notation]], this is the default comma represented by two [[tina]]s.
In [[Sagittal notation]], this is the default comma represented by two [[tina]]s.
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== Commatic relations ==
== Commatic relations ==
In terms of commas, it is the difference between the following superparticular pairs:
In terms of commas, it is the difference between the following superparticular pairs:
* [[540/539]] and [[595/594]]
* [[540/539]] and [[595/594]]
* [[729/728]] and [[833/832]]
* [[729/728]] and [[833/832]]
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It factors into the following superparticular pair:  
It factors into the following superparticular pair:  
* [[9801/9800]] and [[14400/14399]]
* [[9801/9800]] and [[14400/14399]]


== Temperaments ==
== 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. [[80edo]] represents both 9/7 and 17/8 within 0.1 cents, so it and many [[80th-octave temperaments]] temper out the chlorisma.
[[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. [[80edo]] represents both 9/7 and 17/8 within 0.1 cents, so it and many [[80th-octave temperaments]] temper out the chlorisma.


== Etymology ==
== Etymology ==
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== See also ==
== See also ==
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]
* [[Unnoticeable comma]]


[[Category:Chlorismic]]
[[Category:Chlorismic]]
[[Category:Commas with unknown etymology]]
[[Category:Commas with unknown etymology]]

Revision as of 07:54, 29 March 2026

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 norm (log2 nd) 25.0193
Weil norm (log2 max(n, d)) 25.0196
Wilson norm (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 about 0.297 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 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. 80edo represents both 9/7 and 17/8 within 0.1 cents, so it and many 80th-octave temperaments temper out the chlorisma.

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