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 amount by which a stack of three [[9/7]]'s exceeds [[17/8]], or the amount by which a stack of three [[7/6]]'s falls short of [[27/17]]. Equivalently, it is the difference between [[18/17]] and [[343/324]], or between [[24/17]] and [[343/243]].  
'''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]].  


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.
Line 11: Line 10:
== 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]]
Line 18: Line 16:
* [[4914/4913]] and [[31213/31212]]
* [[4914/4913]] and [[31213/31212]]


It factors into the following suparparticular pairs:  
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.  
[[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.
 
=== Chloric ===
[[Subgroup]]: 2.3.7.17
 
{{Mapping|legend=2| 1 0 0 3 | 0 1 0 6 | 0 0 1 -3 }}
: mapping generators: ~2, ~3, ~7
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9952{{c}}, ~3/2 = 701.9358{{c}}, ~7/4 = 968.8729{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9344{{c}}, ~7/4 = 968.8712{{c}}
 
{{Optimal ET sequence|legend=1| 14, 22, 36, 94, 99, 130, 135, 171, 364, 400, 571, 971, 2378, 2549, 2949, 3920 }}
 
[[Badness]] (Sintel): 0.0174
 
=== Chlorismic ===
[[Subgroup]]: 2.3.5.7.11.13.17
 
[[Mapping]]: <br>
{| class="right-all"
|-
| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 3 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 6 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || -3 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
|-
| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
|}
: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1199.9952{{c}}, ~3/2 = 701.9358{{c}}, ~5/4 = 386.3232{{c}}, ~7/4 = 968.8729{{c}}, ~11/8 = 551.3322{{c}}, ~13/8 = 840.5419{{c}}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9344{{c}}, ~5/4 = 386.3194{{c}}, ~7/4 = 968.8712{{c}}, ~11/8 = 551.3264{{c}}, ~13/8 = 840.5367{{c}}
 
{{Optimal ET sequence|legend=1| 19, 22, 27eg, 41, 49fg, 50, 58, 72, 121, 149, 166g, 171, 193, 198g, 224g, 243e, 270, 364, 373g, 400, 422, 494, 742, 764, 814, 935, 1084, 1106, 1178, 1236, 1506, 2000, 2414, 2684, 3178, 3920, 4684, 5498, 10182d, 14102dg, 14174d, 15680dg, 19600dg }} *
 
<nowiki/> * [[optimal patent val]]: [[14916edo|14916]]
 
[[Badness]] (Sintel): 1.13


== Etymology ==
== Etymology ==
The chlorisma was named by [[User:Jerdle|Jerdle]] in 2021. Despite the similar name, it has no relation to the later-named [[Chlorine]] temperament.  
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 ==
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]
* [[Unnoticeable comma]]


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

Latest revision as of 08:19, 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 amount by which a stack of three 9/7's exceeds 17/8, or the amount by which a stack of three 7/6's falls short of 27/17. Equivalently, it is the difference between 18/17 and 343/324, or between 24/17 and 343/243.

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.

Chloric

Subgroup: 2.3.7.17

Subgroup-val mapping: [⟨1 0 0 3], ⟨0 1 0 6], ⟨0 0 1 -3]]

mapping generators: ~2, ~3, ~7

Optimal tunings:

  • WE: ~2 = 1199.9952 ¢, ~3/2 = 701.9358 ¢, ~7/4 = 968.8729 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9344 ¢, ~7/4 = 968.8712 ¢

Optimal ET sequence: 14, 22, 36, 94, 99, 130, 135, 171, 364, 400, 571, 971, 2378, 2549, 2949, 3920

Badness (Sintel): 0.0174

Chlorismic

Subgroup: 2.3.5.7.11.13.17

Mapping:

[⟨ 1 0 0 0 0 0 3 ],
⟨ 0 1 0 0 0 0 6 ],
⟨ 0 0 1 0 0 0 0 ],
⟨ 0 0 0 1 0 0 -3 ],
⟨ 0 0 0 0 1 0 0 ],
⟨ 0 0 0 0 0 1 0 ]]
mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

Optimal tunings:

  • WE: ~2 = 1199.9952 ¢, ~3/2 = 701.9358 ¢, ~5/4 = 386.3232 ¢, ~7/4 = 968.8729 ¢, ~11/8 = 551.3322 ¢, ~13/8 = 840.5419 ¢
  • CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9344 ¢, ~5/4 = 386.3194 ¢, ~7/4 = 968.8712 ¢, ~11/8 = 551.3264 ¢, ~13/8 = 840.5367 ¢

Optimal ET sequence: 19, 22, 27eg, 41, 49fg, 50, 58, 72, 121, 149, 166g, 171, 193, 198g, 224g, 243e, 270, 364, 373g, 400, 422, 494, 742, 764, 814, 935, 1084, 1106, 1178, 1236, 1506, 2000, 2414, 2684, 3178, 3920, 4684, 5498, 10182d, 14102dg, 14174d, 15680dg, 19600dg *

* optimal patent val: 14916

Badness (Sintel): 1.13

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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