Francium: Created page with "{{Infobox Interval | Ratio = 9251/9250 | Name = harchisma | Color name = 37u29oo1og³1
thisubitweno-alotrigu unison | Comma = yes }} '''9251/9250''', the '''harchisma''', is a 37-limit superparticular comma of about 0.19 cents. == Commatic relationships == This comma is the difference between the following superparticular pairs: * 841/840 and 925/924 * 1276/1275 and 1480/1479 * 2001/2000 and 2553..."

2025-04-10T18:50:01Z

Created page with "{{Infobox Interval | Ratio = 9251/9250 | Name = harchisma | Color name = 37u29oo1og31 thisubitweno-alotrigu unison | Comma = yes }} '''9251/9250''', the '''harchisma''', is a 37-limit superparticular comma of about 0.19 cents. == Commatic relationships == This comma is the difference between the following superparticular pairs: * 841/840 and 925/924 * 1276/1275 and 1480/1479 * 2001/2000 and 2553..."

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{{Infobox Interval
| Ratio = 9251/9250
| Name = harchisma
| Color name = 37u29oo1og31 thisubitweno-alotrigu unison
| Comma = yes
}}

'''9251/9250''', the '''harchisma''', is a [[37-limit]] [[superparticular interval|superparticular comma]] of about 0.19 [[cent]]s.

== Commatic relationships ==
This comma is the difference between the following superparticular pairs:
* [[841/840]] and [[925/924]]
* [[1276/1275]] and [[1480/1479]]
* [[2001/2000]] and [[2553/2552]]

It can be factored into the following superparticular ratios:
* [[9361/9360]] and [[787176/787175]]
* [[9801/9800]] and [[164836/164835]]
* [[10626/10625]] and [[71485/71484]]
* [[13456/13455]] and [[29601/29600]]

== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''harchismic'''. Using the 2.5.11.29.37 subgroup leads to the rank-4 temperament '''harchic'''.

=== Harchic ===

[[Subgroup]]: 2.5.11.29.37

[[Comma list]]: 9251/9250

[[Mapping]]: 
{| class="right-all"
|-
| [⟨ || 1 || 2 || 3 || 4 || 4 || ],
|-
| ⟨ || 0 || 1 || 0 || 0 || -3 || ],
|-
| ⟨ || 0 || 0 || 1 || 0 || 1 || ],
|-
| ⟨ || 0 || 0 || 0 || 1 || 2 || ]]
|}

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~5/4 = 386.330, ~11/8 = 551.306, 29/16 = 1029.529

{{Optimal ET sequence|legend=1| 5ejl, 6, 9, 13, 15, 22, 28, 37, 65, 103l, 108, 131, 140, 159, 168, 196, 233, 364, 379, 401, 407, 444, 640, 1084, 1724, 2873, 3041, 3513, 4153, 4597, 5237 }}

[[Badness]] (Sintel): 0.011

== Etymology ==
This comma was named by [[Francium]] in 2025. It refers to {{W|9251 Harch}}, the asteroid, which in turn was named after Ann P. Harch, an scientist at the Cornell University.

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

9251/9250 - Revision history