925/924: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
VisualWikitext
Francium (talk | contribs)
4,862 edits
Created page with "{{Infobox Interval | Ratio = 925/924 | Name = alphonsinisma | Color name = 37o1uryy1 <br> thisoluruyoyo unison | Comma = yes }} '''925/924''', the '''alphonsinisma''', is a [..."
 
m FloraC moved page Alphonsinisma to 925/924 over redirect: 6-digit ratios are okay as page titles
 
(One intermediate revision by one other user not shown)
Line 35: Line 35:


== Temperaments ==
== Temperaments ==
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''alphonsinismic'''. Using the 2.3.5.7.11.37 subgroup leads to the rank-5 temperament '''alphonsic'''.
Tempering out this comma in the full 37-limit leads to the rank-11 temperament '''alphonsinismic'''. Using the 2.3.5.7.11.37 subgroup leads to the rank-5 temperament '''alphonsinic'''.


=== Alphonsismic ===
=== Alphonsinismic ===


[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37
[[Subgroup]]: 2.3.5.7.11.13.17.19.23.29.31.37
Line 71: Line 71:
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036
[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036


=== Alphonsic ===
=== Alphonsinic ===


[[Subgroup]]: 2.3.5.7.11.37
[[Subgroup]]: 2.3.5.7.11.37

Latest revision as of 14:18, 7 January 2025

Interval information
Ratio 925/924
Subgroup monzo 2.3.5.7.11.37 [-2 -1 2 -1 -1 1⟩
Size in cents 1.872617 ¢
Name alphonsinisma
Color name 37o1uryy1
thisoluruyoyo unison
FJS name [math]\displaystyle{ \text{d}{-2}^{5,5,37}_{7,11} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 19.7051
Weil norm (log2 max(n, d)) 19.7066
Wilson norm (sopfr(nd)) 72
Comma size unnoticeable
Open this interval in xen-calc

925/924, the alphonsinisma, is a 37-limit superparticular comma of about 1.9 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

It can be factored into the following superparticular intervals:

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament alphonsinismic. Using the 2.3.5.7.11.37 subgroup leads to the rank-5 temperament alphonsinic.

Alphonsinismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 925/924

Mapping:

[⟨ 1 1 2 2 3 3 4 4 4 4 4 4 ],
⟨ 0 1 0 0 0 0 0 0 0 0 0 1 ],
⟨ 0 0 1 0 0 0 0 0 0 0 0 -2 ],
⟨ 0 0 0 1 0 0 0 0 0 0 0 1 ],
⟨ 0 0 0 0 1 0 0 0 0 0 0 1 ],
⟨ 0 0 0 0 0 1 0 0 0 0 0 0 ],
⟨ 0 0 0 0 0 0 1 0 0 0 0 0 ],
⟨ 0 0 0 0 0 0 0 1 0 0 0 0 ],
⟨ 0 0 0 0 0 0 0 0 1 0 0 0 ],
⟨ 0 0 0 0 0 0 0 0 0 1 0 0 ],
⟨ 0 0 0 0 0 0 0 0 0 0 1 0 ]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

Alphonsinic

Subgroup: 2.3.5.7.11.37

Comma list: 925/924

Mapping:

[⟨ 1 1 2 2 3 4 ],
⟨ 0 1 0 0 0 1 ],
⟨ 0 0 1 0 0 -2 ],
⟨ 0 0 0 1 0 1 ],
⟨ 0 0 0 0 1 1 ]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.021, ~5/4 = 386.030, ~7/4 = 969.034, ~11/8 = 551.633

Optimal ET sequence: 7d, 8d, 9l, 10e, 12el, 12, 15, 19el, 19, 22, 27e, 31, 41, 50, 53, 60el, 72, 130, 152, 224, 311, 342l, 463, 494, 566l, 805l, 877l

Etymology

This comma was named by Francium in 2025. It refers to 925 Alphonsina, the asteroid, which in turn was named after two Spanish kings.

See also

Retrieved from "https://en.xen.wiki/index.php?title=925/924&oldid=175044"