1225/1224

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Interval information
Ratio 1225/1224
Factorization 2-3 × 3-2 × 52 × 72 × 17-1
Monzo [-3 -2 2 2 0 0 -1
Size in cents 1.4138294¢
Name noellisma
Color name 17uzzyy1, subizoyo 1sn,
Subizoyo comma
FJS name [math]\text{A1}^{5,5,7,7}_{17}[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 20.516
Weil height (log2 max(n, d)) 20.5171
Wilson height (sopfr (nd)) 53
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.45078 bits
Comma size unnoticeable
S-expressions S35,
S49 × S50
open this interval in xen-calc

1225/1224, the noellisma, is a 17-limit (also 2.3.5.7.17 subgroup) comma measuring about 1.41 cents. It is the difference between 35/34 and 36/35, and between 49/48 and 51/50.

Commatic relations

This comma is the difference between the following superparticular pairs:

It factors into the following superparticular pairs:

Temperaments

Tempering out this comma in the 17-limit results in the rank-6 noellismic temperament, or in the 2.3.5.7.17 subgroup, the rank-4 noellic temperament. In either case 18/17 is split into two equal parts, each representing 35/34~36/35. You may find a list of good equal temperaments that support these temperaments below.

Noellic

Subgroup: 2.3.5.7.17

Sval mapping[1 0 0 0 -3], 0 1 0 0 -2], 0 0 1 0 2], 0 0 0 1 2]]

sval mapping generators: ~2, ~3, ~5, ~7

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468

Optimal ET sequence19g, 22, 27g, 31, 41g, 46, 53, 68, 72, 99, 171, 581, 653, 752, 824, 995, 1576, 1747, 1918d

Noellismic

Subgroup: 2.3.5.7.11.13.17

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 702.0440, ~5/4 = 386.1228, ~7/4 = 968.5468, ~11/8 = 551.3179, ~13/8 = 840.5277

Optimal ET sequence19eg, 22, 26, 27eg, 31, 41g, 45efg, 46, 68, 72, 103, 121, 140, 171, 190g, 212g, 217, 224, 270, 311, 414, 441, 460, 581, 995, 1265, 1648cd, 1846g, 1918d

Etymology

The noellisma was named by Flora Canou in 2022. The name derives from Noel, for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.

See also