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 n⋅d) 20.516
Weil height (max(n, d)) 1225
Benedetti height (n⋅d) 1499400
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.40662 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

In terms of commas, it 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 noellismic temperament, where 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 this temperament below.

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 GPV 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 name derives from Noel, for the numerator or the denominator, when written in decimal system, is reminiscent of the date of Christmas.

See also