1225/1224

 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 $\text{A1}^{5,5,7,7}_{17}$ 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, $\sqrt{n\cdot d}$) ~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.