1225/1224

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	1.413829¢
Name	noellisma
Color name	17uzzyy1, subizoyo 1sn, Subizoyo comma
FJS name	[math]\displaystyle{ \text{A1}^{5,5,7,7}_{17} }[/math]
Special properties	square superparticular, reduced
Tenney norm (log2 nd)	20.516
Weil norm (log2 max(n, d))	20.5171
Wilson norm (sopfr(nd))	53
Comma size	unnoticeable
S-expressions	S35, S49⋅S50
Open this interval in xen-calc

1225/1224, the noellisma, is an unnoticeable 17-limit (also 2.3.5.7.17-subgroup) comma measuring about 1.41 cents. It is the amount by which a stack of two 7/6 subminor thirds exceeds 34/25, and the amount by which a stack of two 35/24 subfifths exceeds 17/8, one octave above 17/16. It is also 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:

• 273/272 and 351/350
• 325/324 and 442/441
• 375/374 and 540/539
• 385/384 and 561/560
• 595/594 and 1156/1155
• 625/624 and 1275/1274
• 715/714 and 1716/1715
• 833/832 and 2601/2600
• 1089/1088 and 9801/9800

It factors into the following superparticular pairs:

• 2401/2400 and 2500/2499
• 2058/2057 and 3025/3024
• 1701/1700 and 4375/4374
• 1275/1274 and 31213/31212

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.

Since 1225/1224 factors as (2401/2400)⋅(2500/2499), it would make sense to temper them both out, so noellic can be further tempered to a simple extension of breed that adds prime 17, though it loses accuracy when compared to breed.

Noellic

Subgroup: 2.3.5.7.17

Subgroup-val mapping: [⟨1 0 0 0 -3], ⟨0 1 0 0 -2], ⟨0 0 1 0 2], ⟨0 0 0 1 2]]

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

Optimal tunings:

• WE: ~2 = 1200.0477 ¢, ~3/2 = 701.9872 ¢, ~5/4 = 386.0466 ¢, ~7/4 = 968.4796 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9993 ¢, ~5/4 = 386.0746 ¢, ~7/4 = 968.4911 ¢

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

Badness (Sintel): 0.0985

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 tunings:

• WE: ~2 = 1200.0477 ¢, ~3/2 = 701.9872 ¢, ~5/4 = 386.0466 ¢, ~7/4 = 968.4796 ¢, ~11/8 = 551.1747 ¢, ~13/8 = 840.3844 ¢
• CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9993 ¢, ~5/4 = 386.0746 ¢, ~7/4 = 968.4911 ¢, ~11/8 = 551.2309 ¢, ~13/8 = 840.4346 ¢

Optimal ET sequence: 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

Badness (Sintel): 0.578

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

• List of superparticular intervals