6480/6479

6480/6479, the scarlattisma, is a 31-limit superparticular comma of about 0.27 cents.

Interval information

Ratio	6480/6479
Factorization	24 × 34 × 5 × 11-1 × 19-1 × 31-1
Monzo	[4 4 1 0 -1 0 0 -1 0 0 -1⟩
Size in cents	0.2671864¢
Name	scarlattisma
Color name	31u19u1uy1 thiwunuluyo unison
FJS name	[math]\displaystyle{ \text{A1}^{5}_{11,19,31} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	25.3233
Weil norm (log2 max(n, d))	25.3236
Wilson norm (sopfr(nd))	86
Comma size	unnoticeable
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Commatic relationships

This comma is the difference between the following superparticular pairs:

• 210/209 and 217/216
• 324/323 and 341/340
• 540/539 and 589/588
• 837/836 and 961/960
• 2025/2024 and 2945/2944
• 2300/2299 and 3565/3564
• 2376/2375 and 3751/3750
• 3060/3059 and 5797/5796
• 3136/3135 and 6076/6075

It can be factored into the following superparticular commas:

• 6656/6655 and 245025/245024
• 6670/6669 and 227448/227447
• 6728/6727 and 175770/175769
• 6860/6859 and 116964/116963
• 8526/8525 and 27000/26999
• 8960/8959 and 23409/23408
• 9425/9424 and 20736/20735
• 11781/11780 and 14400/14399
• 12636/12635 and 13300/13299

Temperaments

Tempering out this comma in the full 31-limit leads to the rank-10 temperament scarlattismic. Using the 2.3.5.11.19.31 subgroup leads to the rank-5 temperament scarlattic.

Scarlattismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

Comma list: 6480/6479

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.928, ~5/4 = 386.299, ~7/4 = 968.826, ~11/8 = 551.350, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.561, ~23/16 = 628.274, ~29/16 = 1029.577

Scarlattic

Subgroup: 2.3.5.11.19.31

Comma list: 6480/6479

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.928, ~5/4 = 386.299, ~11/8 = 551.350, ~19/16 = 297.561

Optimal ET sequence: 7k, 9k, 12, 14c, 15k, 22h, 24, 38, 41, 65, 152, 190, 217, 255, 270, 335, 407, 422, 487, 525, 612, 677, 988, 1243, 1395, 1665, 1730, 2407, 3395k, 3650, 4072k, 5315, 7045k, 7722hk, 9452hk

Etymology

The scarlattisma was named by Francium in 2024. It refers to 6480 Scarlatti, the asteroid. Which in turn was named after an Italian composer.

See also

• Unnoticeable comma
• List of superparticular intervals