Scarlattisma
| 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 | 0.26718637¢ |
| Name | scarlattisma |
| Color name | 31u19u1uy1 thiwunuluyo unison |
| FJS name | [math]\text{A1}^{5}_{11,19,31}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 25.3233 |
| Weil height (log2 max(n, d)) | 25.3236 |
| Wilson height (sopfr(nd)) | 86 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.19976 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
6480/6479, the scarlattisma, is a 31-limit superparticular comma of about 0.27 cents.
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
| [⟨ | 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
| [⟨ | 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.