Veederisma
| Ratio | 3510/3509 |
| Factorization | 2 × 33 × 5 × 11-2 × 13 × 29-1 |
| Monzo | [1 3 1 0 -2 1 0 0 0 -1⟩ |
| Size in cents | 0.49329935¢ |
| Name | veederisma |
| Color name | 29u3o1uuy1 twenutholuluyo unison |
| FJS name | [math]\text{A1}^{5,13}_{11,11,29}[/math] |
| Special properties | superparticular, reduced |
| Tenney height (log2 nd) | 23.5541 |
| Weil height (log2 max(n, d)) | 23.5545 |
| Wilson height (sopfr(nd)) | 80 |
| Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20049 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
3510/3509, the veederisma, is a 29-limit superparticular comma of about 0.49 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
It can be factored into the following superparticular commas:
- 4641/4640 and 14400/14399
- 5083/5082 and 11340/11339
- 6656/6655 and 7425/7424
Temperaments
Tempering out this comma in the full 29-limit leads to the rank-9 temperament veederismic. Using the 2.3.5.11.13.29 subgroup leads to the rank-5 temperament veederic.
Veederismic
Subgroup: 2.3.5.7.11.13.17.19.23.29
Comma list: 3510/3509
| [⟨ | 1 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | 4 | 3 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.922, ~5/4 = 386.290, ~7/4 = 968.826, ~11/8 = 551.422, ~13/8 = 840.468, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274
Veederic
Subgroup: 2.3.5.11.13.29
Comma list: 3510/3509
| [⟨ | 1 | 1 | 2 | 3 | 3 | 3 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.922, ~5/4 = 386.290, ~11/8 = 551.422, ~13/8 = 840.468
Optimal ET sequence: 7fjj, 7, 14cfjj, 15f, 15jj, 16j, 17c, 22, 24, 31, 34, 41, 53j, 58, 65, 80, 87, 145j, 159, 183, 224, 270, 311, 407, 494, 901, 1395, 2296, 3749e, 4243ej, 5144ej, 6045ej, 6539ej
Etymology
The veederisma was named by Francium in 2024. It refers to 3510 Veeder, the asteroid. Which was in turn named after an American astronomer.