1666/1665
| Interval information |
thisusozozogu 2nd
reduced
(Shannon, [math]\sqrt{nd}[/math])
1666/1665, the gentisma, is a 37-limit superparticular comma of about 1.04 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 112/111 and 120/119
- 136/135 and 148/147
- 196/195 and 222/221
- 408/407 and 540/539
- 595/594 and 925/924
- 784/783 and 1480/1479
- 833/832 and 1665/1664
It can be factored into the following superparticular intervals:
- 1683/1682 and 164836/164835
- 1701/1700 and 80920/80919
- 1729/1728 and 45696/45695
- 1768/1767 and 28861/28860
- 1925/1924 and 12376/12375
- 2176/2175 and 7105/7104
- 2295/2294 and 6076/6075
- 2401/2400 and 5440/5439
- 2431/2430 and 5292/5291
- 2737/2736 and 4256/4255
- 3136/3135 and 3553/3552
- 3220/3219 and 3451/3450
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament gentismic. Using the 2.3.5.7.17.37 subgroup leads to the rank-5 temperament gentic.
Gentic
Subgroup: 2.3.5.7.17.37
Comma list: 1666/1665
| [⟨ | 1 | 1 | 2 | 2 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -2 | ], |
| ⟨ | 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 = 702.013, ~5/4 = 386.375, ~7/4 = 968.645, ~17/16 = 104.764
Optimal ET sequence: 5g, 7dgll, 8d, 9, 10, 12, 19gl, 19, 22, 27g, 31l, 39dgl, 41gl, 49gl, 50, 58, 60l, 68, 72, 99, 171, 311, 400, 472, 482, 571, 711, 882
Etymology
This comma was named by Francium in 2025. It refers to 1666 van Gent, the asteroid, which in turn was named after Hendrik van Gent, a Dutch astronomer.