3220/3219
| Interval information |
thisutwenutwethozoyo unison
reduced
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
3220/3219, the murayamisma, is a 37-limit superparticular comma of about 0.54 cents.
Commatic relationships
This comma is the difference between the following superparticular pairs:
- 112/111 and 116/115
- 175/174 and 185/184
- 552/551 and 666/665
- 630/629 and 783/782
- 667/666 and 841/840
- 784/783 and 1036/1035
- 1000/999 and 1450/1449
- 1288/1287 and 2146/2145
- 1480/1479 and 2738/2737
It can be factored into the following superparticular ratios:
- 3249/3248 and 360640/360639
- 3250/3249 and 348726/348725
- 3381/3380 and 67600/67599
- 3510/3509 and 38962/38961
- 3565/3564 and 33264/33263
- 3626/3625 and 28750/28749
- 4186/4185 and 13950/13949
- 4256/4255 and 13225/13224
- 4960/4959 and 9177/9176
- 5440/5439 and 7889/7888
- 5888/5887 and 7105/7104
Temperaments
Tempering out this comma in the full 37-limit leads to the rank-11 temperament murayamismic. Using the 2.3.5.7.23.29.37 subgroup leads to the rank-6 temperament murayamic.
Murayamic
Subgroup: 2.3.5.7.23.29.37
Comma list: 3220/3219
| [⟨ | 1 | 1 | 2 | 2 | 4 | 4 | 5 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 0 | 1 | -1 | ]] |
Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.971, ~5/4 = 386.280, ~7/4 = 968.777, ~23/16 = 628.148, ~29/16 = 1029.723
Optimal ET sequence: 5j, 7dijj, 8dijj, 9ij, 9, 10j, 12, 12ij, 15, 19il, 19, 22, 31, 39dijl, 41l, 53j, 60l, 72, 77, 80, 84, 99, 224, 289l, 311, 373, 410, 472, 571, 612, 711, 783, 882, 1007, 1106, 1889, 1988l, 2501, 2600, 4489jl
Badness (Sintel): 0.108
Etymology
This comma was named by Francium in 2025. It refers to 3220 Murayama, the asteroid, which in turn was named after Sadao Murayama, a Japanese astronomer.