6930/6929

Interval information

Ratio	6930/6929
Subgroup monzo	2.3.5.7.11.13.41 [1 2 1 1 1 -2 -1⟩
Size in cents	0.2498353 ¢
Name	bedanisma
Color name	41u3uu1ozy1 fowuthuthulozoyo unison
FJS name	[math]\displaystyle{ \text{A1}^{5,7,11}_{13,13,41} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	25.5171
Weil norm (log2 max(n, d))	25.5173
Wilson norm (sopfr(nd))	98
Comma size	unnoticeable
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6930/6929, the bedanisma, is a 41-limit superparticular comma of about 0.25 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 165/164 and 169/168
• 616/615 and 676/675
• 1353/1352 and 1681/1680
• 1600/1599 and 2080/2079
• 2625/2624 and 4225/4224

It can be factored into the following superparticular ratios:

• 7176/7175 and 202125/202124
• 7425/7424 and 103936/103935
• 10648/10647 and 19845/19844
• 11440/11439 and 17577/17576
• 11935/11934 and 16524/16523

Temperaments

Tempering out this comma in the full 41-limit leads to the rank-12 temperament bedanismic. Using the 2.3.5.7.11.13.41 subgroup leads to the rank-6 temperament bedanic.

Bedanic

Subgroup: 2.3.5.7.11.13.41

Comma list: 6930/6929

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.944, ~5/4 = 386.302, ~7/4 = 968.809, ~11/8 = 551.293, ~13/8 = 840.585

Optimal ET sequence: 5e, 7m, 8dmm, 9, 10, 12f, 14cf, 15, 16m, 17cm, 19em, 24m, 24d, 26, 29, 34dm, 38dfm, 41m, 45efmm, 46m, 49f, 53, 58, 72, 87, 111, 121m, 130m, 140, 183m, 190m, 198, 224, 270, 311, 373, 422, 441, 460, 494, 684m, 805, 814, 954, 1178, 1236, 1506m, 1730, 1817, 2190, 4007, 5185, 6110, 6197, 6691m, 8881m

Badness (Sintel): 0.191

Etymology

This comma was named by Francium in 2025. It refers to the postal code of Bedano, Switzerland.

See also

• Unnoticeable comma
• List of superparticular intervals