1332/1331

Interval information

Ratio	1332/1331
Subgroup monzo	2.3.11.37 [2 2 -3 1⟩
Size in cents	1.300213¢
Name	Marconisma
Color name	37o1u32 thisotrilu 2nd
FJS name	[math]\displaystyle{ \text{A1}^{37}_{11,11,11} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	20.7577
Weil height (log2 max(n, d))	20.7588
Wilson height (sopfr(nd))	80
Comma size	unnoticeable
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1332/1331, the marconisma, is a 37-limit superparticular comma of about 1.3 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 111/110 and 121/120
• 243/242 and 297/296

It can be factored into following superparticular commas:

• 1365/1364 and 55056/55055
• 1369/1368 and 49248/49247
• 1480/1479 and 13311/13310
• 1665/1664 and 6656/6655
• 2058/2057 and 3774/3773
• 2146/2145 and 3510/3509
• 2553/2552 and 2784/2783

Temperaments

Tempering out this comma in the full 37-limit leads to the rank-11 temperament marconismic. Using the 2.3.11.37 subgroup leads to the rank-3 temperament marconic.

Marconismic

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

Comma list: 1332/1331

Mapping:

[⟨	1	1	2	2	3	3	4	4	4	4	4	5	],
⟨	0	1	0	0	0	0	0	0	0	0	0	-2	],
⟨	0	0	1	0	0	0	0	0	0	0	0	0	],
⟨	0	0	0	1	0	0	0	0	0	0	0	0	],
⟨	0	0	0	0	1	0	0	0	0	0	0	3	],
⟨	0	0	0	0	0	1	0	0	0	0	0	0	],
⟨	0	0	0	0	0	0	1	0	0	0	0	0	],
⟨	0	0	0	0	0	0	0	1	0	0	0	0	],
⟨	0	0	0	0	0	0	0	0	1	0	0	0	],
⟨	0	0	0	0	0	0	0	0	0	1	0	0	],
⟨	0	0	0	0	0	0	0	0	0	0	1	0	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.910, ~5/4 = 386.314, ~7/4 = 968.826, ~11/8 = 551.640, ~13/8 = 840.528, ~17/16 = 104.955, ~19/16 = 297.513, ~23/16 = 628.274, ~29/16 = 1029.577, ~31/16 = 1145.036

Optimal ET sequence: 6h, 7dfghijjk, 8d, 8di, 9gijk, 9k, 9, 10hil, 12fghhijkll, 14cfgghhiijjkkl, 14cfggiijjkkl, 14cfggjjkkl, 14cfjjkkl, 14cfjjl, 15, 15gk, 16j, 17cgk, 17cghk, 22ijl, 22il, 24ij, 24i, 24, 29gjkll, 31fghjk, 34dhjkl, 38dfijkkl, 38dfijl, 41, 41i, 46l, 56, 58hikl, 65d, 72hijk, 72ijk, 72, 80, 80k, 103hil, 103hl, 121ikl, 145jkl, 152fj, 152fgj, 159k, 183k, 183, 190gl, 217l, 224, 239, 248h, 270l, 279, 296, 311k, 311, 472f, 472, 487, 535k, 552g, 566gjl, 624jk, 711, 718, 814k, 814, 863efgjk, 935, 1096j, 1125l, …

Marconic

Subgroup: 2.3.11.37

Comma list: 1332/1331

Mapping:

[⟨	1	1	3	5	],
⟨	0	1	0	-2	],
⟨	0	0	1	3	]]

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.910, ~11/8 = 551.640

Optimal ET sequence: 7, 15, 17, 24, 104, 111, 128, 135, 152, 176, 200, 359, 383, 535, 559, 1142, 1901e

Etymology

The marconisma was named by Francium in 2024. It refers to the asteroid 1332 Marconia. Which was in turn named after an Italian electrical engineer.

See also

• Unnoticeable comma
• List of superparticular intervals