1026/1025

Interval information

Ratio	1026/1025
Subgroup monzo	2.3.5.19.41 [1 3 -2 1 -1⟩
Size in cents	1.688185¢
Name	ingridisma
Color name	41u19ogg2 fowunogugu 2nd
FJS name	[math]\text{d2}^{19}_{5,5,41}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	20.0042
Weil height (log2 max(n, d))	20.0056
Wilson height (sopfr(nd))	81
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.22484 bits
Comma size	unnoticeable
Open this interval in xen-calc

1026/1025, the ingridisma, is a 41-limit superparticular comma of about 1.7 cents.

Commatic relationships

This comma is the difference between the following superparticular pairs:

• 76/75 and 82/81
• 171/170 and 205/204
• 288/287 and 400/399
• 513/512 and 1025/1024

It can be factored into the following superparticular ratios:

• 1036/1035 and 106191/106190
• 1045/1044 and 56376/56375
• 1197/1196 and 7176/7175
• 1216/1215 and 6561/6560
• 1296/1295 and 4921/4920
• 1395/1394 and 3876/3875
• 1596/1595 and 2871/2870
• 1701/1700 and 2584/2583
• 1805/1804 and 2376/2375

Temperaments

Tempering out this comma in the full 41-limit leads to the rank-12 temperament ingridismic. Using the 2.3.5.19.41 subgroup leads to the rank-4 temperament ingridic.

Ingridic

Subgroup: 2.3.5.19.41

Comma list: 1026/1025

Mapping:

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

Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.815, ~5/4 = 386.514, ~19/16 = 297.178

Optimal ET sequence: 5h, 7hm, 12, 19, 26, 27, 31, 38m, 41, 46hm, 53, 118, 164, 171, 202, 217, 270, 335, 472, 525, 590, 807

Badness (Sintel): 0.063

Etymology

This comma was named by Francium in 2025. It refers to 1026 Ingrid, which in turn was named after a niece of German astronomer Albrecht Kahrstedt.

See also

• Unnoticeable comma
• List of superparticular intervals