7429/7425

Interval information

Ratio	7429/7425
Factorization	3-3 × 5-2 × 11-1 × 17 × 19 × 23
Monzo	[0 -3 -2 0 -1 0 1 1 1⟩
Size in cents	0.9324002¢
Name	gordaitisma
Color name	23o19o17o1ugg3 twethonosolugugu 3rd
FJS name	[math]\text{d2}^{17,19,23}_{5,5,11}[/math]
Special properties	reduced
Tenney height (log2 nd)	25.7171
Weil height (log2 max(n, d))	25.7179
Wilson height (sopfr(nd))	89
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20635 bits
Comma size	unnoticeable
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7429/7425, the gordaitisma, is a 23-limit (also 3.5.11.17.19.23 subgroup) unnoticeable comma of about 0.93 cents.

Commatic relationships

This comma is the difference between the following intervals:

• 392/391 and 7448/7425
• 595/594 and 875/874

It can be factored into the following ratios:

• 1863/1862 and 601426/601425
• 2024/2023 and 653429/653400
• 2185/2184 and 12376/12375
• 2431/2430 and 7866/7865
• 2737/2736 and 5776/5775
• 2926/2925 and 5083/5082
• 152881/152880 and 193648/193545

Temperaments

Tempering out this comma in the full 23-limit leads to the rank-8 temperament gordaitismic. Using the 3.5.11.17.19.23 subgroup leads to the rank-5 temperament gordaite.

Gordaite

Subgroup: 3.5.11.17.19.23

Comma list: 7429/7425

Mapping:

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

Optimal tuning (CTE): ~3 = 1\1, ~5/3 = 884.472, ~11/9 = 347.534, ~17/9 = 1100.870, ~19/9 = 1293.413

Optimal ET sequence: b6g, b7h, b8eh, b10, b13g, b15, b18, b24, b26, b28, b60, b71, b88, b116, b131, b159, b185, b219, b237, b247, b316, b368, b404, b432, b553, b684, b712, b800, b1116, b1484, b1512, b1828, b2497gi, b2628, b5809ghii, b5837gghii

Etymology

This comma was named by Francium in 2025. It refers to Gordaite, the mineral.

See also

• Unnoticeable comma