8075/8073

Interval information

Ratio	8075/8073
Factorization	3-3 × 52 × 13-1 × 17 × 19 × 23-1
Monzo	[0 -3 2 0 0 -1 1 1 -1⟩
Size in cents	0.4288417¢
Name	hagendorfisma
Color name	23u19o17o3uyy1 twethunosothuyoyo unison
FJS name	[math]\text{m2}^{5,5,17,19}_{13,23}[/math]
Special properties	reduced
Tenney height (log2 nd)	25.9581
Weil height (log2 max(n, d))	25.9585
Wilson height (sopfr(nd))	91
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.20081 bits
Comma size	unnoticeable
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8075/8073, the hagendorfisma, is a 23-limit (also 3.5.13.17.19.23 subgroup) unnoticeable comma of about 0.43 cents.

Commatic relationships

This comma is the difference between the following intervals:

• 897/896 and 8075/8064
• 1275/1274 and 1863/1862
• 2300/2299 and 42500/42471
• 3381/3380 and 79135/79092

It can be factored into the following ratios:

• 4096/4095 and 282625/282624
• 4200/4199 and 104329/104328
• 4375/4374 and 52326/52325
• 4693/4692 and 28900/28899
• 6175/6174 and 11662/11661
• 14875/14872 and 21736/21735
• 19551/19550 and 361250/361179
• 44965/44954 and 328510/328509
• 104272/104247 and 126225/126224

Temperaments

Tempering out this comma in the full 23-limit leads to the rank-8 temperament hagendorfismic. Using the 3.5.13.17.19.23 subgroup leads to the rank-5 temperament hagendorfite.

Hagendorfite

Subgroup: 3.5.13.17.19.23

Comma list: 8075/8073

Mapping:

[⟨	1	1	2	2	2	1	],
⟨	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 = 884.308, ~13/9 = 636.683, ~17/9 = 1100.966, ~19/9 = 1293.517

Optimal ET sequence: b6, b7, b9i, b11f, b13g, b15, b17, b24, b26, b28, b37i, b41, b52, b62, b69, b116, b131, b185, b299, b316, b385, b553, b684, b753, b869, b938, b1028, b1213, b1413, b1897, b1966, b2994, b3179, b4592, b4960h, b5145, b5276, b6489, b7242h, b8455gh

Etymology

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

See also

• Unnoticeable comma