1445/1444

Interval information

Ratio	1445/1444
Factorization	2-2 × 5 × 172 × 19-2
Monzo	[-2 0 1 0 0 0 2 -2⟩
Size in cents	1.198501¢
Name	aureusma
Color name	19uu17ooy1, nunusosoyo unison
FJS name	[math]\text{P1}^{5,17,17}_{19,19}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	20.9927
Weil height (log2 max(n, d))	20.9937
Wilson height (sopfr(nd))	81
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.21165 bits
Comma size	unnoticeable
S-expression	S17 / S19
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1445/1444, the aureusma, is a 19-limit (also 2.5.17.19 subgroup) unnoticeable comma measuring about 1.20 cents. It is the difference between 5/4 and a stack of two 19/17's. It is also the difference between 153/152 and 171/170.

Commatic relations

This comma is the difference between the following superparticular pairs:

• 153/152 and 171/170
• 1156/1155 and 5776/5775
• 1275/1274 and 10830/10829

It factors into the following superparticular pairs:

• 2601/2600 and 3250/3249
• 1540/1539 and 23409/23408
• 1521/1520 and 28900/28899

Temperaments

Tempering out this comma in the 19-limit leads to the rank-7 aureusmic temperament, or in the 2.5.17.19 subgroup, the rank-3 aureus temperament. In either case it results in 5/4 being split into two 19/17's, and enables the essentially tempered aureusmic chords.

Etymology

The aureusma was named by Flora Canou in 2021. It comes from Latin aureus ("golden"), for its possible association with golden meantone.

See also

• Unnoticeable comma
• List of superparticular intervals