1445/1444: Difference between revisions

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'''1445/1444''', the '''aureusma''', is a [[19-limit]] (also 2.5.17.19 subgroup) [[unnoticeable comma]] measuring about 1.20 [[cent]]s. 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]].  
'''1445/1444''', the '''aureusma''', is a [[19-limit]] (also 2.5.17.19 subgroup) [[unnoticeable comma]] measuring about 1.20 [[cent]]s. 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]].  


The term comes from Latin ''[[Wiktionary: aureus #Latin|aureus]]'', meaning golden, for its possible association with [[golden meantone]].  
== 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]].  


== Temperaments ==
== Etymology ==
Tempering out this comma results in 5/4 being split into two 19/17's, and enables the essentially tempered '''aureusmic chords'''.  
The aureusma was named by [[Flora Canou]] in 2021. It comes from Latin ''[[Wiktionary: aureus #Latin|aureus]]'' ("golden"), for its possible association with [[golden meantone]].  


== See also ==
== See also ==

Revision as of 08:54, 11 May 2023

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
FJS name [math]\displaystyle{ \text{P1}^{5,17,17}_{19,19} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 20.9927
Weil norm (log2 max(n, d)) 20.9937
Wilson norm (sopfr(nd)) 81
Comma size unnoticeable
S-expression S17/S19
Open this interval in xen-calc

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.

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