625/624: Difference between revisions

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'''625/624''', the '''tunbarsma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] comma with a value of roughly 2.77 [[cent]]s. Tempering out this comma not only equates [[25/24]] with [[26/25]] – splitting [[13/12]] in half and going part of the way towards splitting the [[9/8]] whole tone into three (the other comma that needs to be tempered in order to finish this job is [[676/675]]) – but also equates [[39/32]] with the interval that results from stacking four [[5/4]] major thirds then octave-reducing.
'''625/624''', the '''tunbarsma''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] comma with a value of roughly 2.77 [[cent]]s. Tempering out this comma not only equates [[25/24]] with [[26/25]] – splitting [[13/12]] in half and going part of the way towards splitting the [[9/8]] whole tone into three (the other comma that needs to be tempered in order to finish this job is [[676/675]]) – but also equates [[39/32]] with the interval that results from stacking four [[5/4]] major thirds then octave-reducing.
In terms of commas, it is the difference between
* [[325/324]] and [[676/675]]
* [[385/384]] and [[1001/1000]]
It can be factored into
* [[1575/1573]] and [[3025/3024]]
* [[2200/2197]] and [[4225/4224]]
* [[729/728]] and [[4375/4374]]
In the 17-limit, it can be factored into
* [[1225/1224]] and [[1275/1274]]
== See also ==
* [[Unnoticeable comma]]


[[Category:13-limit]]
[[Category:13-limit]]

Revision as of 15:55, 15 August 2022

Interval information
Ratio 625/624
Factorization 2-4 × 3-1 × 54 × 13-1
Monzo [-4 -1 4 0 0 -1
Size in cents 2.772193¢
Name tunbarsma
FJS name [math]\displaystyle{ \text{dd}{-2}^{5,5,5,5}_{13} }[/math]
Special properties square superparticular,
reduced
Tenney height (log2 nd) 18.5731
Weil height (log2 max(n, d)) 18.5754
Wilson height (sopfr(nd)) 44
Open this interval in xen-calc

625/624, the tunbarsma, is an unnoticeable 13-limit comma with a value of roughly 2.77 cents. Tempering out this comma not only equates 25/24 with 26/25 – splitting 13/12 in half and going part of the way towards splitting the 9/8 whole tone into three (the other comma that needs to be tempered in order to finish this job is 676/675) – but also equates 39/32 with the interval that results from stacking four 5/4 major thirds then octave-reducing.

In terms of commas, it is the difference between

It can be factored into

In the 17-limit, it can be factored into

See also