625/624: Difference between revisions

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Created page with "{{Infobox Interval | Icon = | Ratio = 625/624 | Monzo = -4 -1 4 0 0 -1 | Cents = 2.77219 | Name = vinctrias comma, <br> vinctriasma | Color name = | FJS name = | Sound = }}..."
 
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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = tunbarsma
| Ratio = 625/624
| Color name = 3uy<sup>4</sup>-2, Thuquadyo comma
| Monzo = -4 -1 4 0 0 -1
| Comma = yes
| Cents = 2.77219
| Name = vinctrias comma, <br> vinctriasma
| Color name =
| FJS name =
| Sound =  
}}
}}


'''625/624''', currently dubbed the '''vinctrias comma''' or '''vinctriasma''', is an [[unnoticeable comma|unnoticable]] [[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]]; tempering out both gives [[cata]]) – but also equates [[39/32]] with the interval that results from stacking four [[5/4]] major thirds then octave-reducing.


The term "vinctrias", from which both of this comma's names are derived, is a portmanteau of Latin ''vincire'' (to ''bind'', to ''tie up'') and Latin ''trias'' (referring to the the number three or to a triad) that was coined in reference to the fact that 625/624 is tempered out in such well-known temperaments as Catakleismic, Tritikleismic, Quadritikleismic, Octoid, Benediction, Sqrtphi, Ekadash, Countercata, Widefourth, Portentious, Yajna, Enlil, Hanuman, Marvel and Agni, and to how tempering it out simulataneously equates different kinds of neutral third and goes part of the way towards dividing the whole tone into thirds.
In terms of commas, it is the difference between
* [[325/324]] and [[676/675]]
* [[385/384]] and [[1001/1000]]


[[Category:13-limit]]
It can be factored into
[[Category:Unnoticeable comma]]
* [[1575/1573]] and [[3025/3024]]
[[Category:Superparticular]]
* [[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:Tunbarsmic]]
[[Category:Commas with unknown etymology]]

Latest revision as of 03:10, 4 November 2024

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
Color name 3uy4-2, Thuquadyo comma
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
Comma size unnoticeable
S-expression S25
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; tempering out both gives cata) – 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

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