625/624: Difference between revisions

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removed tentative names- found the name "tunbarsma" on the Wiki
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| Monzo = -4 -1 4 0 0 -1
| Monzo = -4 -1 4 0 0 -1
| Cents = 2.77219
| Cents = 2.77219
| Name = vinctrias comma, <br> vinctriasma
| Name = tunbarsma
| Color name =  
| Color name =  
| FJS name =  
| FJS name =  
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}}
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'''625/624''', 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|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.
 
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.


[[Category:13-limit]]
[[Category:13-limit]]
[[Category:Unnoticeable comma]]
[[Category:Unnoticeable comma]]
[[Category:Superparticular]]
[[Category:Superparticular]]

Revision as of 23:49, 26 December 2020

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 norm (log2 nd) 18.5731
Weil norm (log2 max(n, d)) 18.5754
Wilson norm (sopfr(nd)) 44
Open this interval in xen-calc

625/624, the tunbarsma, is an unnoticable 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.

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