Gaster comma: Difference between revisions

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The '''gaster comma''' is a 5-limit [[unnoticeable comma]] measuring about 0.7995 cents. It is the difference between a stack of seventeen [[9/8]]s and a stack of nineteen [[10/9]]s, (9/8)<sup>17</sup>/(10/9)<sup>19</sup> = {{monzo|-70 72 -19}} (quadbila-negu).
The '''gaster comma''' is a 5-limit [[unnoticeable comma]] measuring about 0.7995 cents. It is the difference between a stack of seventeen [[9/8]]s and a stack of nineteen [[10/9]]s, (9/8)<sup>17</sup>/(10/9)<sup>19</sup> = {{monzo|-70 72 -19}} (quadbila-negu).


It can also be described as the difference between eighteen [[81/80]]<nowiki/>s and [[5/4]].  
It can also be described as the difference between eighteen [[81/80]]<nowiki/>s and [[5/4]]. It is the [[Don Page comma]] between 9/8 and 10/9.


== Temperaments ==
== Temperaments ==
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== Ratio ==
== Ratio ==
'''22528399544939174411840147874772641 / 22517998136852480000000000000000000'''
'''22528399544939174411840147874772641 / 22517998136852480000000000000000000'''
[[Category:Commas with unknown etymology]]

Latest revision as of 19:02, 21 February 2025

Interval information
Factorization 2-70 × 372 × 5-19
Monzo [-70 72 -19
Size in cents 0.7994989¢
Name gaster comma
Color name L8g19-3, quadbila-negu negative 3rd
FJS name [math]\displaystyle{ \text{M}{-3}_{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 228.234
Weil norm (log2 max(n, d)) 228.235
Wilson norm (sopfr(nd)) 451
Comma size unnoticeable
Open this interval in xen-calc

The gaster comma is a 5-limit unnoticeable comma measuring about 0.7995 cents. It is the difference between a stack of seventeen 9/8s and a stack of nineteen 10/9s, (9/8)17/(10/9)19 = [-70 72 -19 (quadbila-negu).

It can also be described as the difference between eighteen 81/80s and 5/4. It is the Don Page comma between 9/8 and 10/9.

Temperaments

Equal temperaments which temper out this comma include 111, 113, 224, 335, 559, 783, 1342, 1901, 3243 and others.

The gaster comma is tempered out by the gaster temperament.

Ratio

22528399544939174411840147874772641 / 22517998136852480000000000000000000