6175/6174: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Xenllium (talk | contribs)
mNo edit summary
+commatic relations
Line 4: Line 4:
| Comma = yes
| Comma = yes
}}
}}
'''6175/6174''', the '''neonewtisma''' or '''neonewt comma''', is a [[19-limit]] [[Superparticular ratio|superparticular comma]] of about 0.28 [[cent]]s. It is the amount by which a stack consisting of [[7/5]], [[9/5]], [[14/13]] and [[28/19]] falls short of two [[octave]]s. By tempering it out is defined the '''neonewtismic temperament''', which enables the [[neonewtismic chords]].
'''6175/6174''', the '''neonewtisma''' or '''neonewt comma''', is an [[unnoticeable comma|unnoticeable]] [[19-limit]] (also 2.3.5.7.13.19-[[subgroup]]) [[superparticular]] [[comma]] of about 0.28 [[cent]]s. It is the amount by which a stack consisting of [[7/5]], [[9/5]], [[14/13]] and [[28/19]] falls short of two [[octave]]s. By tempering it out is defined the '''neonewtismic temperament''', which enables the [[neonewtismic chords]].
 
== Commatic relations ==
This comma is the difference between the following superparticular pairs:
* [[190/189]] and [[196/195]]
* [[325/324]] and [[343/342]] *
* [[442/441]] and [[476/475]]
* [[1716/1715]] and [[2376/2375]]
* [[1729/1728]] and [[2401/2400]] *
* [[2080/2079]] and [[3136/3135]]
* [[2500/2499]] and [[4200/4199]]
* [[3025/3024]] and [[5929/5928]]
* [[3250/3249]] and [[6860/6859]] *
* [[4225/4224]] and [[13377/13376]]
* [[5776/5775]] and [[89376/89375]]
* [[5832/5831]] and [[104976/104975]]
* [[5985/5984]] and [[194481/194480]]
 
It factors into the following superparticular pairs:
* [[10830/10829]] and [[14365/14364]]
 
<nowiki/>* relation within the 2.3.5.7.13.19 subgroup


== Etymology ==
== Etymology ==
Line 10: Line 31:


== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]


[[Category:Neonewtismic]]
[[Category:Neonewtismic]]

Revision as of 14:04, 5 November 2024

Interval information
Ratio 6175/6174
Factorization 2-1 × 3-2 × 52 × 7-3 × 13 × 19
Monzo [-1 -2 2 -3 0 1 0 1
Size in cents 0.2803845¢
Names neonewt comma,
neonewtisma
Color name 19o3or3yy-2,
nothotriru-ayoyo negative 2nd,
Nothotriru-ayoyo comma
FJS name [math]\displaystyle{ \text{m}{-2}^{5,5,13,19}_{7,7,7} }[/math]
Special properties superparticular,
reduced
Tenney norm (log2 nd) 25.1842
Weil norm (log2 max(n, d)) 25.1844
Wilson norm (sopfr(nd)) 71
Comma size unnoticeable
Open this interval in xen-calc

6175/6174, the neonewtisma or neonewt comma, is an unnoticeable 19-limit (also 2.3.5.7.13.19-subgroup) superparticular comma of about 0.28 cents. It is the amount by which a stack consisting of 7/5, 9/5, 14/13 and 28/19 falls short of two octaves. By tempering it out is defined the neonewtismic temperament, which enables the neonewtismic chords.

Commatic relations

This comma is the difference between the following superparticular pairs:

It factors into the following superparticular pairs:

* relation within the 2.3.5.7.13.19 subgroup

Etymology

The names neonewtisma and neonewt comma were named by Xenllium in 2023. The rank-three temperament which tempers out 2080/2079, 2401/2400 and 4096/4095 (lif temperament, 41&130&140) can be extended to the 2.3.5.7.11.13.19 subgroup by tempering out 1216/1215, 1729/1728, 2926/2925, 3136/3135 or 6175/6174, and the rank-two 2.3.5.7.11.13.19 subgroup 41&270 temperament (neonewt) also supports it.

See also