Septimal enneadeca: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Godtone (talk | contribs)
Created page with "{{Infobox Interval | Monzo = -37 57 0 -19 | Name = septimal enneadeca | Comma = yes }} {{Monzo| -37 57 0 -19 }}, the '''septimal enneadeca''' or '''19-tone-comma''', is an int..."
 
Lériendil (talk | contribs)
No edit summary
 
(6 intermediate revisions by 3 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Ratio = 1 570 042 899 082 081 611 640 534 563 /<br>1 566 652 225 014 704 215 735 402 496
| Monzo = -37 57 0 -19
| Monzo = -37 57 0 -19
| Name = septimal enneadeca
| Name = septimal enneadeca
| Comma = yes
| Comma = yes
}}
}}
{{Monzo| -37 57 0 -19 }}, the '''septimal enneadeca''' or '''19-tone-comma''', is an interval of 2.816 cents which is the amount by which nineteen [[28/27]]'s fall short of an octave, that is, 2/(28/27)<sup>19</sup>.
The '''septimal enneadeca''' ({{monzo|legend=1| -37 57 0 -19 }}), is an interval of 3.743 [[cent]]s which is the amount by which nineteen [[28/27]]'s fall short of an octave, that is, 2/(28/27)<sup>19</sup>.


== Temperaments ==
== Temperaments ==
=== Septimal enneadecal ===
Because of how accurately [[19edo]] approximates [[6/5]], there is no real reason to not also temper out the [[enneadeca]] with the septimal enneadeca, leading to the 7-limit version of [[enneadecal]].
This temperament is a no-5's temperament in the 7-limit; contrast with 7-limit [[enneadecal]], which adds a mapping for 5 by tempering the [[enneadeca]].


[[Subgroup]]: 2.3.7
==== Enneadecal ====
 
See [[Ragismic microtemperaments #Enneadecal]].
Mapping: {{Mapping| 19 0 -37 | 0 1 3}}
 
[[CTE]] generators: ~28/27 = 1\19, ~3 = 1901.906
 
[[Patent val]] EDOs < 400: 19, 152, 171, 190, 323
 
==== [[Enneadecal]] ====
[[Subgroup]]: 2.3.5.7
 
{{Mapping|legend=1| 19 0 14 -37 | 0 1 1 3 }}
 
See: [[Enneadecal]]


== See also ==
== See also ==
* [[Unnoticeable comma]]
* [[Unnoticeable comma]]
* [[Septimal enneadeca]]
* [[Enneadeca]]


[[Category:Enneadecal]]
[[Category:Enneadecal]]

Latest revision as of 10:32, 25 August 2024

Interval information
Ratio 1 570 042 899 082 081 611 640 534 563 /
1 566 652 225 014 704 215 735 402 496
Factorization 2-37 × 357 × 7-19
Monzo [-37 57 0 -19
Size in cents 3.742826¢
Name septimal enneadeca
FJS name [math]\displaystyle{ \text{13d}{-13}_{7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 180.683
Weil norm (log2 max(n, d)) 180.686
Wilson norm (sopfr(nd)) 378
Comma size small
Open this interval in xen-calc

The septimal enneadeca (monzo[-37 57 0 -19), is an interval of 3.743 cents which is the amount by which nineteen 28/27's fall short of an octave, that is, 2/(28/27)19.

Temperaments

Because of how accurately 19edo approximates 6/5, there is no real reason to not also temper out the enneadeca with the septimal enneadeca, leading to the 7-limit version of enneadecal.

Enneadecal

See Ragismic microtemperaments #Enneadecal.

See also