Septimal enneadeca: Difference between revisions

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"Septimal enneadecal" can't be used to contrast "7-limit enneadecal", contracted to "septienneadecal"
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{{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, septienneadeca
| Name = septimal enneadeca
| Comma = yes
| Comma = yes
}}
}}
The '''septimal enneadeca''' or '''septienneadeca''' ({{monzo|legend=1| -37 57 0 -19 }}), is an interval of 2.816 [[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>.
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 ==
=== Septienneadecal ===
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 out the [[enneadeca]].
 
[[Subgroup]]: 2.3.7
 
{{Mapping|legend=1| 19 0 -37 | 0 1 3 }}
 
: mapping generators: ~28/27, ~3
 
[[Optimal tuning]] ([[CTE]]): ~28/27 = 1\19, ~3/2 = 701.906 (~{{monzo| 14 -23 0 8 }} = 6.969)
 
{{Optimal ET sequence|legend=1| 19, …, 152, 171, 494, 665, 836, 1007, 1843, 2850, 6707, 9557 }}
 
[[Badness]]: 0.00146


==== Enneadecal ====
==== 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

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