Septimal enneadeca: Difference between revisions

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| Ratio = 1 570 042 899 082 081 611 640 534 563 / 1 566 652 225 014 704 215 735 402 496

| Monzo = -37 57 0 -19

| Name = septimal enneadeca~~, septienneadeca~~

| Name = septimal enneadeca

| 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)19.

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)19.

== 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 ====

@@ Line 2: / Line 2: @@
 | 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
-| Name = septimal enneadeca, septienneadeca
+| Name = septimal enneadeca
 | 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 ==
-=== 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 ====