Septimal enneadeca: Difference between revisions

Line 1:

{{Infobox Interval

| Monzo = -37 57 0 -19

| Name = septimal enneadeca

| Name = septimal enneadeca, septienneadeca

| 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''' 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>.

== Temperaments ==

=== ~~Septimal enneadecal~~ ===

=== Septienneadecal ===

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]].

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:~~ {{Mapping| 19 0 -37 | 0 1 3}}

~~[[CTE]]~~ generators: ~28/27 ~~= 1\19~~, ~3 ~~= 1901.906~~

: mapping generators: ~28/27, ~3

[[~~Patent val~~]] ~~EDOs < 400~~: 19, ~~152, 171, 190, 323~~

[[Optimal tuning]] ([[CTE]]): ~28/27 = 1\19, ~3/2 = 701.906 (~{{monzo| 14 -23 0 8 }} = 6.969)

=~~=== [[Enneadecal]] ====~~

{{Optimal ET sequence|legend=1| 19, …, 152, 171, 494, 665, 836, 1007, 1843, 2850, 6707, 9557 }}

~~[[Subgroup]]: 2.3.5.7~~

~~{{Mapping|legend=1| 19~~ 0 ~~14 -37 | 0 1 1 3 }}~~

[[Badness]]: 0.00146

See: [[Enneadecal]]

==== Enneadecal ====

See [[Ragismic microtemperaments #Enneadecal]].

== See also ==

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Monzo = -37 57 0 -19
-| Name = septimal enneadeca
+| Name = septimal enneadeca, septienneadeca
 | 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''' 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>.
 == Temperaments ==
-=== Septimal enneadecal ===
+=== Septienneadecal ===
-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]].
+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: {{Mapping| 19 0 -37 | 0 1 3}}
+{{Mapping|legend=1| 19 0 -37 | 0 1 3 }}
-[[CTE]] generators: ~28/27 = 1\19, ~3 = 1901.906
+: mapping generators: ~28/27, ~3
-[[Patent val]] EDOs < 400: 19, 152, 171, 190, 323
+[[Optimal tuning]] ([[CTE]]): ~28/27 = 1\19, ~3/2 = 701.906 (~{{monzo| 14 -23 0 8 }} = 6.969)
-==== [[Enneadecal]] ====
+{{Optimal ET sequence|legend=1| 19, …, 152, 171, 494, 665, 836, 1007, 1843, 2850, 6707, 9557 }}
-[[Subgroup]]: 2.3.5.7
-{{Mapping|legend=1| 19 0 14 -37 | 0 1 1 3 }}
+[[Badness]]: 0.00146
-See: [[Enneadecal]]
+==== Enneadecal ====
+See [[Ragismic microtemperaments #Enneadecal]].
 == See also ==