289/288: Difference between revisions

(10 intermediate revisions by 3 users not shown)

Line 1:

{{Infobox Interval

| Name = semitonisma

| Name = semitonisma, septendecimal semitones comma, septendecimal 6-cent comma

| Color name = 17oo2, soso 2nd,<br>Soso comma

| Comma = yes

Line 20:

== Temperaments ==

Tempering out this comma results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.

Tempering out this comma in the full 17-limit results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.

=== Semitonic ===

See [[No-fives subgroup temperaments #Semitonic]].

=== Semitonismic ===

Line 45:

Line 48:

[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8

{{Optimal ET sequence|legend=1| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}

{{Optimal ET sequence|legend=1| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}*

~~=== Semitonic ===~~

~~[[Subgroup]]: 2.3.17~~

~~{{Mapping|legend=2| 2 0 5 | 0 1 1 }}~~

~~: sval mapping generators: ~17/12, ~3~~

~~[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)~~

~~{{Optimal ET sequence~~|~~legend=1| 12, 58, 70, 82, 94, 106, 118, 224g }}~~

<nowiki>*</nowiki> [[optimal patent val]]: [[280edo|280]]

== Etymology ==

Line 66:

Line 60:

[[Category:Semitonismic]]

[[Category:Commas named for the intervals they stack]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = semitonisma
+| Name = semitonisma, septendecimal semitones comma, septendecimal 6-cent comma
 | Color name = 17oo2, soso 2nd,<br>Soso comma
 | Comma = yes
@@ Line 20: / Line 20: @@
 == Temperaments ==
-Tempering out this comma results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.
+Tempering out this comma in the full 17-limit results in the rank-6 '''semitonismic temperament''', or in the 2.3.17 subgroup, the rank-2 '''semitonic temperament'''. In either case the [[octave]] is split into two equal parts, each representing 17/12~24/17, and thus so is the whole tone, each representing 17/16~18/17. Odd edos cannot temper it out.
+=== Semitonic ===
+See [[No-fives subgroup temperaments #Semitonic]].
 === Semitonismic ===
@@ Line 45: / Line 48: @@
 [[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472, 5/4, 7/4, 11/8, 13/8
-{{Optimal ET sequence|legend=1| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}
+{{Optimal ET sequence|legend=1| 34d, 38df, 46, 58, 72, 130, 140, 190g, 212g, 270g, 342fg, 402defgg, 460gg, 532dfggg, 672defggg }}*
-=== Semitonic ===
-[[Subgroup]]: 2.3.17
-{{Mapping|legend=2| 2 0 5 | 0 1 1 }}
-: sval mapping generators: ~17/12, ~3
-[[Optimal tuning]] ([[CTE]]): ~17/12 = 1\2, ~3/2 = 702.3472 (~17/16 = 102.3472)
-{{Optimal ET sequence|legend=1| 12, 58, 70, 82, 94, 106, 118, 224g }}
+<nowiki>*</nowiki> [[optimal patent val]]: [[280edo|280]]
 == Etymology ==
@@ Line 66: / Line 60: @@
 [[Category:Semitonismic]]
+[[Category:Commas named for the intervals they stack]]