81/20: Difference between revisions

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{{Infobox Interval

| Name = syntonic octave

| Name = syntonic double octave

| Color name = g15, gu double octave

}}

The ratio of '''81/20''' is the distance between the 81st and 20th harmonic, which can be seen as an [[octave]] that is augmented by a syntonic comma ([[81/80]]). This interval spans the size of about 2421.5 cents. It is also the result of stacking ~~4 [~~[[6/5]]]'s and 3 [[5/4]]'s. This suggests that an octave stretch of half a syntonic comma is a good way to optimise a diatonic scale for pure thirds.

The ratio of '''81/20''' is the distance between the 81st and 20th [[harmonic]], which can be seen as a [[4/1|double octave]] that is augmented by a syntonic comma ([[81/80]]). This interval spans the size of about 2421.5 cents. It is also the result of stacking four [[6/5]]'s and three [[5/4]]'s. This suggests that an [[octave stretch]] of half a syntonic comma is a good way to optimise a [[diatonic scale]] for [[just intonation|pure]] thirds, resulting in whole tones of approximately 193 cents and [[semitone (interval region)|semitones]] of 122.

[[~~Category:Octave~~]]

~~{{todo|expand|categorize}}~~

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = syntonic octave
+| Name = syntonic double octave
 | Color name = g15, gu double octave
 }}
-The ratio of '''81/20''' is the distance between the 81st and 20th harmonic, which can be seen as an [[octave]] that is augmented by a syntonic comma ([[81/80]]). This interval spans the size of about 2421.5 cents. It is also the result of stacking 4 [[[6/5]]]'s and 3 [[5/4]]'s. This suggests that an octave stretch of half a syntonic comma is a good way to optimise a diatonic scale for pure thirds.
+The ratio of '''81/20''' is the distance between the 81st and 20th [[harmonic]], which can be seen as a [[4/1|double octave]] that is augmented by a syntonic comma ([[81/80]]). This interval spans the size of about 2421.5 cents. It is also the result of stacking four [[6/5]]'s and three [[5/4]]'s. This suggests that an [[octave stretch]] of half a syntonic comma is a good way to optimise a [[diatonic scale]] for [[just intonation|pure]] thirds, resulting in whole tones of approximately 193 cents and [[semitone (interval region)|semitones]] of 122.
-[[Category:Octave]]
-{{todo|expand|categorize}}