10/9: Difference between revisions

In 5-limit Just Intonation, 10/9 is a small whole tone of about 182.4¢. It is a superparticular interval, as you can find it in the harmonic series between the 9th and the 10th overtones. It is one of two essential whole tones in the 5-limit; the other one is 9/8 (about 203.9¢), which is 81/80 (about 21.5¢) higher than 10/9. 9/8 is an octave-reduced overtone, and it is closer to 12edo's single whole step of 200¢. Thus, 9/8 is more familiar and less difficult to tune by ear than 10/9.

The first three notes of a JI major scale -- 1/1, 9/8, 5/4 -- move by a step of 9/8 followed by a step of 10/9 (or alternatively 1/1, 10/9, 5/4 -- move by a step of 10/9 followed by a step of 9/8). In systems where 81/80 is tempered out (in 12edo, 19edo, 31edo and other meantone systems) that distinction is lost and this sounds like two equal-sized steps. In strict JI, the difference is tiny and hard to notice at first.

See also Gallery of Just Intervals

@@ Line 1: / Line 1: @@
-'''10/9'''
+{{Infobox Interval
-|1 -2 1&gt;
+| Icon =
+| Ratio = 10/9
+| Monzo = 1 -2 1
+| Cents = 182.40371
+| Name = small whole tone
+| Sound = jid_10_9_pluck_adu_dr220.mp3
+}}
-.40371 cents
+In [[5-limit]] [[Just Intonation]], '''10/9''' is a small whole tone of about 182.4¢. It is a [[superparticular]] interval, as you can find it in the harmonic series between the 9th and the 10th overtones. It is one of two essential whole tones in the 5-limit; the other one is [[9/8]] (about 203.9¢), which is [[81/80]] (about 21.5¢) higher than 10/9. 9/8 is an octave-reduced overtone, and it is closer to [[12edo|12edo]]'s single whole step of 200¢. Thus, 9/8 is more familiar and less difficult to tune by ear than 10/9.
-[[File:jid_10_9_pluck_adu_dr220.mp3]] [[:File:jid_10_9_pluck_adu_dr220.mp3|sound sample]]
+The first three notes of a JI major scale -- 1/1, 9/8, 5/4 -- move by a step of 9/8 followed by a step of 10/9 (or alternatively 1/1, 10/9, 5/4 -- move by a step of 10/9 followed by a step of 9/8). In systems where 81/80 is tempered out (in 12edo, [[19edo]], [[31edo]] and other [[meantone]] systems) that distinction is lost and this sounds like two equal-sized steps. In strict JI, the difference is tiny and hard to notice at first.
-In [[5-limit|5-limit]] [[Just_intonation|Just Intonation]], 10/9 is a small whole tone of about 182.4¢. It is a [[superparticular|superparticular]] interval, as you can find it in the harmonic series between the 9th and the 10th overtones. It is one of two essential whole tones in the 5-limit; the other one is [[9/8|9/8]] (about 203.9¢), which is [[81/80|81/80]] (about 21.5¢) higher than 10/9. 9/8 is an octave-reduced overtone, and it is closer to [[12edo|12edo]]'s single whole step of 200¢. Thus, 9/8 is more familiar and less difficult to tune by ear than 10/9.
+:''See also [[Gallery of Just Intervals]]''
-The first three notes of a JI major scale -- 1/1, 9/8, 5/4 -- move by a step of 9/8 followed by a step of 10/9 (or alternatively 1/1, 10/9, 5/4 -- move by a step of 10/9 followed by a step of 9/8). In systems where 81/80 is tempered out (in 12edo, [[19edo|19edo]], [[31edo|31edo]] and other [[Meantone|meantone]] systems) that distinction is lost and this sounds like two equal-sized steps. In strict JI, the difference is tiny and hard to notice at first.
+[[Category:5-limit]]
-See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:5-limit]]
 [[Category:interval]]
 [[Category:just_interval]]

10/9: Difference between revisions

Revision as of 22:25, 11 October 2018

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