10/9: Difference between revisions

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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.

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 hard to notice at first.

== See also ==

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 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.
+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 hard to notice at first.
 == See also ==