10/9: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = small whole tone, classic(al) whole tone, ptolemaic whole tone

~~| Ratio = 10/9~~

~~| Monzo = 1 -2 1~~

~~| Cents = 182.40371~~

| Name = small whole tone

| Color name = y2, yo 2nd

| Sound = jid_10_9_pluck_adu_dr220.mp3

}}

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.

In [[5-limit]] [[just intonation]], '''10/9''' is the '''small''', '''classic(al)''', or '''ptolemaic whole tone'''<ref>For reference, see [[5-limit]]. </ref> 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 may be hard to notice at first.

:''See also [[Gallery of ~~Just Intervals~~]]''

== Temperaments ==

The following [[linear temperament]]s are [[generate]]d by a [[~]]10/9:

* [[Porcupine]]

* [[Minortone]]

== See also ==

* [[Decaononic]] - temperament which sets the tone to this interval, instead of to 9/8

* [[9/5]] – its [[octave complement]]

* [[27/20]] – its [[fifth complement]]

* [[6/5]] – its [[fourth complement]]

* [[Gallery of just intervals]]

== Notes ==

~~[[Category:5-limit]]~~

~~[[Category:Interval ratio]]~~

~~[[Category:Just interval]]~~

~~[[Category:Listen]]~~

[[Category:Second]]

[[Category:Whole tone]]

[[Category:Tritave-reduced harmonics]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = small whole tone, classic(al) whole tone, ptolemaic whole tone
-| Ratio = 10/9
-| Monzo = 1 -2 1
-| Cents = 182.40371
-| Name = small whole tone
 | Color name = y2, yo 2nd
 | Sound = jid_10_9_pluck_adu_dr220.mp3
 }}
+{{Wikipedia|Major second}}
-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.
+In [[5-limit]] [[just intonation]], '''10/9''' is the '''small''', '''classic(al)''', or '''ptolemaic whole tone'''<ref>For reference, see [[5-limit]]. </ref> 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 may be hard to notice at first.
-:''See also [[Gallery of Just Intervals]]''
+== Temperaments ==
+The following [[linear temperament]]s are [[generate]]d by a [[~]]10/9:
+* [[Porcupine]]
+* [[Minortone]]
+{{todo|complete list}}
+== See also ==
+* [[Decaononic]] - temperament which sets the tone to this interval, instead of to 9/8
+* [[9/5]] – its [[octave complement]]
+* [[27/20]] – its [[fifth complement]]
+* [[6/5]] – its [[fourth complement]]
+* [[Gallery of just intervals]]
+== Notes ==
+<references/>
-[[Category:5-limit]]
-[[Category:Interval ratio]]
-[[Category:Just interval]]
-[[Category:Listen]]
 [[Category:Second]]
 [[Category:Whole tone]]
+[[Category:Tritave-reduced harmonics]]