10/9: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = small whole tone, classic(al) whole tone, ptolemaic whole tone | |||
| Name = small whole tone | |||
| Color name = y2, yo 2nd | | Color name = y2, yo 2nd | ||
| Sound = jid_10_9_pluck_adu_dr220.mp3 | | Sound = jid_10_9_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{Wikipedia|Major second}} | |||
In [[5-limit]] [[ | 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 | 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. | ||
== Temperaments == | |||
The following [[linear temperament]]s are [[generate]]d by a [[~]]10/9: | |||
* [[Porcupine]] | |||
* [[Minortone]] | |||
{{todo|complete list}} | |||
== See also == | == See also == | ||
* [[Decaononic]] - temperament which sets the tone to this interval, instead of to 9/8 | |||
* [[9/5]] – its [[octave complement]] | * [[9/5]] – its [[octave complement]] | ||
* [[27/20]] – its [[fifth complement]] | * [[27/20]] – its [[fifth complement]] | ||
* [[6/5]] – its [[fourth complement]] | * [[6/5]] – its [[fourth complement]] | ||
* [[Gallery of | * [[Gallery of just intervals]] | ||
== Notes == | |||
<references/> | |||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Whole tone]] | [[Category:Whole tone]] | ||
[[Category: | [[Category:Tritave-reduced harmonics]] | ||
Latest revision as of 03:39, 3 August 2025
| Interval information |
classic(al) whole tone,
ptolemaic whole tone
reduced
[sound info]
In 5-limit just intonation, 10/9 is the small, classic(al), or ptolemaic whole tone[1] 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 may be hard to notice at first.
Temperaments
The following linear temperaments are generated by a ~10/9:
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