25/24: Difference between revisions
-"chroma"; +"dicot comma". Chroma is ever more general than this interval. 17edo -> 7edo since the latter is more typical |
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'''25/24''', the '''just chromatic semitone''', '''classic(al) chromatic semitone''' or '''diptolemaic chromatic semitone''', 70.672{{cent}}, is the [[superparticular]] ratio which marks the difference between the [[5-limit]] seconds, [[16/15]] and [[10/9]], thirds, [[6/5]] and [[5/4]], sixths, [[8/5]] and [[5/3]], and sevenths, [[9/5]] and [[15/8]]. It is therefore the amount which sharpens or flattens a 5-limit second, third, sixth, or seventh, and when notating 5-limit just intonation it can be associated with the sharp or flat symbol, and along with an additional symbol for the [[81/80]] comma, it can be used for a complete system of [[5-limit]] notation as an extension of diatonic. | |||
'''25/24''', the '''just chromatic semitone''', '''classic(al) chromatic semitone''' or '''diptolemaic chromatic semitone''', 70.672{{cent}}, is the [[superparticular]] ratio which marks the difference between the [[5-limit]] seconds, [[16/15]] and [[10/9 | |||
== Approximation == | == Approximation == | ||
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== Temperaments == | == Temperaments == | ||
If 25/24 is treated as a comma to be tempered out, it may be called the '''dicot comma'''. Doing so leads to the [[dicot]] temperament, where the distinction between major and minor thirds are removed and | If 25/24 is treated as a comma to be tempered out, it may be called the '''dicot comma'''. Doing so leads to the [[dicot]] temperament, where the distinction between 5-limit major and minor thirds are removed and there is only a single neutral interval functioning as both, as in [[7edo]], [[10edo]], and [[17edo]]. See [[dicot family]] for the rank-2 family where it is tempered out. | ||
== See also == | == See also == | ||
* [[36/25]] – its [[fifth complement]] | * [[36/25]] – its [[fifth complement]] | ||
* [[48/25]] – its [[octave complement]] | * [[48/25]] – its [[octave complement]] | ||
* [[Sqrt(25/24)]] – its exact half | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Medium comma]] | * [[Medium comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Chromatic semitone]] – a generalising concept for the [[diatonic]] scale | * [[Chromatic semitone]] – a generalising concept for the [[5L 2s|diatonic]] scale | ||
* [[Chroma]] – a generalising concept for all [[mos]] scales | * [[Chroma]] – a generalising concept for all [[mos]] scales | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Third tone]] | [[Category:Third tone]] | ||
[[Category:Dicot]] | |||
[[Category:Commas named for how they divide the fifth]] | |||
Latest revision as of 06:00, 4 August 2025
| Interval information |
classic(al) chromatic semitone,
diptolemaic chromatic semitone,
dicot comma
reduced
[sound info]
25/24, the just chromatic semitone, classic(al) chromatic semitone or diptolemaic chromatic semitone, 70.672 ¢, is the superparticular ratio which marks the difference between the 5-limit seconds, 16/15 and 10/9, thirds, 6/5 and 5/4, sixths, 8/5 and 5/3, and sevenths, 9/5 and 15/8. It is therefore the amount which sharpens or flattens a 5-limit second, third, sixth, or seventh, and when notating 5-limit just intonation it can be associated with the sharp or flat symbol, and along with an additional symbol for the 81/80 comma, it can be used for a complete system of 5-limit notation as an extension of diatonic.
Approximation
25/24 is very accurately approximated by 17edo's 1\17 (70.588 ¢). In fact, the interval that results from stacking seventeen 25/24 chromatic semitones reduced by an octave is the septendecima, only 1.428 ¢ in size.
Temperaments
If 25/24 is treated as a comma to be tempered out, it may be called the dicot comma. Doing so leads to the dicot temperament, where the distinction between 5-limit major and minor thirds are removed and there is only a single neutral interval functioning as both, as in 7edo, 10edo, and 17edo. See dicot family for the rank-2 family where it is tempered out.
See also
- 36/25 – its fifth complement
- 48/25 – its octave complement
- Sqrt(25/24) – its exact half
- Gallery of just intervals
- Medium comma
- List of superparticular intervals
- Chromatic semitone – a generalising concept for the diatonic scale
- Chroma – a generalising concept for all mos scales