25/24: Difference between revisions
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-"chroma"; +"dicot comma". Chroma is ever more general than this interval. 17edo -> 7edo since the latter is more typical |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, | | Name = just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, dicot comma | ||
| Color name = yy1, yoyo unison | | Color name = yy1, yoyo unison | ||
| Sound = jid_25_24_pluck_adu_dr220.mp3 | | Sound = jid_25_24_pluck_adu_dr220.mp3 | ||
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}} | }} | ||
'''25/24''', the '''just chromatic semitone''', '''classic(al) chromatic semitone''' or '''diptolemaic chromatic semitone''' | '''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]], [[27/25]] and [[9/8]], thirds, [[6/5]] and [[5/4]], sixths, [[8/5]] and [[5/3]], and sevenths, [[16/9]] and [[50/27]], and [[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. | ||
== Approximation == | == Approximation == | ||
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== Temperaments == | == Temperaments == | ||
If 25/24 is treated as a comma to be tempered out, | 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 get only a single neutral interval in their place, as in [[7edo]] and [[10edo]]. 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]] | ||
* [[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 | ||
* [[ | * [[Chroma]] – a generalising concept for all [[mos]] scales | ||
* [[Sqrt(25/24)]] – its exact half | * [[Sqrt(25/24)]] – its exact half | ||
Revision as of 15:29, 26 January 2023
| 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, 27/25 and 9/8, thirds, 6/5 and 5/4, sixths, 8/5 and 5/3, and sevenths, 16/9 and 50/27, and 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.
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 major and minor thirds are removed and get only a single neutral interval in their place, as in 7edo and 10edo. 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
- 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
- Sqrt(25/24) – its exact half