25/24: Difference between revisions
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Wikispaces>Sarzadoce **Imported revision 245079399 - Original comment: ** |
Hotcrystal0 (talk | contribs) correcting this |
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{{interwiki | |||
| de = 25/24 | |||
| en = 25/24 | |||
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{{Infobox Interval | |||
| Name = just chromatic semitone, classic(al) chromatic semitone, diptolemaic chromatic semitone, dicot comma | |||
| Color name = yy1, yoyo unison | |||
| Sound = jid_25_24_pluck_adu_dr220.mp3 | |||
| Comma = yes | |||
}} | |||
'''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. | |||
== Approximation == | |||
25/24 is very accurately approximated by [[17edo]]'s 1\17 (70.588{{cent}}), though 17edo does not represent it as such, actually [[tempering out]] 25/24 by [[patent val]] (though [[34edo]] represents it as 1\17 consistently). In fact, the interval that results from stacking seventeen 25/24 chromatic semitones reduced by an octave is the [[septendecima]], only 1.431{{cent}} in size. | |||
{{Interval edo approximation|25/24}} | |||
== 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]] [[exotemperament]], 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 [[5L 2s|diatonic]] scale | |||
* [[Chroma]] – a generalising concept for all [[mos]] scales | |||
[[Category:Chroma]] | |||
[[Category:Semitone]] | |||
[[Category:Third tone]] | |||
[[Category:Dicot]] | |||
[[Category:Commas named for how they divide the fifth]] | |||
Latest revision as of 20:31, 18 March 2026
| 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 ¢), though 17edo does not represent it as such, actually tempering out 25/24 by patent val (though 34edo represents it as 1\17 consistently). In fact, the interval that results from stacking seventeen 25/24 chromatic semitones reduced by an octave is the septendecima, only 1.431 ¢ in size.
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 16 | 1\16 | 75.00 | +4.33 | +5.77 |
| 17 | 1\17 | 70.59 | -0.08 | -0.12 |
| 18 | 1\18 | 66.67 | -4.01 | -6.01 |
| 33 | 2\33 | 72.73 | +2.05 | +5.65 |
| 34 | 2\34 | 70.59 | -0.08 | -0.24 |
| 35 | 2\35 | 68.57 | -2.10 | -6.13 |
| 50 | 3\50 | 72.00 | +1.33 | +5.53 |
| 51 | 3\51 | 70.59 | -0.08 | -0.36 |
| 52 | 3\52 | 69.23 | -1.44 | -6.25 |
| 67 | 4\67 | 71.64 | +0.97 | +5.41 |
| 68 | 4\68 | 70.59 | -0.08 | -0.48 |
| 69 | 4\69 | 69.57 | -1.11 | -6.37 |
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 exotemperament, 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