25/24: Difference between revisions
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'''25/24''', the '''classic''' or '''just chromatic semitone''' (short: '''chroma'''), 70.672 cents, is the [[superparticular]] ratio which marks the difference between the 5-limit thirds, [[6/5]] and [[5/4]], | '''25/24''', the '''classic''' or '''just chromatic semitone''' (short: '''chroma'''), 70.672 cents, 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== | ||
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. | 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 == | ==Temperaments== | ||
If 25/24 is treated as a comma to be tempered out, you remove the distinction between major and minor thirds and get only a single neutral interval in their place as in [[dicot family]], and edos like [[10edo]] or [[17edo]]. | If 25/24 is treated as a comma to be tempered out, you remove the distinction between major and minor thirds and get only a single neutral interval in their place as in [[dicot family]], and edos like [[10edo]] or [[17edo]]. | ||
== See also == | ==See also== | ||
* [[36/25]] – its [[fifth complement]] | * [[36/25]] – its [[fifth complement]] | ||
* [[48/25]] – its [[octave complement]] | *[[48/25]] – its [[octave complement]] | ||
* [[Dicot family]], where it is tempered out | *[[Dicot family]], where it is tempered out | ||
* [[Gallery of just intervals]] | *[[Gallery of just intervals]] | ||
* [[Medium comma]] | *[[Medium comma]] | ||
* [[List of superparticular intervals]] | *[[List of superparticular intervals]] | ||
* [[Chroma]] – a generalising concept for [[MOS]] scales | *[[Chroma]] – a generalising concept for [[MOS]] scales | ||
* [[2187/2048]] – the Pythagorean chromatic semitone | *[[2187/2048]] – the Pythagorean chromatic semitone | ||
[[Category:5-limit]] | [[Category:5-limit]] | ||
Revision as of 01:17, 25 October 2021
| Interval information |
chroma
reduced
[sound info]
25/24, the classic or just chromatic semitone (short: chroma), 70.672 cents, 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, you remove the distinction between major and minor thirds and get only a single neutral interval in their place as in dicot family, and edos like 10edo or 17edo.
See also
- 36/25 – its fifth complement
- 48/25 – its octave complement
- Dicot family, where it is tempered out
- Gallery of just intervals
- Medium comma
- List of superparticular intervals
- Chroma – a generalising concept for MOS scales
- 2187/2048 – the Pythagorean chromatic semitone