2187/2048: Difference between revisions
Jump to navigation
Jump to search
added color name |
Never seen "Pythagorean major chroma" attested, replaced with Pythagorean chroma; +"whitewood comma"; +approximation |
||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| Name = apotome, Pythagorean chromatic semitone | | Name = apotome, Pythagorean chroma, Pythagorean chromatic semitone, whitewood comma | ||
| Color name = Lw1, lawa unison | | Color name = Lw1, lawa unison | ||
| Sound = jid_2187_2048_pluck_adu_dr220.mp3 | | Sound = jid_2187_2048_pluck_adu_dr220.mp3 | ||
| Line 7: | Line 7: | ||
{{Wikipedia|Semitone#Pythagorean tuning}} | {{Wikipedia|Semitone#Pythagorean tuning}} | ||
'''2187/2048''', the '''apotome''', also known as the '''Pythagorean chromatic semitone''' or the '''Pythagorean | '''2187/2048''', the '''apotome''', also known as the '''Pythagorean chromatic semitone''' or the '''Pythagorean chroma''', is the [[chromatic semitone]] in the [[Pythagorean tuning]]. It is the [[3-limit]] interval between seven perfect just fifths ([[3/2]]) and four octaves ([[2/1]]): 3<sup>7</sup>/2<sup>11</sup> = 2187/2048, and measures about 113.7¢. Unlike the situation in [[meantone]] tunings, it is larger, not smaller, than the corresponding diatonic semitone, which is the Pythagorean minor second of [[256/243]]. | ||
== | == Approximation == | ||
When | This interval is well approximated by any tuning generated with accurate octaves and fifths. For example, [[53edo|4\53]] is a very good approximation. | ||
== Temperaments == | |||
When this ratio is taken as a comma to be tempered in the 5-limit, it produces the [[whitewood]] temperament, and it may be called the '''whitewood comma'''. See [[apotome family]] for extensions thereof. | |||
== See also == | == See also == | ||
| Line 16: | Line 19: | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Large comma]] | * [[Large comma]] | ||
* [[25/24]] – classic chromatic semitone | * [[25/24]] – classic chromatic semitone | ||
| Line 22: | Line 24: | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category: | [[Category:Whitewood]] | ||
Revision as of 09:57, 21 December 2022
| Interval information |
Pythagorean chroma,
Pythagorean chromatic semitone,
whitewood comma
reduced harmonic
[sound info]
2187/2048, the apotome, also known as the Pythagorean chromatic semitone or the Pythagorean chroma, is the chromatic semitone in the Pythagorean tuning. It is the 3-limit interval between seven perfect just fifths (3/2) and four octaves (2/1): 37/211 = 2187/2048, and measures about 113.7¢. Unlike the situation in meantone tunings, it is larger, not smaller, than the corresponding diatonic semitone, which is the Pythagorean minor second of 256/243.
Approximation
This interval is well approximated by any tuning generated with accurate octaves and fifths. For example, 4\53 is a very good approximation.
Temperaments
When this ratio is taken as a comma to be tempered in the 5-limit, it produces the whitewood temperament, and it may be called the whitewood comma. See apotome family for extensions thereof.
See also
- 4096/2187 – its octave complement
- Gallery of just intervals
- Large comma
- 25/24 – classic chromatic semitone