2187/2048: Difference between revisions

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'''2187/2048'''
{{Infobox Interval
|-11 7>
| Ratio = 2187/2048
| Monzo = -11 7
| Cents = 113.6850
| Name = Apotome, <br>Pythagorean chromatic semitone
| Sound = jid_2187_2048_pluck_adu_dr220.mp3
| FJS name = A1
}}


113.6850 cents
The '''apotome''', also known as the '''Pythagorean chromatic semitone''' or the '''Pythagorean major semitone''', is the interval 3<sup>7</sup>/2<sup>11</sup> = 2187/2048 which is the chromatic semitone in the [[Pythagorean tuning|Pythagorean]] ([[3-limit]]) version of the diatonic scale. 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]]. It measures about 113.7¢ and can be generated by stacking seven [[3/2]] perfect fifths and octave-reducing the resulting interval.


[[File:jid_2187_2048_pluck_adu_dr220.mp3]] [[:File:jid_2187_2048_pluck_adu_dr220.mp3|sound sample]]
== See also ==
 
* [[Gallery of Just Intervals]]
The ''apotome'', also known as the Pythagorean chromatic semitone or the Pythagorean major semitone, is the interval 3^7/2^11 = 2187/2048 which is the chromatic semitone in the Pythagorean (3-limit) version of the diatonic scale. 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|256/243]]. It measures about 113.7¢ and can be generated by stacking seven [[3/2|3/2]] perfect fifths and octave-reducing the resulting interval.
* [[Large commas]]
 
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[Comma|comma]]

Revision as of 05:27, 17 August 2020

Interval information
Ratio 2187/2048
Factorization 2-11 × 37
Monzo [-11 7⟩
Size in cents 113.685¢
Names Apotome,
Pythagorean chromatic semitone
FJS name [math]\displaystyle{ \text{A1} }[/math]
Special properties reduced,
reduced harmonic
Tenney height (log2 nd) 22.0947
Weil height (log2 max(n, d)) 22.1895
Wilson height (sopfr(nd)) 43

[sound info]
Open this interval in xen-calc

The apotome, also known as the Pythagorean chromatic semitone or the Pythagorean major semitone, is the interval 37/211 = 2187/2048 which is the chromatic semitone in the Pythagorean (3-limit) version of the diatonic scale. 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. It measures about 113.7¢ and can be generated by stacking seven 3/2 perfect fifths and octave-reducing the resulting interval.

See also

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