22/21: Difference between revisions
m Comma = yes (listed on medium commas page for a long time) |
Rework; +"undecimal minor semitone", +"pentacircle minor second" and reasons |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = small undecimal semitone | | Name = small undecimal semitone, undecimal minor semitone, pentacircle minor second | ||
| Color name = 1or1, loru unison | | Color name = 1or1, loru unison | ||
| Sound = jid_22_21_pluck_adu_dr220.mp3 | | Sound = jid_22_21_pluck_adu_dr220.mp3 | ||
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}} | }} | ||
'''22/21''' is a small [[superparticular]] | '''22/21''' is a small [[superparticular]] [[semitone]] of about 80.5¢ that appears in [[11-limit]] [[just intonation]], commonly known as the '''small undecimal semitone''', or '''undecimal minor semitone'''. It makes the difference between the 21st and 22nd [[harmonic]]s. | ||
In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect unison, as it is the stack of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. However, it is only flat of the [[256/243|Pythagorean minor second (256/243)]] by a [[896/891|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle minor second'''. | |||
Further more, it is close in size to [[21/20]], a 7-limit superparticular interval most commonly treated as a minor second, differing from it by [[441/440]], about 3.9¢. The single degree of [[88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440. | |||
== Approximation == | |||
10 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s. | 10 steps of [[149edo]] appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using [[relative cent]]s. | ||
Revision as of 08:32, 25 October 2024
| Interval information |
undecimal minor semitone,
pentacircle minor second
reduced
[sound info]
22/21 is a small superparticular semitone of about 80.5¢ that appears in 11-limit just intonation, commonly known as the small undecimal semitone, or undecimal minor semitone. It makes the difference between the 21st and 22nd harmonics.
In many notation systems (e.g. FJS, HEJI), it is an imperfect unison, as it is the stack of an undecimal quartertone (33/32) and a septimal comma (64/63), neither of which changes the scale degree or quality. However, it is only flat of the Pythagorean minor second (256/243) by a pentacircle comma (896/891). For this reason it could be called the pentacircle minor second.
Further more, it is close in size to 21/20, a 7-limit superparticular interval most commonly treated as a minor second, differing from it by 441/440, about 3.9¢. The single degree of 88cET can function as both 21/20 and 22/21, thus tempering out 441/440.
Approximation
10 steps of 149edo appoximate 22/21 with a precision of about 1 part in 15 million, or 1 part in 100000 when measured using relative cents.