22/21: Difference between revisions
m Normalising usage of Infobox Interval |
Removed obvious fact, added two differences between two intervals Tags: Mobile edit Mobile web edit Advanced mobile edit |
||
| (4 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
{{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 | ||
| Comma = yes | |||
}} | }} | ||
'''22/21''' is a small [[superparticular]] [[semitone (interval region)|semitone]] of about 80.5¢ that appears in [[11-limit]] [[just intonation]], commonly known as the '''small undecimal semitone''', or '''undecimal minor semitone'''. It is the difference between [[12/11]] and [[8/7]], or between [[7/6]] and [[11/9]]. | |||
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'''. | |||
The single degree of [[88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440. | Furthermore, 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. | ||
Latest revision as of 11:13, 9 April 2025
| 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 is the difference between 12/11 and 8/7, or between 7/6 and 11/9.
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.
Furthermore, 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.