21/11: Difference between revisions
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{{Infobox Interval | |||
| Name = large undecimal diminished octave, undecimal major seventh, pentacircle major seventh | |||
| Color name = 1uz8, luzo 8ve | |||
| Sound = jid_21_11_pluck_adu_dr220.mp3 | |||
}} | |||
'''21/11''', commonly known as the '''large undecimal diminished octave''', is an [[11-limit]] interval, and the octave complement of [[22/21]]. | |||
In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect octave, as it is the octave minus a stack consisting 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 sharp of the [[243/128|Pythagorean major seventh (243/128)]] by a [[896/891|pentacircle comma (896/891)]]. For this reason it could be called the '''pentacircle major seventh'''. | |||
Of note is that the Huygens-Fokker Foundation dubs this interval the '''undecimal major seventh''', which also makes sense, resulting in this interval being perhaps best classified as a "sevtave" – a type of cross between a seventh and an octave. | |||
[[ | == Approximation == | ||
{{Interval edo approximation|21/11}} | |||
== See also == | |||
| | * [[22/21]] – its [[octave complement]] | ||
[[Category:Octave]] | |||
[[Category:Diminished octave]] | |||
[[Category:Seventh]] | |||
[[Category:Major seventh]] | |||
[[Category:Over-11 intervals]] | |||
Latest revision as of 13:05, 3 November 2025
| Interval information |
undecimal major seventh,
pentacircle major seventh
[sound info]
21/11, commonly known as the large undecimal diminished octave, is an 11-limit interval, and the octave complement of 22/21.
In many notation systems (e.g. FJS, HEJI), it is an imperfect octave, as it is the octave minus a stack consisting 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 sharp of the Pythagorean major seventh (243/128) by a pentacircle comma (896/891). For this reason it could be called the pentacircle major seventh.
Of note is that the Huygens-Fokker Foundation dubs this interval the undecimal major seventh, which also makes sense, resulting in this interval being perhaps best classified as a "sevtave" – a type of cross between a seventh and an octave.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 14 | 13\14 | 1114.29 | -5.18 | -6.04 |
| 15 | 14\15 | 1120.00 | +0.54 | +0.67 |
| 16 | 15\16 | 1125.00 | +5.54 | +7.38 |
| 29 | 27\29 | 1117.24 | -2.22 | -5.37 |
| 30 | 28\30 | 1120.00 | +0.54 | +1.34 |
| 31 | 29\31 | 1122.58 | +3.12 | +8.05 |
| 44 | 41\44 | 1118.18 | -1.28 | -4.70 |
| 45 | 42\45 | 1120.00 | +0.54 | +2.01 |
| 46 | 43\46 | 1121.74 | +2.28 | +8.73 |
| 59 | 55\59 | 1118.64 | -0.82 | -4.03 |
| 60 | 56\60 | 1120.00 | +0.54 | +2.69 |
| 61 | 57\61 | 1121.31 | +1.85 | +9.40 |
| 74 | 69\74 | 1118.92 | -0.54 | -3.35 |
| 75 | 70\75 | 1120.00 | +0.54 | +3.36 |
See also
- 22/21 – its octave complement