11/8: Difference between revisions
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In [[11-limit]] [[just intonation]], '''11/8''' is an '''undecimal [[superfourth]]''' of about 551.3[[cent|¢]]. This interval has [https://en.wikipedia.org/wiki/Major_fourth_and_minor_fifth also been referred to] as the '''major fourth'''. Furthermore, as stacks of this interval form a core axis of Alpharabian tuning (see [[User:Aura/Aura's Ideas on Tonality #11-limit Axis Functionality]]), it can also be somewhat similarly dubbed the | In [[11-limit]] [[just intonation]], '''11/8''' is an '''undecimal [[superfourth]]''' of about 551.3[[cent|¢]]. This interval has [https://en.wikipedia.org/wiki/Major_fourth_and_minor_fifth also been referred to] as the '''major fourth'''. Furthermore, as stacks of this interval form a core axis of Alpharabian tuning (see [[User:Aura/Aura's Ideas on Tonality #11-limit Axis Functionality]]), it can also be somewhat similarly dubbed the '''Alpharabian paramajor fourth''' or even the '''just paramajor fourth'''. | ||
This interval is the simplest superfourth in JI, and, falling about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced overtone, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the much stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3). It is very well-represented in [[24edo]], making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. | This interval is the simplest superfourth in JI, and, falling about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced overtone, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the much stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3). It is very well-represented in [[24edo]], making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. | ||
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== See also == | == See also == | ||
Revision as of 06:04, 27 October 2020
| Interval information |
major fourth,
Alpharabian paramajor fourth,
just paramajor fourth
reduced harmonic
[sound info]
In 11-limit just intonation, 11/8 is an undecimal superfourth of about 551.3¢. This interval has also been referred to as the major fourth. Furthermore, as stacks of this interval form a core axis of Alpharabian tuning (see User:Aura/Aura's Ideas on Tonality #11-limit Axis Functionality), it can also be somewhat similarly dubbed the Alpharabian paramajor fourth or even the just paramajor fourth.
This interval is the simplest superfourth in JI, and, falling about halfway between 12edo's perfect fourth and tritone, it is very xenharmonic. As an octave-reduced overtone, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the much stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3). It is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12.
Approximations by EDOs
Following EDOs (up to 200) contain good approximations[1] of the interval 11/8. Errors are given by magnitude, the arrows in the table show if the EDO representation is sharp (↑) or flat (↓).
| EDO | deg\edo | Absolute error (¢) |
Relative error (r¢) |
↕ | Equally acceptable multiples [2] |
|---|---|---|---|---|---|
| 11 | 5\11 | 5.8634 | 5.3748 | ↓ | |
| 13 | 6\13 | 2.5282 | 2.7389 | ↑ | 12\26 |
| 24 | 11\24 | 1.3179 | 2.6359 | ↓ | 22\48 |
| 37 | 17\37 | 0.0334 | 0.1030 | ↑ | 34\74, 51\111, 68\148, 85\185 |
| 50 | 23\50 | 0.6821 | 2.8419 | ↑ | 46\100 |
| 61 | 28\61 | 0.4983 | 2.5329 | ↓ | 56\122 |
| 63 | 29\63 | 1.0630 | 5.5808 | ↑ | |
| 85 | 39\85 | 0.7297 | 5.1688 | ↓ | |
| 87 | 40\87 | 0.4062 | 2.9449 | ↑ | 80\174 |
| 98 | 45\98 | 0.2975 | 2.4299 | ↓ | 90\196 |
| 124 | 57\124 | 0.2950 | 3.0479 | ↑ | |
| 135 | 62\135 | 0.2068 | 2.3269 | ↓ | |
| 137 | 63\137 | 0.5069 | 5.7868 | ↑ | |
| 159 | 73\159 | 0.3745 | 4.9627 | ↓ | |
| 161 | 74\161 | 0.2349 | 3.1509 | ↑ | |
| 172 | 79\172 | 0.1552 | 2.2238 | ↓ | |
| 198 | 91\198 | 0.1972 | 3.2540 | ↑ |