11/7: Difference between revisions

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11/7 is [[22/21]] (about 80.5¢) above the [[3/2]] perfect fifth, allowing the possibility of a resolution down by a step from 11/7 to 3/2.
11/7 is [[22/21]] (about 80.5¢) above the [[3/2]] perfect fifth, allowing the possibility of a resolution down by a step from 11/7 to 3/2.
== Approximations by EDOs ==
Following [[EDO]]s (up to 200) contain good approximations<ref>error magnitude below 7, both, absolute (in ¢) and relative (in r¢)</ref> of the interval 11/7. Errors are given by magnitude, the arrows in the table show if the EDO representation is sharp (&uarr;) or flat (&darr;).
{| class="wikitable sortable right-1 center-2 right-3 right-4 center-5"
|-
! [[EDO]]
! class="unsortable" | deg\edo
! Absolute <br> error ([[Cent|¢]])
! Relative <br> error ([[Relative cent|r¢]])
! &#8597;
! class="unsortable" | Equally acceptable multiples <ref>Super EDOs up to 200 within the same error tolerance</ref>
|-
|  [[20edo|20]]  ||  13\20  || 2.4920 || 4.1534 || &darr; ||
|-
|  [[23edo|23]]  ||  15\23  || 0.1167 || 0.2236 || &uarr; ||  [[46edo|30\46]], [[69edo|45\69]], [[92edo|60\92]], [[115edo|75\115]], [[138edo|90\138]], [[161edo|105\161]], [[184edo|120\184]]
|-
|  [[26edo|26]]  ||  17\26  || 2.1233 || 4.6006 || &uarr; ||
|-
|  [[43edo|43]]  ||  28\43  || 1.0967 || 3.9298 || &darr; ||
|-
|  [[49edo|49]]  ||  32\49  || 1.1814 || 4.8242 || &uarr; ||
|-
|  [[66edo|66]]  ||  43\66  || 0.6739 || 3.7062 || &darr; ||
|-
|  [[72edo|72]]  ||  47\72  || 0.8413 || 5.0478 || &uarr; ||
|-
|  [[89edo|89]]  ||  58\89  || 0.4696 || 3.4826 || &darr; ||  [[178edo|116\178]]
|-
|  [[95edo|95]]  ||  62\95  || 0.6659 || 5.2714 || &uarr; ||
|-
| [[112edo|112]] ||  73\112 || 0.3492 || 3.2590 || &darr; ||
|-
| [[118edo|118]] ||  77\118 || 0.5588 || 5.4950 || &uarr; ||
|-
| [[135edo|135]] ||  88\135 || 0.2698 || 3.0354 || &darr; ||
|-
| [[141edo|141]] ||  92\141 || 0.4867 || 5.7186 || &uarr; ||
|-
| [[158edo|158]] || 103\158 || 0.2136 || 2.8118 || &darr; ||
|-
| [[164edo|164]] || 107\164 || 0.4348 || 5.9422 || &uarr; ||
|-
| [[181edo|181]] || 118\181 || 0.1716 || 2.5882 || &darr; ||
|-
| [[187edo|187]] || 122\187 || 0.3957 || 6.1658 || &uarr; ||
|}
<references/>


== See also ==
== See also ==

Revision as of 12:20, 25 October 2020

Interval information
Ratio 11/7
Factorization 7-1 × 11
Monzo [0 0 0 -1 1⟩
Size in cents 782.492 ¢
Names undecimal minor sixth,
undecimal augmented fifth
Color name 1or5, loru 5th
FJS name [math]\displaystyle{ \text{P5}^{11}_{7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 6.26679
Weil norm (log2 max(n, d)) 6.91886
Wilson norm (sopfr(nd)) 18

[sound info]
Open this interval in xen-calc

In 11-limit just intonation, 11/7 is an undecimal minor sixth, measuring about 782.5¢. It is the inversion of 14/11, the undecimal major third.

11/7 is flat of the Pythagorean minor sixth of 128/81 (about 792.2¢) by a pentacircle comma, 896/891. It is flat of the 5-limit minor sixth of 8/5 (about 813.7¢) by 56/55. It is sharp of the 7-limit subminor sixth of 14/9 (about 764.9¢) by a mothwellsma, 99/98. And finally, it is sharp of the classic augmented fifth of 25/16 (about 772.6¢) by a valinorsma, 176/175.

11/7 is 22/21 (about 80.5¢) above the 3/2 perfect fifth, allowing the possibility of a resolution down by a step from 11/7 to 3/2.

Approximations by EDOs

Following EDOs (up to 200) contain good approximations[1] of the interval 11/7. 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]
20 13\20 2.4920 4.1534 ↓
23 15\23 0.1167 0.2236 ↑ 30\46, 45\69, 60\92, 75\115, 90\138, 105\161, 120\184
26 17\26 2.1233 4.6006 ↑
43 28\43 1.0967 3.9298 ↓
49 32\49 1.1814 4.8242 ↑
66 43\66 0.6739 3.7062 ↓
72 47\72 0.8413 5.0478 ↑
89 58\89 0.4696 3.4826 ↓ 116\178
95 62\95 0.6659 5.2714 ↑
112 73\112 0.3492 3.2590 ↓
118 77\118 0.5588 5.4950 ↑
135 88\135 0.2698 3.0354 ↓
141 92\141 0.4867 5.7186 ↑
158 103\158 0.2136 2.8118 ↓
164 107\164 0.4348 5.9422 ↑
181 118\181 0.1716 2.5882 ↓
187 122\187 0.3957 6.1658 ↑
  1. ↑ error magnitude below 7, both, absolute (in ¢) and relative (in r¢)
  2. ↑ Super EDOs up to 200 within the same error tolerance

See also

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