3/2: Difference between revisions

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'''3/2''' is the [[frequency ratio]] of the [[just perfect fifth]]. What tunes it well, is one of variants of [[12edo]] or [[17edo]] (such as [[24edo]], [[34edo]] and 36edo). Other edos tune it well too (5, 7, 29, 41, 53, 200). But not all edos are like this. 35edo is great for 2, 5, 7, 9, 11 and 17 but fails on 3.
'''3/2''' is the [[frequency ratio]] of the [[just perfect fifth]]. What tunes it well, is one of variants of [[12edo]] or [[17edo]] (such as [[24edo]], [[34edo]] and 36edo). Other edos tune it well too (5, 7, 29, 41, 53, 200). But not all edos are like this. 35edo is great for 2, 5, 7, 9, 11 and 17 but fails on 3.
== 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 3/2. 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>
|-
|  [[12edo|12]]  ||  7\12  || 1.9550 || 1.9550 || &darr; || [[24edo|14\24]], [[36edo|21\36]]
|-
|  [[17edo|17]]  ||  10\17  || 3.9274 || 5.5637 || &uarr; ||
|-
|  [[29edo|29]]  ||  17\29  || 1.4933 || 3.6087 || &uarr; ||
|-
|  [[41edo|41]]  ||  24\41  || 0.4840 || 1.6537 || &uarr; || [[82edo|48\82]], [[123edo|72\123]], [[164edo|96\164]]
|-
|  [[53edo|53]]  ||  31\53  || 0.0682 || 0.3013 || &darr; || [[106edo|62\106]], [[159edo|93\159]]
|-
|  [[65edo|65]]  ||  38\65  || 0.4165 || 2.2563 || &darr; || [[130edo|76\130]], [[195edo|114\195]]
|-
|  [[70edo|70]]  ||  41\70  || 0.9021 || 5.2625 || &uarr; ||
|-
|  [[77edo|77]]  ||  45\77  || 0.6563 || 4.2113 || &darr; ||
|-
|  [[89edo|89]]  ||  52\89  || 0.8314 || 6.1663 || &darr; ||
|-
|  [[94edo|94]]  ||  55\94  || 0.1727 || 1.3525 || &uarr; || [[188edo|110\188]]
|-
| [[111edo|111]] ||  65\111 || 0.7477 || 6.9162 || &uarr; ||
|-
| [[118edo|118]] ||  69\118 || 0.2601 || 2.5575 || &darr; ||
|-
| [[135edo|135]] ||  79\135 || 0.2672 || 3.0062 || &uarr; ||
|-
| [[142edo|142]] ||  83\142 || 0.5466 || 6.4675 || &darr; ||
|-
| [[147edo|147]] ||  86\147 || 0.0858 || 1.0512 || &uarr; ||
|-
| [[171edo|171]] || 100\171 || 0.2006 || 2.8588 || &darr; ||
|-
| [[176edo|176]] || 103\176 || 0.3177 || 4.6600 || &uarr; ||
|-
| [[183edo|183]] || 107\183 || 0.3157 || 4.8138 || &darr; ||
|-
| [[200edo|200]] || 117\200 || 0.0450 || 0.7500 || &uarr; ||
|-
|}
<references/>


== See also ==
== See also ==
* [[Gallery of Just Intervals]]
* [[Gallery of Just Intervals]]
* [[4/3]] – its [[octave complement]]
* [[4/3]] – its [[octave complement]]

Revision as of 16:15, 25 October 2020

Interval information
Ratio 3/2
Factorization 2-1 × 3
Monzo [-1 1⟩
Size in cents 701.955¢
Name just perfect fifth
Color name w5, wa 5th
FJS name [math]\displaystyle{ \text{P5} }[/math]
Special properties superparticular,
reduced,
reduced harmonic
Tenney height (log2 nd) 2.58496
Weil height (log2 max(n, d)) 3.16993
Wilson height (sopfr(nd)) 5

[sound info]
Open this interval in xen-calc
Main article: Just perfect fifth

3/2 is the frequency ratio of the just perfect fifth. What tunes it well, is one of variants of 12edo or 17edo (such as 24edo, 34edo and 36edo). Other edos tune it well too (5, 7, 29, 41, 53, 200). But not all edos are like this. 35edo is great for 2, 5, 7, 9, 11 and 17 but fails on 3.

Approximations by EDOs

Following EDOs (up to 200) contain good approximations[1] of the interval 3/2. 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]
12 7\12 1.9550 1.9550 ↓ 14\24, 21\36
17 10\17 3.9274 5.5637 ↑
29 17\29 1.4933 3.6087 ↑
41 24\41 0.4840 1.6537 ↑ 48\82, 72\123, 96\164
53 31\53 0.0682 0.3013 ↓ 62\106, 93\159
65 38\65 0.4165 2.2563 ↓ 76\130, 114\195
70 41\70 0.9021 5.2625 ↑
77 45\77 0.6563 4.2113 ↓
89 52\89 0.8314 6.1663 ↓
94 55\94 0.1727 1.3525 ↑ 110\188
111 65\111 0.7477 6.9162 ↑
118 69\118 0.2601 2.5575 ↓
135 79\135 0.2672 3.0062 ↑
142 83\142 0.5466 6.4675 ↓
147 86\147 0.0858 1.0512 ↑
171 100\171 0.2006 2.8588 ↓
176 103\176 0.3177 4.6600 ↑
183 107\183 0.3157 4.8138 ↓
200 117\200 0.0450 0.7500 ↑
  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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