20/17: Difference between revisions

Interval information
Ratio	20/17
Factorization	22 × 5 × 17-1
Monzo	[2 0 1 0 0 0 -1⟩
Size in cents	281.3583¢
Name	diatismic minor third
Color name	17uy2, suyo 2nd
FJS name	[math]\displaystyle{ \text{A2}^{5}_{17} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	8.40939
Weil norm (log2 max(n, d))	8.64386
Wilson norm (sopfr(nd))	26
	https://en.xen.wiki/w/File:Jid_20_17_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

Latest revision as of 13:11, 3 November 2025

In 17-limit just intonation, 20/17 is the diatismic minor third, measuring about 281.4 ¢. It falls short of the Pythagorean minor third (32/27) by a diatisma (136/135), hence the name. It is the mediant of 7/6 and 13/11, as it is (7 + 13)/(6 + 11). It is found in the harmonic series between the 17th and 20th harmonics.

Edo approximations for 20/17 (281.36 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	1\4	300.00	+18.64	+6.21
13	3\13	276.92	-4.44	-4.80
17	4\17	282.35	+0.99	+1.41
21	5\21	285.71	+4.36	+7.62
26	6\26	276.92	-4.44	-9.61
30	7\30	280.00	-1.36	-3.40
34	8\34	282.35	+0.99	+2.82
38	9\38	284.21	+2.85	+9.03
43	10\43	279.07	-2.29	-8.20
47	11\47	280.85	-0.51	-1.99
51	12\51	282.35	+0.99	+4.23
60	14\60	280.00	-1.36	-6.79
64	15\64	281.25	-0.11	-0.58
68	16\68	282.35	+0.99	+5.64
77	18\77	280.52	-0.84	-5.38

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = diatismic minor third
-| Ratio = 20/17
-| Monzo = 2 0 1 0 0 0 -1
-| Cents = 281.3583
-| Name = septendecimal minor third
 | Sound = jid_20_17_pluck_adu_dr220.mp3
 | Color name = 17uy2, suyo 2nd
 }}
-In [[17-limit]] [[Just Intonation]], '''20/17''' is the "septendecimal minor third", measuring about 281.4¢. It is the [[mediant]] between [[7/6]] and [[13/11]], as it is (7+13)/(6+11). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 20th harmonics.
-See:
+In [[17-limit]] [[just intonation]], '''20/17''' is the '''diatismic minor third''', measuring about 281.4{{cent}}. It falls short of the [[32/27|Pythagorean minor third (32/27)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of [[7/6]] and [[13/11]], as it is (7 + 13)/(6 + 11). It is found in the [[harmonic series]] between the 17th and 20th [[harmonic]]s.
+== Approximation ==
+{{Interval edo approximation|20/17}}
+== See also ==
+* [[17/10]] – its [[octave complement]]
+* [[51/40]] – its [[fifth complement]]
+* [[17/15]] – its [[fourth complement]]
 * [[17edo|4\17]] (282.353 cents)
-* [[17/10]] the [[octave complement]]
+* [[Gallery of just intervals]]
-* [[Gallery of Just Intervals]]
-[[Category:17-limit]]
+[[Category:Third]]
-[[Category:interval]]
+[[Category:Minor third]]
-[[Category:just_interval]]
+[[Category:Diatismic]]
-[[Category:minor_third]]
-[[Category:septendecimal]]