17/10: Difference between revisions

Interval information
Ratio	17/10
Factorization	2-1 × 5-1 × 17
Monzo	[-1 0 -1 0 0 0 1⟩
Size in cents	918.6417¢
Name	diatismic major sixth
Color name	17og7, sogu 7th
FJS name	[math]\displaystyle{ \text{d7}^{17}_{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	7.40939
Weil norm (log2 max(n, d))	8.17493
Wilson norm (sopfr(nd))	24
	https://en.xen.wiki/w/File:Jid_17_10_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

Latest revision as of 13:14, 3 November 2025

In 17-limit just Intonation, 17/10 is the diatismic major sixth, measuring about 918.6¢. It exceeds the Pythagorean major sixth (27/16) by a diatisma (136/135), hence the name. It is the mediant of 5/3 and 12/7. Its octave complement is 20/17, the diatismic minor third.

Edo approximations for 17/10 (918.64 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
4	3\4	900.00	-18.64	-6.21
13	10\13	923.08	+4.44	+4.80
17	13\17	917.65	-0.99	-1.41
21	16\21	914.29	-4.36	-7.62
26	20\26	923.08	+4.44	+9.61
30	23\30	920.00	+1.36	+3.40
34	26\34	917.65	-0.99	-2.82
38	29\38	915.79	-2.85	-9.03
43	33\43	920.93	+2.29	+8.20
47	36\47	919.15	+0.51	+1.99
51	39\51	917.65	-0.99	-4.23
60	46\60	920.00	+1.36	+6.79
64	49\64	918.75	+0.11	+0.58
68	52\68	917.65	-0.99	-5.64
77	59\77	919.48	+0.84	+5.38

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = diatismic major sixth
-| Ratio = 17/10
-| Monzo = -1 0 -1 0 0 0 1
-| Cents = 918.64170
-| Name = septendecimal major sixth
 | Sound = jid_17_10_pluck_adu_dr220.mp3
 | Color name = 17og7, sogu 7th
 }}
-In [[17-limit]] [[just Intonation]], '''17/10''' is the '''septendecimal major sixth''', measuring about 918.6¢. It is the [[mediant]] between [[5/3]] and [[12/7]]. Its [[octave complement]] is [[20/17]], the "septendecimal minor third".
+In [[17-limit]] [[just Intonation]], '''17/10''' is the '''diatismic major sixth''', measuring about 918.6¢. It exceeds the [[27/16|Pythagorean major sixth (27/16)]] by a [[136/135|diatisma (136/135)]], hence the name. It is the [[mediant]] of [[5/3]] and [[12/7]]. Its [[octave complement]] is [[20/17]], the diatismic minor third.
+== Approximation ==
+{{Interval edo approximation|17/10}}
 == See also ==
@@ Line 18: / Line 16: @@
 * [[Gallery of just intervals]]
-[[Category:17-limit]]
+[[Category:Sixth]]
-[[Category:Interval ratio]]
-[[Category:Just interval]]
 [[Category:Major sixth]]
-[[Category:Sixth]]
+[[Category:Diatismic]]
-[[Category:Pages with internal sound examples]]