17ed4: Difference between revisions

Revision as of 22:00, 20 March 2023

Prime factorization

17 (prime)

Step size

141.179 ¢

Octave

8\17ed40001/10000 (1129.43 ¢)
(semiconvergent)

Twelfth

13\17ed40001/10000 (1835.33 ¢)

Consistency limit

3

Distinct consistency limit

3

17ed4 is the equal division of the double octave into 17 parts of 141.18 cents each, corresponding to 8.5edo or every second step of 17edo.

TBA

Approximation of harmonics in 51ed64
Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+70.6	-66.7	-0.0	+37.2	+3.9	+19.4	+70.6	+7.9	-33.4	-57.2	-66.7
Error	Relative (%)	+50.0	-47.2	-0.0	+26.4	+2.8	+13.7	+50.0	+5.6	-23.6	-40.5	-47.2
Steps (reduced)		9 (9)	13 (13)	17 (17)	20 (20)	22 (22)	24 (24)	26 (26)	27 (27)	28 (28)	29 (29)	30 (30)

#	Cents	Approximate ratios	17edo notation
0	0.00	1/1	C
1	141.18	13/12, 12/11, 14/13, 25/23	C#
2	282.36	13/11, 7/6	Eb
3	423.54	32/25, 9/7, 14/11, 33/26, 23/18	E
4	564.72	11/8, 18/13, 32/23	^F
5	705.90	3/2, 32/21	G
6	847.08	13/8, 18/11, 23/14	G#, vA
7	988.26	16/9, 7/4, 25/14, 44/25, 23/13	Bb
8	1129.44	25/13, 48/25, 27/14, 64/33, 23/12	B
9	1270.62	15/7	^C
10	1411.80	16/7	D
11	1552.98	12/5, 5/2	vE
12	1694.16	8/3	F
13	1835.34	3/1	F#
14	1976.52	16/5	^G, Ab
15	2117.70	10/3	A
16	2258.88	11/3	vB
17	2400.00	4/1	C

@@ Line 1: / Line 1: @@
-{{Infobox ET|51ed64}}
+{{Infobox ET|17ed40001/10000}}
-<!--Using ED64 as temporary solution until Infobox ET starts working with ED4s-->
+<!--Using ED40001/10000 as temporary solution until Infobox ET starts working with ED4s-->
 '''17ed4''' is the [[Ed4|equal division of the double octave]] into 17 parts of 141.18 [[cent|cents]] each, corresponding to 8.5edo or every second step of [[17edo]].
 ==Theory==