17edf

← 16edf

17edf

18edf →

Prime factorization	17 (prime)
Step size	41.2915¢
Octave	29\17edf (1197.45¢) (semiconvergent)
Twelfth	46\17edf (1899.41¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	6

17EDF is the Division of the just perfect fifth into 17 equal parts. It is related to 29 edo, but with the 3/2 rather than the 2/1 being just. The octave is about 2.5474 cents compressed and the step size is about 41.2915 cents. Unlike 29edo, it is only consistent up to the 6-integer-limit, with discrepancy for the 7th harmonic.

Lookalikes: 29edo, 46edt

Intervals

Degree	Cents	Approx. ratios of the 15-odd-limit
0	0.0000	1/1
1	41.2915	25/24~33/32~56/55~81/80
2	82.5829	21/20
3	123.8744	16/15, 15/14, 14/13, 13/12
4	165.1659	12/11, 11/10
5	206.4574	9/8
6	248.7488	8/7, 7/6, 15/13
7·	289.0403	13/11
8	330.3318	6/5, 11/9
9	371.6232	5/4, 16/13
10	412.9147	14/11
11	455.2062	9/7, 13/10
12·	495.4976	4/3
13	536.7891	11/8, 15/11
14	578.0806	7/5, 18/13
15	619.3721	10/7, 13/9
16	660.6635	16/11, 22/15
17·	701.9550	3/2
18	743.2465	14/9, 20/13
19	784.5379	11/7
20	825.8294	8/5, 13/8
21	867.1209	5/3, 18/11
22·	908.4124	22/13
23	949.7038	7/4, 12/7, 26/15
24	990.9952	16/9
25	1032.3287	11/6, 20/11
26	1073.5782	15/8, 28/15, 13/7, 24/13
27	1114.8697	40/21
28	1156.1612	48/25~64/33~55/28 ~160/81
29	1197.4526	2/1
30	1238.7441	25/12~33/16~112/55~81/40
31	1280.0356	21/10
32	1321.3271	32/15, 15/7, 28/13, 13/6
33	1362.6185	24/11, 11/5
34	1403.9100	9/4

Scale tree

If 4\7 (four degrees of 7EDO) is at one extreme and 3\5 (three degrees of 5EDO) is at the other, all other possible 5L 2s scales exist in a continuum between them. You can chop this continuum up by taking "freshman sums" of the two edges - adding together the numerators, then adding together the denominators (i.e. adding them together as if you would be adding the complex numbers analogous real and imaginary parts). Thus, between 4\7 and 3\5 you have (4+3)\(7+5) = 7\12, seven degrees of 12EDO.

If we carry this freshman-summing out a little further, new, larger EDOs pop up in our continuum.

Generator range: 40.33613 cents (4\7/17 = 4\119) to 42.35294 cents (3\5/17 = 3\85)

Fifth							Cents	Comments
4\7							40.3361
						27\47	40.5507
					23\40		40.5882
						42\73	40.6124
				19\33			40.6417
						53\92	40.6650
					34\59		40.6780
						49\85	40.6920
			15\26				40.7240
						56\97	40.7520
					41\71		40.7622
						67\116	40.7708
				26\45			40.7843	Flattone is in this region
						63\109	40.7897
					37\64		40.8088
						48\83	40.8221
		11\19					40.8669
						51\88	40.90
					40\69		40.9207
						69\119	40.9293
				29\50			40.9412
						76\131	40.95195	Golden meantone (696.2145¢)
					47\81		40.9586
						65\112	40.6994
			18\31				40.9867	Meantone is in this region
						61\105	41.0084
					43\74		41.1075
						68\117	41.0256
				25\43			41.0397
						57\98	41.0564
					32\55		41.0695
						39\67	41.0887
	7\12						41.1765
						38\65	41.2670
					31\53		41.2875	The fifth closest to a just 3/2 for EDOs less than 200
						55\94	41.3016	Garibaldi / Cassandra
				24\41			41.3199
						65\111	41.33545
					41\70		41.3445
						58\99	41.3547
			17\29				41.3793
						61\104	41.4027
					44\75		41.4118
						71\121	41.4195	Golden neogothic (704.0956¢)
				27\46			41.4322	Neogothic is in this region
						64\109	41.4463
					37\63		41.4566
						47\80	41.4706
		10\17					41.5225
						43\73	41.5764
					33\56		41.5966
						56\95	41.6099
				23\39			41.6290
						59\100	41.6471
					36\61		41.6586
						49\83	41.6726
			13\22				41.7112	Archy is in this region
						42\71	41.7564	The generator closest to a just 14/11 for EDOs less than 3400
					29\49		41.7768
						45\76	41.7957
				16\27			41.8301
						35\59	41.8744
					19\32		41.9118
						22\37	41.9714
3\5							42.3529

Tunings above 7\12 on this chart are called "negative tunings" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 11\19) and 1/4-comma (close to 18\31). As these tunings approach 4\7, the majors become flatter and the minors become sharper.