1ed17/16

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1ed17/16

2ed17/16 →

Prime factorization	n/a
Step size	104.955 ¢
Octave	11\1ed17/16 (1154.51 ¢)
Twelfth	18\1ed17/16 (1889.2 ¢)
Consistency limit	3
Distinct consistency limit	3

1 equal division of 17/16 (abbreviated 1ed17/16) is a nonoctave tuning system that uses equal steps of 17/16, or about 105 ¢.

Harmonics

Approximation of harmonics in 1ed17/16

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-45.5	-12.8	+14.0	+47.5	+46.7	-10.3	-31.5	-25.5	+2.0	+46.9	+1.2
	Relative (%)	-43.3	-12.2	+13.3	+45.2	+44.5	-9.8	-30.0	-24.3	+1.9	+44.7	+1.2
Step		11	18	23	27	30	32	34	36	38	40	41

Approximation of harmonics in 1ed17/16 (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-32.4	+49.2	+34.7	+27.9	+27.9	+33.9	+45.3	-43.5	-23.0	+1.4	+29.4
	Relative (%)	-30.9	+46.9	+33.1	+26.6	+26.6	+32.3	+43.2	-41.4	-21.9	+1.3	+28.0
Step		42	44	45	46	47	48	49	49	50	51	52

Note that this tuning is fairly close to 18edt, although by patent val mapping 18edt maps ~17/16 inconsistently to 2\18edt instead of 1\18edt, while 1ed17/16 maps its own equave even more inconsistently, to 3\1ed17/16.

Intervals

Many intervals in 1ed17/16 are mapped inconsistently (including 17/16 itself, as noted above). The table of intervals by direct approximation differs considerably from the table of intervals by patent val mapping.

By direct approximation (even if inconsistent)

Steps	Cents	Approximate ratios
0	0.0	1/1
1	105.0	16/15, 17/16, 18/17
2	209.9	9/8, 26/23, 17/15
3	314.9	6/5
4	419.8	14/11, 23/18
5	524.8	19/14, 23/17, 27/20
6	629.7	13/9, 23/16
7	734.7	23/15, 26/17, 32/21
8	839.6	13/8, 21/13, 34/21
9	945.6	19/11, 26/15
10	1049.6	11/6
11	1154.5	35/18, 39/20
12	1259.5	35/17, 33/16, 27/13

By patent val mapping

Steps	Cents	Approximate ratios
0	0	1/1
1	105	14/13, 21/20, 22/21, 23/22
2	209.9	10/9, 17/15, 19/17
3	314.9	23/19
4	419.8	9/7, 19/15, 22/17
5	524.8	15/11, 23/17
6	629.7	10/7, 13/9
7	734.7	17/11, 20/13, 23/15
8	839.6	21/13
9	944.6	17/10, 19/11
10	1049.6	13/7
11	1154.5
12	1259.5	21/10, 23/11

(The above table is implemented as {{Interval table|12ed582622237229761/281474976710656}}, the value used being (17/16)¹².)

Instruments

A Lumatone mapping for 1ed17/16 is available.

Music

Bryan Deister

• equal step 17/16 (2025)

See also

• 18edt — relative edt