19ed5

← 18ed5

19ed5

20ed5 →

Prime factorization	19 (prime)
Step size	146.648¢
Octave	8\19ed5 (1173.18¢)
Twelfth	13\19ed5 (1906.43¢) (convergent)
Consistency limit	7
Distinct consistency limit	3

Division of the 5th harmonic into 19 equal parts (19ED5) is related to the Bohlen-Pierce scale, but with the 5/1 rather than the 3/1 being just. The step size is about 146.6481 cents, corresponding to 8.1829 EDO. It provides 5, 7, 13, and 15-odd-limit minimax generator for the bohpier temperament.

Intervals

degree	cents value	corresponding JI intervals	comments
0	0.0000	exact 1/1
1	146.6481	49/45
2	293.2962	13/11
3	439.9443	9/7
4	586.5924	7/5
5	733.2405	49/32
6	879.8885	5/3
7	1026.5366	9/5
8	1173.1847	63/32
9	1319.8328	15/7
10	1466.4809	7/3
11	1613.1290	28/11
12	1759.7771	11/4
13	1906.4252	3/1
14	2053.0733	49/15
15	2199.7214	32/9
16	2346.3694	35/9
17	2493.0175	21/5
18	2639.6656	32/7
19	2786.3137	exact 5/1	just major third plus two octaves

Harmonics

Approximation of harmonics in 19ed5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-26.8	+4.5	-53.6	+0.0	-22.3	+4.1	+66.2	+8.9	-26.8	-45.2	-49.2
	Relative (%)	-18.3	+3.0	-36.6	+0.0	-15.2	+2.8	+45.1	+6.1	-18.3	-30.8	-33.5
Steps (reduced)		8 (8)	13 (13)	16 (16)	19 (0)	21 (2)	23 (4)	25 (6)	26 (7)	27 (8)	28 (9)	29 (10)

Approximation of harmonics in 19ed5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-41.1	-22.7	+4.5	+39.4	-65.6	-17.9	+35.2	-53.6	+8.6	-72.0	-2.3
	Relative (%)	-28.0	-15.5	+3.0	+26.9	-44.7	-12.2	+24.0	-36.6	+5.8	-49.1	-1.6
Steps (reduced)		30 (11)	31 (12)	32 (13)	33 (14)	33 (14)	34 (15)	35 (16)	35 (16)	36 (17)	36 (17)	37 (18)

See also

• 13ED3: relative ED3 (Bohlen-Pierce scale)
• 23ED7: relative ED7