106ed6

← 105ed6

106ed6

107ed6 →

Prime factorization	2 × 53
Step size	29.2637 ¢
Octave	41\106ed6 (1199.81 ¢) (convergent)
Twelfth	65\106ed6 (1902.14 ¢) (convergent)
Consistency limit	16
Distinct consistency limit	10

106 equal divisions of the 6th harmonic (abbreviated 106ed6) is a nonoctave tuning system that divides the interval of 6/1 into 106 equal parts of about 29.3 ¢ each. Each step represents a frequency ratio of 6^1/106, or the 106th root of 6.

Theory

106ed6 is very nearly identical to 41edo, but with the 6/1 rather than the 2/1 being just. The octave is about 0.19 cents compressed. Like 41edo, 106ed6 is consistent to the 16-integer-limit.

Harmonics

Approximation of harmonics in 106ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-0.2	+0.2	-0.4	-6.3	+0.0	-3.5	-0.6	+0.4	-6.4	+4.1	-0.2
	Relative (%)	-0.6	+0.6	-1.3	-21.4	+0.0	-12.0	-1.9	+1.3	-22.0	+14.1	-0.6
Steps (reduced)		41 (41)	65 (65)	82 (82)	95 (95)	106 (0)	115 (9)	123 (17)	130 (24)	136 (30)	142 (36)	147 (41)

Approximation of harmonics in 106ed6 (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+7.6	-3.7	-6.1	-0.7	+11.4	+0.2	-5.6	-6.6	-3.3	+3.9	-14.5	-0.4
	Relative (%)	+25.8	-12.6	-20.8	-2.6	+38.8	+0.6	-19.2	-22.7	-11.3	+13.5	-49.5	-1.3
Steps (reduced)		152 (46)	156 (50)	160 (54)	164 (58)	168 (62)	171 (65)	174 (68)	177 (71)	180 (74)	183 (77)	185 (79)	188 (82)

See also

• 24edf – relative edf
• 41edo – relative edo
• 65edt – relative edt
• 95ed5 – relative ed5