13edt

13EDT divides the tritave (3/1) into 13 equal parts of 146.304 cents each, corresponding to 8.202EDO. It is the equal-tempered version of the well-known Bohlen-Pierce scale. In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as bohpier temperament. It is less impressive in higher p-limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 (26EDT, 39EDT and 52EDT) come to the fore.

Below is a plot of the no-twos Z-function, in terms of which 13EDT is the fourth no-twos zeta peak EDT.

Theory

Approximation of prime intervals in 13-EDT

Prime interval		2	3	5	7	11	13	17	19
Error	absolute (¢)	-29.6	0.0	-6.5	-3.8	-54.8	-51.4	+69.4	+23.1
	relative (%)	-20	0	-4	-3	-37	-35	+47	+16
Patent val		8	13	19	23	28	30	34	35
Fifthspan		-1	0	-4	+2	+3	+6	-1	-6

• Intervals of BP
• Relationship between Bohlen-Pierce and octave-ful temperaments

Intervals

See also: Bohlen-p_et

Steps	Cents	Hekts	BP nonatonic degree	Corresponding JI intervals	Comments	Generator for...
1	146.3	100	A1/m2	27/25~49/45
2	292.6	200	M2/d3	25/21		Sirius
3	438.9	300	A2/P3/d4	9/7		Linear BP
4	585.2	400	A3/m4/d5	7/5		Canopus
5	731.5	500	M4/m5	75/49	false 3/2	false Father
6	877.8	600	A4/M5	5/3		Arcturus
7	1024.1	700	A5/m6/d7	9/5		Arcturus
8	1170.4	800	M6/m7	49/25	false 2/1	false Father
9	1316.7	900	A6/M7/d8	15/7		Canopus
10	1463.0	1000	P8/d9	7/3		Linear BP
11	1609.3	1100	A8/m9	63/25		Sirius
12	1755.7	1200	M9/d10	25/9~135/49
13	1902.0	1300	A9/P10	3/1	Tritave

JI approximation

Regular temperament properties

Main article: Bohlen-Pierce § Regular temperament properties

See also

• Catalog of 3.5.7 subgroup rank two temperaments
• 19ED5: relative ED5
• 23ED7: relative ED7