Tetrahanson

The tetrahanson temperament is a nonoctave kleismic temperament, tempering out the kleisma in the 4.3.5 subgroup and repeating at the double octave 4/1. It is generated by 5/3 and, like in normal hanson temperament, 6 of them make a 4/3. Tetrahanson does not contain any 5-limit major or minor triads, but it does have different voicings of them (3:4:5 and 12:15:20), which, to a 12edo-accustomed listener, can make it sound like the root is the real root and the perfect fifth above it at the same time.

For technical information see Subgroup temperaments#Tetrahanson.

Interval chain

Generators	Cents (CTE)	Approximate ratios
-7	1019.413	9/5
-6	1902.354	3/1
-5	385.295	5/4
-4	1268.236	25/12
-3	2151.177	125/36
-2	634.118	36/25
-1	1517.059	12/5
0	0.000	1/1
1	882.941	5/3
2	1765.882	25/9
3	248.823	144/125
4	1131.764	48/25
5	2014.705	16/5
6	497.646	4/3
7	1380.587	20/9

Tetrahanson on tritave

In tritave-repeating tetrahanson (3.4.5 subgroup), 36/25 actually represents 1\3edt, which makes the 3rd-tritave period.

b39 & b15

	3.4.5	3.5.11	3.5.13
CWE	883.071	879.416	883.808
Badness	0.155	2.708	0.069
	3.4.5.11	3.4.5.13	3.5.11.13
CWE	880.672	882.854	879.352
Badness	0.384	0.066	0.44

# (mingen)	Period 0		Period 1		Period 2
	Cents*	Approximate Ratios	Cents*	Approximate Ratios	Cents*	Approximate Ratios
-1	1652.9	13/5	384.9	5/4	1018.9	9/5
0	0.0	1/1	634.0	36/25,13/9	1268.0	25/12,27/13
1	249.1	125/108,15/13	883.1	5/3	1517.1	12/5
2	498.2	4/3	1132.2	48/25,25/13	1766.1	25/9
3	747.3	20/13	1381.2	20/9,11/5	113.3	16/15,55/52
4	996.3	16/9,44/25	1630.3	64/25,33/13	362.4	100/81,16/13,11/9