Dubhe

Dubhe is a temperament in the 3.5.7.17 subgroup generated by a sharp ~17/15 (or equivalently a flat ~45/17). As a weak extension of BPS, it tempers out the sensamagic comma, 245/243, while splitting the BPS generator of ~9/7 in two (by tempering out 2025/2023) so that a stack of two generators represents 9/7, and a stack of four generators represents 5/3 in addition to 81/49, which generates MOS scales of 8L 1s and 9L 8s against the tritave. The "canonical" tuning for the generator is 3\26edt, representing the double Bohlen-Pierce scale, but a range of other tunings are valid, including 2\17edt and 5\43edt.

For technical data, see No-twos subgroup temperaments#Dubhe.

Interval chains

In the below, tritave-reduced harmonics below 243 are indicated in bold. All ratios are considered to be in the 287-throdd limit.

Dubhe

#	Cents*	Approximate Ratios
		3.5.7.17 subgroup
-12	1160.5	49/25, 243/125
-11	1380.8	189/85
-10	1601.1	63/25
-9	1821.4	49/17, 243/85, 357/125
-8	139.7	27/25, 49/45
-7	360.0	21/17, 153/125
-6	580.3	7/5, 243/175
-5	800.6	27/17, 119/75, 245/153
-4	1020.8	9/5, 49/27
-3	1241.1	35/17, 51/25, 243/119
-2	1461.4	7/3, 81/35
-1	1681.7	45/17, 119/45, 459/175
0	0.0	1/1, 245/243
1	220.3	17/15, 135/119, 175/153
2	440.6	9/7, 35/27
3	660.9	25/17, 51/35, 119/81
4	881.1	5/3, 81/49
5	1101.4	17/9, 225/119, 459/245
6	1321.7	15/7, 175/81
7	1542.0	17/7, 125/51
8	1762.2	25/9, 135/49
9	80.5	51/49, 85/81, 125/119
10	300.8	25/21
11	521.1	85/63
12	741.4	75/49, 125/81
13	961.7	85/49
14	1181.9	125/63

Tuning spectrum

Edt Generator	Eigenmonzo (Unchanged-interval)	Generator (¢)	Comments
	17/15	216.687	Untempered tuning
4\35		217.366
	7/3	217.542	1/2-fidesma
7\61		218.257
10\87		218.616
	49/45	219.316
3\26		219.456	Double Bohlen-Pierce
	7/5	219.907
		220.170	DR 3:5:7
11\95		220.226
	25/21	220.380
8\69		220.518
	5/3	221.090
5\43		221.158
7\60		221.895
	175/81	222.272
9\77		222.306
2\17		223.759
	35/27	224.637