Equal temperament names

Here are my examples for ambiguous equal temperaments following
Herman's naming scheme. The "p" is for "prime" or "patent" and other
letters go through the alphabet and primes starting with "a" for 3,
"b" for 5, and so on.

I produced these by hand. There may be mistakes. The first of each
pair should have the lowest badness but I'm not sure I was strict
about that. What I did is search for equal temperaments on my
website, and from the first however-many-it-gives (31?) look for
duplicates. The "n-cent badness" refers to Cangwu badness measured in
cents the way my website does it. It's quite likely there are
non-patent vals without duplicates that therefore didn't get flagged
as ambiguous. It should be easy to search automatically for such
cases but I didn't.

Some interesting points to note: 46 never comes out as ambiguous
although it's inconsistent from the 9(?)-limit. 34 is famously
inconsistent but only duplicated in the 7-limit. 24 as well -- never
on this list and it does sometimes come up in the top-whatever lists.

Use a monospaced font for optimal satisfaction.

5-limit 10-cent badness

2p = <2, 3, 5]
2b = <2, 3, 4]

5p = <5, 8, 12]
5b = <5, 8, 11]

5-limit 5-cent badness

17b = <17, 27, 40]
17p = <17, 27, 39]

7-limit 10-cent badness

7c = <7, 11, 16, 19]
7p = <7, 11, 16, 20]

12p = <12, 19, 28, 34]
12c = <12, 19, 28, 33]

2bc = <2, 3, 4, 5]
2p = <2, 3, 5, 6]

3c = <3, 5, 7, 9]
3p = <3, 5, 7, 8]

5p = <5, 8, 12, 14]
5b = <5, 8, 11, 14]

17b = <17, 27, 40, 48]
17p = <17, 27, 39, 48]

7-limit 5-cent badness

7-pair again

34c = <34, 54, 79, 96]
34p = <34, 54, 79, 95]

11-limit 10-cent badness

10p = <10, 16, 23, 28, 35]
10d = <10, 16, 23, 28, 34]

3cd = <3, 5, 7, 9, 11]
3p = <3, 5, 7, 8, 10]

4d = <4, 6, 9, 11, 13]
4p = <4, 6, 9, 11, 14]

5p = <5, 8, 12, 14, 17]
5d = <5, 8, 12, 14, 18]

12p = <12, 19, 28, 34, 42]
12d = <12, 19, 28, 34, 41]

2p = <2, 3, 5, 6, 7]
2bcd = <2, 3, 4, 5, 6]

11-limit, 5-cent badness

12 pair again
5 pair again

7c = <7, 11, 16, 19, 24]
7p = <7, 11, 16, 20, 24]

19p = <19, 30, 44, 53, 66]
19d = <19, 30, 44, 53, 65]

13-limit, 10-cent badness

12e = <12, 19, 28, 34, 42, 45]
12p = <12, 19, 28, 34, 42, 44]
12d = <12, 19, 28, 34, 41, 44]

15p = <15, 24, 35, 42, 52, 56]
15e = <15, 24, 35, 42, 52, 55]

10p = <10, 16, 23, 28, 35, 37]
10d = <10, 16, 23, 28, 34, 37]

7p = <7, 11, 16, 20, 24, 26]
7c = <7, 11, 16, 19, 24, 26]
7ce = <7, 11, 16, 19, 24, 25]

19p = <19, 30, 44, 53, 66, 70]
19d = <19, 30, 44, 53, 65, 70]

14e = <14, 22, 32, 39, 48, 51]
14p = <14, 22, 32, 39, 48, 52]

5d = <5, 8, 12, 14, 18, 19]
5p = <5, 8, 12, 14, 17, 19]

22p = <22, 35, 51, 62, 76, 81]
22e = <22, 35, 51, 62, 76, 82]

3cde = <3, 5, 7, 9, 11, 12]
3cd = <3, 5, 7, 9, 11, 11]

13-limit 5-cent badness

31p = <31, 49, 72, 87, 107, 115]
31e = <31, 49, 72, 87, 107, 114]

12e = <12, 19, 28, 34, 42, 45]
12p = <12, 19, 28, 34, 42, 44]

19p = <19, 30, 44, 53, 66, 70]
19d = <19, 30, 44, 53, 65, 70]

10p = <10, 16, 23, 28, 35, 37]
10d = <10, 16, 23, 28, 34, 37]

22p = <22, 35, 51, 62, 76, 81]
22e = <22, 35, 51, 62, 76, 82]

7p = <7, 11, 16, 20, 24, 26]
7c = <7, 11, 16, 19, 24, 26]

13-limit 2-cent badness

31 pair again
19 pair again
22 pair again

13-limit 1-cent badness

19 pair again

17-limit 5-cent

22p = <22, 35, 51, 62, 76, 81, 90]
22e = <22, 35, 51, 62, 76, 82, 90]

19d = <19, 30, 44, 53, 65, 70, 77]
19f = <19, 30, 44, 53, 66, 70, 77]
19p = <19, 30, 44, 53, 66, 70, 78]

12e = <12, 19, 28, 34, 42, 45, 49]
12p = <12, 19, 28, 34, 42, 44, 49]

15f = <15, 24, 35, 42, 52, 56, 62]
15p = <15, 24, 35, 42, 52, 56, 61]

9p = <9, 14, 21, 25, 31, 33, 37]
9f = <9, 14, 21, 25, 31, 33, 36]

17-limit 2-cent

22 pair again

17-limit 1-cent

118p = <118, 187, 274, 331, 408, 437, 482]
118e = <118, 187, 274, 331, 408, 436, 482]

19-limit 5-cent

9p = <9, 14, 21, 25, 31, 33, 37, 38]
9f = <9, 14, 21, 25, 31, 33, 36, 38]

15f = <15, 24, 35, 42, 52, 56, 62, 64]
15p = <15, 24, 35, 42, 52, 56, 61, 64]

22eg = <22, 35, 51, 62, 76, 82, 90, 94]
22p = <22, 35, 51, 62, 76, 81, 90, 93]
22g = <22, 35, 51, 62, 76, 81, 90, 94]

10g = <10, 16, 23, 28, 35, 37, 41, 43]
10p = <10, 16, 23, 28, 35, 37, 41, 42]

8cg = <8, 13, 19, 23, 28, 30, 33, 35]
8c = <8, 13, 19, 23, 28, 30, 33, 34]

19-limit 2-cent

72p = <72, 114, 167, 202, 249, 266, 294, 306]
72g = <72, 114, 167, 202, 249, 266, 294, 305]

41p = <41, 65, 95, 115, 142, 152, 168, 174]
41f = <41, 65, 95, 115, 142, 152, 167, 174]

53p = <53, 84, 123, 149, 183, 196, 217, 225]
53f = <53, 84, 123, 149, 183, 196, 216, 225]

19-limit 1-cent

72 pair again

Graham