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For any equal temperament, there are technically an unlimited number of different abstract regular temperaments that it "supports" in the sense of tempering out all the same commas, thus allowing music in the non-equal temperament to be faithfully and mechanically played in the equal temperament.

However, some of these non-equal regular temperaments become exactly the same as each other when tuned to the equal temperament. For example, in 12edo, pajara and injera become the same, even though in anything other than 12 they are distinct temperaments.

Two temperaments are called "edo-distinct" if they remain distinct even when tuned to the same equal temperament. For rank-2, it turns out that the number of edo-distinct rank-2 temperaments in N-edo is floor(N/2); that is, N/2 if N is even and (N-1)/2 if N is odd.

Rank-2 lists

12
12f
15

16

17
17c
19

22

24

26

27
27e
29

31

34
34d
41

43

46

50

53

58

72


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17