Lists of edo-distinct temperaments: Difference between revisions

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For any [[~~Equal|~~equal]] ~~temperament~~, there are technically an unlimited number of different [[~~Abstract_regular_temperament|~~abstract regular temperaments]] that it "[[support]]s" 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.

For any [[equal temperament]], there are technically an unlimited number of different [[abstract regular temperaments]] that it "[[support]]s" 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|~~12edo]], [[~~pajara|~~pajara]] and [[~~Injera|~~injera]] become the same, even though in anything other than 12 they are distinct temperaments.

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.

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=~~

== Rank-2 lists ==

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[[Category:Lists]]

[[Category:Lists of edo-distinct temperaments| ]]

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-For any [[Equal|equal]] temperament, there are technically an unlimited number of different [[Abstract_regular_temperament|abstract regular temperaments]] that it "[[support]]s" 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.
+For any [[equal temperament]], there are technically an unlimited number of different [[abstract regular temperaments]] that it "[[support]]s" 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|12edo]], [[pajara|pajara]] and [[Injera|injera]] become the same, even though in anything other than 12 they are distinct temperaments.
+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.
+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=
+== Rank-2 lists ==
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-==No fives==
+=== No-fives ===
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-[[Category:Lists]]
+[[Category:Lists of edo-distinct temperaments| ]] <!-- main article -->