Domain basis: Difference between revisions

Line 59:

= Interval bases for temperaments =

In the context of a [[regular temperament]], an interval basis serves as a minimal representation of all the intervals this temperament can temper (some of which it completely [[tempers out]]). The full set of these possible-to-temper intervals is called the '''interval subspace'''; it is a ''sub''space~~, not a space, because~~ the ''full'' interval space ~~would include~~ all conceivable intervals, even those outside the temperament.

In the context of a [[regular temperament]], an interval basis serves as a minimal representation of all the intervals this temperament can temper (some of which it completely [[tempers out]]). The full set of these possible-to-temper intervals is called the '''interval subspace'''; it is a ''sub''space with respect to the ''full'' interval space which includes all conceivable intervals, even those outside the temperament.

So, for instance, a temperament in the 2.3.5 interval subspace cannot temper the intervals 7/6 or 11/8, because there is no way to represent either of those intervals using only the primes 2, 3, and 5. It could, however, temper 6/5, 5/4, 10/9, or 9/8, etc., because those intervals ''can'' be represented using only those three primes.

@@ Line 59: / Line 59: @@
 = Interval bases for temperaments =
-In the context of a [[regular temperament]], an interval basis serves as a minimal representation of all the intervals this temperament can temper (some of which it completely [[tempers out]]). The full set of these possible-to-temper intervals is called the '''interval subspace'''; it is a ''sub''space, not a space, because the ''full'' interval space would include all conceivable intervals, even those outside the temperament.
+In the context of a [[regular temperament]], an interval basis serves as a minimal representation of all the intervals this temperament can temper (some of which it completely [[tempers out]]). The full set of these possible-to-temper intervals is called the '''interval subspace'''; it is a ''sub''space with respect to the ''full'' interval space which includes all conceivable intervals, even those outside the temperament.
 So, for instance, a temperament in the 2.3.5 interval subspace cannot temper the intervals 7/6 or 11/8, because there is no way to represent either of those intervals using only the primes 2, 3, and 5. It could, however, temper 6/5, 5/4, 10/9, or 9/8, etc., because those intervals ''can'' be represented using only those three primes.