Subgroup monzos and vals: Difference between revisions

Line 1:

A '''subgroup monzo''' is a monzo whose elements refer to powers of ~~arbitrary~~ "basis elements" in JI (specified rationals such as 2, 3, 35, and 13/11 which are combined to form the set of intervals in a [[subgroup]]), rather than strictly to ordered primes. For cases where the basis elements are all prime numbers, a subgroup monzo can be seen as "abbreviating" entries from a standard monzo: for example, the monzo [0 0 -1 0 0 1⟩ (13/5) may be abbreviated to the subgroup monzo 5.13 [-1 1⟩. However, subgroup monzos can refer to intervals in subgroups whose basis elements are not primes, for example 2.3.13/5 [1 -1 1⟩ for 26/15. In that case, conversion to and from a subgroup monzo is a little more complicated, and is covered in the next section.

A '''subgroup monzo''' is a monzo whose elements refer to powers of the "basis elements" of a JI subgroup (specified rationals such as 2, 3, 35, and 13/11 which are combined to form the set of intervals in a [[subgroup]]), rather than strictly to ordered primes. For cases where the basis elements are all prime numbers, a subgroup monzo can be seen as "abbreviating" entries from a standard monzo: for example, the monzo [0 0 -1 0 0 1⟩ (13/5) may be abbreviated to the subgroup monzo 5.13 [-1 1⟩. However, subgroup monzos can refer to intervals in subgroups whose basis elements are not primes, for example 2.3.13/5 [1 -1 1⟩ for 26/15. In that case, conversion to and from a subgroup monzo is a little more complicated, and is covered in the next section.

A '''subgroup val''' is like a standard val, but the entries are the mappings of subgroup basis elements rather than strictly of primes (and can be derived from a standard val by applying the val to the basis intervals). Since converting to a subgroup val loses information, there is no clear way to convert a subgroup val back to a standard val.

@@ Line 1: / Line 1: @@
 {{Breadcrumb|Monzo|}}{{Breadcrumb|Val|}}
-A '''subgroup monzo''' is a monzo whose elements refer to powers of arbitrary "basis elements" in JI (specified rationals such as 2, 3, 35, and 13/11 which are combined to form the set of intervals in a [[subgroup]]), rather than strictly to ordered primes. For cases where the basis elements are all prime numbers, a subgroup monzo can be seen as "abbreviating" entries from a standard monzo: for example, the monzo [0 0 -1 0 0 1⟩ (13/5) may be abbreviated to the subgroup monzo 5.13 [-1 1⟩. However, subgroup monzos can refer to intervals in subgroups whose basis elements are not primes, for example 2.3.13/5 [1 -1 1⟩ for 26/15. In that case, conversion to and from a subgroup monzo is a little more complicated, and is covered in the next section.
+A '''subgroup monzo''' is a monzo whose elements refer to powers of the "basis elements" of a JI subgroup (specified rationals such as 2, 3, 35, and 13/11 which are combined to form the set of intervals in a [[subgroup]]), rather than strictly to ordered primes. For cases where the basis elements are all prime numbers, a subgroup monzo can be seen as "abbreviating" entries from a standard monzo: for example, the monzo [0 0 -1 0 0 1⟩ (13/5) may be abbreviated to the subgroup monzo 5.13 [-1 1⟩. However, subgroup monzos can refer to intervals in subgroups whose basis elements are not primes, for example 2.3.13/5 [1 -1 1⟩ for 26/15. In that case, conversion to and from a subgroup monzo is a little more complicated, and is covered in the next section.
 A '''subgroup val''' is like a standard val, but the entries are the mappings of subgroup basis elements rather than strictly of primes (and can be derived from a standard val by applying the val to the basis intervals). Since converting to a subgroup val loses information, there is no clear way to convert a subgroup val back to a standard val.