Subgroup monzos and vals: Difference between revisions

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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.

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			{{Breadcrumb\|Monzo}}

	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 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.