Subgroup monzos and vals: Difference between revisions

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~~{{Breadcrumb|Monzo|}}{{Breadcrumb|Val|}}~~

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 [[prime interval|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 {{monzo| 0 0 -1 0 0 1 }} (13/5) may be abbreviated to the subgroup monzo 5.13 {{monzo| -1 1 }}. However, subgroup monzos can refer to intervals in subgroups whose basis elements are not primes, for example 2.3.13/5 {{monzo| 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.

Revision as of 10:28, 17 May 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 24,098 edits - abuse of quotation marks. Adopt template: monzo. Unhighlight elementary methods. It quickly gets complex when the numbers are large. Move it to the bottom. Also move the step-by-step tutorial to a collapsed box ← Older edit		Latest revision as of 10:28, 17 May 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 24,098 edits m - breadcrumbs (this isn't a subpage).
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	~~{{Breadcrumb\|Monzo\|}}{{Breadcrumb\|Val\|}}~~

	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 [[prime interval\|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 {{monzo\| 0 0 -1 0 0 1 }} (13/5) may be abbreviated to the subgroup monzo 5.13 {{monzo\| -1 1 }}. However, subgroup monzos can refer to intervals in subgroups whose basis elements are not primes, for example 2.3.13/5 {{monzo\| 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 [[prime interval\|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 {{monzo\| 0 0 -1 0 0 1 }} (13/5) may be abbreviated to the subgroup monzo 5.13 {{monzo\| -1 1 }}. However, subgroup monzos can refer to intervals in subgroups whose basis elements are not primes, for example 2.3.13/5 {{monzo\| 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.