Just intonation subgroup: Difference between revisions
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There are three categories of subgroups: | There are three categories of subgroups: | ||
* Prime subgroups (e.g. 2.3.7) contain only primes | * '''Prime subgroups''' (e.g. 2.3.7) contain only primes | ||
* Composite subgroups (e.g. 2.9.5) contain composite numbers and perhaps prime numbers too | * '''Composite subgroups''' (e.g. 2.9.5) contain composite numbers and perhaps prime numbers too | ||
* Fractional subgroups (e.g. 2.3.7/5) contain fractional numbers and perhaps prime and/or composite numbers too | * '''Fractional subgroups''' (e.g. 2.3.7/5) contain fractional numbers and perhaps prime and/or composite numbers too | ||
For composite and fractional subgroups, not all combinations of numbers are mathematically valid [[basis|bases]] for subgroups. For example, 2.3.9 has a redundant generator 9, and both 2.3.15 and 2.3.5/3 can be simplified to 2.3.5. | For composite and fractional subgroups, not all combinations of numbers are mathematically valid [[basis|bases]] for subgroups. For example, 2.3.9 has a redundant generator 9, and both 2.3.15 and 2.3.5/3 can be simplified to 2.3.5. | ||