Just intonation subgroup: Difference between revisions
"In the strict sense": subgroups include full prime limits, not including them is but a convention |
Rational -> fractional |
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* Prime subgroups (e.g. 2.3.7) contain only primes | * Prime subgroups (e.g. 2.3.7) contain only primes | ||
* Composite subgroups (e.g. 2.5.9) contain composite numbers and perhaps prime numbers too | * Composite subgroups (e.g. 2.5.9) 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 | ||
For composite and | 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. | ||
A prime subgroup that does not omit any primes < ''p'' (e.g. 2.3.5, 2.3.5.7, 2.3.5.7.11, etc. but not 2.3.7 or 3.5.7) is simply called 5-limit JI, 7-limit JI, etc. It is customary of just intonation subgroups to refer only to prime subgroups that do omit such primes, as well as the other two categories. | A prime subgroup that does not omit any primes < ''p'' (e.g. 2.3.5, 2.3.5.7, 2.3.5.7.11, etc. but not 2.3.7 or 3.5.7) is simply called 5-limit JI, 7-limit JI, etc. It is customary of just intonation subgroups to refer only to prime subgroups that do omit such primes, as well as the other two categories. | ||