secondary generator definition

there was a need to supplement the definition of "generator",
which my Dictionary had as a generator of a scale, with a
secondary definition describing the generator of a kernel.

Gene, if you already posted your definition of "generator",
i'm sorry i can't recall it now.

this is what i added:

http://www.ixpres.com/interval/dict/generator.htm

>> In periodicity-block theory, there are small intervals
> called unison-vectors, a select few of which are able to
> generate a kernel, which in JI is the periodicity-block
> enclosing a finite set of ratios on the lattice.

corrections, additions, etc.

-monz

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--- In tuning-math@y..., "monz" <joemonz@y...> wrote:
>
> there was a need to supplement the definition of "generator",
> which my Dictionary had as a generator of a scale, with a
> secondary definition describing the generator of a kernel.
>
> Gene, if you already posted your definition of "generator",
> i'm sorry i can't recall it now.
>
> this is what i added:
>
> http://www.ixpres.com/interval/dict/generator.htm
>
> >> In periodicity-block theory, there are small intervals
> > called unison-vectors, a select few of which are able to
> > generate a kernel, which in JI is the periodicity-block
> > enclosing a finite set of ratios on the lattice.

what does this have to do with the definition of 'generator'??

--- In tuning-math@y..., "paulerlich" <paul@s...> wrote:

> what does this have to do with the definition of 'generator'??

I've been using "generator" in its meaning from the theory of finitely-generated abelian groups, in which sense both the generators of a kernel or the generators of a temperament are generators.