Talk:Periods and generators

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Stacks of Generators

"Stacks of Generators" appears on this page and several other pages and creates considerable confusion, especially on other pages.

In principle, on the page of the original definition "stack of generators" can be understood correctly, but only in this context. It would work if the notion of the "generator" was segregated from the notion of the "result of generation". Without it, the generator is understood in two different senses: 1) as the interval, 2) and as the result of adding an interval to some tone repeatedly, something which could be understood not as interval, but "interval instance". Actually it's just "tone", but in its abstract understanding, abstracted out from its base frequency. Then the "chain" would be a chain of tones.

When "stack of generators" is used another context, it makes things much less clear, because the plural form of "generators" suggests that it can be a set of different intervals. That is, in a separate context nothing tells the reader that this is the same interval, applied to some tone or not. The links don't make things much better.

I seriously suggest re-phrasing this part.

I didn't find stacks of generators on this page, but I absolutely agree in your critique. It should be rephrased when it tries to say generator and at the same time to build the inner image of the process generating stacks of the same interval. --Xenwolf (talk) 08:19, 1 December 2020 (UTC)
PS: signing is now easier than before: in the edit bar, there is a button for it. --Xenwolf (talk) 08:19, 1 December 2020 (UTC)

Get it; thank you for the note. — SA, Wednesday 2020 December 2, 05:51 UTC

You probably meant "chain of generators" or "generator chain"? But chain is not better than stack. --Xenwolf (talk) 08:22, 1 December 2020 (UTC)

No, I did not mean anything related to stack vs. chain. Where? Please also read next paragraph. — SA, Wednesday 2020 December 2, 05:49 UTC

Here is the real use of the generators: it is simply a basis made of 1, 2 or more different intervals, or rational numbers, which is the same in the given context. Due to the commutative commutative properties of the rational number arithmetic, we can take a base frequency and multiply it by any number of numbers from the generator set any number of times in any order, we obtain resulting frequency. If we apply the same operation to the base frequency in all possible combination, we obtain the resulting set of frequencies "generated" from a base frequency with a given generator set. This way, the set of the generators is not a "stack" and not a "chain". — SA, Wednesday 2020 December 2, 05:49 UTC