Talk:Periods and generators: Difference between revisions
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: 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. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:19, 1 December 2020 (UTC) <br> <small> PS: signing is now easier than before: in the edit bar, there is a button for it. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:19, 1 December 2020 (UTC) </small> | : 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. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:19, 1 December 2020 (UTC) <br> <small> PS: signing is now easier than before: in the edit bar, there is a button for it. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:19, 1 December 2020 (UTC) </small> | ||
:: <small>Get it; thank you for the note. — [[User:SAKryukov|SA]], ''Wednesday 2020 December 2, 05:51 UTC''</small> | :: <small>Get it; thank you for the note. — [[User:SAKryukov|SA]], ''Wednesday 2020 December 2, 05:51 UTC''</small> | ||
:: In fact, "same interval" can be figured out from the explanation on this particular page, but well-known concept of ''generators'' in well-known representation is different, please also see "Real use of generators" below. — [[User:SAKryukov|SA]], ''Wednesday 2020 December 2, 05:58 UTC'' | |||
:: You probably meant "chain of generators" or "generator chain"? But chain is not better than stack. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:22, 1 December 2020 (UTC) | :: You probably meant "chain of generators" or "generator chain"? But chain is not better than stack. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 08:22, 1 December 2020 (UTC) | ||
::: No, I did not mean anything related to stack vs. chain. Where? Please also read | ::: No, I did not mean anything related to stack vs. chain. Where? Please also read the new section "Real use of generators" below. — [[User:SAKryukov|SA]], ''Wednesday 2020 December 2, 05:49 UTC'' | ||
== Real use of generators == | |||
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 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". — [[User:SAKryukov|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 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". — [[User:SAKryukov|SA]], ''Wednesday 2020 December 2, 05:49 UTC'' | ||