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
- 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. — SA, Wednesday 2020 December 2, 05:58 UTC
- No, I did not mean anything related to stack vs. chain. Where? Please also read the new section "Real use of generators" below. — 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". — SA, Wednesday 2020 December 2, 05:49 UTC
That's why the val form has exactly the same structure as the "Monzo" structure. In both cases, we consider the ordered subset of numbers, For Monzo, this is first N prime numbers (N is called "limit", as in "5-limit") and assign an integer power to each of them. Also, for Monzo, some of the powers are negative. For val, it is defined over the set of interval, each of the interval can itself be represented as a Monzo instance, or not. The examples of val I can see the in these lectures clearly indicate that the author actually meant this well-known concept of val, and not anything like "stacks" or "chains". "Chain" is a common word which can be used in concrete examples of data, but it would be a characteristic of some particular presentation of some particular instance of the instance of a frequency generated using a particular val, but not the val itself, and not even the particular instance of the generation, because the change in order would not change anything essential. Note that the string representation of val is sequential, but this is only a feature of the notation of it (only because prime numbers themselves are omitted); it does not characterize the informatics of the val object itself. — SA, Wednesday 2020 December 2, 06:19 UTC
On top of that, it is always good to understand, that Monzo and val is merely the game of notations, no different from any other possible notation. At the same time, the concept of the generator itself is essential and does not rely on its presentation. A generator is a subset of prime numbers. When we also assign a set of powers over the set of the prime numbers, are obtain a way of generating of a single frequency from a single base frequency, and this object can be called, for example, "generation", or "generator instance", formally speaking, the cardinal number of the set of such instances is that of the set of natural number, it is an infinite set. — SA, Wednesday 2020 December 2, 06:19 UTC