Talk:Periods and generators: Difference between revisions
Essential vs notational |
m Monzo vs val, minor correction |
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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'' | ||
That's why the ''val'' form has exactly the same structure as the "Monzo" structure. In both cases, we consider the ordered subset of first N prime numbers (N is called "limit", as in "5-limit") and assign an integer power to each of them. | 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. — [[User:SAKryukov|SA]], ''Wednesday 2020 December 2, 06:19 UTC''ti | ||
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 [https://en.wikipedia.org/wiki/Cardinal_number cardinal number] of the set of such instances is that of the set of natural number, it is an infinite set. — [[User:SAKryukov|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 [https://en.wikipedia.org/wiki/Cardinal_number cardinal number] of the set of such instances is that of the set of natural number, it is an infinite set. — [[User:SAKryukov|SA]], ''Wednesday 2020 December 2, 06:19 UTC'' | ||