SAKryukov

:::::::::::::::::::::: Oh yes, I know all about that.  In fact, while some consonances- such as those involving sum tones and difference tones- are based on a linear mathematical relationship (as noted by [[User:CritDeathX|Sam Pulley]] in [[User talk:CritDeathX #Ideas of Consonance|a conversation we had about the matter]]), there is an equivalent type of consonances that seems to be based on what I call a "contralinear" mathematical relationship- these particular tones being what I call "contrasum" and "contradifference" tones.  We seem to need a new set of mathematical symbols in order to shorten the process of solving the mathematical problems involved in finding these contralinear tones.  For example, a 10:12:15 minor triad is identical to a pitch relationship in which the frequencies are related the the following mathematical relationship 1/4:1/5:1/6.  In order to solve for the contrasum and contradifference tones with the current set of mathematical relationships, we would currently need to take the multiplicative inverse of each of the fractions in the 1/4:1/5:1/6 ratio, solve for sum and difference tones among the resulting whole number ratios, and then take the multiplicative inverse of the answers we get- or something like that. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 21:34, 7 December 2020 (UTC)

::::::::::::::::: Now, about the problem, how "exactly to program complicated tonal values". First, the problems are solved using the "divide and conquer" method and "separation of concerns". In particular, tone values can be abstracted from the technical means of sound production. Another thing is: it's good to "think by hands". (In our case, "hands" is the generalization of several things: hands, fingers, hearing, etc.) When you don't understand how to solve the problem, of, course, think about understanding but also start working with incomplete understanding and uncertainties. As you try, you can get a better feeling of the problem, will be able to get rid of some illusionary ideas and get new ones... Moreover, in some analogous ways, I many times recommended people to... avoid reading literature. Here is what I mean: it's good to try to solve a problem from scratch by yourself. Why? First, you won't miss a pretty rare chance of inventing something really new. More realistically, when you read, you don't quite understand reading at first, because the illusionary understanding is quite common, besides, you can be affected by some well-established ideas and reduce your chances for a fresh look. And when you tried hard and broke some of your teeth at the problem, you can use what you learned, and then you will ready with much better understanding. — [[User:SAKryukov|SA]], ''Monday 2020 December 7, 04:01 UTC''