AllyPike wrote: ↑Sun Jun 23, 2019 5:31 am
3 is a magic number according to School house rock. There’s a song. Three is culturally significant across the world. 1/3 is an infinite number. 3/4 is the time signature for most lullabies in European music and the sexy waltz. Should we be paying more attention to the third? I’m not really sure how it matters because I’m struggling with whether or not we should accept any human imperatives in terms of ethics, but we all have some moral imperative to go positive. Nature sort of does too. Negative charges move towards positive (particle theory). Human cultures have binary too. But cultures threes and thirds strongly. What does this affinity towards 1/3 mean? We can’t answer but can you direct me towards scholars or philosophers who identify 1/3?
Zero, one, two, and three, play the most significant roles in reality in ALL areas of real life. I think that the 'third' factor, as signified by '-1-' and 'Impenitent' here gives good examples. I think the magic
of a third is due to "contradiction" (which literally comes from meaning, "with a third (factor)", where we normally assume balance or symmetry in reality ('even' concept). I think of it similar in logic with respect to Zero, One, and Infinity. A third suffices as a kind of 'trigger' to do more or look elsewhere (like a new dimension) regarding things and so is a 'constructive' type of thing.
As for music, I am not exactly sure what you mean unless you are referencing the general blues 1-3-4 pattern of a major scale that is most common in all music but most uniquely specific in relatively 'easy' music. Since much of 'rock' permits anyone to participate, the reduced most common form of it is of that 1-3-4 pattern to be most universally appealing.
The Pythagoreans were the ones most involved in making sense of these things where this also relates to the first 'physics' revolving around dividing a string into differing standing waves. But this includes as much the concepts of unison and binary concepts. The division into 12 semi-tones is of the prime factors of 1, 2, and 3. The common denominator would normally have been 6 (rather than 12) but they noticed that you have to count both sides of where some 'bridge' is created. For example, a 'dominant' note of a major scale (a fifth) is included because its 'complement' of all eight notes even of the major scale is equivalent to a third below. That is a 'fifth' can be thought of as (-3 + eight*) where '8' is the 'octave'. The complete 12 notes derives from halfing the length of a string twice (= 4) plus the odd division of splitting the wire into three. But also note that 1/3 of the length of a string is equal to 1/2 of what remains and where the Pythagoreans may have ended up treating a full 'chronological' division into (2 x 2 x 3 = 12 semitones).
Although we think of primes as numbers we use, every number can be treated as the sum of multiples of 2 and multiples of 3. Thus the 'magic' of these numbers to be minimally necessary.
If you are extending this to rhythm, the same thing applies. We can create more than 12 notes divisions of tones and have bars measuring more than thirds by using the same concept (2x + 3y) relationships.
Was this what you were thinking about?
Edit: I had to change "8" into the word "eight" because the stupid priority of social media html turns the eight with a following closed bracket into a smiley face. Does anyone know what the means is here to force a character explicitly to be what you type when it uses combined symbols to represent unique codes?
Edit 2: changed 'many' to 'ALL'. I think the 'third' is significant in all areas necessarily about reality. I also need to add,
Yes, to your question, for overt clarity. But you still need the prior 0, 1, and 2 concepts. I would also include infinity. But you can also think of the third as (1 + 2). So the equation I gave as (2x + 3y) might better be rendered as [2x + (2 + 1)y] and even more clear, make x or y be recursive and include either a power of zero to allow for '1' or add a third term such as "(2 - 1)z". Then you might summarize all realities regarding integers as having the form,
[(2-1)z + 2x + (2+1)y].
Musicians of the past from different cultures have extended the division beyond 12 semitones and so can have more divisions to any number of desired scales. Even if we don't directly use them in most 'western' music, we still do indirectly where we use instruments that permit continuity, such as a bend of a string in a guitar solo that can make a tone outside of the mere 12 divisions.