Hi Ray welcome back to BAUT (I guess you were introduced to it a couple years ago when our member
ExpErdMann referenced your analysis of the GPS stations), we've met
on Usenet
Quote:
Originally Posted by rtomes
It took a while before I noticed that the first four cycles that I had used were related in frequency in exactly the same was as the four notes in a major chord.
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I know this is not new to you (I see you've created wiki pages on just intonation and similar subjects), but I find this point fascinating.
The notes of a major chord are in a ratio of 4:5:6:8 (I assume those are the four that you meant) but that just means that they are integer harmonics of a note two octaves lower. In other words, the 1, in 1:2:3:4:5:6. (and, of course, the 1:2 is the same as the 4:8, and the 2:3 the same as 4:6, sorta explaining why the 7 is left off
)
There are two dfferent ways that such harmonics can arise. The fundamental unit can be multiplied, or it can be divided. For example, if our day is the fundamental unit, we find that another unit (the week) works best if it is an integer multiple (7, as opposed to 7.3) of our fundamental unit. Another unit (the hour) works best if it is an integer fractional part (1/24) of a day. Both the week and hour are artificial, but we find them in society over and over. The only thing that needs explaining is the
day--which explanation naturally relates our relationship to space.
I think the harmonics arise often enough, naturally, but the key is the explanation of some fundamental unit, why it occurs, why it exists to force the others.