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Originally Posted by naethoven  Wes, Louden 1 is 1:1.4:1.9. I know musically 1.4 is good, and musically 1.9 is good. But together, don't 1.4 and 1.9 make a perfect 4th? Please explain this to me, maybe I'm not understanding correctly.
Thanks,
Nathan Webb |
Wow, Nathan, good observation. It is true, and for this reason I much prefer something other than 1.9 when I'm using 1.4. Like maybe 1.8, or 1.7. These are round numbers, by the way, but these two options would give you approx. the major 3rd and the minor 3rd.
It's okay to speak in terms of approximations when dealing with musical intervals, because musical intervals are not fixed in stone to begin with. Only for a hundred years or so has the Western world been fairly rigidly tied to the equal temperament system. When you get into just intonation and other tuning systems, there are very many versions of each of the intervals, depending upon what ratios are used to create them (by way of string or tube lengths, etc.) For instance the ratio (interval) between the 5th harmonic and the 6th harmonic is a minor third (5 : 6). But the ratio between the 6th harmonic and the 7th harmonic is also a minor third (6 : 7). The ear hears both as minor thirds, even though one ratio is 1 : 1.2 and the other ratio is 1 : 1.17. Equal temperament compromises and places the minor third at approx. 1 : 1.19.
Some people may think it strange to speak of ratios as musical intervals, since doing so concentrates on the 12 relatively fixed intervals between the numbers 1 and 2, at the expense of all of the other infinite possibilities. But the truth is, once microtuning in taken into account, the infinite possibilities open right back up, and it surely helps to have those 12 guideposts or grid lines along the way. It's like the 12 hours of the clock - sure there are lots and lots of minutes in the day, but it helps to simplify things to first say which hour it is you're talking about.
But getting back to your question, it is important to pay attention to the third leg of the triangle, meaning the ratio between the width and length. Given a ratio of height to width (e.g. 1 : 1.4) and height to length (e.g. 1 : 1.9), you just divide 1.9 by 1.4 to see what the third ratio is. And this ratio is just as important as the other two, I promise you.
--Wes