Quote:
Originally Posted by
PaulP
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I take it we're more interested in just intonation when we talk about rooms
as musical instruments and that we priviledge dissonnant intervals for the
ratios ?
Paul P
The reason I use just intonation intervals for discussion purposes is simply that they are easy to represent as whole number ratios. A just intonation perfect 5th is simply a 3 : 2 ratio, whereas an equal termpered perfect 5th is the 12th root of 2 raised to the 7th power. See what I mean? You lose a lot of people talking about equal tempered intervals.
And the truth is, it doesn't really matter anyway. I'm not saying that all room ratios should be tuned to musical intervals per se. What I am saying is that the 12 musical divisions of the octave are the easiest and best way to discuss and work with room ratios because 1) the 12 tones represent a logarithmic division of the 2 : 1 (octave) ratio, which is more useful than a linear division, and 2) we are, after all, talking about creating rooms for musical listening and production, so I feel it helps to work within a musical context when designing and creating these rooms.
So while I may start out with a just major third ratio between height and width ( 1 : 1.25), I always feel free to move that to the equal tempered 3rd ( 1 : 1.26) if it helps to bring the numbers into balance. The bass waves aren't going to notice an inch here or there, but they will respond to a change from a perfect 5th to a diminished 5th, let's say. So, in other words, a 1 : 1.4 ratio is good (just intonation), a 1 : 1.414 ratio is good ( equal temperament), but a 1 : 1.5 interval (or it's equal tempered counterpart) is bad.
As to your other question about dissonant intervals being better than consonant ones, I would say the answer to that is a bit more nuanced. If we define consonance as Harry Partch ( and others) have, then the simpler the whole number ratio, the more consonant the ratio. So the most consonant ratio is 1 : 1, followed by 2 : 1, 3 : 2, 4 : 3, 5 : 4, etc. I think this is a reasonable definition, since many musicians, mathematicians, and golden ears have tended to agree on this point for centuries.
I would agree that it's best to avoid the very consonant, low integer ratios for room dimensions for obvious reasons. A 1: 1 or 2 : 1 ratio is going to get you into obvious trouble. But a 5 : 4 ratio is actually a very good ratio, for instance. That's because it happens to be approximately one third of the way around the Circle of 5ths, and lends very even spacing to the lowest axial modes, as well as distributing the modal harmonics evenly throughout the musical keys.
So the best way I can briefly state it is to say this: Very low low integer ratios are to be avoided, but other simple integer ratios can be used to create intentionally "musical" spacing of the modal resonances.
-Wes