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Old 08-03-2007, 09:11 AM
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David Powell David Powell is offline
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Quote:
Originally Posted by Jeff Moote View Post
David,

While I respect what you're doing, I really think you're over thinking it - or at least over thinking certain aspects and missing others.

One thing to mention is that you seem to be equating constructive interference of waves and consonant sounds, if I'm not reading you incorrectly. Even if one ignores that a note sounds with significant amplitude on more than just the fundamental, a more constructive relationship between fundamentals doesn't necessarily mean a more consonant sound. Psychoacoustics is the major factor at play, and unfortunately that brings this way outside the realm of physics.

The point is that to use your chord example, you can tune a chord (say, a major triad) and that is very different than tuning a major third and a minor third on their own - so the intervals you choose in the chord to create the most consonant sound will not be the same you'd choose for either on their own.

To take this discussion further off topic, I'll mention the notion that composers and musicologists have held that different keys have different "colours". They absolutely DO NOT - with the emphasis on "absolutely" On a piano tuned to 12ET (I'll use it for reference at first) all keys sound identical. On an instrument of flexible temperament such as strings, as long as the player continues to play just temperament all keys will sound the same, in terms of dissonance. Wind instruments are kind of in between since they generally use just temperament but are somewhat limited by the key of their instrument (unless for example you have a set of natural trumpets - one for every key!). All this combined still points to keys being identical - so where does the idea come from? My guess is that it's more related to instrumentation and variation in timbre: certain keys lend themselves to various instruments playing in different parts of their range. This means that depending on the key, certain instruments are limited to some subset of the timbres they are capable of. When this is summed in an ensemble context some keys may begin to take on a "colour" which leads to the ideas mentioned above. This also explains why there is not universal agreement on this - one composer hears a given key as one thing, and another differently. This could be as simple as one composer preferring a different orchestration leading to that key taking on a certain colour. Even if we limit both composers to the use of their pianos, both pianos are not identical and are certainly tuned differently - for this reason the dissonance may be distributed differently giving them an impression of something about keys, as they hear them.


To bring this back on topic, I think one reason why fifths work better on the bass in the context of other string instruments is that you have a broader range of notes in each position on the neck allowing for different timbres which blend differently. This doesn't explain anything about the supposed increased resonance of the instrument itself though. For that I would come back to the physics of the harmonic relationships, so if you want to do any ****ysis this would be where I'd do it, and not between the bass and other instruments. In doing that we cannot leave out the natural resonances of our instrument either. It could be just that the instrument resonates differently when tuned in fifths as the wood is under different types of stresses, and this is another barrier to ****ysis because it is not as objective. Once you add the varying harmonic response of a single vibrating string to the simple fundamental ****ysis, and then consider the resonating wood (which is not unchanging over time) the task becomes increasingly complicated. There's easily enough material for 10 theses in mechanical engineering, but is this really worth the trouble?? Maybe if you need a topic for your doctoral thesis! As a musician it seems sensible to try the tuning myself, or at bare minimum listen to others using it (which is how it started for me) and if you like the results then it's good. If not, then keep using fourths.
Well, I'm not sure what you are talking about when you say consonant sounds, so I'm definitely missing that. I do know what I mean about constructive sound wave interference of two or more frequencies. When the sine waves are laid over each other in a perfect simple ratio, one can hear that as a new wave form. Did you look at the chart on the bazantar site?

If you bow two strings you can find some of those off the half step (sometimes called quarter tones). Anyway, it is easy to find some of the more unusual ratios just by ear while gradually changing the pitch of one string while droning the other string. I know how those harmonizing ratios sound and it has everything to do with constructive interference characteristics of the sound waves. I really don't know if psycho-acoustics has anything to do with what I'm talking about. It may. The phenomenon I'm talking about is the same thing that allows me to tune one note on an instrument and then tune the whole thing. It is the same constructive interference I'm hearing when two notes are in tune. I don't think the "color" thing about keys is easy to talk about in any certain terms. Nor do I think that it is of any consequence in the way that I'd like to look at the resonance / constructive interference differences between the tuning.

I would like you to explain the "consonant sound" definition. I couldn't find anything that referenced that terminology or explained it. Depending on the definition, it may or may not have anything to do with what I'm talking about.

I really think if the increased resonance is something that is experienced in an ensemble with other strings, we will miss what's happening without including all the strings in the ensemble in the physical ****ysis. Sure, there should be a pattern just looking at one instrument tuned in fifths, but we need to consider the implications of all of them playing chords at once. Not chords on one instrument, but chords where one plays the tonic, another the third, another the fifth. What changes on the bass between the two tunings is not the pitch played, but the position and string it winds up being played on. Tuning in fifths should not change the stresses on the instrument if we choose strings that give the same overall tension result. That must be kept constant. If there is anything that seems "instrument dependent", in other words it works differently on this bass than that one, the the idea is pretty much invalid. If the tuning itself generally improves something, the effect should be universal across instruments as long as we hold everything else constant. If tension is part of the effect, then the effect is not due to tuning in 5ths and could be achieved by 4th tunings and just using a different set of strings. If an instrument resonates differently, it has to be because of the different series of partials that result on the open strings and on the relation to a specific stopped note before it has much to do with 5th tunings. FYI, I wasn't going to use any instruments in the ****ysis, I was going to chart the partial series of the notes and look at the frequency relationships / ratios. If this turns into something that is instrument dependent in any way, the concept is lost completely and it is just a novelty tuning. I don't think it will take ten mechanical engineers to show what I'm talking about. It will take some time and a calculator, that's about it. In my mind it is not complicated if we stick to a theoretical ****ysis. When we leave the theoretical ****ysis and start considering different instruments, etc., then any meaningful ****ysis is impossible. If a theoretical ****ysis shows up nothing, then I don't think there is anything there dependable. You can try it on this or that instrument and see what you get in the real world, but constructive interference is something that I have found (and how, given physics, could it be different? Sound has it's laws and it abides them.) is the same no matter what one uses to generate the pitches, as long as the pitches generated also generate a partial series of resonances based on the pure harmonic series. To me what wouldn't be worth the trouble is stringing up my instrument differently without having some theoretical foundation for why.

What I am looking for is a general improvement in resonance that can be specifically related to nothing but the tuning difference. That is a problem worked out on paper. My hunch is that there could be something there, that it will probably be somewhat key dependent;- that it also could require playing the notes on each instrument in a specific position and string. It won't prove or disprove anything, but it might point in a direction.

Last edited by David Powell; 08-03-2007 at 09:25 AM.
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