The Bass in Fifths

[Jeff Moote]

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.