If we wish to discuss tone, perhaps there’s no better place to begin than with the Tone Ranger himself:

Fast Tube by Casper

Mr. Johnson is a low church musician, yet his musical ability should satisfy even the most high church among us. He’s on anyone’s list of the world’s greatest living guitarists. Shema and I saw him last year–I first saw him in the 80’s– and he was top-notch, a true musical pioneer who refused to play his hits and rather played all new music, with few exceptions. This angered a few in the crowd around us, but I thought it spoke well of him.

Regardless, did you notice the astounding range of tone in the clip above generated by one musician limited to one setup? Let’s dispense with the standard joke, first.

Do you know how to shut a guitarist up?  Give him sheet music 🙂 

There’s some truth to it, actually. At the street level-gasp!-guitarists play by ear, by chord, by scale, and by tone. Tone is a beautiful thing, and one some pianists, for example, often don’t pay much attention to, in terms of striving to constantly search out new tones, by virtue of the inherent tonal limitations of their instrument. [EDITOR’s NOTE: TA’s genteel and mannerly good friend CD is not one of these pianist types referred to above. I recently heard a beautiful and soulful guitar piece of hers in addition to her piano work.]  Here’s what I mean:

I currently have five guitars: a Gibson Les Paul Studio, an 80’s model Guild solidbody, a Fender Stratacoustic, an Ibanez RG, and a Peavy double neck, 12 on top, 6 on bottom. This, disregarding all other factors, creates a tonal treasure chest with only the quick switch of a quarter-inch cord. Each guitar has its own reach, its own sound, its own character. But that’s only where it begins. Take the Les Paul, for instance. It has three settings, that corresponds to different combinations of the two pickups. That is colored by four volume and tone knobs that each range from 0-10. So, if my math is correct…forget it, I’m not going to do the math. Suffice it to say there are an astounding permutation of settings on only one instrument. The combinations, all of which directly affect tone, are staggering.

But that’s not all, because the manner in which the instrument is played directly affects the tone as well. Did you notice in the clip that Mr. Johnson sometimes picks with the pick, sometimes uses the pads of his fingers, sometimes uses his fingernails, sometimes uses both pick harmonics and finger harmonics, sometimes uses the palm of his right hand for muting, sometimes forms the notes differently with his left hand, all with different pressures and intensities at the point of attack on the strings?

But that’s not all. Did you notice the array of amplifiers behind him? They’ll all have a seemingly infinite range of settings, as well as their own inherent tone that differs from all other amplifiers. How about the rack at his feet? There’s a wealth of tone generating devices there I won’t go into. The point should be overdone by now. The guitarist is unique among all instrumentalists in his ability to generate tone. True, the synth has a similar capability, but the synth operates with digital sampling, which is a problem we will address in a later post. At any rate, the synth is not generating tone, it’s reproducing digitally sampled tones. Rest assured, we at The Areopagus did not miss CD’s following statement from her first post: I like tribal music, Bach, 20^th century composers, and digital ambiance. Hey kids, if you’re needing an example of oxymoron for your English class, here it is: digital ambiance. We intend to hold CD’s feet to the fire for validating the great digital wasteland. [EDITOR’s NOTE: Disregard that last statement, please. As part of this series, TA has intended from the start to argue forcefully, yet very politely, genteel, and mannerly, that the digital revolution–the extremely mathematical digital revolution–has had deleterious effects on music in several ways. We believe CD must mean something very different by the phrase digital ambiance than we understand by it. We’re confident she’ll correct us.]

So, if you add all the combinations of tone available to the guitarist, it’s a staggering thought. But, so what? Well, here’s what. Tone can be expressed mathematically, much like color can, but it cannot be explained mathematically. Thus, we will enter tone in as our second line of evidence that demonstrates that music is not explainable by mathematics.

Here’s what I mean. What does the phrase light at a wavelength of 475 nanometres mean to you? If you answered blue, good for you. But what if I ask, what is blue like? An answer such as blue is like a 475 nm wavelength of light is woefully inadequate. It tells me nothing, except a mathematical equivalent for my perception of blue. But I’m not asking for a mathematical equivalent, I’m asking you what blue is like. How does it strike you? How does it make you feel? What’s your experience of blue?

And it’s the same for tone. What’s tone like? If you offer me a mathematical equivalent for tone in response to that question, I’ll inform you, regrettably, that you’ve missed the whole point of music. Tone is king, and math doesn’t explain it, nor can it.

The only things that explain tone are statements like the following:

It’s the way a Fender Strat sounds through a Marshall. It’s the way a flute sounds. It’s the way a harpsichord sounds. Ad nauseum. It’s tone, man. You got it, or you don’t. The only remaining question, as in part II, is whether we add tone through our perception, God adds it as some weird form of occasionalism, or whether tone is a property of the music itself.

With tone, though I believe we were successful with mood, I think this question will be more easily demonstrated. Tone, unlike mood, possesses an expressable [note that we feel mood is as well, but it’s limited to the mathematics of interval intrinsic to differing musics, not in the soundwaves themselves as tone may be] mathematical correspondence to the physical properties of the music created by the instrument, or even a human voice. Hence, tone enters our minds in accordance with a corresponding physical description, in the same manner as blue enters our minds as described by light at a wavelength of 475 nanometers. Yet, blue is not light at a wavelength of 475 nanometers, and tone is not whatever mathematical equivalence is ascribed to it.

Ironically, then, I believe this mathematical correspondence will create all sorts of undesired philosophic problems for S>S if the attempt is made to maintain that music is indeed mathematical. In my view, tone will enter the mind perhaps as some sort of quale, like blueness, with a direct mathematical equivalent, yet it will not be reducible to physical causation. It will be, as argued in part II, music functioning precisely as God designed it: we will encounter the beauty of good tone just as we encounter the beauty of color in a sunset.

To avoid naturalism, S>S’s view seems to require that the spiritual component of humans adds something to the music in order to interpret the experience. All fine and good, as that is exactly what TA’s does, except for a crucial difference. TA’s has the spiritual experience correlated to the physical phenomena; S>S seems to require either some weird form of occasionalism on the part of God or the human spirit to account for the consistency of experience, or a denial that we all experience blueness and tone in the same manner–IOW, that where in the same instance where I hear a raunchy, distorted tone, you hear the textured tone of a french horn, despite each of us apprehending the identical mathematical soundwave signature.

With the mathematical equivalence of tone not in doubt, it seems most plausible that normal, rational observers would experience the same mathematically descripted physical properties in similar manners throughout all times and places. Otherwise, we’ve embraced a near total skepticism. Since the property of tone thusly derives from the music, and since the mathematical descriptor of this extremely important musical property, tone, cannot wholly account for our experience, and certainly not the beauty of it, we conclude that music is not primarily mathematics.

In closing, we might also briefly add that the mathematics of the sort capable of describing tone are not pragmatically accessible to musicians when they are performing in the same manner intervals are, if they are accessible at all. Theoretically, a musician might be able beforehand to chart out all the variance of tone within a musical piece (think of the nightmare an orchestra would create), but practically, the mathematics involved here seem beyond any practical value with the exception of those who work at Digitech, and the like.

Next we’ll look at rhythm.