Friday, July 08, 2005

Embrace the artificial

Over at A Monk's Musical Musings, Hucbald has been showing the physical generation of various chords in tonal progressions. I found myself writing a very long comment in one of his posts, and decided to subject all of my readers to a comprehensive look at this question. Theorists through the centuries have attempted to prove that tonality is the ultimate language of music because tonality is based upon natural principles of physics and psychology. The psychology side is rather messy, so I will wait to address that one.

The physical side comes from claims that tonality is based upon the harmonic series. Since the first sixteen harmonics can make the major scale (we'll ignore harmonics 7 and 14 right now) from the tonic/fundamental, this must mean that the major scale has special significance, something that resonates right from the very nature of the notes played by acoustical instruments.

Notice that this means of generation says nothing about the minor scale (any of the three). For Helmholtz, this means that minor keys are inferior to major keys, as they are distortions from the pure generation. Rameau tried to generate the minor scale from two different fundamentals, called the "co-generation" theory. This still makes the minor scale a second class citizen to the major scale, since it requires help from a second note to generate all of its notes. Riemann believed in "undertones", patterns of frequencies that follow the same pattern as the harmonic series except going down from the fundamental instead of up. (Hucbald mentions one of his teachers, so I'm pulling out Harrison, one of my History-of-Theory teachers.) With this new series, the minor scale can be generated. However, undertones have no physical basis, despite Riemann's claims of having heard them.

The problem is that in practice, minor keys are not treated as inferior to major keys by tonal composers, and indeed are not preferenced in perception/cognition studies either. All attempts to physically generate the scale are unsatisfactory at best, and plain wacko at worst. So, when practice conflicts with theory, the theory must be questioned. (Right, PZ?) I say that we should embrace the fact that such a complex and vigorous language is the result of artifice rather than from the happenstances of physics. Long live art!


Hucbald said...

Hi Scott,

For some reason I can't read your blog because I get microscopically small blue letters on a brown patterned background. I have this same issue with every blog that uses this particular combination. I'm a Mac guy and use Safari, so that may be the problem (Some complain about my white letters on black, but it looks fine to me). Anyway, thanks for linking to me, and I'll try the blog on IE next time.

Hucbald said...


IE works fine here. Sorry about that. As I said in my response to you over at my place (Thanks again for linking), rationalizations by theorists about the origin of the minor modes are just that: Rationalizations. But, the minor mode exists (And some of us prefer it to major), so you "gotta pick one", no? For me, the minor as a reflection of the major via the undertone concept is as good an artifice as any, and is displayed in nature anytime you view a sunset over a body of water. So I choose that one. Arbitrarily, of course, but it "works for me".

And Riemann was a towering giant of a theorist, but he jumped the shark when he claimed to hear "Undertones": THEY DO NOT EXIST IN NATURE.


Scott D. Strader said...

Some questions and comments:

- You say that the harmonic series cannot be used to generate any of the three minor scales: isn't the natural minor simply a modal view of the major?

- I had never heard of the "undertone" thing. It sounds completely idiotic when examined from a physical basis. I'll have to read more about Reimann though.

- Can't the minor scales be viewed as dissonant alterations of the major? This would be similar to how the natural minor is a modal alteration, but the natural's alteration is that of emphasis and not tone. This wouldn't make minors second-class citizens but instead "differently enabled" citizens: the major is notable for its harmonic series consonance, the minors for their subtle dissonance.

- Finally, thanks for the link to Monk's site. Nice.

Scott Spiegelberg said...

I argue that you don't have to pick a rationalization, if you accept that diatonic collections are no more natural than any other type of collection (Pentatonic, octatonic, whole tone, chromatic, etc). All collections are artifical inventions, so no rationalization is necessary.

Scott Spiegelberg said...

Scott, the point of generating tonality from the harmonic series is to show that the pitches used are supported by the timbre of the notes. In the case of the minor scales, it cannot be generated so the root and fundamental are the same. If it is viewed as a rotation of the major scale, then it is inferior (a la Helmholtz). For a long time dissonance was considered a weakness, until Schoenberg's salvo declaring the emancipation of the dissonance. So theoretical explorations of tonality would not be happy with the explanation that the minor tonality is a distortion of the major tonality, yet they are both equal.

Scott D. Strader said...

We may be arguing in circles: you're arguing against what's commonly taught, and I'm arguing for what I specifically was taught. Maybe.

I don't see the rotation explanation as inferior, but I'll have to read Helmholz to understand his rationalization. The rotation gives us the natural minor; added accidentals (the leading tone being the most important) alter it to be closer to its parallel major, giving us the harmonic and melodic minors. Instead of a “distortion of the major,” I think of it more as a connection to the major. I'm not sure that the root differing from the fundamental should be considered a deficiency--but that again may be what's commonly taught. I don't see how this “rationalization” weakens the connection between tonality and the physics of the harmonic series. Although one question I do have is how the aeolean mode survived to be used frequently while the other modes are used less frequently. Maybe this is the arbitrariness that you're suggesting.

Regarding dissonance: the definition of dissonance has been continually changing, from the absence of harmony (IIRC), to the acceptance of only parallel motion, to the restriction to only certain parallel motion, etc. Wasn't it composers' bumping against those definitions that changed what was acceptable dissonance (ultimately progressing to the complete freedom that we have today)? Even with today's acceptance, a minor second is going to vibrate in our ears the way that an octave doesn't. While the current freedom of dissonance could suggest that everything is equally natural, couldn't the progression from tonal consonance to atonal dissonance suggest a modification of what's natural?

You also brought up other collections of notes unrelated to the harmonic series (although, I would exclude the pentatonic scale for reasons similar to the minor mode). Aren't these interesting for their differences from tonality? I consider tonality natural and these other scales man-made without using those labels as a value judgment. Just as with dissonance, we progressed from tonality and what I consider natural to these different scales (although I have to admit that I'm not that well versed in world music and non-western origins).

Possibly unnecessary disclaimer: I'm certainly not trying to be pedantic with my details on theory and history (I wouldn't dare). We're talking such basic concepts that my reviewing the basics helps me define my position and beliefs.

Scott Spiegelberg said...

Scott, you may interested to know that J.S. Bach and his contemporaries considered the Dorian mode to be the true minor mode, rather than the Aeolean mode. Renaissance theory traces a varying number of modes described/used, from four to six to twelve to sixteen(!), back to nine, and finally the radical suggestion that there are only two. (I probably missed some, it has been ten years since I took History of Theory.)

Ask yourself why you think tonality is natural. Pre-tonal Western music had a history of about 700 years; tonal music a history of 400 years (or 500 hundred, if you argue that popular genres produced today still count).

I've shown the difficulties in claiming an acoustic basis for the naturalness of tonality, as it conflicts with practice. The generation of minor has to be secondary, as major must be generated first. There is no way to directly generate minor from the harmonic series, thus its secondary status as a natural language.

You are probably more comfortable with the tonal language, as is (almost) everyone raised in the contemporary Western music tradition. This is just like people speaking their native language best, because they were emersed in it during crucial developmental periods. But that doesn't make English more "natural" than other languages.

PZ Myers said...


Although it may be more a matter of tweaking the theory to accommodate a special case, less than fully questioning it.

Anonymous said...

Scott D Strader Quote

Although one question I do have is how the aeolean mode survived to be used frequently while the other modes are used less frequently. Maybe this is the arbitrariness that you're suggesting.

Hi !
This is something I've just come across in my studies.The reason is the position of the Tritone Interval.In the Mayor Ionian mode the triton occurs between its fourth and seventh note.The tritone is unstable and seeks resolution.In the major mode it resolves on the third and the eigth.....key notes of the Tonal 'Home' Traid.In the Aelion mode the Tritone occurs between the 2nd and 6th.It can resolve on the 3rd on the 5th....again the resolution brings the mode back to notes strongly associated with the Tonal centre.
These are the only two modes in which the Tritone resolves on key notes of its 'home' base.In Lydian for example the Triton occurs between the 1st and 4th notes.This makes the mode highly unstable as its root / Home is part of the Tritone and seeks active resolution !!!.
Hope this helps a bit.Great blog by the way....