J. P. Kirnberger: phenomenology and historical music theory
Kris Shaffer, Sound and Mind, May 2007

I was struck a couple weeks ago by a couple of passages in J. P. Kirnberger's Die Kunst des reinen Satzes (The Art of Strict Composition), specifically in the chapter on modulation. Though the ideas in this chapter were commonly held by composers and teachers of composition, this treatise from 1771-79 gives the earliest theoretical explanation of key relations I have seen which appeals to distinctly phenomenological principles.

This is noteworthy today not only because this passage demonstrates that a phenomenological approach to musical perception is not a recent development, but also because Kirnberger lays out the asymmetry of key relationships. That is, the cognitive distance between C major and F major, for example, is larger when moving from C to F than from F to C. This principle (supported by experimental data from Krumhansl--to come in another post in the near future) preemptively undercuts the possibility of a geometric representation of musical space, which is all the rage these days (for example, 3 articles about Dmitri Tymoczko's recent work here, here, and here), at least as far as key relationships are concerned. Thus, this passage has served me well in recent weeks in framing my thoughts and discussion of the theories of David Temperley, Carol Krumhansl, Fred Lerdahl, David Lewin, and others who approach a theory of musical space based on principles or data from cognitive musicology.

Here are two brief passages from Kirnberger's chapter on Modulation. They will also prove to be useful background information for some of my upcoming posts, particularly the review of Carol Krumhansl's Cognitive Foundations of Musical Pitch, which I am currently in the middle of writing. Enjoy!

Passage 1, on establishing a key:

Here it is particularly important to note, as was already done above, that each key has its essential degrees which define it and its mode. These essential degrees are contained in the tonic triad. Thus, when such a triad occurs at the beginning of a composition or a period, the ear is directed to that key [center] and mode.

Only in cases where the ear is already used to a key to which all notes of the new triad belong is one uncertain whether or not the root of this triad should be considered as a tonic. For example, if an ear that is accustomed to C major hears a G major triad, this triad has nothing that points to a new key, because all its notes also belong to the C major scale. This, for the ear to kean toward G major, it would be necessary to introduce a note foreign to the key of C major shortly before or immediately thereafter.

For this reason the tonic triad is sufficient to announce the key only at the beginning of a piece, before the ear is accustomed to any scale. However, if one goes from one key to another, the triad in the new key must be preceded or immediately followed by a note foreign to the former key. This note, which is essential to the new key, erases, so to speak, the feeling of the old key. How this can be accomplished will be clearly demonstrated in the course of this chapter.

Passage 2, on key distance in modulation:

It is self-evident that those keys whose scales have most notes in common are most closely related. So it can be said that the key of C major is closely related to G major, since they differe only by one note; although C major has an F while G has an F-sharp, all other pitches are the same. On the other hand the keys of C major and F-sharp major are almost diametrically opposed, since they have only a single pitch in common.

However, two keys can differ by only one note and still be only slightly related. This happens when the note is entirely contrary to the nature of the other key. For example, C major and F major differ by just one note, which is B in C major and B-flat in F major. However, this B is indispensable to C major, since it is the leading tone of the key. By changing this pitch, the C major scale suffers more than if any other note were to be changed. Therefore the key of F major is farther removed from C major than one in which a less essential note is changed.