source file: mills2.txt Date: Fri, 6 Dec 1996 06:50:45 -0800 Subject: Three views on the fourth From: Eric Lyon I finally got around to Bill Alves's excellent response to my Bach Italian Concerto post which I repost here as it definitely bears re-reading. I wrote: >>If we flip to the last four bars of the first movement of >>JS Bach's Italian Concerto,we are presented with a big fat I(6/4) chord >>on the downbeat. Question: do you hear this simultaneity as >>a consonance or a dissonance? I can only speak for myself; >>I hear it as a flaming dissonance which Bach briefly savors >>by abruptly slowing the rhythm after 12 bars of steady 16th notes. Bill Alves wrote: >I'm afraid that I do not hear it as a dissonance. There are several >historical reasons why the fourth was treated as a dissonance, but I think >one is that the systems of common-practice counterpoint used "dissonance" >interchangeably with "tension." Certainly this is not the case, and >something Babbitt I think fails to represent accurately in his zeal to >expose the arbitrary nature of common-practice counterpoint rules. >Can you have tension in tonal music without dissonance? Clearly so. >Dunstable and some other early 15th century composers wrote very beautiful >music with few or no dissonances, yet the music seems to me to have tension >and release about it. There are some important points here which I strongly second. Although I believe we do hear the passage differently in subtle ways, I suspect our structural hearing is similar with greater differences in terminology than concept. In particular we both agree that there needs to be greater precision in using the word "dissonance" and that there needs to be a very clear distinction between dissonance due to the spectral, intervallic, and overtone complexity of a given chord or time-slice, and tension (as Bill uses the term) owing to contextual factors such as syntax, stylistic norms, rhythm, density, etc. The fourth is an especially interesting interval since it is treated as a "switch-hitter" in traditional tonal music theory - it's not considered a dissonance in a 6/3 (first inversion) triad, but is considered a dissonance in certain contrapuntal contexts. In this case I think Bill's description of it in the 4-3 suspension as a non-dissonance is in conflict with the traditional contrapuntal labelling (of course not all suspensions contain dissonance, eg 6-5s), but is consistent with the more specialized, sonority-local use of "dissonance" described above which seems to be more commonly adopted in discussions of consonance and dissonance with respect to tuning systems. The issue of "correctness" is of course much less important than bringing us to closer understanding of musical phenomena and Bill's remarks certainly add clarity and perspective to both the specific Bach example and the more general issue of treatment of fourths in tonal music. In that spirit, let me introduce one more way of viewing the fourth - Heinrich Schenker's, which as I recall from "The Will of the Tone", is based on an abstract view of the triad as the foundation of both linear and harmonic motion. Schenker interprets the overtone series as a "hint" to the artist who takes the triad and discards the rest of the inconvenient (to his theory) overtones. The triad and the facility to move in tonal space as defined by the triad becomes the composer's "a priori". I can't recall the example Schenker gives for tonal space, but the opening melody for Bach's Brandenburg #3 is an excellent example: despite neighboring notes everywhere, it is evident that the melody is unambiguously outlining a tonic triad. >From Schenker's point of view, a fourth might be heard as dissonant owing to its melodic status as a passing tone in the interval sequence 5-4-3, since the reference tonal space is 5-3, i.e. the upper half of the triad outlined over the bass. It's difficult to discuss hierarchies of tone without being tempted to say that some notes are more "important" than others, which is subtly different from saying that some notes have more structural weight, or different syntactic function. So rather than call the fourth in the above context "dissonant" it is perhaps better to call it "unstable" in the same way that a sentence like "I walked my ..." is unstable at the point I broke it off. >Because the fifth of the chord is on the bottom, the 6/4 chord is not as >stable as the 5/3. Some theorists say this is because the 3rd harmonic of >the lowest note forms a dissonance with the other two notes of the triad. >There may be something to that, but of course Bach never thought of it that >way. It is easier to think of it as 6/4 "resolving" to 5/3, the same way >5/4 would resolve to 5/3. Agreed. I would add to this that in a tonal context, the I(6/4) chord takes on considerable tension, since it does not in fact function as a I chord at all (despite contain containing precisely the full set of pitches from the tonic chord). Instead the driving feature of this chord is its bass note, degree V, and the chord functions as a precursor to V. Therefore through purely syntactic function, the chord, despite being consonant takes on a double instability: it is a stand-in for the dominant - a tonally unstable region, but made even more unstable by the fact that the dominant has not yet arrived but is imminent. This to me is a beginning of an explanation as to how two sonorities, one clearly more inherently dissonant than the other, can have their inherent dissonant properties overridden by other contextual features of the music, such that the less dissonant sonority takes on a high degree of tension in the music, and the considerably more dissonant sonority takes on a less tense position. As Bill concisely states: >Musical styles are created as a way of manipulating the physics and >perception of sound towards artistic ends. It occurs to me that technical discussions of compositional deployment of contrapuntal principles push the bandwidth boundaries of email groups. Perhaps for that reason we haven't seen too many such discussions, although I recall a few enlightening posts on the interaction between tunings and voice leading by Gary Morrison quite awhile ago. Nonetheless, I'm a counterpoint nut and would be very happy to see more such postings by other members. Eric Lyon eric@iamas.ac.jp http://www.iamas.ac.jp/~eric Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 6 Dec 1996 16:15 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA21771; Thu, 5 Dec 1996 11:03:14 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA21259 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id CAA18013; Thu, 5 Dec 1996 02:03:12 -0800 Date: Thu, 5 Dec 1996 02:03:12 -0800 Message-Id: <961205100108_71670.2576_HHB21-12@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu