Wednesday, February 20, 2013

Consonance and Dissonance

I tracked down the abstract for that University of Melbourne study on music that has been reported in various places and that I have written a couple of posts on. I often find that journalistic reporting on research is so confused it is hard to tell what is really going on. So let's have a look at that abstract. Here it is:

Consonance and Pitch.

By McLachlan, Neil; Marco, David; Light, Maria; Wilson, Sarah
Journal of Experimental Psychology: General, Jan 7 , 2013, No Pagination Specified.
To date, no consensus exists in the literature as to theories of consonance and dissonance. Experimental data collected over the last century have raised questions about the dominant theories that are based on frequency relationships between the harmonics of music chords. This study provides experimental evidence that strongly challenges these theories and suggests a new theory of dissonance based on relationships between pitch perception and recognition. Experiment 1 shows that dissonance does not increase with increasing numbers of harmonics in chords as predicted by Helmholtz's (1863/1954) roughness theory, nor does it increase with fewer pitch-matching errors as predicted by Stumpf's (1898) tonal fusion theory. Dissonance was strongly correlated with pitch-matching error for chords, which in turn was reduced by chord familiarity and greater music training. This led to the proposition that long-term memory templates for common chords assist the perception of pitches in chords by providing an estimate of the chord intervals from spectral information. When recognition mechanisms based on these templates fail, the spectral pitch estimate is inconsistent with the period of the waveform, leading to cognitive incongruence and the negative affect of dissonance. The cognitive incongruence theory of dissonance was rigorously tested in Experiment 2, in which nonmusicians were trained to match the pitches of a random selection of 2-pitch chords. After 10 training sessions, they rated the chords they had learned to pitch match as less dissonant than the unlearned chords, irrespective of their tuning, providing strong support for a cognitive mechanism of dissonance.
 The first thing I notice is that I was correct in assuming Helmholtz was one of the people they were disagreeing with. I suppose this is all reasonable from a scientist's point of view? Perhaps my commentor Joel could weigh in here. But I find a lot of things perplexing. First of all, the opening sentence: "To date, no consensus exists in the literature as to theories of consonance and dissonance." What literature are they referring to? Certainly not the theoretical literature in music that abounds in discussion of consonance and dissonance. By "theories" of consonance and dissonance they must be referring to theories of the listener's reception or perception of consonance and dissonance. OK. Then they refer to the "frequency relationships between the harmonics of music chords". What this means is unclear. A chord in music is the simultaneous sounding of two or more notes. Typically chords are triads or tetrads. Yes, every note, in a chord or alone, has harmonics, that is, the overtone series, but what the "frequency relationships between the harmonics of music chords" is, is a mystery to me. Most of the rest I find unclear as well. But perhaps that is due to my ignorance of the scientific context.

Here is how a musician and composer looks at consonance and dissonance. All intervals are divided up into consonant and dissonant, but the line between them has changed over time. If we go back far enough, every interval except the perfect ones (fourth, fifth and octave) was considered more or less dissonant. In actual use this meant that while you could use other intervals, you couldn't end with anything other than a perfect one. Dissonances like thirds and sixths, had to be passing. Later on, thirds and sixths were accepted as consonant, though the minor third was often not considered suitable in a final chord, so a major third was substituted resulting in a tierce de Picardy. As chords with an added seventh developed, found very useful for the added tension they provided cadences, the seventh and tritone were used more and more--though again, they were used in a chord normally passing to a consonant tonic harmony: GBDF (the tritone lies between the B and the F) going to CEGC. The most dissonant intervals have always been the tritone and the minor second, but we find them in constant use during the whole common practice period. However, for most of this period they were used in specific ways and resolved in specific ways. In the late 19th and early 20th century, their use became more and more frequent and the resolution more and more ambiguous until finally the whole notion of consonant and dissonant was tossed out with the development of 12-tone music.

What I find problematic with the researcher's approach is that they seem to take no account of the context. But I can't imagine understanding anything much about consonance and dissonance without context. A C major triad can sound harsh and dissonant in just the right (or wrong!) context. Here is the beginning of the Piano Sonata op 106 by Beethoven, nicknamed the "Hammerklavier" which begins with a simple B flat chord, though sounding quite bold and 'crunchy':

It's all in the context...


Joel Lo said...

Well… as I see it:

Yes, “literature” means “scientific literature” and yes, the theories of dissonance and consonance refer strictly to Psychoacoustics (perception).

"Frequency relationships between the harmonics of music chords" (Oh my God, I can’t believe they wrote it like that) If it is what I think it is, then you know it as well. Yes, it’s about overtones… or the other notes that come “naturally” with a certain note. But scientifically, this subject it’s all about mathematics (numbers). You know that every note has a frequency (a physic property of waves), like the A we use to tune: the frequency is 440 kHz. Since always it is known that there are mathematical relationships between these frequencies in the notes forming intervals, or chords which sound either “naturally pleasant” (consonant) or dissonant. They found mathematical patterns to judge “dissonant” or “consonant” objectively. So then… scientists used to think that there’s a “natural” perception of harmony, dissonance and so on… and that it could be explained with these rules, with these “relationships”.

Hmm… sometimes I get a little lost with their use of the concepts: “pitch” “harmonics” “chords” “intervals” “notes”.

I think I could explain more things in the abstract but that would be a monster-comment here. Hehehe. Judging from your comments on your previous post, I think you got the idea. Specially on the Experiment 2: the more you are habituated to dissonant chords or the more you know the notes they’re made with blah blah blah… the more you are capable of enjoying this until-now-considered “displeasing” chords or intervals.

The reason of why the authors may sound so proud of their work, it’s that they challenge the theory that says that consonance is naturally pleasant (beyond the circumstances). And then, it could be suggested for example that if a new human being, since his gestation in the womb and during childhood only could have contact with “dissonance”, the individual would develop these “templates” which would make him love dissonance and be aversive to consonant music. Of course, such an experiment I think is impossible to run.

I’m with you; I think they’re not overturning anything… yet. Personally, I’m on the other site (I think that it makes sense evolutionary speaking, that consonance is naturally pleasing).

And yes, Bryan… you’re going to have that problem all the time. It’s not that researchers try to “generalize” things, but when studying a phenomenon, they have to isolate the subject in a very “pure” state so they can evaluate objectively the parameters. This time is the sheer dissonance and consonance they we’re working on… not the context they’re present in music. They’re never going to say when it is right or wrong to use dissonance or consonance (when it’s pleasant or not), they’re just trying to understand the natural, physiological operation of the brain.


Bryan Townsend said...

Greetings Joel! And thanks for an excellent comment. Yes, they are dealing with mathematical relationships between different pitches. But this is what puzzles me: they don't seem to want to admit that it is easier to hear simple relationships as consonant than more complex relationships. Referring to the Wikipedia article on acoustics we learn that the fifth relationship is 4:3 while the major seventh is 16:15. No mystery there as to why a major seventh sounds more dissonant than a perfect fifth.

Thanks for making the point that the implication of their "finding" is that we could make people love dissonance by training them from birth. Again, this is the "blank slate" dogma so beloved of scientists doing this kind of research.

But are they actually coming to understand the natural, physiological operation of the brain better?