So in this next lesson we're going to consider a third way of thinking about consonance and dissonance, and this is in terms of biology. And just by way of sort of introducing this and comparing it to what Helmholtz had to say on the subject, it doesn't really make a whole lot of sense that we would like something because of the absence of an annoyance. That would be kind of the same as kind of saying that we liked sweet things because they weren't sour, and that just doesn't really hold much water as an explanation. The biological explanation of consonance is predicated on what we like and dislike in music based on the biological fact that generally in any sensory modality, what we like or dislike has to do with its biological value for us. So let's think about that in terms of what we talked about earlier, that the biological value for tonality comes from the human voice. Identifying the human voice because of its value in social communication, its biological value in getting along in the world, ultimately in surviving and reproducing. Just to remind you of that, the argument was that we developed a sense of tonality in the first place because the major tonal sounds that we hear in nature are conspecific vocal sounds. And those vocal sounds, whether pre-lingual or lingual, are critical in human communication and have been a major driving force biologically as well as linguistically, and ultimately in the language that we use today. So let's go back and ask sampling speech whether we find evidence of musical ratios, of musical tone combinations, of musical dyads, in speech itself. So we talked about this before, the TIMIT, Texas Instrument MIT speech corpus, as a database that people have used. And I showed you this slide before. Let me just remind you that this is the time signal of a sentence spoken in American English. And this is taking a little tonal snippet out of this, 100 milliseconds, showing you the amplitude variation which is systematic, the tone variation, over this 100 millisecond interval that we talked about before. And this is taking that same snippet and turning it into a spectrum. You remember that the spectrum is plotting the amplitude of the sound against its frequency as an indicator of what the frequencies that are prevalent in this snippet are. And you remember we said before that these are the formants in speech, that these sequence of systematically repeating frequencies are the harmonic series at the fundamental, the first harmonic, second harmonic and so on. So we can ask the question using the TIMIT database. In a compilation of speech, a compilation of thousands of these snippets, is there any evidence of musical tonality? If we just take the pitches in different elements of speech, so for example, if we just take the pitch of this tone or this tone and ask how these varying pitches are related to music, the answer is they're really not related to music at all. The up and down of the pitches in speech, the singsonginess of speech, isn't musical in the sense of hitting musical intervals, the intervals of a chromatic scale, for example. We just don't see any of those intervals in speech. They don't come out of an analysis of pitch in speech. But what they do come out of is an analysis of speech spectra. And let me show you how that works by taking that speech corpus and asking, is there in our experience with ordinary speech, are we exposed to chromatic scale tones? And the answer is yes, but in a kind of a subtle way. So here is the analysis of many thousand snippets, spectra, of speech that I just described to you. And this is those snippets normalized over an octave, over a single octave, to ask, as we go across an octave, are there emphases in the occurrence of tones, and tonal relationships in particular, in normal speech that exemplify musical intervals? So this is unison. This is, as you see here, the named intervals of the chromatic scale, most of them, not all of them, for reasons that are more technical than anything else. But these red arrows are indicating the frequency intervals as ratios of the chromatic scale tones. And you can see that where the chromatic scale tones occur in this analysis of speech, speech corpus, a lot of speech normalized in terms of its pitches so they're all in the same scale whether it's a woman talking, a man talking and so on. That these red arrows show a bump over an octave where there is clearly some exposure to the chromatic scale intervals in normal speech. Here's the keyboard, just for comparison, to remind you of the ratios of the musical tones and their names and their expression or there exemplification on the keyboard. But the bottom line of this is that in normal speech, we are being exposed to ratios from the harmonics that are occurring in speech spectra. We are being exposed routinely to musical ratios. Where those ratios are coming from is a complicated issue that I'm not going to go into. But they're there, and it's important to recognize that as part of our normal exposure to speech, we hear ratios that are musical intervals. Not in the prosody of speech, but in the relationship of the harmonics in speech. So let's go back to what we talked about before, which is the harmonic series and the importance of recognizing human speech by virtue of its main identifying characteristic. Its main identifying characteristic being, in addition to its pitch level, in addition to its timbre, the main identifier of human speech as opposed to some other sound is its expression of a uniform harmonic series. Remember harmonic series being the fundamental frequency and integer multiples of that fundamental frequency. So here's a diagram of a harmonic series. So here is the fundamental, the first harmonic, the second harmonic, third harmonic and so on. Let's say that the fundamental frequency is 100 hertz, so this would be 200 hertz, 300 hertz, 400 hertz and so on, just as an example. The point of showing you this is that the biological argument for recognizing human vocalization and consonance emerging from that is that when you take the scale degrees of the chromatic scale and ask, how do they play out in terms of the consonance and dissonance of the scale degrees in terms of their harmonic correspondence? That is, whether the harmonics of one tone correspond to the harmonics of another tone. You get a very good ranking of consonance on this biological basis, the idea being that we recognize human speech based on the expression of a uniform harmonic series. And that the more constant tones exemplify human speech far better than the relatively dissonant tones in the chromatic scale, and that that's the reason why we find some tone combinations consonant and other dissonant. So let's look at that. This is unison. Remember unison is playing two tones together. So the harmonic correspondence in unison is gonna be complete, 100%. So here's, again, our harmonic series, these tick marks indicating the sequential harmonics in the series, and here the white circle is indicating a tone played with that tonic harmonic series. That's the same tone. And of course, it's going to correspond every time there is a tone, let's say we're playing them on two pianos, every time there's a harmonic on one piano, there is a corresponding harmonic on the other one. That's unison, by definition. And the argument would be that it's the most consonant, as we saw looking at the ranking of consonance in those studies that were done around the turn of the 19th and 20th century, it's the most consonant. The next most consonant tone is the octave, and the octave has every second harmonic in exact correspondence with the fundamental of the tonic, with the sequence of harmonics in the tonic. So it's 50% coincidence, and that's the second most consonant tone. The next most consonant tone combination is the perfect fifth. The perfect fifth has a every third, one out of three tones in common. So perfect fifth is here shown in orange, and you can see that every third harmonic in the tonic is in correspondence for the fifth. And so on, down the ranking of consonance, with the fourth being the next most corresponding tone combination. The major third being the next one, the major sixth being the next one and so on down the whole chromatic scale. And this ranking based on the correspondence of the harmonics gives you the ranking of consonance quite well. So this is a complicated slide, one that we're going to come back to and talk about some more. But the main point I want you to grasp for the moment is just that when you think about consonance in terms of biology, and identifying human speech because of its biological value. That's gonna be an enemy, a potential mate, somebody who's telling you something important about where the food source is in human evolution. Identifying human speech is critical and the argument is that the consonance derives from the relative similarity of a tone combination to the uniform harmonic series that exemplifies, that characterizes human speech. The closer it is, the more we like it. The further it is, the more dissonant the tone combinations down here at the minor second, major seventh and so on, the less we're going to like it. We're not going to dislike it entirely, because it's still indicative of human speech, but it's less indicative than the consonant combinations at the octave, at unison, the octave and major fifth, for example. So let's just sum up the major points that we've covered today. The first point I made was that music is hard to define. There are many definitions that you'll find in music theory books or dictionaries, but they all have the aspect of tonality, timing, aesthetic appeal, and emotional appeal probably deriving from that aesthetic appeal. The second point I made was that the phenomenology of tonal music, the list of phenomena to be explained that we're going to be talking about and that I've started talking about in today's module, they remain largely unexplained. The central issue in tonality is why we like some tone combinations and melodies and harmonies better than others. That's consonance and dissonance. And the possible explanations that we talked about, and they're not exhaustive, but these are the main ones that people have considered. The possibilities are a mathematical explanation that began with Pythagoras, but that goes on today because of the appeal to mathematicians in particular of explaining music in these terms. We talked about Helmholtz, the major figure in the 19th century who put music on a physical basis, trying to explain consonance and dissonance in this way. And then we ended up with a biological explanation of tonal music that in the next couple of modules we're gonna go on exploring further. As what seems to me at least, the most plausible reason for not only consonance and dissonance but all of the list of the phenomena in tonal music that otherwise remain unexplained. So next time we're going to go on talking more specifically about musical scales, how they're used, and some reasons why particular scales have been preferred over the history of music. This is really a basic issue that we'll turn to next.
