Now in this lesson let's turn to an explanation of that question. Why are only a relatively a few dozen scales used whether you're considering western music or music in other cultures. The number of scales is limited. Given that there could be billions of scales if you just take the pitch intervals over an octave that we can discriminate, or even limit those to five or seven note combinations. There are huge numbers of possible scales. Why do we use only these few? And the only answer I know of that makes any sense is a biological explanation of scale preference, and let me try and briefly explain what that is. So you remember I said before, but now I'm going to come back to it and focus on it a little bit more clearly, that the issue that makes a tone consonant. And the same idea would apply to a scale, which is a collection of intervals as opposed to a dyad, just one interval. A tonic and a note above it. Now we're talking about a whole collection of intervals. Five note collections pentatonic scales. Seven note collections, heptatonic, diatonic scales, etc. So let's take as an example, a particular scale. This is the pentatonic minor scale, and ask, is the reason we like scales and are limited to a relatively small number of scales in music usage worldwide and historically, because of the scale's vocal similarity? The argument was before and is still, that vocal similarity is critical in consonance, in the use of scales and other aspects of music because of the biological value of recognizing vocal utterances coming from human beings which is the source of tonal sounds, and our evolutionary environment. And at the value of recognising those sounds would have been pre-eminent in the evolution of human, the human species and the evolution of our tonal sense. So the idea here is that the use of a small number of scales today stems from the fact that relatively few combinations of tones can have sufficient vocal similarity to count as something that we want to hear, like to hear, that is biologically advantageous to hear. So let's take the pentatonic minor scale. There are 15 different possible combinations of intervals in that five interval, six note scale. And they are listed here as these 15 intervals and they're each named. And you'll see that some of these intervals are repeated. And you can ask for each of the possible intervals in this or any scale, I've done it for a large number of scales. You can ask for the tones in that scale, what is their vocal similarity? What is their degree of agreement with a harmonic series? Again, the harmonic series being the chief identifier of a human vocalization. So, you can ask, for example, for a minor third, what is the percentage similarity of a minor third, the tonic play with a minor third interval in terms of the conformity of that combination to a uniform harmonic series, to a single harmonic series. And the answer is 33%. You can take the octave for example, and ask what's the conformance of inactive? The tonic note played with the twice the frequency of the tonic note. That's the definition of an octave. So there you have correspondence of those two notes. A 100% of the time the two harmonics are overlapping. Every harmonic in the series of the tonic note has a correspondence with every other harmonic in the note an octave above it, so you can go down this list and compare all of the possible intervals in a scale like this with respect to their harmonic correspondence. How often does the tonic harmonic series correspond with a harmonic in the tone that's being played above it? And that average similarity for the minor scale or any scale could be calculated numerically on this basis. And the idea is that the greater this value the greater the similarity will be. So the trick in this is comparing the harmonic overlap of the two notes that are being played and then taking the whole collection that forms the scale and asking how does that scale rank in terms of its correspondence with a harmonic series. The idea being that, the more the overlap, the greater the similarity to a single harmonic series, the greater the identification with vocal utterances would be, the more constant that the intervals that comprise that scale are going to be, and the more attractive that scale will be in total, taking all of the intervals, in this case, the five intervals of minor pentatonic scale. But, you can analyse any scale on this basis, and the result of that is really remarkable. So, let's just take a look at that so here are the top ten five-note scales ranked in that wave. One example being what I've just showed you and here are the top ten seven-note scales ranked in that way that is in terms of their relative vocal similarity. And these rankings, it's easy to do this with computer algorithms these days. This couldn't have been done too many decades ago. The upshot of that is that the ranking fits beautifully with the scales that are actually used and explains why it is that we like only a relative handful of scales whether our culture is western, eastern or some other tradition. So, I won't go through the names of these different scales, but sufficive to say that the top ten ranked five note scales are all scales that are recognized in Eastern, Western, other musical cultures as scales that are commonly used. So the same is true of the top ten seven-note scales. And the upshot is that the scales that are used in music are those with the greatest vocal similarity. That is, the ones that are closest in their collective identify, to a uniform single harmonic series, that enable us to, biologically speaking, recognize human vocalization. So, the answer to the question, why are there just a few of these scales that we use today, a few dozen of scales worldwide. The answer is that as you move away from the top ten, in these two categories, you get further and further from vocal similarity. You get further and further from the ability of the collection of tones just as we talked about for the single tones. In consonance you get further and further away from the ability of that tone collection to conform to the ability to recognize you get further and further away from the ability of that tone collection to identify human vocalization and it just becomes less and less attractive to it. More and more murky in a biological sense and the argument in that context is that the reason we like such a small number of scales or use such a small number of scales that's just historical fact. Is because relatively few have sufficient identity of the harmonic series that characterizes human vocalization to make it useful and in that sense attractive.
