Harmony in ancient music – and the wonder of taunting kids
Some 3400 year old ancient Ugaritic tablets from what is now Syria revealed a complete song deciphered by Prof Kilmer from University of California. The thing is there were twice as many notes as word syllables, but when the notes were matched to the syllables, they doubled up into logical harmonies, suggesting that this hymn was sung in polyphonic parts. A corollary to this is that the scale was actually a diatonic scale – like our present day ‘major’ scale – one of many modes (like major, minor, myxolidian, dorian etc). However there are many musicologists who think that the diatonic scale was only invented by the ancient Greeks about 2000 years ago.
click on the image to take you to the site – and if you click this image there you will be able to hear a midi file of the ancient song.
Of course, anyone who has heard Fijians or Papua New Guineans singing would recognise immediately that you don’t have to be musically literate to sing complex harmonies. Robert Fink wrote a book in 1970 called “The Origin of Music” in which he articulated the view that there is a natural foundation to the diatonic scale – a view that has actually been around for a while, and is readily discernable to any fretless stringed instrument player. I first heard about it in 1984, while listening to some radio lectures by a musicologist that my recollection suggests was Robert Haas, that the diatonic scale is what happens when you take the main three musical harmonic overtones, build on their overtones and arrange them in linear sequence.
The human ear is quite amazing – and childrens’ ears are able to distinguish most of the overtones without difficulty. It works like this:
If you take a string, say one tuned to the note ‘C’ and play it, you will get not only that note, but a whole series of other notes that make up its harmonics – these are the overtone series. The first of these is derived from the string being halved which yields the octave above the note – so it is another ‘C’. This is the strongest reinforcement of the note, so it is the most readily discernable and gives strength to the note. The next occurs at the one third point, and this generates a note a fifth above the tonic (the note ‘G’) – this is called the ‘dominant’ and it is the first different note to be heard. the next occurs at the one quarter point and yields a note a fourth above the dominant – it is another octave ‘C’ – so it still reinforces the tonic note.
Now it gets interesting… the next overtone is where the string is divided into fifths, yielding a note a third above the tonic – this is called the ‘sub-dominant’ – the note ‘E’, as it is strong but not as strong as the dominant. The next harmonic divides the string into sixths, making a note a third above the E which is another ‘G’ – now we start to see a pattern. By this time the tonic note – ‘C’ has been reinforced three times, while the dominant has been reinforced twice and the sub-dominant once.
The next overtone on our C string is where the string is divided into sevenths, yielding now a ‘B-flat’. As the string is divided into eighths we get another ‘C’ which again reinforces the tonic note.
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But now we notice a wonderful thing. Have you heard children taunting each other? have you heard them chanting ‘Nyah, nah, ni nyah nah…’ Why is this a taunting tune the world over? And why is this remarkable? Look at the harmonic overtones that are not the tonic note, and look at the first three without repetitions – play them if you have an instrument to hand. The notes will be: G down to E, then up to B-flat. Try playing G,E,G,E,G,E,B-flat,G and hear that taunting tune. Think for a moment about the sophistication of children’s ears to pick up the first four harmonics and then recognise that they can represent weakness by singing or chanting the first three overtones that do not reinforce the tonic note!
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Are we amazed yet? there’s more.
Let’s continue the arithmetic progression up the harmonics. The next in the series is where the string is divided into ninths – this gives us a ‘D’ or supertonic as it is one whole tone above the tonic note. Divide the string into tenths and we get an ‘E’ which reinforces the earlier E – with all this reinforcement, that is why a Major chord based on C will be C,E,G – as these most strongly reinforce the note – any other combination will sound weaker, because there will be interference as weaker harmonics are being emphasised – hence a minor chord sounds weaker or even a little sad, as against the strong happy sound of a major chord.
back to our progression – the next overtone divides the string into elevenths giving us an F-sharp. Finally, with the twelfth harmonic, we get another ‘G’. We have seen that some notes keep getting reinforced, and others don’t.
Fink points out that the most audible overtones have some simple ratios – 2:1 for the octave, 2:3 for the fifth (or dominant), and the fourth note of the scale (whose first different overtone is the octave) with a ratio of 3:4. If we draw out the first three different overtones of these three notes and lay them out in sequence, we get: voila! a major scale.
He goes on to explain how some of the other types of scale came into existence, but for me the interesting thing is that the scale is based on the sheer physics of sound – and that our ears are perceptive enough to pick out natural harmonies.
Cheers
Jerry
