The Nature of Quarter-tones:
Natural Scale vs. Tempered Scale

Like all other wind instruments, the Naï is fixed in pitch (should the player be adopting the proper technique, of course). So, when our next instrument came to be invented, the ancient Egyptian Harp, it simply continued the existing tradition, playing along with its elder kin. But with the advent of the following genre of instruments, the ancient Egyptian Lute, the time was ripe for a totally different ride...

     The lute's strings must have got our priests/scientists all crazy! They finally got hold of a suitable research tool that helped them understand the exact nature of the Harmonic Series, which they had first noticed embodied in the Naï. But they also came to realise that the latter's intervals do not exactly conform to the eternal, physical rules of Mother Nature. Those purists of old, in their relentless quest for being one with the Universe, could never swallow the compound ratios of the Naï; 3/4 is all right, but 76/99, for example, would be utterly unforgivable! Thus, the idea of the Natural Scale was born (note that physis in Greek meant Nature, and so, Natural in this context really meant Physical, i.e. physically/mathematically correct, bearing in mind that physics, geometry, mathematics, astronomy and music formed one compound whole at that time).

     And to facilitate practising this rigorous, mathematically correct version of tone-making technique, my ancestors devised a cunning system of drawn frets for their lutes, calculated to the nearest quarter of a comma. Now, the comma was in fact defined as the smallest audibly recognisable interval, and is mathematically equivalent to 1/81 of the initial string length. In other words, if we started with a string of length X, emitting a tone T, to reach a tone T+ that is one comma above T, we would have to shorten the original length X by an amount equal to 1/81 of it (stopped with a finger of the left hand, like with the violin), and pluck the remaining 80/81. Practically, though, the only cases where such one-comma-apart drawn frets would exist were the following pairs: C#/Db, F#/Gb and G#/Ab. Another larger unit was used for the rest of the instrument's length of neck: the Limma, which is equivalent to 3 3/4 of commas (it was certainly more convenient than if the entire length were divided into commas; I should know: I tried this system on my lute). Using those mathematically pure intervals of the Natural Scale (or Scales, really) meant one could use subtle variations of any given, fixed scale to provide for more expressive power. A natural, i.e. mathematically correct, Eb, in C minor for example, would be rendered more depressing if it was played one or two commas less, and vice versa. But things were never left to the player's whims, though; rigorous discipline was the norm, in case you didn't know...

     Later on, the Arabs got to learn all about these things, and endeavoured to continue the glorious traditions. As a matter of fact, veteran musicians still maintain that certain scales have their Eb a tiny bit shifted in one direction, while other scales have it shifted in the other direction, but it all seems more like fossilised knowledge, certainly not the vibrant, living idiom it once used to be. Because ever since we were occupied by the Greek more than 200 years B.C. (then the Persians, the Romans, ... etc., up until we obtained our freedom in 1952!!), our creativity was generally stifled. Continuing the traditions was done through personal efforts of individuals (and went away with their departure), not establishments or institutions any more, not academic ones at any rate. Not even when, in 1932, the First Conference on Arabic Music was held in Cairo, attended by a host of Egyptian, Arab and orientalist musicologists from all around the world.

     By then, the western Equally Tempered Scale had become the norm (we got to know the occidental musical traditions more closely with the opening of the first, older Opera House that was built to celebrate the inauguration of the Suez Canal, for which Verdi's Aïda was conceived). And a quarter-tone came to be defined as half of a semitone, thus 50 cents.

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