Choral singing of folklore and folk song, as well as religious and ceremonial chanting, have a wonderful unifying effect on the tribe, clan, village or whatever practising it. Such forms of choral singing have been found and studied in hunter-gatherer and agricultural societies all over the world, and undoubtedly pre-date civilisation and the earliest musical instruments by thousands or tens of thousands of years. Indeed, the earliest instruments may have resulted from attempts to mimic artificially what the human voice had long been doing.
A tonic of any frequency (ie pitch) may be established by a singer, simply by the choice of an arbitrary note 1 and the singing of it. Thus note 1 of a scale:
1 . . . . . . . .
Once this tonic was established, the easiest note next to come was probably the octave, (the eighth, or note 8) because its frequency is exactly double that of the tonic.
1 . . . . . . 8 .
The next easiest note for the choral singers to find was probably the fifth, with its simple 3/2 frequency ratio to the tonic. It is a fifth (ie four diatonic scale notes) above the tonic.
1 . . . 5 . . 8 .
The next likely could have been the fourth, (tonic/fourth frequency ratio = 3/4) which is also a fifth below the octave: when the fourth is set as a tonic, the octave becomes its fifth above. Thus the combinations 1 + 5 and 4 + 8 are both power chords in their own right, and can be used as such in choral singing.
1 . . 4 5 . . 8 .
Then the third (tonic/third = 4/5) completes the tonic triad: 1-3-5
1 . 3 4 5 . . 8 .
And the next could have been the sixth, (tonic/sixth ~ 10/17) to complete the subdominant triad of 4-6-8.
1 . 3 4 5 6 . 8 .
Addition of the second gives us the 5 + 2 combination: yet another note pair to use in our choral harmonie: (tonic/second ~ 9/10.)
1 2 3 4 5 6 . 8 .
Finally, the seventh gives us the complete dominant triad of 5-7-9, given that the ninth is simply the octave of the second:
1 2 3 4 5 6 7 8 (9)
(Tonic/seventh ~ 1/1.9 ~ 53/100)
And so early choral singers, located without access to tuneable instruments, could have produced a diatonic scale. Taking the notes 1 to 8 making each of them a tonic in turn, leads on by the same process to a complete chromatic scale, which once tempered, gives us the modern chromatic scale as found on the keyboard.
Another possible way to the diatonic major scale was via its power chords, each one having the simplest frequency ratio possible: 2/3. Thus from the tonic-fifth pair (eg C4-G4) and the fourth-octave (eg F4-C5) as discussed above, our fore-singers could have progressed fairly easily and logically to any and all of the other power chord combinations: 2-6: (eg D4-A4); 3-7: (eg E4-B4); 5-9: (eg G4-D5); 6-10: (eg A4-E5) and so on, remembering that the simplest step onwards is from any given note to its octave above or below.
Thus the full diatonic major scale 1-2-3-4-5-6-7-8 (eg C4-D4-E4-F4-G4-A4-B4-C5 could have been filled out, with the power-chord combinations seen above serving also as the basis for the discovery of minor and other scales.
The beginning musician commonly begins with scales and then moves on to study chords. My view is that in the historical development of music, the scales more likely arose out of preceding chords.
There is a great distance in time between the first plucked or bowed string, the construction of the first whistle, the blowing of the first trumpet shell or conch and the construction of an instrument of sufficient quality to play basic chords or a basic major scale. The finding and setting of fret distances on fretted instruments, the discovery of the best string lengths for harps, and where holes should be bored in flutes, etc did not come easily.
But excellent human voices and singers have been around for millennia: presumably since the appearance of our species around 200,000 years ago. Choral singing of sorts may have been for an even longer period as complex vocalisations probably went back a fair way into our primate ancestry. We no longer have other species of the genus Homo to study in live situations, but complex and harmonic vocalisation and vocal communication could have been important to them. Never mind Swiss mountain yodellers: witness species like howler monkeys.
Robert Fink has an alternative view that the diatonic scale was discovered through the harmonics of vibrating strings. It can be found at:
http://www.greenwych.ca/natbasis.htm
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