By John Lambert, Esq. 319 
The intervals of the Diatonic Scale, whether subdivided into 
Tetracords, according to the earlier system of the Greeks; into 
Hexacords, as afterwards was the case; or into Octaves, as at the 
present day, are all founded upon certain laws of vibration, known 
to the Greeks no less than to the Musicians of the Middle Age; and 
the only difference between the Scales of the two consisted in this: 
that the latter added another note to the Scale below the A, which 
they designated by the Greek I’, or Gamma, from which the Scale 
came to be termed Gamut, just as the word Alphabet is derived 
from the two first Greek letters, Alpha and Beta. 
Nothing can be clearer than the description of the Scale given 
by Guido d’ Arrezzo, the great Musician of the eleventh century, 
in his celebrated treatise, the Micrologus.' It is to be found in his 
third chapter, ‘‘ On the disposition of the notes on the Monochord;” 
the Monochord being an instrument, consisting of a single string 
stretched over a piece of wood. He says, “the Gamma, or starting 
point, being in the first place fixed upon, then divide the inter- 
mediate space between it and the end of the string into nine equal 
parts, and at the termination of the first division place the letter A, 
from which all the ancients began their Scale. Then from A to 
the end, calculate the ninth part, in the same manner, and place 
at that point the letter B. After this, returning to the Gamma, 
divide the string into four equal parts, and at the end of the first 
part you will find the note C. By a similar division by four, as with 
the Gamma, is found C; so in relation with A, you will find D; with 
B, E; with C, F; with D, G; and with E, aabove; which process 
being worked out, all the intermediate intervals will be discovered 
in due order: so that, for example, if you divide the string from B 
to the end into two equal parts, you will find the Octave b above; 
a similar division from C will give the ¢ above: and so you may go 
on, almost without limit, either above or below.” 
The Scale, thus constructed, is, as you will perceive, purely 
Diatonic, without accidentals. There was, however, one accidental 
admitted, viz., b flat, which was introduced in order to obviate what 
the ancients considered the false relation between F and b natural, 
1 Scriptores Musicw. Gerbert. Vol. I. “oa 
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