A Philosophical Essay of Musick

being so frequent, and the distances of the intermediate pulses being proportional, the mixture is very pleasing; this is the principal chordIn this context, "chord" refers to a musical interval or a harmonious sound rather than a three-note triad. called the fifth.

Where the terms of coincidenceThe points where the vibrations of two different notes align or "hit" at the same time. are further apart—as when it is only the fourth, fifth, or sixth pulses of the treble that coincide with the third, fourth, and fifth pulses of the bass—the mixture is still pleasing and produces chords. These chords are more or less perfect according to how frequently their pulses coincide.

• Coincidence upon every fourth pulse of the treble is the fourth.
• Every fifth pulse is the major third original: "third sharp".
• Every sixth pulse is the minor third original: "third flat".
• When the fifth pulse of the treble aligns with the third of the bass, it is a major sixth original: "sixth sharp".
• The eighth pulse of the treble aligning with the fifth of the bass makes a minor sixth original: "sixth flat".

That these chords have their pulses in such proportional alignment is demonstrable by the division of the monochordA historical scientific instrument consisting of a single string stretched over a soundboard with a movable bridge, used to measure musical intervals.. When the string is stopped at 1/2 its length, it gives an octave; at 1/3, it gives a fifth; at 1/4, it gives a fourth; at 1/5, it gives a major third; at 1/6, it gives a minor third; at 3/5, it gives a major sixth; and at 5/8, it gives a minor sixth. This is agreed upon by all who have ever written about music; therefore, I shall say no more about it.

It may seem strange that a coincidence in this manner should unite sounds, and that the four or five pulses that do not align should not cause more interference than the single coincident pulse could reconcile. It may also seem strange that a coincidence between the eighth pulse of the treble and the fifth of the bass should make the sounds agreeable, despite the variance of all the pulses in between.

But this will be very clear when it is observed that the intermediate pulses do not hinder the harmony at all. They are all placed in such a manner, in relation to one another, that where any of them pull the pulses of the concording string in one direction, there are others that—by being just as far in the other direction—set them right again. They are in balance