A treatise of the natural grounds and principles of harmony by William Holder ...

CHAP. III. Of Consonancy and Dissonancy.

COnsonancy and Dissonancy are the Result of the Agreement, mixture or uniting (or the contrary) of the undulated Motions of the Ayr or Medium, caused by the Vibrations by which the Sounds of distinct Tunes are made. And those are more or less capable of such Mixture or Co-in∣cidence according to the Proportion of the Measures of Velocity in which they are made, i.e. according as they are more or less commensurate. This I might well set down as a Postulatum. But I shall by several Instances indea∣vour to illustrate the undulating Mo∣tions or Undulations of the Ayr; and confirm what is said of their Agree∣ment and Disagreements. And first

the Undulations, by somewhat we see in other Liquids.

Let a Stone drop into the Middle of a small Pond of standing Water when it is quiet, you shall see a Motion forthwith impressed upon the Water, passing and dilating from that Center where the Stone fell, in circular Waves one within another, still propagated from the Center, spreading till they reach and dash against the Banks, and then returning, if the force of the Mo∣tion be sufficient, and meeting those inner Circles which pursue the same Course, without giving them any Check.

And if you drop a Stone in another place, from that Centre will likewise spread round Waves; which meeting the other, will quietly pass them, each moving forwards in its own proper Figure.

The like is better experimented in Quick-silver, which being a more

dense Body, continues its Motions longer, and may be placed nearer your Eye. If you try it in a pretty large round Vessel, suppose of a foot Diameter, the Waves will keep their own Motion forward and backward, and quietly pass by one another as they meet. Something of this may be seen in a long narrow Passage, where there is not room to advance in Circles.

Make a wooden Trough or long Box, suppose of two Inches broad, and two deep, and twenty long. Fill it three Quarters or half full of Quick-silver, and place it Horizontally, when it is at quiet, give it with your Finger a little patt at one End, and it will impress a Motion of a ridgid Wave across, which will pass on to the other End, and dashing against it, return in the same Manner, and dash against the hether End, and go back again, and thus backward and forward, till

the Motion cease. Now if after you have set this Motion on foot, you cause such another, you shall see each Wave keep its regular Course; and when they meet one another, pass on without any Reluctancy.

I do not say these Experiments are full to my purpose, because these be∣ing upon single Bodies, are not suffi∣cient to express the Disagreements of Disproportionate Motions caused by different Vibrations of different sound∣ing Bodies; but these may serve to illustrate those invisible Undulations of Ayr. And how a Voice reflected by the Walls of a Room, or by Ec∣cho being of adequate Vibrations, re∣turns from the Wall, and meets the commensurate Undulations passing forwards, without hindring one ano∣ther.

But there are Instances which fur∣ther confirm the Reasons of Conso∣nancy and Dissonancy, by the Mani∣fest

agreeing or disagreeing Measures of Motions already spoken of.

It hath been a common Practice to imitate a Tabour and Pipe upon an Organ. Sound together two discord∣ing Keys (the base Keys will shew it best, because their Vibrations are slow∣er) let them, for Example, be Ga∣mut with Gamut sharp, or F Faut sharp, or all three together. Though these of themselves should be exceeding smooth and well voyced Pipes; yet, when struck together, there will be such a Battel in the Ayr between their disproportioned Motions, such a Clat∣ter and Thumping, that it will be like the beating of a Drum, while a Jigg is played to it with the other hand. If you cease this, and sound a full Close of Concords, it will appear surprizingly smooth and sweet, which shews how Discords well placed, set off Concords in Composition. But I bring this Instance to shew, how strong

and vehement these undulating Moti∣ons are, and how they correspond with the Vibrations by which they are made.

It may be worth the while, to re∣late an Experiment upon which I hap∣pened. Being in an Arched sound∣ing Room near a shrill Bell of a House Clock, when the Alarm struck, I whistled to it, which I did with ease in the same Tune with the Bell, but, indeavouring to whistle a Note higher or lower, the Sound of the Bell and its cross Motions were so predominant, that my Breath and Lips were check'd so, that I could not whistle at all, nor make any Sound of it in that discor∣ding Tune. After, I sounded a shrill whistling Pipe, which was out of tune to the Bell, and their Motions so clashed, that they seemed to sound like switching one another in the Ayr.

Galileo, from this Doctrine of Pen∣dulums, easily and naturally explains

the so much admired sympathy of Consonant strings; one (though un∣touch'd) moving when the other is struck. It is perceptible in Strings of the same, or another Instrument, by trembling so as to shake off a Straw laid upon the other String: But in the same Instrument, it may be made ve∣ry visible, as in a Bass-viol. Strike one of the lower Strings with the Bow, hard and strong, and if any of the other Strings be Unison or Octave to it, you shall plainly see it vibrate, and continue to doe so, as long as you continue the Stroke of your Bow, and, all the while, the other Strings which are dissonant, rest quiet.

The Reason hereof is this. When you strike your String, the Progressive sound of it strikes and starts all the other Strings, and every of them makes a Movement in its own pro∣per Vibration. The Consonant string, keeping measure in its Vibrations with

those of the sounding String hath its Motion continued, and propagated by continual agreeing Pulses or Strokes of the other. Whereas the Remainder of the Dissonant strings having no help, but being checked by the cross Mo∣tions of the sounding String, are con∣strained to remain still and quiet. Like as, if you stand before a Pendulum, and blow gently upon it as it passeth from you, and so again in its next Courses keeping exact time with it, it is most easily continued in its Motion. But if you blow irregularly in Measures different from the Measure of the Mo∣tion of the Pendulum, and so most frequently blow against it, the Moti∣on of it will be so checked, that it must quickly cease.

And here we may take notice, (as hath been hinted before) that this also confirms the aforesaid Equality of the Time of Vibrations to the last, for that the small and weak Vibrations of

the sympathizing String are regulated and continued by the Pulses of the greater and stronger Vibrations of the sounding String, which proves, that notwithstanding that Disparity of Range, they are commensurate in the Time of their Motion.

This Experiment is ancient: I find it in Aristides Quintilianus a Greek Au∣thour, who is supposed to have been contemporary with Plutarch. But the Reason of it deduced from the Pendu∣lum, is new, and first discovered by Galileo.

It is an ordinary Trial, to find out the Tune of a Beer-glass without stri∣king it, by holding it near your Mouth, and humming loud to it, in several single Tunes, and when you at last hitt upon the Tune of the Glass, it will tremble and Eccho to you. Which shews the Consent and Uniformity of Vibrations of the same Tune, though in several Bodies.

To close this Chapter. I may con∣clude that Consonancy is the Passage of several Tuneable sounds through the Medium, frequently mixing and uniting in their undulated Motions, caused by the well proportioned com∣mensurate Vibrations of the sonorous Bodies, and consequently arriving smooth, and sweet, and pleasant to the Ear. On the contrary, Dissonan∣cy is from disproportionate Motions of Sounds, not mixing, but jarring and clashing as they pass, and arriving to the Ear Harsh, and Grating, and Of∣fensive. And this, in the next Chap∣ter shall be more amply explained.

Now, what Concords and Discords are thus produced, and in use, in or∣der to Harmony, I shall next consi∣der.