Then, too, it seems narrow-minded to allow

Ex. 10.

and forbid

Ex. II.

Having got thus far, some malcontents say, you allow the first inversion of the diminished triad, why do you not allow the first inversion of the augmented triad? Or again, cannot we include the six-four in the scheme? Theorists shake their heads and say, 'No, it is not expedient'.

Some, again, try to palliate the malcontents by attempting to make the subject more practical. They write examples for instruments. Then the inquisitive pupil wants to know why he has to obey the laws of melodic progression in reference to voices when writing for instruments. Over and above all this, what authority has Dr. Jones or Dr. Smith for extending or restricting laws, or for inventing them?

It will thus be seen that this attitude towards Strict Counterpoint places the technique upon an impossible basis. No one is going to be coerced into using one chord a bar because Dr. Jones says it is good for him, nor into using two for the same reason. But some one will say, you have only touched upon a few of the rules of Strict Counterpoint. Consider the many upon which there is complete agreement, as for example, that quavers must only be used on the second or fourth crotchet of the bar, that they must be approached and quitted by step, that all discords of suspension must resolve on the third crotchet of the bar, and so forth. All that need be said here is that whatever tests are applied to prove or disprove theory in one case will be applied to all cases. We are not willing to accept any dogma on the authority of any theorist or any body of theorists.

4. We have seen how harmonic progression came to be

restricted and melodic progression extended. But it will at once occur to us that we ought to find out how it is that textbooks can contain such examples as

At (a) is an implied six-four,

at (b) is the first inversion of the dominant seventh.

Either these things are wrong or else there is some flaw in the statement of the harmonic resource of Strict Counterpoint.

We are only to use common chords and their first inversions and the first inversion of the diminished triad. Then how does it come about that the following are given in text-books?—

Ex. 13.

(1)

-O

(3)

(1) is a dominant thirteenth,

(2) is a six-four,

(3) is an added sixth.

We may explain (1) by saying that B, E, and D are unessential notes. That being so, the student may add a fourth part, thus:

Ex. 14.

and so expose the mechanical nature of his teaching. At present there does not seem to be any clue to the explanation of this apparent conflict of theory.

Now the malcontents, or the 'agitators' shall we call them, in the sphere of Strict Counterpoint must have asked themselves some such questions as these:

(a) Why is a semibreve Canto Fermo used in Strict Counterpoint?

(b) Why is the harmonic scheme so restricted ?

(c) Why are there so many melodic restrictions? Such questions would occur to any intelligent student. The unsatisfactory answer of the Macfarren school of thought we have already detailed. But we must also explain its ulterior basis.

It is stated that Counterpoint stands in the same relation to music that Euclid does to architecture. Now Euclid starts with some few postulates and axioms which exhibit the following features: the postulates are of such a nature that no one could say such things cannot be granted; for instance, that a straight line may be drawn from any one point to any other point. He simply demands what suffices to carry out his proposals. This, in Counterpoint, corresponds to the granting of the use of staves, clefs, notes, and so forth.

Now the necessary characteristics of axioms are:

(1) They should be self-evident; that is, their truth should not require proof.

(2) They should be fundamental; that is, their truth should not be derivable from any truth simpler than themselves.

(3) They should supply a basis for the establishment of further truths.

To take only three fundamental points in Counterpoint, it cannot be said that the following are axioms:

(1) That only common chords and their first inversions and the first inversion of the diminished triad are to be used. (2) That the Canto Fermo is to be a semibreve C.F.

(3) That each semibreve represents one chord.

It is possible then that these three statements are false. If

so, how came they to be made, and how can we prove them to be false? The earliest treatises on Counterpoint belong to the period when Counterpoint was the only method of composition known, i.e. the Polyphonic Period, and the treatise on Counterpoint was to the student of those days what the harmony book is to the present-day student-his means of learning the current technique. Modern harmony represents two aspects of combined sound-the harmonic and the contrapuntal. Then, the cynic will at once say, you intend to teach the one as it is and the other as it was in the sixteenth century-an absurd combination. We will deal with that later; but we will at once say that it is not so absurd as teaching the one as it is and the other as it is not and never was. That is the real crux of the whole matter. The system of some theorists cannot be verified from the practice of any period, but is a confusion of the old with the new, due to a want of historical research.

5. We shall get some light on the subject if we put our minds back to the sixteenth century. Let us, in the first instance, examine a piece of composition of the period :