in like manner has major intervals only, excepting the third and sixth, which are minor. As we know how major intervals are changed into minor, we can easily convert major scales into minor. We need only depress the third and sixth. For example,C major, c-d-e-f-g-a-b-c into C minor, c-d-eb-f-g-ab-b-c

Here we find that the succession of tones makes the following steps:

d

eb

g

ab

b

No doubt these successions of tones are softer than that with the extreme second; but the idea of one mode is entirely destroyed-the sixth is as well ab as a, the seventh bb as b, therefore the pretended scale should be declared to be a double foundation or two scales; or again, both successions of tones should be mixed together, thus:

c-d-eb-f-g-ap-a-bb-b-c which would form a scale, half diatonic, half chromatic, but which would disagree too much with itself to answer the object. This will be shewn more distinctly in the Theory of Harmony, and also in the first part of the Author's Instructions in Composition.

par

It is quite another question, whether the composer may not in ticular cases (in order to make the succession more soft and flowing) deviate from the systematic progression, No. 47, and so arrange his tones as in No. 48, or other different ways. The rules of composition allow him this liberty, and moreover shew him how and on what grounds he should use it. The teacher may therefore permit his pupil (in order to acquire ease and readiness in playing and singing) to use the flowing forms in conjunction with the fundamental scale, nay, even to use them preferably for technical practice, in order that the harsh effect of the

Why have we formed our two scales in th manner and no other? why has the major, maj intervals only? and why in the minor are the thi and sixth alone minor? These questions will a be answered hereafter: for the present it is sufficien to know the real construction of each, and to lear their succession of sounds.

SEVENTH SECTION-THE MAJOR AND MINOR SCALES OR KEYS.

We have already remarked, that the intervals may be made to proceed from any degree, whether from d or e, or d as well as from c. Therefore we can form from "any degree at will, all the major and minor intervals, as we have done at page 17, merely as an example.

Consequently we can construct our scales on every tone, as well as upon c, d or eb, &c.

The representation of a major or minor key or scale on determined degrees, we call THE SCALE.

There are, therefore major scales and minor scales,
that is, one of each for every tone of our system.
How many tones are there in our system?
First-the seven root tones-

db-eb-gb-ab-bb

in short, every tone might have been called by three different names. But by so doing, we should not have acquired new tones, but only additional names.

How can we now construct the different scales ? We fix upon all the degrees from that one with which we have chosen to begin, and compare the succession of tones and semitones with the model successions as above, whether the intervals be for the major, 1, 1, 1⁄2, 1, 1, 1, 1⁄2 tones, and for the minor, 1, 1, 1, 1, 1, 1, tones.

Where the step is too small, we must raise, and where too large, we must depress the upper tones to the right measure.

If it be desired, for example, to write down the major scale of a, or

A, MAJOR.

We put down first of all, the degrees from a, thus,— a-b-c-de-f-g-a

Now, we examine the intervals step by step, a-b is right, a tone; b-c is only a semitone, but should be a whole tone; therefore we raise c to c, and so get the tone b-c. The distance between c-d and d-e is correct. Now a whole tone must come again, but e-ƒ is only a semitone; we must there

systematic scale may not have a torporific and annoying influence on the pupil by too frequent repetition. But this concession to particular cases in composition and to kind feeling towards the pupil, must not be construed into a departure from the true and indispensable system.

and then measure the steps. Here we find ab-b too large for a tone, and must therefore lower it to bb; so we must proceed and shall finally get the scale

ab-bb-c-db-eb—ƒ—g—ab

In like manner, we can now form any minor scale. We get it, however, much more easily when we know the major scale of the same tone; for in that case, without any more measuring, we have only to depress the third and sixth. In order to change* A major, for example, into A minor,

ab-bb-cb-db-eb—ƒb-g—ab

Now only, have we a fully established foundation for any musical composition. We can now say whether it is altogether or chiefly in the major or minor key, and to what particular major or minor scale it belongs; that the composition is in A major, or A minor, in the usual technical expression.

Commonly (not without exceptions) a composition proceeds in one key, and if it abandon that key, for a time, to move into another, it returns to the original key, for its close. It will facilitate our comprehension and performance of a composition, if we know in what key it is written.

EIGHTH SECTION-COMBINATION OF ALL THE SCALES.

We cannot deny that the mode of constructing the scales, as set forth in the preceding section, is minute and circuitous: particularly if the operation is to be often repeated. We require, therefore, a more convenient process, by which we may in a moment, produce in our imagination at pleasure, any one, or all such similar arrangements.

What is the meaning of imagining or conceiving

a scale?

Perceiving which degrees in it are to be raised or

*This operation must become familiar to every person who wishes to be, in any degree, fundamentally instructed. But we urgently recommend to the beginner for the first cultivation of the ear and the imagination, to play diligently C major, and then the other major scales and lastly to seek out the minor scales, by the ear only, with a pianoforte. If he thinks he has found a scale correctly, let him name the tones, taking the names from the next following degrees-thus, for example, not calling the second tone in A major from a, a, but bb, since the degree of a is already occupied. Then let him measure the distance of his steps and prove the correctness of his discovery. He may begin this exercise with the more convenient tones G, D, A, E, F, BD, ED, Ab, but he must work with diligence. The time dedicated to this object will greatly profit musical conception; more by far than simple intellectual comprehension of what we have said above, or mere learning by rote, with which alone many teachers content themselves.

C major is the normal major scale which requires neither elevation nor depression, since it contains nothing but the seven original tones,

C-D-E-F-G-A-B

We begin, therefore, with C, place it as the beginning, and put a nought over it, as a sign that in it, nothing is to be either raised or depressed. Then we write after C, the fifth degree from it, in ascending, G, and each succeeding fifth degree upwards, until we come again to C. Lastly, we mark out of the line, the fifth degree before C, thus :F. 0

CGDAEBFC

:

with twelve raisings. But b is enharmonically the same as C.

We are now, therefore, returned through all the twelve major scales, to the first C again; and by steps of fifths only. This representation of the scales, is called the CIRCLE OF FIFTHS.

But we know that scales may be also produced by depressed degrees. We formed in that manner A major, page 20. What are the contents of these scales? Depressing is the opposite of raising. Consequently the contrary operation will give us the scales with depressed degrees. We write, therefore, the circle of fifths towards the left hand, in contrary order, C-F-B, &c. and know that in C major there is no depression; in F major, one degree will be depressed; in the next scale, two degrees, and so forth. We remember also, that (as formerly in the raising) every depression will be continued for the following scale. Here is our new plan,

F

b

7 6 5 4 3 2 1 0 CGDA EBF C

But how do we find which degree is to be each time lowered? Each time that which is to the left in the plan.* Therefore, in F major, b is lowered to bb. Now, we see immediately, that the next scale cannot be B, but Bb major. In Bb major, in the first place, bb is retained, and e depressed to eb; consequently, the following scale is not E major but Eb major. While we proceed in this manner, our former plan assumes this form

We see, therefore, that in Ep major there appear three depressed degrees, bb, eb and ab; in Db, five, bb, eb, ab, db, gb; in Cb, seven, bb, eb, ab, db, gb, cb and fb.

If we would proceed further, we should find after Cb major, Fb major with eight; Bbb major with nine; Ebb with ten; Apb with eleven; and Dbb with twelve depressions. But Dbb is enharmonically the same as C major, consequently we have here also completed the circuit of the chain of fifths, and returned to its beginning. By these plans, by the circle of fifths with elevations, and that with depres

This seems arbitrary and not in agreement with the supposition that in the depression the contrary effect occurs to what takes place in the elevation. But this seems only; because for the sake of brevity, we did not pursue the circle of fifths to the end: if we were to continue it from page 20, we should find

sions, we are in a condition to point out immediately and surely, any major scale, at pleasure. It is very easy to form the scales, which have few elevations or depressions,-more tedious naturally to arrange those which have many.† But here we meet, most joyfully, the reflection that the scales with so many changes are quite superfluous.

Let us place here for example :

0 1 2 3 4 5 6 7 8 9 10 11 12 C G Ꭰ A E B F C G D A E B Dbb Abb Ebb Bbb Fb Cb Gỗ Db Ab Eb Bb F C 12 11 10 9 8 7 6 5 4 3 2 1 0

Comparing the above scales, with sharps, together with those with flats, we find—

Dbb with 12 depressions is the same as C major without change
Abb 11
Ebb 10

G

with 1 raising

D

2

Who would trouble himself with twelve, or ten, or seven changes in Dbb or B, Ebb or A, Cb or C, when he finds the same scales, without any change, or with only two or five changes. We shall therefore, in general, make no use of those scales which have seven or more changes. The greatest indispensable number of changes is six; that is, six sharps in F major, and as many flats in Gb major; which scales are also enharmonically

+ Mr. Logier's method of exemplifying to and impressing on a number of pupils the collective scales, is very ingenious. He turns towards them his left hand, open; calls the arm (the trunk of the hand) C, and this, the trunk scale; the thumb G, the first finger D, the second A, the third E, and the fourth B.-The index finger of the right hand F. The Trunk exhibits no sign. The next tone G receives a sharp. Here the right index finger is raised and therefore indicates F. The following tone D receives a second sharp, C. Here the Trunk (the arm) is referred to. The next following tone, A, receives a third sharp, G. Here the left thumb is pointed out, and so forth. On the other hand, F receives its flat from the foresaid little finger, which represents B, and so forth. The name, circle of fifths, may indeed be considered more appropriate to a method which conveys us round through all the scales back again to the point whence we started. I will not omit that some have preferred the scales to be represented in the form of a circle, somewhat in this way

fx, gx, CX, In B major, the twelfth raising appears and points according to the second sign) to a which therefore becomes ax.

If it be desired to change back B major to E major, the last elevation to ax must revert to a and therefore ax be lowered; then we have again the above succession E. The depression has therefore fallen on the tone to the left before E, the scale which we sought. Now, B major is nothing but C major, E major nothing but F major; a'x is enharmonically the same as b, and a as bb. Äs, in order to form E major from B, we were obliged to depress a x into a so in order to form F major from C major, we must depress b into bb; and that is what we did above.

and to exemplify with this figure what we have detailed in the text.

In order to fix deeper the recollection of the number of changes required in any scale, let it be remarked that the changes of two enharmonic scales amount constantly, when added together, to twelve. For example, B or Dbb has each twelve changes, while C has none; Ebb has ten and D two; D has nine and E three. If, therefore, the number of changes in one scale be known, the number for the other is manifest.-Deduct the known from 12. Thus G Major has one, conse quently Abb must have eleven.

the same. Only in particular and rare cases, will there be reasonable occasion for a step beyond; excepting perhaps, to C major, with seven sharps, or Cb major, with as many flats. This latter procedure is especially advisable, if we have been beforehand in a scale with many sharps or flats, and desire to pass to another with the same kind of changes. If we had been, for example, in B or in F major, and wished to pass to C or D major, it would be manifestly more eligible" to add two or one to the five or six sharps already present, than to remove these latter by so many naturals, and then replace them with five flats. In the first manner one or two signs would be wanted; in the latter ten or eleven. This will become more clearly seen in the following section.

Let it

all the signatures of the most usual scales. be remarked that the sharps and flats make their appearance in the same succession, as we found them in the circle of fifths (page 21): first, F and then C; or first, Bb then Eb, &c.

"The signature influences not only the octave where it may chance to be written, but all the degrees which it concerns, in whatever octave they may be. In G major, for example, not only the two-lined f, but every f wherever it may be, is converted into f

If, however, the effect of the signature is to be suspended for a time, if, for example, in G major,

be desired not to be used, but f instead of it, a natural is placed before the note; and here we see this sign (), for the first time practically applied.

51.

In this passage, for example, the three first f's are considered as f, by virtue of the signature; but the fourth is considered really as f, by virtue of the natural which is placed before it, and not as f. So also, if a piece of music is to leave its scale, the sig

nature of that scale must be contradicted, and the signature of the new scale inserted. This may be done in the course of the music and in the middle of the line of notes. Here for example

52.

we see the signature of D major, and some notes which seem to be the close of a passage in D major. Now, the movement is to proceed in Bb major; the sharps then of D major are contradicted, and the two flats of Bb major are inserted.

Sometimes a partial contradiction alone is required: that is, if from a scale with many sharps we pass to one with fewer sharps, or from a scale with many flats to one with less. In this case, contradicting the superfluous signs is sufficient; as for example at (a), where a transition is made from B major

53.

(a

to D major. But for the sake of clearness, we add, as in (b), those signs whose effect is to continue; in order that the player may not imagine, at the appearance of so many naturals, that the whole signature is contradicted.

A similar proceeding is adopted if it be required to pass from a scale with few flats or sharps to one which has many from D major, or Bb major, with two sharps or flats, to E or Ab major, with four changes each. In this case, it would be sufficient, strictly speaking, to inscribe the two new signs, for example :

to be part of a longer movement in D major. Now, we see at (a) the tone C, which in D major does not exist. But at (b) we meet Cagain. We have not left D major for a long period, and therefore do not change the signature: we only give the C note a natural, and the next time it appears, a sharp again. Such is the case also at (c) and (d,) where we make Bbfrom B, and again turn Bb into B.

2. THE MINOR SCALES OR KEYS. One peculiar law determines the signature of the minor scales. They are not signatured as their place in the succession of TONES would require, but Every minor scale has the signature of the major scale, which is situated a minor third above it.* Therefore, A minor is not, as one might expect (consisting of a-b-c-d-e-f-g), signatured with a sharp before g, neither is D minor (d-ef —g-a-bb-c), signatured with a c or a bp: but A minor has the signature of C, that is, none at all, and D minor that of F major: for C lies a minor third over A, and F a minor third above D. Here

the signatures of the most useful minor scales. The signature of E minor is the same as that of G major, D minor as that of F major, B minor as that of D major, and so forth.

Two scales (one major and the other minor),

which have the same signature, are calledRELATIVE SCALES.

The relative major of a minor key lies, as we have seen, a minor third higher: therefore the relative minor of every major scale lies a minor third lower than its relative major. The relative minor of Ab major, for example, was F minor; the relative minor of B major must be G minor-of Db major, Bb

minor-and so forth. all the relative scales, signatures.

"Thus we know how to find and how to mark their

signature were two sharps, the key must be eit D major or B minor. If, therefore, the last tone, the lowest tone of the last harmony, were B, should consider that, according to custom, the key which the movement belonged was B minor.

But what is to be done for the degrees in comp sitions in a minor key, which degrees the signatu their proper sharp or flat in the course of the con does not affect? They each receive individual position. So, for example, in D minor, the signatu only makes Bb; but it contains also C. So ofte then, as this latter note occurs, it is marked wit a sharp.

Why this extraordinary manner of giving signa tures to the minor scales which call them out of thei proper names? We are certainly obliged to conform to it, because it is the general custom; but we canno do so contentedly, unless we perceive a reasonabl ground for the custom. At present, we shall allege only what follows.

-d, c and bb, ƒ, bb, and eb,

In the first place, an exact signature for the minor scales would occasion many inconveniences. Two minor scales would require both flats and sharps; for example,D—e—f-g-a-bb-c G-a-bb-c-d-eb-f-g, whereby the accustomed and natural development visible in the signatures of the major mode, is abandoned. The others, for example,A-b-c-d-e-j E-f -g- A- -b-cC-d-eb

F-g-ab-bb-c-db

-a,

g

f and d

ab_b—c, eb and ab, -e-f,.. bb, ab, and db, would receive one, two, or more sharps and flats for signatures, as if they were quite unknown major keys. How many errors would creep in-how often would the signature of A minor be mistaken for that of G major, and that of F minor for that of Eb major,

since in the major, the number alone, of the flats or sharps, decides of itself.† It would be necessary, therefore, to inspect and observe much more closely. This would, at the same time, be much more troublesome than in the major scales; for in these latter, the sharps and flats follow each other constantly in fifths,-after the sharp of F, those of C and G must follow, &c. Of the flats, that of B must be the first, and those of E and A must follow. This regular progression vastly facilitates the apprehension; and nothing of the kind is exhibited in the signatures of the minor scales.

Therefore it has been proposed to change in the minor signature those degrees, by naturals, which had been raised or depressed in the same tonic major, or the relative minor; for example, A minor and C minor to be marked thus:

But setting aside that this principle would not apply throughout (D minor and G minor could not be so represented), it is contrary to good sense to apply a natural when previously no elevation nor depression has taken place.