In the second place, most compositions (especially those of considerable length, to which the signature is of most importance) do not remain in one key, but pass to others, and generally, indeed, to those most convenient to them—that is, which do not stray too far from the original key. A signature, therefore, which is favorable for the development of the nearest related scale, must have evidently the preference. Which scale, then, lies nearest to a minor scale,-its own major, or its relative key? The latter, since from this, the minor varies in only one degree, while from its own major it differs in two⚫ thus, C minor, for example,

Major C-d-e-f-g-a-b-c-d—e, Minor C-d-eb-ƒ—g—ab-b-c▬d—eb, Major Eb-ƒ—g-ab-bb—c—d—eb, differs from C major in two tones (eb and ab), but from Eb major in only one.*

(B) CHIEF POINTS OF THE SCALE.

We have seen that a scale may be formed on every tone. This tone is the first, the foundation of all the tones in the scale which is grounded on and named after it. In this sense it is called peculiarly THE TONIC.

The fifth degree in each scale (the major fifth of the scale) is called

THE DOMINANT,

the governing degree. We shall not understand fully, why it enjoys this name, until we have entered into the study of Harmony. We will merely point out now, that the dominant is the tone by which and to which we proceed step by step in the circle of fifths. From C, for example, to G, from G to D, G and D are the dominants. In the circle of fifths we go from C to G and from G to D.

But there is also a circle of fifths proceeding from depressions, which leads us step by step by a descending series; thus, from C to F, from F to Bb. And in scales with sharps, this reverse method can be practised also; thus, from D to G and from G to C. Referring then again to the scale, we shall observe the major fifth under the tonic, and call it THE SUBDOMINANT.

In contradistinction to which, the dominant is sometimes called the

SUPERDOMINANT. We will further note two denominations, which, however, are of less importance. The third degree in each scale (the third of the tonic), is called the MEDIANT.

We will for the moment say only, that it lies between the tonic and the dominant, and is the means of binding, as it were, or combining both these together. The manner of action in this union, and of what importance it is, will not be manifest until we come to the study of Harmony. In like manner, the third under the tonic, the medium of combina

* A third and more important reason, which determines a minor key to pass rather to its relative major than to its own (A minor rather to C major than to A major), belongs to the study of composition. It is, that its own major would be less effective in operation, because, whether in major or minor, the most important degrees (the tonic and dominant) and that busy harmony, (the chord of the dominant,) are common to both, while the relative key gives quite a new set.

tion between it and the subdominant, is therefore called the SUBMEDIANT,

and in contradistinction to this, the mediant is called the SUPERMEDIANT.

Therefore, in C major, e is the mediant, and a the submediant; e is the medium between c and 9, and a between fand c. In C minor, eb is the mediant, and ab the submediant: the first is the medium between c and 9, the second between ƒ and c.†

(C)

RELATIONSHIP OF THE SCALES.

If we return to the preceding section, in which we formed all the scales, after and with each other, we find indeed that every scale differs from the other, but some more and some less. If we compare, for example, C major with G major,— cdefg-a-bcd

g-a- -b—c—d·- -e f-g we see they differ from each other in one tone only: C major has f, and G major f: all the other degrees they have in common. Let us compare on the other hand C major, suppose with E major,-a-b -C d- e ·a -b-c

c-d-e-f

-e

and we see that the two scales differ from each other in four degrees C major has f, c, g, d, while E major has f, c, g and d. Two scales which have several tones in common,"are called

RELATED.

Now, we have just seen that this relationship may be nearer or more distant, according to the number of tones which the scales may have in common. There are, therefore, several

DEGREES OF RELATIONSHIP.

In fine, we have ourselves found out several ways in which scales are mutually connected. We found the major scales linked together in the form of the circle of fifths, the minor scales with their relative keys and with their own major scales. There must be, therefore, three kinds of relationship:

1. RELATIONSHIP OF THE MAJOR SCALES. Here the circle of fifths shews us the relationships, with their grades. The scales, lying immediately next adjoining to each other in the circle of fifths, differ from each other only in one tone; therefore they are in the first degree of relationship towards each other. We see here,

b

6 5 4 3 2 1 0 1 2 3 4 5 6 Gb Db Ab Eb Bb F C G D A E B.F the united circle of fifths of the sharp and flat scales (so far as we found them indispensable), and we perceive that each scale has its neighbour right and left, as its nearest relative next to itself. C major, for example, has for relative of the first degree, G major and F major: in like manner, E major has

It is scarcely worth mentioning that all these names belong to each tone, in one determined scale only; and that one and the same tone, in different scales, bears quite a different character. For example, we called a, above, the submediant, that is, of C major: in F major it would be the mediant; in D the dominant; in E the subdominant; in A major or minor it would be the tonic.

for relatives of the first degree, B major and A major next to it. Which are the nearest relatives of Ğþ major? On one side Db major, on the other Cb major, in lieu of which we can set down B major ;* and in the same way F major is related on the one side to B major, and on the other to C major (for which we can place D major,) in the first degree.

Relatives of the second degree, are those, one step more distant from each other; for example, from D major on one side of C major to Bb major on the other. In this manner we may when necessary ascertain all degrees of relationship.

2. RELATIONSHIP OF THE RELATIVE KEYS. The relative scales are in the first degree of relationship, for they differ from each other only in one tone So, therefore, C major and A minor, C minor and Eb major, &c., are relatives in the first degree.

If we combine this manner of relationship with the previous one, a new species of relative connexion becomes manifest among the scales. We have found in the first place, that every major scale is related to both its neighbouring major keys in the first degree, and moreover with its relative scale in the same degree; for example, C major with G major, F major, and A minor. Now the major scales, G major and F major, are again related to their relative scales (E minor and D minor) in the first degree; consequently we may consider these minor scales as relatives in the second degree of the first major scale, C major. This figure shews it :C major.

Here we have a table of affinities of the first degree, as G major, F major, and A minor; of the second degree, as D major, E minor, Bb major and D minor; of the third degree, as B minor and G minor. But it is not necessary for us to follow these affinities so far, still less, farther.

3. RELATIONSHIP OF THE MINOR SCALES WITH THEIR MAJOR SCALES, AND AMONG THEMSELVES. We have already learned (page 24) that every minor scale differs from its own scale in two degrees, the

While the student is mastering the above open and broad relationships, we must not omit remarking for the benefit of those more deeply versed in music, that in the region of the scales, there lie many quite different, we might almost say sympathetic interweavings. They exist, for example, in the scales now under consideration, whose tonics lie at the distance of a third from each other, such as C major with A minor, and Ab major, with E minor, and Eb major, &c. Simply from the outward point of view it is certain that B major (instead of CP) and C (instead of Db) must be called the nearest relatives to Go major. This point of view suffices for early tuition. A precocious knowledge of deeper matters would remain fruitless, or only create a fantastic juggle of ideas.

third and sixth. Hence we should consider them as related in the second degree.

But a particular circumstance intervenes, to draw the bonds of union closer. This is, that major and minor have in common, the most important part of every scale; the

TONIC, DOMINANT, AND SUBDOMINANT, and this (as we shall see in the study of Harmony) is so influential, that we are obliged to consider them as related in the first degree.

And so we do consider the minor scales among themselves, which stand towards each other in the relationship of tonic and dominant or subdominant, as nearest related, by virtue of the internal affinity of the tonic, dominant, and subdominant. So A minor avails us as next related to E minor and D minor, although it differs from them not in one point only, but even in three; as we here shew:- D-e-f-g-a-bb- -d-e-ƒ-g- a

a-b

a -b- od-e -a-b -C

APPENDIX OF ECCLESIASTICAL MODES.

In the preceding sections we have represented the modes and scales as they are now used in our system of music.

But this system has not long been the most general. In the sixteenth and seventeenth centuries, a system entirely different was universally prevalent, which we call the

SYSTEM OF ECCLESIASTICAL MODES, or Church Scales. According to the fashion of those days, it was assumed to be (and by preference), the system of Greek scales. The scales were Greek and were called by the names of the ancient Greek, scales, although they had nothing else in common with, nor other resemblance to, them, than their

These scales could also be formed on other degrees; for example, the Æolic on G,

g—a—bb—c▬d—eb—ƒ—g

and in fine, it was allowed to employ foreign scales also under certain relationships. Besides the tones c, d, e, f, g, a and b, there were also present bb and ebf, c and g. The tuning, however, of the whole system of tones was different from ours and in such a manner, that f and g, could not be used as gb, db gb, db or ab, nor could bb and eb be employed as a or d * This old system, differing from ours, more especially in its principles of modulation, is not merely a matter of historical record; but in its application in our days, particularly to Church music, it is become a matter of peculiar interest. For we possess abundance of Church chants (and they are our best), which were composed under the dominion of the old system, and cannot be well and surely performed without a knowledge of it. But intimate acquaintance with this branch, belongs to the study of composition,† where it enters into immediate operation. must limit the (we confess) very superficial account we have given of this matter. We will merely add, as perhaps a slight insight, the most eligible kind of closing cadence for each of the Ecclesiastical Modes, which may in some measure serve to give a feeble conception of them,

Here we

4. Lydian.

*No temperament was then admitted in the tuning (Obs: page 7) as with us-bb and eb were too deep for a and d; and f, c, and g were too high for gb, d, and ap. The difference between greater and lesser semitones was, with them, real (Note, page 16).

+ The necessary instruction on this subject is in Part I. of Instructions for Composition.

FIRST SECTION-THE VALUE OF TONES.

We have already said in the introduction, that every tone must have some duration, longer or shorter; and that the time given or ascribed to any tone is called its value.

The value of a tone is that duration of time allowed to it, relatively to the amount or quantity of time allowed to other tones, It is not absolute time, that is attributed to any tone (so that this tone is to last so many seconds, while that is to last such another number of seconds), but a certain proportion of time when compared with other tones: that is, one tone shall last twice, thrice, or more times as long as another, or vice versa, shall last one half, one third or a still smaller portion of the duration of another.

The most simple division is by the number two. With that, we will begin.

But what if we have tones to note of longer duration than a semibreve? For this object we have three expedients.

In the first place we find that formerly, notes of longer duration were used. In the period of measurable music,† when value and division into

* I have attempted here-and elsewhere-to give a descriptive English name for a German compound word; there being, as I believe, no exact equivalent single word in English for the German. The liberty allowed to every one in Germany of composing what words they please or may judge convenient, renders literal translation from the German, at times, very difficult, if not impossible, without circumlocution or descriptive invention. It must, however, be conceded to Dr. Marx, that his explanations are so strikingly plain and minutely exact, that it matters not what name you put at the head of a section or paragraph: you see the object before you, call it what you will. A rare talent, this; far beyond the choice of a name. If I am not so perspicuous in English, the fault is mine-the Doctor is broad daylight.-TRANSLATOR.

+ A nearer insight into this matter is given in the Universal Lexicon, der Tonkunst. We have said sufficient for this place. The name, measurable music (musica mensurabilis or mensurata) signifies music brought into measurable condition, which originated from the longs and shorts of the words in church music. The first teacher of this method, whose name has descended to us, was Frank, of Cologne, until the sixteenth and seventeenth centuries, when the old system of notation or measurable method, was superseded by the present system of bars. The music contradistinguished from the musica mensurata, was the musica plana, or the cantus planus, the church song, which proceeded chiefly by one or two notes. The measured theory was, however, extremely intricate and unpractical.

bars were first reduced to order, notes of the following form were in use:

Maxima or duplex longa,

Longa,

Brevis,

◇ Semibrevis, Minima,

From the Minima is derived our minim, as may be guessed at once; from the Semibrevis our semibreve. Therefore we may use the

Brevis,

which has with us the value of

Two SEMIBREVES.

The longer notes are not used in modern music. Secondly, when we want to lengthen a note in a manner not feasible by the preceding system, we use the

BIND.

This is done by repeating the note until we make up the amount of value which we desire, and then binding them together by a sign in the curve of a bow, which indicates that the notes are not to be considered as separate, but as one note, whose value is equal to the sum of the values of all the notes so bound. If we wished, for example, a sound to continue during the value of four semibreves, we should write thus :

if it should last the time of seven or five crotchets,

After the representation of division by two, we are led to expect from the division by three, that a semibreve would be divided into three thirds, a third into three ninths, and so forth: and that for these thirds and ninths a peculiarly formed note would be introduced. This, however, is not the case, as it would have encumbered our measurement with a perplexing mass of names and signs. The division by three, however, has not been left unaccomplished.

If it be desired to signify a third of a unit, we use the same names and signs as in the division by two; but with the understanding that, not two, but three of the parts. shall be valued as one.

A group of the three notes which are to have the value of two, is called a

Custom, however, has in the meantime decided otherwise. The name of sextriplet is used for both the representations, and most frequently for that which we wished to call double triplet, as the other form in reality much more rarely appears.

Accordingly, we can now use the division by two and three, in