# Letters to a Young Lady (Czerny)/Letter 7

LETTER VII.
(SOME MONTHS LATER.)
RUDIMENTS OF THOROUGH-BASS.
It is with great pleasure that I now fulfil the desire which you expressed that I would give you some preliminary notion of Harmony or Thorough-bass, to facilitate the study of it, when you, by and by, commence with your worthy teacher this very necessary and interesting science on a more extended scale.
First of all, I will endeavour, by the following explanations, to give you as clear an idea as possible of what thorough-bass or harmony is, and to what purpose it serves.
Music consists of melody and harmony. When, for example, a female sings quite alone, without any accompaniment, her song is pure, simple melody. When another female singer, with a somewhat deeper voice, accompanies the first with a different, but still agreeably sounding melody, this will form music in two parts, which may also be called two-part harmony.
​When to these two voices a third person, with a high male voice, adds his accompaniment, there arises a harmony in three parts.
Lastly, imagine a deep male or bass voice, by way of accompaniment, and we shall have a harmony in four parts, in which each part sings a different melody, and nevertheless the whole together sounds harmonious and pleasing to the ear. You will easily imagine, Miss, that the three singers who accompany the first do not sing at hazard, and merely what may strike them; for this would produce a horrible discordance: consequently the chords of which this four-part harmony consists, are arranged by the composer according to certain rules, in order to produce that fine effect.
Those rules are just what we are taught to know by thorough-bass; and consequently the theory of harmony consists in shewing—
1st. What chords are possible in music; and,
2nd. How these chords must succeed each other in a regular manner, so as to give to each melody the necessary harmonic ground-work, or accompaniment.
“But,” you will ask, “in the pieces which I play, whole lines often occur, in which there are no chords, and nothing but running or skipping passages in one hand, while the other strikes single notes; or there are passages in ​both hands. Does all this too arise from thorough-bass?”
Exactly so, Miss; for all these passages are nothing but varied or arpeggioed chords: and, in all music, no bar occurs which does not repose on this foundation.
Even the fullest chords, which often consist of ten, nay, even of twenty or thirty notes, are for the most part formed from four essential, that is, really different notes. The rest are only duplications of them.
If we consider the following example in four parts,
and afterwards this,
we shall readily perceive that the second example is only an extended duplication of the first, that it consists of the same chords, and consequently contains only four real parts.
​We shall now give some examples in which these chords are varied and broken into arpeggios.
A composer must have studied thorough-bass well; as otherwise he would, in every composition, entangle himself in irregular, and therefore irresoluble, discords. And, even to the player and practical musician, this science ought not to remain unknown; for it is equally useful and pleasant to be able to account to oneself, as to how far each composition may justly lay claim to intrinsic merit; and because thorough-bass is of the greatest assistance in extemporizing, playing at sight, and accompanying.
But before we learn to know the chords, we must see from what they are constructed.
Each chord must consist of at least three notes, sounded together. When we strike only two notes together, it is not a chord, but merely an interval.
There are ten such intervals in music, which here follow; C being always taken as the lower note or root.
With respect to these intervals, the following remarks are to be made:
1st. Any key which we choose to fix upon, may serve as a root or bottom note to all these intervals; and consequently they may take place in all keys and in all octaves.
2ndly. They receive their names from the greater or less distance from their root, and that according to the number of degrees by which they are removed from it. Thus, for example, the third is distant three degrees of the diatonic scale from the lower note or root; the fifth, five degrees; the sixth, six degrees; and so on.
3rdly. The unison (or like sound) is no interval; but it must be so considered in thorough-bass, because two different parts occasionally take one and the same note.
4thly. When we strike intervals separated by still wider distances than the tenth,—as, for example,
such intervals are merely fourths, fifths, sixths, ​sevenths, &c. taken one or more octaves higher; and even the most remote distances, extending through all the octaves, make no difference in this respect. Even the tenth is nothing but a third taken an octave higher.
5thly. The ninth is also, in truth, but a second taken an octave higher; but, in thorough-bass, it is used in a different manner in both forms; and it is therefore named sometimes in the one way, sometimes in the other.
6thly. All intervals are computed and sought for from the lower note upwards,—that is, in the direction from the bass towards the treble,—and never in the reverse way, or from the upper note downwards. Their inversions will be explained afterwards.
7thly. The above scheme of intervals I have written on C as a root, and therefore in the key of C major; and, as I proceed, I shall also give all the subsequent examples in one key only, generally that of C major or A minor.
It is, however, of the greatest importance that you should transpose all these examples into all the other keys, and that too in writing; for which purpose, your having learned to copy music will be very useful. It is to be remembered here, that all the examples in a major key can only be transposed into major keys; and, similarly, all the examples in minor, only into minor keys. Thus, as the ​preceding scheme of intervals is formed from the diatonic scale of C major, it can only be written in this way in all the rest of the major keys; and the key-note of the scale selected must always be taken as the root from which all the intervals must be sought for in ascending.
By way of illustration, I shall give you a similar diagram in A♭ major.
And similarly in all other major keys.
You know, Miss, that every note may be raised or depressed by means of the ♯, ♭, ♮, 𝄪, 𝄫. And as this is naturally possible also with respect to every interval, each of them admits of three, or even four different kinds; and this difference is indicated and determined by the epithets, diminished, minor (or false), major (or perfect), and superfluous, as may be seen in the following table:
The tenth is the same as the third.
You will observe, Miss, that many different intervals, when struck, are taken on the very same keys. For example, the superfluous second and the minor third; or the superfluous fourth and the false fifth, &c.
But, in thorough-bass, these intervals are distinguished from one another in two ways:
1st. Because each of them requires, for its ​accompaniments, quite different notes, which therefore form quite different chords; and
2ndly. Because each is resolved in quite another manner. You will shortly learn this difference more fully.
You will also have further remarked, that, in each species of interval, the notes retain the same alphabetical names, whether it is minor, major, or superfluous; the difference is produced merely by the marks of transposition, whether ♯ or ♭.
Here follows the same scheme of intervals in two more keys.
In the last example you will observe, with regard to the diminished sixth and diminished seventh, that these two intervals in D♭ cannot be produced in any other manner than by raising the bottom note or root.
In transposing these examples, you must observe this in each key, whenever, owing to the too great number of sharps or flats, these intervals cannot be produced in any other manner.
And now, Miss, I leave it to your diligence to impress all this thoroughly on your mind, by writing it and committing it to memory; and in our next we shall occupy ourselves with the formation of chords.