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The Triads of the Major Scale.
§ 4. If we construct a triad on each successive degree of the diatonic major scale, we obtain the following chords:
On the 1-st, 4-th and 5-th degree we find major triads:
These triads, representing the most essential constituents of the major scale, bear the names of those degrees of the scale, on which they are based.
§ 5. It has just been said that these three major triads form the most essential constituents of the major scale. Verily they contain all the diatonic degrees of the scale; and, being most closely related to one another, they indicate clearly and unmistakeably the key and further suffice for the harmonic accompaniment of any melody that does not surpass the limits of the key in question. Their mutual affinity is easily demonstrated by the degree of relation existing between the several scales to which they belong. The triads on the 4-th and 5-th degrees, while they are respectively the Subdominant and Dominant in the harmony of the given key, are at the same time the tonic triads of those keys, which, in the so-called "Circle of Fifths" are nearest to the given key. So that the inner relationship of the three major triads in the harmony of the major scale is in direct proportion to the degree of relationship of the three successive keys in the Circle of Fifths (their Tetrachords being common).
§ 6. In the major scale minor triads are also found, namely on the 2-nd, 3-rd and 6-th degrees. The minor Third imparts to these triads a soft, weakened character, hence they cannot command the importance possessed by the major triads. However, they furnish us with a beautiful contrast to the latter, emphasizing their strength! Their mutual affinity is the same as that of the major triads, as they possess the same proximity in the Circle of Fifths.
Of the degree of their relationship to the major triads we may say it is the same as that existing between parallel keys; for the chords on the 1-st and 6-th degrees, the 5-th and 3-rd degree and the 4-th and 2-nd degree respectively are separated by a minor third.
The whole mass of major and minor triads may be grouped into three sets of two triads each:
a) The tonic group viz: the triads on the 1-st and 6-th degrees.
b) The dominant group viz: the triads on the 5-th and 3-rd degrees and
c) The subdominant group viz: the triads on the 4-th and 2-nd degrees.
§ 7. In marked contrast to the other triads stands the diminished triad on the 7-th degree, because of its dissonant character. We shall return to this chord later on, having first entirely mastered the connection of the other six triads.
The Connection of the Triads of the major scale.
§ 8. In music chords are either used in masses, that is with manifold repetitions of one and the same interval—as is the case in compositions for orchestra and Pianoforte—or they are set for several, single, distinct voices. "Four-voiced-writing" is the commonest and most normal form, as it denotes the four different human voices—namely: Soprano, Alto, Tenor and Bass. So, in our study of Harmony we shall keep to this disposition of the voices.
The highest voice—Soprano—and the deepest voice—Bass—are called the two outer voices—the two intermediate voices: Alto and Tenor: the two inner voices.
§ 9. Turning now to the practical application of the above treated chords, we will begin with placing the fundamental tone in the Bass. In the highest voice any of the three tones of the chord, the fundamental tone, the Third or the Fifth may be used. For the two inner voices we will use respectively the intervals of the triad nearest to the Soprano. The C major triad would thus appear as follows:
These three cases are called the positions of the chord. According to the interval of the triad which appears in the Soprano, these positions are called the fundamental position or position of the octave, the position of the Third, and the position of the Fifth.
§ 10. From the above example we see that in each of the three positions the fundamental tone is used twice, while the third and fifth appear but once. Shall this always be the case? By no means! In a free leading of the voices the composer may double any tone of the chord at will. For the present, however, we cannot avail ourselves of this liberty, since according to § 9—we must place the inner voices as close as possible to the upper voice. Indeed, the doubling of the fundamental tone will always be the most common, as it is most natural to the triad).
§ 11. We have already mentioned (§ 6) the internal relationship of the triads of the scale. Now, there is still another and purely external connection of these triads, growing out of the tones they have in common. The triads c, e, g and g, b, d for instance have the tone g in common, while the triad f, a, c shares the tone c with the triad c, e, g. In fact each triad has one or two tones in common with every other triad constructed on steps of the same scale, except in the case where the fundamentals are directly succeeding steps. So: the triad on C has no tone in common with the triads on b. and d; the triad on d. none with the triads on c and e, and so on. The mutual relationship of the triads with regard to their external connection is shown in the following table:
To effect a connection of two triads at once correct and satisfying to the ear, it is necessary to retain the common tone of the triads in the same voice.
Conscientious application of this rule imparts fluency, euphony and unity to the harmony; moreover it enables the pupil to avoid many grave errors, which, otherwise, he would of necessity commit. Take for instance the triad on c in the octave position, and let us connect it successively with other triads containing tones in common with it. Which positions of the new chords must we then choose? Obviously those which enable us to retain the common tone, or tones in the same voice. Consequently the G major triad must appear in position of the third, F major in the position of the fifth, A minor in position of the third and E minor again in position of the fifth.
The progression and position, therefore, of the three upper voices is influenced by the common tones. Meanwhile the Bass may progress upward or downward at liberty. Should we have to choose between a skip of a sixth and one of a third, we prefer the latter).
I Remark. In addition to these examples, which consist in supplying the remaining three voices to a given bass, it is very beneficial to construct a table, which shall contain all the possible connections of all triads with one another, in every position. To this end the example ([??] 13) begun in this paragraph on C should be carried on further. The pupil must not be disheartened, when he finds that at the very beginning of his study 120 chords must be written out in one key alone. In the first place the labor is merely a mechanical one, and in the second place it is important that by thoroughgoing explanations of the rudiments we should dispel at the start the superstitious awe that prevails regarding the so-called "Theory" or "Thorough Bass".
II. Remark: In harmonizing a bass, care should be taken not to lead the voices too high; therefore one must not choose too high a position of the tonic triad at the start.
Connection of Triads, showing no external agreement.
§ 12. In the preceding chapter we spoke of the beauty of harmonies connected by common tones. This absolute completeness in chord-connection, however, does not exclude the admissibility of certain connections, which, while perhaps less pleasing, satisfy us by very reason of their sharpness or coarseness. This we can understand if we consider the aim of Music, which is, to picture the many various emotions of the soul: and these cannot always be expressed by dulcet soothing means. For this reason Harmony admits also such chord-connections, which show no outer relationship—though they may bear an inner relationship to one another. (§ 5).
§ 13. Should we not, when connecting two chords not outwardly related chose again those positions, that permit a melodious, fluent leading of the voices? Should we not, to avoid jumps, lead each voice into the nearest interval, a second up or down? For instance as follows:
Before answering these questions, however, let us see, what different kinds of voice-motions there are.
We perceive the three following kinds:
1) Parallel motion (motus rectus), in which two voices progress in one and the same direction, that is, upwards or downwards.
2) Oblique motion (motus obliquus), in which one voice remains stationary, while the other moves onward:
3) Contrary motion (motus contrarius); one voice progresses upwards, the other downwards.
All these various motions are admissible in every succession of harmonies. Observe, however, the so called Parallelisms occurring in the motus rectus; these are progressions, in which the two voices move not only in the same direction, but also in the same interval; for instance: when two voices progress upward or downward in Seconds or Fourths.
Some of these Parallelisms are indeed very euphonious and, therefore, like the other motions, entirely permissible. Others, however, are to be avoided partly because they do not satisfy the musical ear and again, because they counteract the independent movement of the voices. Such forbidden progressions are Parallel Fifths and Octaves.
Remark. To comprehend clearly the reason for prohibiting parallel Fifths and Octaves, it must be borne in mind that we have to deal not with the massive harmonization of orchestra or piano composition, but with 4 separate independent voices, which do not permit of extensive doubling. Should the question arise whether only parallel octaves and fifths are forbidden, and parallel dissonant intervals permitted, we may add, that for the present we are familiar only with tone-combinations, in which such progressions do not occur. Once for all, then, let it be said that in Harmony progressions of parallel fifths and octaves are prohibited.
Now only are we in a position to answer the question put at the beginning of this paragraph.
If we wish to connect two triads having no external relationship, we can not lead all the voices a second upwards or downwards, as parallel fifths and octaves would arise.
To avoid this fault we must employ contrary motion, without, however, proceeding in great skips.
The fault is by no means corrected, if we replace the step of a second by a skip of a seventh in the opposite direction (contrary motion), as in that case the fifths and octaves really remain.
Moreover, we obtain a very unmelodious skip of a seventh in the Bass.
So we will allow the Bass to retain its melodious step of a second, and, employing contrary motion, lead each of the other voices into the nearest interval of the following chord.
We have now learned, how to connect, within its own limits, all the consonant chords of the major scale in all positions. Besides working out the following written exercises, we chould advise the pupil to form at the piano all manners of chord-combinations in all the keys, in order to master them more thoroughly.
Deviations from rules governing the connection of related triads.
§ 14. In the foregoing exercises we retained the common tone in the same voice, when connecting two chords and thus obtained greater beauty and smoothness in harmonic progressions. We need observe this rule, however, only in so far as it does not hinder us in our true purpose: a free and independent leading of the voices.
This aim we will seek gradually to attain by disregarding at times those restraining rules, whose purpose it was at the start to fortify us against error. Even at this stage we might occasionally do so, provided we thereby improve the voice-leading. Thus it has been said, for example, that the position of the upper voices should not be too high. Now, if we see that this can be avoided by a deviation from the rule in question, we may make such a deviation, observing, however, the necessary precaution. We must bear in mind chiefly the following points:
1) Two triads, however closely related internally and externally, must never directly follow each other in the same position, as parallel fifths and octaves must necessarily occur.
2) The uppermost voice must make no jumps greater than a fourth.
3) In this case the Bass must progress in contrary motion to the upper parts, so that no concealed Fifths and Octaves are formed.
Besides the parallel or open Fifths and Octaves there exist also concealed ones. These occur, when two voices jump in parallel motion into a Fifth or Octave.
These hidden progressions, however, lose their disagreable nature, if the two chords possess a common tone, which remains in the same voice, e. g.
But if this rule is not applied, the concealed Fifths and Octaves sound extremely unpleasant.
Directly we employ contrary motion, which excludes these hidden progressions, the same chord-combinations sound pleasant.
In the following examples therefore, deviations from the rule in question are admissible only, if contrary motion can be employed in the Bass.
If the leading tone, the third of the Dominant triad, is in the Soprano voice, and the Dominant triad is followed by the tonic, the deviation is not permitted, as the tendency of the leading tone is to move upward a halftone into the tonic. Should we find it, however, in one of the inner voices, we may lead it a third downward.
The same holds good for the tonic triad, if succeeded by the sub-dominant triad. In this case the third of the tonic triad partakes of the nature of the leading tone, since these two chords have the same relationship as Dominant to Tonic.
§ 15. A Harmonic Sequence is a chord-progression, in which a motive consisting of two or more chords is repeated a number of times, always on different steps of the scale, thereby giving rise to motion downwards or upwards.
In the repetitions the same arrangement of voices has to prevail as in the motive.
The motive may consist either of several positions of one and the same chord, or of different chords properly connected.
§ 16. At the places marked NB. we find the diminished triad on the 7-th degree. Because of the dissonant interval it contains (the diminished fifth) it must not be used with as much liberty as the other triads of the scale. We will, therefore, indulge in its use only with the greatest precaution. Its use in the Sequence is justified on the ground that the repetition of the motive and the carrying out of the Sequence demand it.
§ 17. It may be stated with regard to the diminished triad, that its use is not absolutely restricted to the Sequence. It may appear, for instance, supported between two related triads, in which case the common tones must unquestionably be retained in the same voices.
Excerpted from Guide To The Practical Study Of Harmony by Peter Ilyitch Tchaikovsky. Copyright © 2005 Dover Publications, Inc.. Excerpted by permission of Dover Publications, Inc..
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