So far we have studied melody and harmony in the music we are playing. Now we shall organize this knowledge into a system to which we can refer in learning new and more difficult pieces.

Scale

Our music today is based upon scales, if we except some ultramodern compositions. The major scale with its half steps between 3 and 4 and between 7 and 8 is the basic scale of our musical system. The minor scale with its half steps between 2 and 3, 5 and 6, and 7 and 8 and a step and a half between 6 and 7 appears to us as a variant of this.

Tones of the Scale

The tones of the scale are called:

Intervals

Intervals are measured from the tonic in the major scale to give the perfect and major intervals. The minor, diminished, and augmented are derived from these.

1-1 perf. prime 1-2 maj. 2nd 1-3 maj. 3rd 1-4 perf. 4th 1-5 perf. 5th 1-6 maj. 6th 1-7 maj. 7th 1-8 perf. octave

1-1$ aug. prime l-2# aug. 2nd l-3# aug. 3rd l-4# aug. 4th l-5# aug. 5th 1-6$ aug. 6th l-7# aug. 7th 1-8$ aug. octave

l-2b min. 2nd 1-3J? min. 3rd 1-4|? dim. 4th l-5b dim. 5th 1-61? min. 6th 1-7J7 min. 7th 1-8b dim. octave

l-2bb dim. 2nd l-3bb dim. 3rd   l-6bb dim. 6th l-7bb dim. 7th

The intervals between the other tones of the scale are:

2-3 maj. 2nd 2-4 min. 3rd 2-5 perf. 4th 2-6 perf. 5th 2-7 maj. 6th 2-8 min. 7th	3-4 min. 2nd 3-5 min. 3rd 3-6 perf. 4th 3-7 perf. 5th 3-8 min. 6th	4-5 maj. 2nd 4-6 maj. 3rd 4-7 aug. 4th 4-8 perf. 5th
5-6 maj. 2nd 5-7 maj. 3rd 5-8 perf. 4th	6-7 maj. 2nd 6-8 min. 3rd	7-8 min. 2nd

Chords

The chords built upon the major scale are:

The chords built upon the minor scale are:

Triads

The major triad is composed of a major 3rd and a perfect 5th. The minor triad is like the major with the 3rd lowered. The diminished triad is like the major with both 3rd and 5th lowered. The augmented triad is like the major with the 5th raised.

eventh Chords

The seventh chords are built by adding a major 7th or a minor 7th or a diminished 7th to one of these four triads. Most of the seventh chords may be found on one of the tones of the major or minor scale; some, however, are constructed only by the use of altered tones. The most important of the seventh chords is the dominant seventh, V7, found on the dominant in both major and minor. It is composed of a major triad and a minor 7th. The other important one, well worth learning, is the diminished seventh, VII°, found on the leading tone in minor. It is composed of a diminished triad and a diminished 7th.

Ninth Chords

The ninth chords are built by adding a major or minor 9th to one of the seventh chords. The most common are the major dominant ninth, built upon the dominant tone of the major scale, and the minor dominant ninth, built upon the dominant tone of the minor scale.

Chords of the eleventh, thirteenth, etc., are built in similar fashion by adding tones above the ninth chords.

Having now examined the gross anatomy of music, we may turn to some of the interesting physiology.

Parallel 5ths
Parallel 5ths are avoided because they sound so crude. Play the progression  Hear how hollow and awkward these 5ths sound. Even when they are more than one step apart. , parallel 5ths jerk one rudely. If one or both of the 5ths are not perfect 5ths, the effect is not nearly as dis­pleasing. And if they are accompanied by other tones which distract the attention from the parallelism, the ear may not notice them, particularly if the other parts are moving in the opposite direction from the fifths. Play them in a great variety of situations and you will gain a sensitivity to their subtle variations. Good composers use them, but use them advisedly. Grieg used them when he portrayed a rough, rocky wilderness; Wagner employed them in similar situa­tions. They are out of place in a quiet mood or with smooth polyphony. When played alone they outrage any ear, and in complicated harmony they weaken the harmonic structure.

Parallel motion is never as strong as movement in opposite directions. Parallel sixths are sweet and tend to be sickish. This was all that was wrong with Sweet Adeline—she was just too sweet. Parallel thirds are almost as bad, but we are more accustomed to them. Parallel octaves, however, are some­times used to accentuate a melody or bass line. If the melody moves upward the bass should move downward or stand still. There are many variations of this; experimentation and keen listening will reveal more than any amount of discussion.

Dissonance from Inversion The inversion of a chord is more dissonant than the funda­mental position, particularly with seventh and ninth chords.

	A		D
	B		B
The ninth chord	D	, when inverted,	A	, sounds as if someone had sat on the
	B		G
	G		F

keys. The cause of the dissonance is obvious. However, if the chord is built up slowly, first presenting its fundamental position and then gradually in­verting into this tight position, the ear senses the logical connection and the chord is not too dissonant. A beautiful illustration is the middle of MacDowell's To a Water Lily, where he builds a chord of the thirteenth so gradually that it sounds no more dissonant than a minor seventh chord. Build these chords and invert them. Oftentimes they will suggest passages from well-known composers.

Modulation by VII7

The diminished seventh chord is found on the leading tone of the minor scale. It is identical with the minor dominant ninth chord with root omitted. The best resolution is to a major or minor chord whose root is a half step above any tone in the diminished seventh chord. This provides an easy modulation to difficult keys, as illustrated by the following progressions.

The strongest harmonic progression occurs when the root drops a 5th to the root of the next chord. Thus VII drops down a 5th to III, which in turn drops down a 5th to VI, which then drops down a 5th to II, which then drops to the dominant and thence to the tonic. This progression is effective when triads are used:

This progression is even more effective when seventh chords are used:

erfect Cadence

The perfect cadence used at the close of many pieces is I—IV—I—V—I. It establishes the key and gives a feeling of finality.

Figuration

Chords are often not played as chords but are rolled in arpeggio fashion:

or as broken arpeggios:

Often a nonharmonic tone is added just above each member of the broken arpeggio series, thus:

This is a favorite figuration with Beethoven. Immediately it suggests many other nonharmonic tones which may be combined with harmonic patterns to make an interesting passage. Analyze these passages as you hear them; they will explain many pieces which you have not been able to play by ear.

The nonharmonic tones are always the most baffling, particularly when they occur on accented beats. They are always related to the harmony or melody somehow. Notes do not just float around in music. A note which had no connection would be sheer nonsense and would sound like a wrong note. Your ear is your best guide to locate the con­nection. The relationship of a tone or chord is always deter­mined by the sound—not by any rule of harmony.

Since these relationships do not sound the same to different theorists there is room for some very interesting discussion. This need not detain you. Play it as you hear it and you will be right. This is your interpretation.

Style

Styles change in harmony and figuration. Most ear players have a style of their own; but any ear player who has progressed this far in the text will have developed many different styles. In popular music the styles change rapidly. From 1890 to 1910 all popular music was harmonized with the three chords of the perfect cadence. Startling chords and wild modulations were next introduced. Since then we have had "blue" chords, sweet chords, boogie woogie, chords of the added sixth, and others too numerous to mention. These styles are always easy to acquire; if they were difficult they could not become popular.

It often helps to note the style of a composer or period. Most of the chords of Mozart and Haydn are simple triads with simple figuration. Beethoven adds the rolling figures and a few nonharmonic tones. Brahms spreads out his rolled chords to uncomfortable dimensions and frequently omits the fifth. Franck adds quantities of nonharmonic tones which are related to the main harmony but frequently obscure it.

Thus we progress into the realm of possibilities in musical structure. Experience is the best teacher, the ear the best guide. This chapter should serve as a reference for basic materials. For further study the student is referred to the regular textbooks on ear training, harmony, and harmonic analysis.

Pieces Suitable or Analysis and Playing

	original key
Minuet from DON JUAN (MOZART)	F
Soldiers’ Chorus from FAUST (GOUNOD)	Bb
Unfold, Ye Portals from REDEMPTION (GOUNOD)	C
Gypsy Rondo (HAYDN)	G
Invitation to the Dance (WEBER)	Db
Angel Scene from HANSEL AND GRETEL          (HUMPERDINCK)	F
Strike up the Band (GERSHWIN)
Quartet from RIGOLETTO (VERDI)	D
To a Wild Rose (MACDOWELL)	A
From an Indian Lodge (MACDOWELL)	C minor
A Deserted Farm (MACDOWELL)	F# minor
A.D. 1620 (MACDOWELL)	G

WHAT TO DO Name the chords in the pieces you know. Play hymns. When you do not happen onto the right harmony, figure out the various possibilities. Play college songs with various harmonizations.

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