Harmony is nothing but a more formal name for chording. In my volunteer choir I once had a bass who tortured me after each rehearsal by sitting at the piano and playing by ear. He would get a melody under way in any key he happened to strike and then search around with the left hand for the "harmony." For him the harmony meant the tonic chord, and once he found it he would wham away regardless of the harmony implied by the melody. I tried to show him that there were other chords and that at least the dominant might be used occasionally to break the monotony. He listened respectfully and learned to find the dominant chord; but a few weeks later he was back to his one-chord harmonization. For him it wasn't worth the bother!

At the other extreme we have the story of Mozart, perhaps the world's greatest musical genius, who, at the age of fifteen, wrote down the entire Allegri Miserere, with all its compli­cated voices, after hearing it only once.

Chord Vocabulary

You and I fall somewhere between these two types in our ability to hear and remember variations in harmony. Just as some people have a vocabulary of only a few hundred words and use them for every purpose, while others have a vocabulary of thousands of words and use precisely the right word in every situation, so some ear players use only three chords to harmonize everything, while others are always searching for a more suitable chord to fit into the harmony. And just as there are synonyms among words, so there are synonyms among chords—never quite the same but able to fit into the situation with a slightly different effect. The master composer selects the very best chord for each situation; and when playing his works, we do well to find that same harmony.

This refinement of harmony develops as we listen keenly to new music. And if we have tried to play a piece but have not been able to find quite the desired chord, we are keenly aware of the fine difference the next time we hear the piece played with that correct chord in its proper place. If we are already familiar with such a chord, we recognize it immedi­ately like an old friend; but if we have never heard it before, the likelihood is we shall not remember it. Consequently, familiarity with harmony is more important to the ear player than it is to the player who finds all his harmonies by looking at notes on a page.

Once we have become proficient with the three basic chords presented in the previous chapter, we may select the other chords according to our own inclination and require­ment. There are not nearly so many chords available in music as most people think. They all fall into a system almost as easily as the colors take their logical place in the spectrum

Major Triad

In the first place we have four different kinds of triads, that is, chords composed of only three tones. The basic one is the major triad—the major chord—which you learned so thoroughly in the previous chapter. This is found by playing 5 3 in any major scale. It remains  a major triad no matter how many times 1 you invert it or double the various tones.

Minor Triad

Now if you take this major triad in fundamental position, 3, and lower the middle tone, the 3rd, just one half-step, you will have a minor triad. You may invert this triad and double its tones and rearrange it to suit yourself; it will remain a minor triad. Practice
forming it and play with it until you easily recognize its sound, and your fingers will find it for you.

Diminished Triad

Form again the minor triad in its fundamental position and then lower the top tone, the 5th, a half-step, and you will have a diminished triad. The sound of this triad is so characteristic that you will easily learn to recognize it, no matter in what position you
hear it. Do not stop long to practice it; it will come easily a little later.

Augmented Triad

The only other triad, the augmented, is formed by raising the 5th of the major triad a half-step. This triad is very seldom used but has been adopted by jazz bands and movie producers to gain a certain bizarre effect.

It is one of the easiest of all chords to find, for the distance between
                                                                                                          G#
its tones is always the same, no matter how it is inverted. Play E, and you
                                                                                                           C
will find that three keys lie unused between C and E and also between E and G#. And, if you invert the triad, three keys remain between G# and C. In other words, the chord does not change its form or effect when it is inverted. Consequently, there are only four possible augmented triads: the ones on C, C# or Db, D, and D# or Eb. The one which you build on E is merely an inversion of the one on C; the one which you build on F is an
                                                                                                               G#   Db
inversion of the one on C#; etc. They are spelled differently, e.g., A or A,
                                                                                                                F     F
But this does not trouble the ear player. Let the note-reader worry about that!

Move any of the tones of these four triads a half-step and you will have either a dissonance or an inversion of one of the other triads. Only these four triads are possible.

Triads in Key

Now let us find how they are related to the scale. Just as we have nouns and verbs in our spoken language which are used as subjects and predicates in our sentences, so we have major and minor triads in music which are used as chords in our keys. We practice the triads by themselves in order that we may use them easily when we play in a definite key or scale. We can use any scale, for they occur in the same manner in every key; but we shall take the key of C, because it is easiest to use all white keys. If we build a triad on each degree of the scale we have:

G	A	B	C	F	E	F	G
E	F	G	A	B	C	D	E
C	D	E	F	G	A	B	C
I	II	III	IV	V	VI	VII	I

These are all the triads possible in the key of C. I, IV, and V are major triads; II, HI, and VI are minor triads; and VII is a diminished triad. There is no augmented triad in the major key. These major, minor, and diminished triads fall in the same order and position in every major key. You will recognize the three major triads as those which you have been using in the perfect cadence—the tonic I, the sub-dominant IV, and the dominant V. A diminished chord is generally marked with a °, and an augmented chord with a +.

Progression

Play these triads up the scale in various keys, and you will soon see how they are related to the key in which you happen to be playing. A regular course in harmony would be neces­sary to work out all the possible good combinations or progressions of these chords. Endless entertainment awaits you, however, if you play around with the triads and let your ear be your guide. Only occasionally stop to figure out what the triad is or what key you are in. Use the inversions freely to get smooth progression. You can modulate from one key to another rapidly, if you will allow one chord to melt into another without trying to stay in a certain key. Some of the progressions will suggest passages from familiar pieces; follow these up persistently. This makes a good game and is fine training for the ear. Eventually you will get into a rut and play the same chords over and over. Then go back to your scale with its triads and figure out a new progression. Play this in various keys, just as you did your cadences, and you will be stimulated to new harmonies and further experimentation.

Circle of Keys

As we have found how the various triads are related in a key, so we may now find how the various keys are related among themselves. This is easily seen by the circle of keys.

As we progress around the circle clockwise, each new key requires one more sharp. The key of C has no sharps or flats, G requires one sharp, D two, etc. As we progress around the circle counterclockwise, each new key requires one more flat.

The order in which the sharps or flats are added follows this same sequence. If one note in the key is sharped, it will be F#; if two notes are sharped, they will be F# and C#; if three notes are sharped, they will be F#, C#, and G#; etc. Similarly, if one note is flatted, it is Bb; if two notes are flatted, they are Bb and Eb ; if three notes are flatted, they are Bb, Eb and Ab ; etc.

Modulation

As we go around the circle clockwise, each new key is a fifth higher. Consequently, when we modulate to the dominant of the key in which we are playing, we merely add one sharp—or remove one flat. This sharp which we add— or flat which we remove—is always on the 7th degree of our new scale, if we are modulating to the dominant.

Similarly, if we wish to modulate to the subdominant, we go counterclockwise, and each new key is a fifth lower, or a fourth higher, and adds one flat or removes one sharp.

The easiest keys for modulation—the nearest related keys— are the keys immediately to the right and left in the circle. The farther away we get, the more difficult is the modulation. This is merely another way of saying that the modulations which require the addition of a considerable number of flats or sharps are more difficult than those which require only one addition or subtraction.

Signature

The group of sharps

or flats

that is employed in any particular

key is known as the signa­ture of that key. In printed music it is placed at the beginning of the score; but for ear players it is seen right on the key­board in the black keys which are used in that key.

There are many ways of modulating from one key to another. It can be done by introducing the new sharp or flat into the melody, or by removing the same. Or a chord which is common to both keys may be employed and then the new key assumed. In any case, it is best to play the cadence in the new key; this always completes the modulation and firmly establishes the new key.

The dominant seventh chord, however, is the quickest and most satisfactory way of effecting a modulation. This famous chord must now be investigated. Without having its name you have probably already stumbled onto it in your experi­mental ventures on the keyboard; and, if so, you have found it very useful.

A seventh chord is a triad with another 3rd added on top. A triad has a root, or fundamental tone, a 3rd, and a 5th. The seventh chord has a root, a 3rd, a 5th, and a 7th. Notice that the 7th lies just one step below the root an octave higher; you can find the 7th of a chord much more easily by going down one step below the root than by going up a 7th. The seventh chord may be inverted just as the triad was inverted; but, since it has four tones, the inversions will be more complicated—and also more interesting.

You will recall that there were four kinds of triads; there are many more kinds of seventh chords. Some of these are very rarely used, and are used only in inversion; but others are just as important as the chords of the cadence. Your ear will select the more useful ones for you.

First let us build a seventh chord on each tone of the scale, just as we built a triad on each tone of the scale. In the key of C we get:

B	C	D	E	F	G	A	B
G	A	B	C	D	E	F	G
E	F	G	A	B	C	D	E
C	D	E	F	G	A	B	C
I7	II7	III7	IV7	V7	VI7	VII7	VIII7

By playing these we find that I7 and IV7 sound alike; they are decidedly coarse and not very usable. We pass them, quickly by. II7, III7, and VI7 also sound alike; they have a rather weak feeling but are very effective in certain sur­roundings. VII7 has no twin; he is a question mark, but—we shall have more to do with him later. V7, however, is the powerful dominant. This is the grandest and most useful of all the seventh chords. This is the modulating chord par excellence. There is only one in each key, and it controls, or dominates the key.

V7

You will now enjoy becoming thoroughly familiar with this dominant seventh chord (V7). Play it in any key and follow it immediately by the tonic, thus:

or

Rearrange the tones as you wish and double them in various arrangements; you will find that the 7th should not be doubled, since it makes the chord sound thin.

After you have tried this progression in all the keys and can find it with ease, try modulating by means of it. Play part of a piece in one key and then modulate to another key. To make the modulation, first decide to which key you want to go, and then figure out the V7 in that key. As soon as you play this V7 in the new key, you will hear the resolution to I in the new key. To be sure that you have completed the modulation, play the perfect cadence in the new key. Then modulate back to the original key by means of the V7 in that key, and play the complete cadence in that key.

Modulation in Sequence

The easiest modulation and the one most used is to the dominant, e.g., from the key of C to the key of G. It is possible, and very good practice, to go completely around the circle of keys in this manner, without stopping to complete the modulation by a cadence in each key. Starting in the key of C, such a series of modulations would begin:

These chords may, of course, be spread over the piano at will; but you will notice that some positions are more satisfying than others. Use your ear keenly to decide which progressions you prefer.

Whenever you happen onto an inversion of a chord or a particular progression which reminds you of something you have heard, stop immediately and take time to investigate the resemblance. The recognition and the use of the chord in con­text will make it of practical value to you much more quickly than any exercise we can devise.

In similar fashion, and with an easier progression for the ear and fingers to pick up, we may modulate around the circle of keys counterclockwise, thus:

After playing these sequential modulations until they almost seem to play themselves, you will be able to arrange similar modulations to other keys, although these other sequences will not include all of the keys. By noticing your progress on the circle of keys, you will be able to see where you are going and why all the keys are not included in such excursions.

You will be kept busy many weeks gaining familiarity with this dominant seventh chord and all its possibilities. Try some of the other seventh chords, if you wish; but you will find that you use the V7 more than all the other seventh chords put together. You are not in danger of wasting time while you work on this chord.

VII7

One other seventh chord, however, is so useful and so easy to master that it will be mentioned here, even though it does not occur among the chords of the major scale, which we listed on page 50. Many other seventh chords may be con­structed by adding various kinds of 7ths to the four different kinds of triads; but the only one worth bothering with at this time is the one known as the diminished seventh (VII7). It is formed by adding a diminished seventh to a diminished triad. We shall leave the explanation of the diminished seventh interval to the chapter on intervals; but we can construct the chord very easily right now. Thus we take G the diminished triad, E, and add the diminished seventh, Bb, and we have the diminished seventh chord                               .

It is the easiest of all seventh chords to construct, if we do not worry about

the spelling, which often involves double sharps
 

and double flats                                      .

No matter how it is inverted, the distance between its tones remains the

same. Play

, and notice that just two keys lie

unused between C# and E, between E and G, between G and Bb, and between Bb and C#. And if the chord is inverted, it does not change its form. Consequently there are only three possible diminished seventh chords: the ones on C, C# or Db, and D. The one which you build on Eb is merely an inversion of the one built on C; the one built on E is an inversion of the one built on C#; etc.

This chord is easily recognized by its undecided and exciting nature. It is the chord which is used in the movies when the villain is chasing the heroine; and no matter how much the chord is inverted and carried up and down the keyboard, it does not lose its villainous character, and the heroine is unsafe until the chord finds its resolution in the arms of a solid major triad. The resolution is easily found, for any major chord whose root is just a half step above any one of the tones of the VII° is a logical resolution. Practice finding the chord quickly. When you want it, you want it in a hurry.

Broken Arpeggio

An interesting and useful variation in practicing these many chords is the broken arpeggio.

	A
	GB
Instead of playing the chord	EB	all at one time, roll it upwards as you invert it
	C

You can roll five notes instead of four, if you wish; but four are more common because they will usually fit into the rhythm better. The broken arpeggio is equally effective when played downward. Another effective arrangement is to play the arpeggio in one hand and smash chords in the other, inverting the latter or jumping from octave to octave to bring terrifying suspense. Of course, any chord may be used for this arpeggio; and in progressions the arpeggio is played first on one chord and then on the chord of its resolution.

Figuration

Other more simple figuration can be discovered with a little experimentation or by listening to various compositions. Most composers have a certain type of figuration which they favor and use consistently throughout their works. Thus Stephen Foster in the original publication for piano of his many songs, Swanee River, My Old Kentucky

Home, Old Black Joe,etc., used the figure	E
instead of playing the notes as a chord. If you are familiar with the chords, no practice is required to make this simple substitution. The inversion works

just as well, thus

Styles in figuration

change, however; and today everyone who plays Stephen Foster adds big chords, octaves, and anything else which will provide interest for the modern listener.

Mozart used this same figuration more frequently than any other in his piano works. This gives the simple background which is so characteristic of Mozart and focuses attention on the beautiful melodies which are spun out through all his compositions. No player in his right mind would think of tampering with these simple, carefully arranged figures; their perfection is Mozart.

Harmonic Melody

Figurations often suggest a melody, or, indeed, are a melody. All bugle calls are nothing more than arrangements of the tones of a major chord. Take the G major chord, the key in which bugles are generally pitched, and, using nothing but the notes of this chord, play Taps, or Reveille, or any other bugle call.

Reversing this process, we often select our chord by noticing what chord is spelled out in the melody. For instance, in Silent Night, notice how the melody tones fall into groups which indicate which chord must be used with them.

Only the encircled tones are not in the chords; the other notes in each little melodic phrase when played together make the desired chord, or at least give two of the desired three notes. The harmony for such a piece is written right out on the keyboard, if one watches the melody in the right hand.

The many new chords and progressions and figurations which we have learned in this chapter should open up an enormous literature to the ear player. Indeed, the entire course of learning to play by ear might stop right here with the advice to play and play and play—always listening keenly. The remaining chapters analyze music from various angles which will help the player to hear things which might otherwise escape his attention. Enjoy the literature.

WHAT TO DO Play the chord sequences until they are thoroughly familiar to both ear and fingers. Play the same, using big chords, arpeggios, and other figuration. Substitute or add new chords to the pieces you learned in previous chapters. Harmonize all the other tunes that were listed on pages 22-24 and 32-33. Those marked with a single dagger (t) modulate to the dominant key. Those marked with two daggers modulate to other keys. Transpose all your pieces to other keys

Are You Ready To Move Onto The Next Lesson? Click Here