Pianists are frequently required to play three equal notes (triplets) with one hand while playing two equal notes (duplets) with the other hand. As you know, a triplet is a group of three equal notes compressed into the time-span normally allotted to two notes. The triplets are written as notes of the duplet value and designated as triplets by a slur or bracket over an italicized Arabic 3.
It is very easy to feel these groupings individually, but sometimes difficult to perform them at the same time. Such simultaneous combinations of diverse time divisions are called artificial rhythms. A duplet and a triplet performed at the same time is called two-against-three. Approached properly, it presents no problem.
The first step in the solution of any artificial rhythm is to find the lowest common denominator of the two numbers involved. In this case they are 2 and 3, so our denominator is 6. Spacing the three notes of the triplet above the six digits at every second digit and the two notes of the duplet below at every third digit will show us the exact relationship of the notes to each other.
The combined notes result in this rhythmic pattern:
Clap this rhythm a number of times. It is the rhythm of the Spanish Dance in Chapter 6 and also of the first Rhythm Drill in Chapter 6.
Now divide it between the hands and tap it on some wooden surface—a table, chair arm, or music rack of the piano—saying rhythmically, “together, right, left, right.”
Do this for a number of measures. Reverse parts, tapping the triplets with the left hand and the duplets with the right hand, and saying, “together, left, right, left.”
When this has become easy, choose two keys on the piano—any two if you are alone, F and C if in class—and, using the second finger of each hand, perform the patterns on the keyboard, still reciting the appropriate words.
Next, count “one, two, and three” for both patterns. Figure 180 shows how this basic counting may be adapted to three different time signatures.
When you have mastered Figure 180, try applying the two-against-three pattern to five-finger patterns and scales.
M. S. McLain
There are several possible artificial rhythms, but the only other one we shall consider is three-against-four. We shall approach it as we did two-against-three—first the lowest common denominator, then the note-groups lined up above and below.
You will notice that although the notes of each group alternate (after the first pair), they are not equidistant from one another. A mathematically exact transcript of this, based on triplets, is possible, but a bit complicated: a much easier, more practicable, and very close approximation is:
“Look! Here comes Santa Claus!” will help you remember it—or make up a sentence of your own.
Clap the rhythm a number of times, then tap it, with each hand taking turns at each part.
Play the pattern on two keys, then apply to five-finger positions and scales. When the two hands have learned to coordinate and can perform at a proper speed, the slight metrical inaccuracy will disappear.
Here is a passage from the beautiful slow movement of Beethoven’s Sonata in F minor, Op. 2, No. 1. Sometimes students avoid playing the movement because of this very section!
One final problem sometimes arises from consecutive or alternating groups of two and three, or three and four. The well known habañera rhythm employs alternating groups of two and three. Several combinations are possible:
First, clap each rhythm for several measures; then, clap one rhythm while other students clap even quarters. After several measures of this, reverse the process.
Never clap an isolated triplet: if you do you will surely be clapping. The way to insure an even distribution of time is to carry the counting over to the next beat:.
Now follow the same steps with alternating note-groups of three and four.
HOMAGE TO MR. CZERNY
The different kinds of accompaniments you have been using are adequate and appropriate for most of the music you will be called on to harmonize. However, you are now sufficiently advanced to consider some other styles which will add greater variety and interest to the music.
Chords on the “off beat.” We have already mentioned this type of accompaniment in connection with Turkey in the Straw in Chapter 9. It is characteristic of early American plantation and country dancing, where one or more persons danced to fiddle or harmonica tunes while the non-dancers participated by clapping hands—and perhaps tapping toes—on the weak beats of the music in a primitive but strong form of syncopation. In addition to Turkey in the Straw, the Arkansas Traveler and Chicken Reel are just such fine old fiddle tunes which can be accompanied in this way.
Skipbass or “bar-room.” If you have ever been fortunate enough to see, in a Western movie, a close-up of the left hand of the piano player in some “Longhorn Saloon,” you will have witnessed an exhibition of amazing dexterity—if somewhat dubious artistry. What this prestidigitator was doing with one hand is what you have been doing with two hands, at half the speed, and calling it “Fancy Strumming”.
There is a trick to such lightning travel between low octave and higher chord. If you could see the close-up of our piano player in very slow motion you would observe that as soon as his hand has struck the low octave it relinquishes the octave span to which it was framed and while traveling upward in midair, assumes the shape of the chord it is about to play so that there is no time lost in searching for notes or framing the hand to the new chord. After striking the chord, the hand immediately relinquishes the chord shape and, on the downward trip while in midair, frames to the octave span. This is one of the reasons you were asked from the earliest lessons to fix the chord shapes and octave span in your hand’s memory.
Practice skipbasses in various keys and with different chord patterns. Do this with exaggerated deliberation and absolutely no waste motion. Gradually work up speed, then harmonize songs for which you deem this kind of accompaniment suitable. Little Minka, Lightly Row, and Dixie are good choices. There are many others which you can find.
Drone bass, or bagpipe effect. This is such an easy accompaniment that you will have to exercise restraint to keep from using it all the time. It consists of a perfect fifth preceded by a short grace note a half step below the upper note. The grace note is so short that some pianists advocate playing all three notes simultaneously but immediately releasing the grace note. It takes a keen ear to detect the difference.
Since the chord has no third it can be employed in either major or minor mode. Naturally, it should only be used where a bagpipe effect is appropriate, but remember that bagpipes are not peculiar to Scotland; they are native to Ireland, Italy, and many other lands. The two tones of the perfect fifth constitute a double pedal point and can be reiterated through various changes of harmony.
Here is another reel to harmonize in this way.
THE IRISH WASHERWOMAN
Drum roll. This is almost as easy as the bagpipe effect. It consists of a gruppetto of three notes leading up scalewise to the tonic. (See gruppetto in the section on embellishments.) It should be played fairly low on the keyboard to simulate a deep drum.
Do not try to articulate the individual notes of the gruppetto. Rather, place all fingers in position and depress the keys by means of a rolling motion toward the thumb. The British Grenadiers invites such an accompaniment.
THE BRITISH GRENADIERS
Descending scale figures. Somewhat more complicated are descending scale figures in the lowest voice. These can be used in a strummed accompaniment as in Figure 188,
or by the left hand alone as in this arrangement of a phrase from The Caissons.
Chords in open position. Until now, when we used block chords in an accompaniment we usually played them with one hand while the other hand took charge of the melody.
In your harmony course you have probably been working in open position for some time, so let us apply this approach to the harmonization of some of our melodies.
While writing in open position is no more difficult than writing in close position, it does seem to be a trifle harder to think chords through when you are playing in open position, but the richer sound of the harmonies—particularly the seventh chords—makes the effort worth while. Incidentally, most hymns are written in open position.
Chords with more (or less) than four parts. There is no reason why a chordal piano accompaniment should be restricted to four parts. As long as you have enough fingers you may play as many notes as you wish. There is even a way of placing your thumb across the crack between two white keys and so striking both keys at the same time, and if your thumb is long enough you can strike two black keys. (Chopin Prelude in C minor, measures 2, 4, 6, 10.)
By the same token the harmonies may be thinned out in places to one or two strategic tones.
To serve as guidelines in such deviations here are a few hints:
1. Give special attention to outside voice lines.
2. If an inner voice is conspicuous, make sure that it moves logically.
3. Avoid “bunching” several notes in the lower register as this produces an effect of thickness.
4. If you strike a “wrong” note do not stumble and correct it, but lead it to a neighbouring “correct” note as if you had merely played a passing tone. Almost any mistake can be made to sound interesting in the texture of a piece of music if it is quit skillfully.
Now let us see (or hear) what adding a few notes can do for the same fragment of Swanee River which we used in Chapter 9 (Figure 135).
Notice that the conspicuous inside voice is led upward toward resolution. In playing the music, bring out such a voice to heighten contrapuntal interest.
The melody in thirds and sixths. Some melodies seem made to be accompanied by another voice a third or sixth lower. Silent Night is one of these. All of it can be played in thirds or sixths with a simple broken chord accompaniment.
Tenths in the bass. We pointed out earlier that playing many notes concentrated in the lower register of the piano produces a thick, muddy effect, just as it does in the orchestra. One solution is to spread what would normally be a triad over the interval of a tenth. This is another version of open position.
Even if your hand is large enough to reach the distance comfortably, arpeggiating the chord adds to its sonority. If your hand is small, swing your wrist in a wide lateral crescent and pivot on the middle note, using your third finger. Such a chord may be substituted for the tonic octave in a skip bass.
Broken tenths (the same open position triads with the fifth omitted) introduced when there is a little time to fill in are the darlings of jazz players.
Boogie basses. In Chapter 10 we referred to a ground bass or ground in connection with the Handel Passacaille. Another name for the multiple repetition of a bass figure under a changing superstructure is basso ostinato. Today in so called “popular music” we have all kinds of boogie basses which are the logical descendants of the old grounds and bassi ostinati. One of these bears such a resemblance to Purcell’s A Ground that we call it Ground Boogie.
This pattern requires great left-hand dexterity. Practice it slowly in several keys, then gradually work up speed. From these I, IV, and V chord components you can fashion an accompaniment to suit your needs.
Compare the basic style of Ground Boogie with Purcell’s composition.
Arr. M. S. McLain
Another type of boogie bass consists of seventh chords played in broken octaves. Again we give the components, which you may rearrange as you see fit. Because the hand must be kept framed to the octaves we will call this Frameup Boogie.
None of these various types of accompaniments needs to be maintained throughout a song or improvisation. In a very short movement it is well to take into account the value of unity, but in a longer undertaking some variety might improve the accompaniment.
There are some places where, for a brief stretch, no accompaniment is needed. This is so if the melody is fairly complicated or if anything in the style of a “break” occurs. For example, the seventh, eleventh, and fifteenth measures of Shortnin’ Bread could very well be left unharmonized. In The Arkansas Traveler all of the next-to-the-last measure and the first beat of the last measure can be left unaccompanied, chords being restored only for the last two melody tones.
Old Irish Air
from County Londonderry
Models. All of the sight-reading studies and shorter solos may be used as models for improvisation. Analyze each to determine its characteristic feature or features.
Such features might be: notes restricted to five-finger positions; single notes in each hand; only chord tones in melody; all diatonic tones used in melody; chords in right hand, melody in left hand; staccato with one hand, legato with the other hand; non-harmonic tones—accented or unaccented; chromatic tones; use of sequences; variations on original melodic pattern.
When you have decided what are the characteristic features of the model, improvise (in another key but with the same number of measures and phrases) incorporating the same elements in your creation.
New resources. In addition to the familiar elements we have mentioned there are other resources which you have not yet drawn on in your improvisation; change of key; modulation; secondary dominants and dominant sevenths; chromatically altered chords; artificial rhythms; freer use of inversions—all of these are at your disposal, so experiment with them.
Change of key. Although some of your improvisation models contain brief changes of key, you have not yet changed key or modulated in your free improvisation. Now, in an eight-or sixteen-measure period, change key, then return to the original key. If the second key is closely related you may or may not use a modulation. If the second key is remote, do modulate. You need not remain in the new key long, but its tonality should be definitely established before you return to the original key.
If you plan to use a modulatory chord, figure it out in advance so that you will not hesitate or fumble when the time comes to use it.
Practice moving from all major and minor keys to closely related keys and to distant keys, with modulation and without modulation.
Avoid favorite keys in which you feel more at ease than in others.
Secondary dominants and dominant sevenths. Secondary dominants and dominant sevenths may sometimes be used in a repeated pattern without causing the melody to become unduly monotonous. Improvise to the pattern in Figure 196. Try it as a solo and as a duet.
You will recognize in the first three phrases the pattern of Figure 131 in Chapter 9. Create other chord patterns which include secondary dominants and dominant sevenths and improvise on them.
Special effects. Occasionally it is fun to experiment with what we might call special effects.
We have already mentioned drone bass and drum roll in our discussion of new accompaniment types, and some time ago we suggested that you improvise on the pentatonic scale.
Some other possibilities are:
a. Use of the Byzantine scale, which is a harmonic minor scale with a raised fourth.
Many Russian composers have used this scale; César Cui in Oriental and Tchaikovsky in March Slav are two examples. In Chapter 4 you encountered it in Club Zara.
b. One hand playing black keys while the other hand plays white keys produces many amusing effects.
c. Polytonality, in which each hand plays in a different key.
d. Whole-tone scales. Less variety is possible with these, but veiled, atmospheric effects can be achieved by using the damper pedal to sustain the tones of either scale complex.
e. Low, spread chords, sustained by the damper pedal while you provide more movement in a higher register. If you have a sostenuto pedal, experiment with this, depressing it just after you have played the note or chord you wish sustained. There is also a way of depressing certain keys silently and in advance of the playing. Then, as you play, these prearranged tones will continue to sound while the others fade away.
f. Pedal point, the use or abuse of which can become a pernicious habit. If one does not use it as a crutch, however, it can be a valuable addition to one’s resources. Especially interesting are the far-ranging chromatic improvisations which can proliferate over a dominant pedal.
g. The double pedal point, which is mandatory in what is dubiously known as “Indian Music.” “Indian Music” consists (off the reservation) of a perfect fifth (usually A and E) reiterated in quarter notes in common time. These thumps are supposed to represent the beat of drums. Over them is a rugged melodic line usually based on the pentatonic scale, with an implied feeling of minor mode.
M. S. McLain
“Indian Music” is believed to be practically irresistable to little boys, and almost every beginners’ “method” book has its entry. Since everyone else tries his hand at “Indian Music” you may as well indulge in it, too. It is rhythmical, easy to improvise, and perhaps you will think it fun. If you can free yourself from the hypnotic effect of A minor with its blank key-signature you will find that E flat minor is an ideal key for your purpose since only black keys need be used; all are available to you, and the effect is of minor mode.
One word of caution: please remember that this genre is a travesty on and a gross injustice to the genuine music of the American Indian.
Extended periods. In the beginning it was important for you to improvise in balanced periods of a predetermined length. Without this discipline the tendency of most improvisers is to drift along haphazardly with no idea of where they are going, and still less concept of beginning-middle-end structure. However, once you can manage an eight-measure phrase or period easily, you are capable of doing almost anything else.
Eight measures can be lengthened to sixteen by means of a half cadence at the end of the first eight-measure period, followed by a repetition with slight changes, or by a repetition in the minor (relative or tonic), or by an exact repetition with a full cadence in place of the half cadence. Then a new and contrasting section of eight-lengthened-to-sixteen measures can follow, and finally a return to the first section: an A B A form.
Irregular phrases. We have stressed four-and eight-measure phrases while you were gaining skill. Now you may consider the many beautiful effects to be gained from phrases of three, five, or even seven measures. A surprising number of folk songs have three-measure phrases. Some phrases have a three-and five-, or five-and three-measure, structure.
Playing from memory is an obvious necessity for every artist pianist and it can be an asset to the functional pianist as well. No one will expect the functional pianist to play a Chopin Etude, but he may often be called upon to play Christmas carols or patriotic songs and if he knows a few of these without having to call for the music book he is in a happy situation.
If you are one of the fortunate few who can glance at a piece of music, perhaps play it through once, and remember it for ever after, we have nothing to say to you but “congratulations!” If you are like the rest of us, however, the following remarks will help.
First of all, remember that the ability to memorize improves with use and deteriorates with disuse.
Pianists memorize in several ways. Our fortunate pianist who looks at a piece of music or plays it once and thereafter knows it is said to visualize it. He has, in all probability, a photographic memory. He can, at will, evoke the image of the music and has only to play from that image. If you show evidence of this gift, develop it to the utmost. It is debatable whether or not it can be acquired if there is no natural gift.
Another means of memorizing is by analysis, which does not mean attaching a name to every chord, although if doing so helps you, by all means do it. Analysis in this context really means a comparison and understanding of the various elements in the composition. The way in which we analyzed sight-reading exercises No. 1 and No. 3 in Chapter 3 (page 35), or the Four Solos in Chapter 4, for the purpose of helping you to play them without looking at your hands, would also aid you in memorizing them. Association also plays a part in this way of memorizing.
Other methods advocated by some pianists are memorizing by hand-position shapes and keyboard feel (a kinesthetic approach) and by fingering. Some pianists memorize away from the piano while traveling on trains and planes or sitting under trees. Our own preference is for a combination of analysis and association, but you must experiment with other methods and combinations to find which suits you best.
Under no circumstance take the lazy way of playing the music over and over, mindlessly, until you “know it by heart”: sometimes you will know it and sometimes you will not. The only thing you can depend on with this kind of “memorizing” is that it will fail you under stress.
Any kind of learning must be reinforced, so, whichever method you adopt, these suggestions will be applicable:
1. Do not memorize the beginning of a composition first. It is usually the easiest part and for this and other reasons is likely to be played more than other parts anyway. Begin by memorizing the most difficult part. In this way you will be reinforcing the memory impression and at the same time gaining finger mastery.
2. Divide the composition into short sections and learn each separately, then combine them into larger units. Pianists sometimes make a mistake or forget in the middle of a work and, unable to “pick themselves up” where the mistake occurred, are forced to return to the beginning. This could be avoided if the pianist, by reason of sectional memorizing, could resume playing two measures back or one measure ahead of the mishap. Moreover, the knowledge that he can do this gives the pianist an increased sense of security.
3. In all music except that in which the hands are closely interrelated, or what is in effect a single line, learning each hand’s part separately can be most helpful. Such practice has the added virtue of uncovering contrapuntal values in the bass which might otherwise be overlooked.
4. It has been said that the test of really knowing a composition is to be able to play it at an excessively slow tempo. Try this.
5. If it is essential that you play a work perfectly from memory, there are two ways in which to insure security. They are toilsome but practically failure-proof. The first is to close your eyes and, away from the piano, go through every note in your mind as if you were playing it on the keyboard. The second way is to write the composition out from beginning to end from memory, and away from the piano.
One reason we have delayed a discussion of memorizing is that we wanted you to become a good sight-reader. There is no reason why one skill should militate against the other, but it is a sad fact that people who memorize readily are frequently poor sight-readers. It is not that memorizing causes them to be inept sight-readers, but that being poor sight-readers, they tend to memorize everything so that they will not have to read.
One last thought: the music is never really yours until you have memorized it.
(Op. 28, No. 20)
TWO-PART INVENTION, NO. I
AMERICA THE BEAUTIFUL
Samuel A. Ward
- Repeat longer phrases than you have done so far. See who, in the class, can retain and repeat the most.
- Repeat short two-voice contrapuntal phrases.
- In a four-voice chord progression repeat the bass part, the alto part, the tenor part.
- After being told the starting tonality, identify the type of modulation being played (V7/V or V7/ii) and the ultimate key.
- As classmates modulate using inversions of V7 chords, identify the inversions being used. To do this, concentrate on the movement of the bass voice. At first you should know what the original and the objective keys are, and the player should pause on the modulatory chord long enough for you to get your bearings. Later, though still knowing the keys, you should be able to identify the chord inversion when it is played in time; still later, you should be able to identify it without prior knowledge of the keys.
- Play and harmonize Prayer of Thanksgiving and The Caissons by ear, and in all keys.
artificial rhythm; skip bass; triplet; duplet; two-against-three; habañera; drone bass; reel; open position; close position; contrapuntal device; break; polytonality.
- Play modulations as skip or waltz basses, and as two-hand broken chords. (See Figure 85)
- Play all seventh chords as arpeggios.
- Play from dictation random triads on degrees of pure, harmonic, and melodic minor scales.
- Play major and minor scales, and triad and seventh chord arpeggios in artificial rhythms. Do this in contrary as well as in parallel motion.
- Prepare accompaniments to the songs or instrumental solos your classmates are studying in their applied course and accompany one another in class.
- Transpose and harmonize songs in school music books.
- Continue sight-reading as suggested in Chapter 10.