Category: Music Theory

How to Tackle Difficult Pieces, Practiced Simply

A.B.’s lesson on 4/3/19 on the first prelude from Book One of the Well Tempered Klavier

Balancing memory with freshness:

Be surprised and delighted with each new chord (which is to say each new measure).  This is to balance out the impregnation of the piece by memory, from having heard and/or played the piece many times.   Instead create a “beginner’s mind” for whom the new chord is fresh, unexpected, and bathed in morning light.  You just don’t know what’s coming.  Memory doesn’t go away but a proportional balance is attained between memory and the unforeseeableness of the future.

The persistence of a single chord through an entire measure:

In this piece it helps that you were formerly an organist, for as long as you hold the keys down on the organ manual the sounds continue unabated, persistently, and without the piano’s ‘decay’.  Hear in your “inner” ear of imagination the five different notes of each measure as a simultaneous ensemble, which continues unbated as a totality from the beginning of the measure to the end of the measure.

A.B. is not satisfied with his control over the evenness of the sounds in a measure:

Take a single measure out of the flow of the piece.  Reiterate the first note of the measure over and over until it “sounds like you want”.  Do this without thinking of the other notes and whether they will match the first note in sonically – in other words this is not yet about evenness between notes).  Then switch to the second note.  Play it ever and over, until, as before, it sounds how you want.  Repeat this procedure for each further note in the measure.  When you play the measure as written you will notice in retrospect that all the notes were even, although you were in no way trying to match them, but instead having each note have its ‘ideal’ sound.  A musician with a  good ear will always be able to tell when a sound has reached a certain ideal perfection, but not through analysis, through an intuitive sense of the sound.

For evenness when one note, occurring between two other notes, is not balanced sound-wise with the others:

In the measure that begins : f2 f3 a3 c4 e4, the c4 was not balanced with the a3 and e4.  I suggested that he hold down the a3 and e4, and while they are being held, repeat c4 over and over.

Another path to evenness: the written notes are part of a larger whole:

In measure one, for example, turn the measure’s notes into a rapid arpeggio that starts, with the highest pitch, e5, descends through the notes of the chord until reaching the bottom note (c4) and without pause re-ascends to the top note.  This creates a more cohesive and integrated motion in your hand.  Once you have this gestalt, you can remain silent during the first part of this arpeggio and start playing in the middle of it, at the note that is supposed sound first in the measure.  Eventually there is no need to pause or mark time for the first half of the arpeggio, it can occur in the inner feelings of the body in just a split second.

Yet another path to evenness:

When a baton twirler causes the baton to make a circle, it is the result of a sequence of different motions all blended together in a one overall fluid motion.  I’m ignorant of the breakdown of those motions, but you can still imagine, yourself as twirling a baton, one cycle every half measure (as the note pattern repeats).

I would sing a sustained line for A.B.:

Sometimes I would sing a sustained melody, one note per measure, starting at the beginning of each measure, made up of the top note of each measure.  Maybe I thought of doing this because I Gounod’s Ave Maria flitted through my mind.  That Gounod may have felt that the Bach begged for a continuous line (adumbrated by Bach made tangible  by Gounod).  The effect that my singing had unconsciously on A.B. was each note of the measure was instinctively made to balance, or fuse sonically, with the sustained note I was singing.

How to bring out the dramatological curve of a piece, even though it was originally played on an instrument of a constant degree of loudness: 

There are not many overtly dramatic moments in the piece that stand out from the monotonous (sic) patterns that repeat every half measure.

And even if we become aware at a certain time of these moments, they will afterwards fade into the background due to the abrasion or erosion of constant playing of the piece.  So  make the most of these moments.

Here is one example.  Chords outlining diminished chords, for instance, happen only a few times in the piece, but each time it does, try to react to the sound of the chord as being jarring, intense, dissonant.  This effect can be gained even without making any change in the loudness of those measures versus the surrounding measures. One can intimate a dramatic curve merely with intent and adumbration in the flow of the notes.

One of my other students, while playing through the Adagio from  Beethoven’s Op 13, came across of a few measures of diminished chords in the passage leading back to the second A section of its ABA form.  She said “diminished chords are ugly”. I said: that’s great, can you make them sound as ugly as possible!

Another example. When an interval of a minor second in the left hand, treat it as an astonishing, unexpected dissonance.

One more example, this time a longer passage:

In the second half of the page there is a long dominant pedal point in the left hand playing g2 (lowest line of bass clef).  As he went from one measure to the next I repeated: “long … long endeavor … never stops … we’re not ‘there’ yet”.

Matching two sounds that are separated in time:

When you play the first half of a measure and get to the highest note, consciously hold its sound in your ear’s memory, so that when you play the same note in the second half of the measure you can match it with the first.

Sometimes a “group” of notes is just one note:

In the last few measures of the prelude, I find that it is not useful to think of groups of four notes, or even two notes, the measures are too ambiguous compared to what has preceded it throughout the piece. My way around this is to play these last measures in “groups of ONE” note.  To promote this I say out loud as i am playing: “One”, “one”, “one” …. “.  Every note bears little allegiance to every other note except when though of in retrospect.

Remember that your pinkie is part of your hand, not a separate appendage:

Often your pinkie seems to be out in right field, detached from the rest of your hand as if it were a separate appendage.  Hold the pinkie in the unity of your whole hand.

Isolating Variables: the sequence of fingers as against the sequence of pitches:

This is in line with what we just said about the pinkie being “held” in the hand.  In measure three A.B. is using fingers 1, 3 then 5 to play g4 d5 and f5.

I asked him to cover the notes g4-a4-b4-c5-d5 with the five fingers of his right hand.  Play it as a cluster and hold it.  And while holding all five notes try to lift the thumb and replay the G, then again while still holding all the notes, raise the third finger and replay the d5, and similarly with the pinkie for f5.  Just focus on an awareness of the identity of which finger you are playing, as if to say “these are the fingers I’m going to use: 1 3 and 5”.  Then use the same fingers but for the written notes (g4 d5 f5).  You hopefully will feel an interesting transference of the awareness of which fingers to use, now mapped onto a different set of fingers.

Isolating Variables: The sensation of evenness as against any physical actions taken to instill evenness, especially when there is a new set of notes:

There is an ’emotional’, a generalized physical sense in the body as a whole, of ‘balance’ among the notes of the keyboard that are played together and in close succession.  As with any feeling, this emotional state can be reproduced at will under different circumstances.  Rather than the details of how to play the next measure evenly, try to reproduce the experience of having this feeling.

This distinction applies to many situations in playing.

For instance: there is the sensation we get of playing an ascending set of pitches.  This feeling can be conjured up even if we are playing a descending set of pitches.  Sometimes doing this is very useful in a Bach fugue to help homogenize two different voices, so that what a second voice is doing does not sound too dissimilar from what a first voice is doing.

Or, a sense of enlarging and getting louder can overlay a series of notes that are getting softer.

Or, a sense of wide space between the fingers in the hand can overlay a passage that involves a series of notes only one half step apart from each other.

Or, the sense of energy that we get from one very dynamic piece or passage from such a piece, and overlaying that feeling of energy onto all passages, slow or fast, loud or soft.

Making a clear connection between two non-adjacent fingers:

There is a measure in the first part where the pianist plays this sequence of notes: b3 c4 e4 g4 c5 … .

Notice that I tapped your fourth finger when you went from your third finger on g4 to the fifth finger on c5, It was meant to show the hand the focus of the ‘connection’ between the fingers playing g4 and c5, more at being located at the connection between the 3rd and 5th fingers.

At another point in the lesson I slid a pencil between his second and fifth finger.  The pencil passed over those two fingers but passed underneath the fingers in between them.  This helped him sense that those two fingers don’t act separately, but more at being the two ends of the plank of a see-saw, and thus the result of one single action.

More about see-saws:

Regardless of what two fingers play one after the other, and regardless of the distance between the notes they play, always an imaginary see-saw plank between the current note’s finger and the next note’s finger.  Add to this image an almost felt, pivot point, midway between the two fingers.  Now pretend you are a very strong person who  can make the two ends of the plank move reciprocally move up and down just by leaning first on one side and then the other side of where the pivot.

Once you are on the second note resulting from the first see-saw, move the see-saw’s location so that it connects this second note with the note that follows it.

To develop the sense of this see-saw, and the ability to relocate it quickly, it may help (using measure one as an example) to do this exercise:

Go back and forth between c4 and e4 (something which I notate as |: c4 e4 :|.  Once that see saw is functioning organically do the same for |: e4 g4 :|, and so on.

Addendum to the previous section:

It is your tendency, when you encounter a problem in a measure, to  just play ahead for quite a long time, and then tend to the problem later.  It is good to balance that tendency out with the ability to not move ahead, maybe only as far as the end of the current measure, and then focus in on tiny details.  Focusing entails a greater degree of  awareness of what is  happening physical and sound-wise, plus  reiterating that tiny detail until it sounds how you want it to sound.

Don’t rob the last note of each measure of its full duration:

A.B. usually tries to rush into the new hand position at the beginning of the next measure.  He feels that he may not have enough time to do it in, and compensates by holding the last note of the current measure a little shorter than the other notes of the measure.  I said “it is always good to try to hold longer whatever note sounds just before a leap, a skip, or a change of hand position.  One can deal with this near the end of the note by continuing to hold it when your hand tells you it is time to let go of it.  There is another way that is just as effective, that is more at being located time-wise at the beginning of the note rather than near the end.  Start the note with the “intention” of holding it longer.

We reached the goal of evenness:

Joe: in general today we have accomplished one of your goals: the sound is now even throughout.  During the attempt to make each note sound clear and close to its ideal sound, you were finding it easier to do this when playing all the notes a little louder than usual.  Often two variables get tied together, “entangled” as it were.  On the hand playing more evenly, on the other playing more loudly.  The latter helps achieve the former, only at some point, you want to separate the  former from depending on the latter.  Once you have effected this separation, the evenness and clear-speaking-ness of each sound, no longer depends on loudness and can occur at any dynamic you choose.

General comment #1:

 Notice that while you tend to try to solve things with specific actions of specific fingers, I almost never suggest a solution that involves the fingers, but relies instead on a more integrated motion of all the parts of the arm from shoulders to hands.

General comment #2:

I think you are evolving from one species of musician into another species: from an organist to a pianist.

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The “Spiral” of Fifths – An Alternative to the Circle of Fifths

The “Spiral” of Fifths – a “self similar fractal”:

If you start a new major scale on the fifth step of any current major scale, the new scale will have one more sharp than the previous scale.  Sometimes this new sharp is in the form of a flat from the previous scale that has been “sharped” into a natural in the new scale.*  Or a sharp from the previous scale that has been ‘sharped’ into a double sharp.  The new sharp always appears om the seventh step of the new scale.

If you start a new major scale on the fourth step of a current major scale, the new scale will have on more flat than the previous scale. Sometimes this new flat is in the form of a natural in the previous  scale which was been “flatted” into a flat in the new scale.  Or a flat from the previous scale has been ‘flatted’ into a double flat.

These two processes (adding one sharp at a time or one flat at a time) can go on forever.  If one keeps adding a sharp, the new scales will begin to contain double sharps, then triple sharps, etc..  If one keeps adding a flat, the new scales begin to have double flats, then triplet flats, etc..

The correct drawing of these two interlocked, and inverse procedures is not a circle of fifths (or fourths) but a spiral of fifths.  Just as interestingly, there is no beginning or ending to this spiral.  There is always another layer of the spiral outside the last layer currently displayed in any representation of this spiral, and so on indefinitely.  Similarly, there is always another layer of the spiral compressed inside the smallest layer of the spiral currently displayed, and so on.

Most of us learned about key signatures using the diagram of the circle of fifths.   Yet, a lot is left unanswered by this image.  It does not explain, for instance why, when you got about half way through the circle sharps somewhat arbitrarily turn into flats.   Why just then and not sooner or later in career of the circle?

Just as a C# means something different than a Db, and just as Cx means something different than D, theoretically there is nothing to prevent us from having a C-triplet-sharp which is different than a D# or Eb.  We may never see a triple sharp throughout our playing lives but it exists as sure as ultraviolet and infrared extend the boundaries of the visible portion of the electromagnetic.**

In the spiral of fifths, if we are located at C Major, then the next seven positions (or “o’clocks”) on the spiral will bear the addition of one more sharp, until at 8 o’clock double sharps start to appear in the scale.  And seven hours later than that “triple sharps” will start to appear, and so on every seven hours.

Similarly with flat.  If we go in the other direction from C Major, the next  seven keys bear the addition of one more flat, until at “4 o’clock’ double  flats begin to appear, and so on every seven o’clocks further inwards around the spiral.

Advantages to the spiral shaped diagram:

We no longer have to treat as arbitrary the point when we switch from flats to sharps, or vice versa.  We can also see the dynamic relationship of sharps and flats to each other, not as having two separate, essential identities, but both as being an expression of the same, single reciprocal principle of flatting and sharping.

If you draw a straight line from any key in the spiral inwards towards the center of the spiral, all the keys that lie along that line are all enharmonic equivalents of each other, moreover the letter of the alphabet in the name of the tonic progresses one letter at a time through the musical alphabet.

The letter “C” is always special:

C major has the distinction of being the only key consisting of only naturals and no sharps.   C sharp major has the distinction of consisting of only  sharps.   C double sharp major has the distinction of consisting of only double sharps.   C-triple sharp major consists only of triple sharps.   Etc..

Going in the other direction: C flat major has the distinction of being the only key consisting of only flats.   C double flat major has the distinction of being the only key consisting of only double flats.  Etc..

* For instance, the key of F major stands to the key of C major as having “one more flat” than the later, the note B-Natural in the C Major Scale being flatted into a B-Flat in the F Major Scale.  Going in the other direction, the “new” sharp in the C Major scale is the B-Natural on the seventh step, which had been, in the F Major scale, a B-Flat.

** A curious thing happens when we have ‘sharped’ C-natural twelve times, so that we now have  C-dodectuple-sharp.  We find that C is its own dodectuple sharp one perfect octave higher.  In the same way we can ‘flat’ C-natural twelve times, and find that C is the dodectuple-flat of itself.   And then the process could continue until we find ourselves beyond the range of frequencies covered by the piano keyboard, going past vintuple sharps or flats (or would it be vigintuple), then centuple, and so on indefinitely.  For there is no lowest or highest frequency that a sound can have in theory.  A frequency of a billion vibrations per second is just as possible theoretically as a frequency of one billionth of one vibration per second.   Whether they are audible is another question.  And at some point when we get down to the size of molecules of air, perhaps there is no higher frequencies physically possible (got to think that one through).

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