Tag: concert piano

Deciding What is Controllable. Also: Transforming the Polyphony of a Gugue

Well Tempered Klavier, Book I, C Major, Prelude

#1

After finishing the piece I simply asked A.B. what he liked and disliked about his rendition.  He mentioned several negative things and then struck on the one thing that I had primarily noticed: that he stopped the harmonic flow of the piece every time he went from the end of one measure to the beginning of the next.   I missed sensing that inexorable connection that energetically pushed me from the chord in one measure to the chord in the next measure.

He said that he had previously tried condensing the piece into a chorale of whole-note chords (each chord took the place of one measure).  However, he had trouble because he couldn’t do it with any speed.   I said that the speed was of the essence of the procedure.  Ideally, each eighth note’s worth of the piece, in terms of its duration, became the duration of one of the chords of the chorale.

Since it was difficult to shift chords that quickly, I recommended to him that he play just the chord a single measure followed by the chord of the next measure, and then stop.   I asked him to play the first chord as if it were a grace note going to the second chord – the latter being held longer.

This he could do.  We repeated the process for each measure going into its next measure.

Now that we had merged two amino acids into a somewhat longer chain of molecules, I asked him to play as written, while I, in the higher treble, waited until he was near the end , but not at the very end, of one measure only then played the chord of that measure as a grace note followed the next measure’s chord.  Only I would get to the second chord before he finished playing the current measure.  That anticipation of my chord connection gave him the necessary push and energy to keep the piece’s harmonic flow going across the bar line.  Then I would remain silent at the second piano until he reached nearly to the end of the new measure at which point I would break in with the chord of the new ‘current’ measure played as a grace note to the chord that governed the measure that was about to start.  And so on.

#2

A.B. remained worried in particular that the pinkie sixteenth note in the right hand at the end of each measure does not connect smoothly to the next sixteenth note in the left hand at the beginning of the next measure.

His default solution was to figure out  exactly how he wants his pinkie to play that note.  I solved his issue by stepping entirely around his approach.  As he played the piece I sang “la la la…”, but starting with 6th 7th and 8th sixteenth notes of one measure and ended with the fifth sixteenth note of the next measure. on notes to the first note.  I then waited too the 6th note of the new measure and began the process of again singing along for 3 + 5 or 8 notes.

In the form I was singing it, with the way I was grouping the notes that I sung versus those I did not sing, I purposely glossing over the connection between the two notes on either side of the bar lines..  It happens automatically.  By spreading a solder, or flux over the end of one measure and the beginning of the next, I effectively made less important the connection of the bar line.

I noticed in my singing that I helped things along by making misplaced crescendo starting on my first note and ending towards the eighth note.  This helped smooth over A.B.’s faulty connection over the bar line.

At this point we moved on to the fugue: transforming the polyphony of a

fugue in C Major, Book One, Well Tempered:

A.B.: why do I find it so difficult to not hold a voice note longer than it is supposed to last, when the note is already meant to continue sounding through a certain number of the next notes in some of the other voices.  For example if the target voice is a quarter note, or longer, and the other voices are enunciating sixteenth notes.

I gave a brief answer: remembering when to lift a sustained note in one voice is the requires the opposite of everything you do right when knowing when to start a note.  It’s the “dark side” of piano technique: it requires doing everything the wrong way; or is it now the right way?

A.B.: why did you do that?  Why was it working?

Joe: I think it is important to have a distinct pre-vision, pre-conception, of what the beginning of the next measure is going to sound like before you get to it.  It is a strange balance of knowing what’s coming and still being surprised by it.

#2

Can we transform the sound the sound of the fugue in the student’s ear?

We experimented using two pianos with re-registering one of the voice of the fugue.  He would choose one voice to play, and transpose either an octave higher or lower than  it was written, while I played the remaining three voices (without the fourth) at the other piano.

Results:  A.B. said:

My voice sounded different than before.  I head it saying and meaning other other things than I had before, but then realizing that it was the same voice with the same names to its notes, just transposed, and that there was at the same time an abiding identity between both versions of the voice, an identity which was preserved, was eternal and fixed  and was impervious to change of octave.   The new stuff that suddenly I heard, in how that voice combined with the other voices, must have been there latent to the note’s names themselves alone, or to say it in another way were just as present as aesthetic and sonic effects when I played that voice in its original octave.

In the future we will have A.B. play just one voice, but in the octave higher than written and the octave lower than written without playing it in the octave is written.  Later again we can transpose one voice by more than one octave.  If it is the soprano voice we can have it sound in the tenor voice’s range or even below the bass voice.  In the case of the bass voice, we can have it sound in the alto voice’s range or so that it is the highest sounding of all the voices.  At any time I can choose to play all four voices and not just three, leaving one voice to him.  Or, he can choose at random to play just the voices, while I play the other two.  Or, three voices.

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What to “bring out” in a Complex Passage

Debussy: First Arabesque: the conclusion to the first of the three main parts.

What is the main melody that one should bring out during the passage that concludes the first part and leads to the middle part of the piece.  A.J. said that when I played it I was doing something that that made it work sound-wise but he couldn’t figure out what i was doing. He assumed that I was emphasizing one of the three layers of melodic motion embedded in the passage. I said, it is more complex than that.  There are three different things going on, but no one of which, by itself, is a significant melody.  it is only in the complex ways the three interact that causes the positive quality that I think you noticed.  The rising quarters in the rh form a melody of no great significance.  The cello=like melody in the left hand does have a singing melody, but by itself it doesn’t seem accomplish that much, as well. Then there are triplets.  Are they important or not? The real question is how to bring them together in a complex fusion that makes the passage glow and excite.

To relate the quarter note melody in the right hand with the triplets in the right hand,  I played gs4-b4, then held the two notes as i added in ds4, which I also held, and lastly added fs4.  If at this point I continue holding those four notes and not go on in the measure,  I realize, after maybe about a second, that those notes add up to a four-note chord with a specific flavor that independently of the single notes of which it is comprised, has its own specific flavor and character.  I might have missed hearing this had i not stopped to listen to the chord after it was finally formed.  The realization of the chord does not come instantaneously to the ear.  We have to patient, and wait for the four notes to all be there (five if you add the bass line).

It is a delayed satisfaction, one that is very desirable, but one that cannot be rushed.  Thus the triplets get their meaning in the  sound mixture by our waiting to hear the result of total participation.  Eventually, when we play the passage, he don’t have to pause on the clock to  wait for the four notes to congeal, we only have to subjectively, in the imagination, make the pause, to bring the four notes to life as members of a single chord, so that, at    the end time-wise, it is not any of the four notes that are significant on their own, but how they loose their identify in the sound color of the chord where they vibrate together – as equals – but to a common good.

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When it’s difficult to get from one chord to another

Sorry to have been out of touch for the past two weeks.    I had cataract surgery and was waiting for my eyes to be able to read the computer screen again.  Anyway, I’m fine now, and the hiatus is over.  But please excuse typos and misspellings.

Consider the situation when we try to connect one chord to another chord, but the second chord is a difficult to get to from the first chord, we can do the following.  The solution ultimately lies in not going from one chord to to a second.  We have to break down this apparent cause and effect within time.  Order in time need not dictate to our imagination order in which our body does things.

We let the hand get used to the second chord before playing the first chord.  We play the second a series of times.  After the first time we move the hand just a little bit away from the keyboard and then find the chord again.  Then we can move the hand right (and then left) along the keyboard, horizontally away from the chord, in gradually increasing distances, and each time find your way spontaneously, without thought, without set-up, to the second chord as if you were already on it.  Eventually your hand ‘remembers’ what that chord feels like, and can return to it from any place at all on or off the keyboard; from any position in all three dimensions that the hand can first be removed to, including for instance from your lap.  Of all these infinite places and positions from which the hand might come to return to that chord, just one such possibility is that the hand is first on the chord that is written first.

Memory is like a glue that adheres to a chord like a familiar friend. Benefiting from this fact, we just have to add in a trick with time.  Instead of the ‘first’ chord being followed by the ‘second’ chord, the second chord is there before the first chord.  we must feel that he have already been there, that the glue of the memory causes our hand to automatically be on the notes of the second chord.  I don’t so much mean that because we have practiced the passage, we get ‘used to’ where the second chord lies.  No, this is different.  This is truly being convinced that you are about to do two totally new things, for the very first time, and yet in spite of that, you act like you already know have been where the second is on the keyboard, tactilely, coverage-wise and finger-wise.

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Leverage and Sound

Chopin, Etude in C# Minor from Opus 25:

Irving’s brother came today.  We wanted to get a rich cello-like / vocal-like tone out of the piano for the notes of the opening “baritone” melody for the left hand.  It is in single notes without accompaniment, so it is very exposed.  We need our entire sound/mechanical tool-kit to keep it resonant and sustained so there isn’t a moment’s break in the flow of the line.   Their softness shouldn’t belie their resonance.

Our first exploration was with leverage, the principle being that the greater the leverage you have over the production of each sound, the more that sound approaches the ideal piano-resonance.

The effectiveness of a lever is a function of how long the lever is and where you place the fulcrum on which to rest it*.  Leverage increases with the length of the lever and how remote the fulcrum is from the end of the lever that, from which in this case, the pianist initiates the motion of the lever.  If, for example, the lever is solely the length of a finger, and the third knuckle is where the fulcrum is, there is little mechanical advantage to depressing the key through the motion of that lever.  If the lever extends back into the wrist, and includes the finger, there is greater leverage on behalf of the movement of finger tip.  So the question is, how we can create the greatest leverage with the human body.

We ended up using a curious combination of several different levers, that ended up being connected one to the other.

The length of the arm, from shoulder to finger tips, while perhaps not the longest lever we can make of the body, is a conveniently long one that is still easily manipulated.

We started by his holding out both his forearms; straight out in front of him so that they parallel with each other and were horizontal to the ground.  We Left a comfortable distance between the two hands, about the same as the distance between the two shoulders.

We then had him move his arms up and down using just the shoulders as pivots.  At their highest points the arms were aiming well above the horizontal, at an angle of about forty five degrees.  At their lowest points the arms were just slightly below the horizontal.

Very soon, we changed it to an oscillating motion between the arms. One arm was at its lowest when the other was at its highest.  And they exchanged these positions.  We did this until he felt a sort of physical exhilaration from all that motion.

The next thing we did was to create a second, more imaginary, lever.  At the same time the arms were moving, we pretended there was the plank of a see-saw that connects the two hands (traversing the empty space between the hands), which, as a result of the arm motions, was itself going up and down as if two people were seated at each end of the see-saw.  The pivot of this imaginary see-saw was exactly half way between the hands, so that neither hand or arm had a mechanical advantage over the other – the advantages were equal.

I also had him imagine a secondary but similar see-saw between his two shoulders, as if an, albeit, small person was seated on each shoulder.  We continued exercising the combination of these levers until he felt a definite exhilaration from making these motions.

We then ‘elected’ his two index fingers as the sole ‘beneficiaries’ of all the motions he was making, so that the each index finger was backed up by the entire arm and contributing see-saws.

While continuing the oscillation of the arms he used alternating index fingers to play first the opening note of the second note.  The solo was no longer distributed solely to the left hand but alternately, from note to note, between one arm lever and the other.  If he played the first note with his left index finger, then he played second note with his right index finger.  Then back to the left index finger to sound the third note, the right again for the fourth note, and so on through the line.

During this procedure the fingers were to never loose their connection to the hand, and on to the wrist, the forearms, the elbows, all the way to the shoulders.

Sometimes the arms had to cross one another, but the more important thing was the swinging motion from one arm to the other regardless of which one was to the right or left of the other.

When he did this with physical abandon fervor, without thinking so much of the ‘proper’ or ‘usual’ way of pushing the notes down, the result, to our joint delight,  was an unusually rich sound, one that he was unaccustomed to getting on single notes.

Even when consecutive notes were ‘next door’ to each, only a half step or whole step away, we did not diminish the feeling of the widest possible see-saw between the arms.  In other words, while the objective distance between the consecutive notes might lessen, the subjective sense of how long that distance was always remained large.

The last step was to preserve the widest and most dynamic sense of an oscillating motion when going not just from one hand to the other, but from one finger of one hand to another finger of the same hand.

* The saying, concerning how levers work, as attributed to Archimedes, is: Give me the place to stand, and I shall move the earth.

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Microtonal Musings

Microtonal Musings:

1: “in tune” or “out of tune”:

The tonally trained ear expects to hear things in a certain way, and clings to that way in spite of gradually mounting evidence that what they are hearing is not tonal but microtonal.

I’ve demonstrated this with a sound experiment in which a major triad (such as C-E-G) is gradually transformed into a minor triad (C-Eb-G) followed by a reverse direction.  The root note and fifth remain constant; the third is gradually lowered over the course of a certain duration until it has fallen a half step, at which point the third starts rising in pitch, at the same rate as it the pitch was lowered, until it is back to its usual position as the third of a major triad.

In this particular experiment the third is lowered (and later raised) at the rate of one hundredth of a semi-tone (a “cent”) every third of a second.

For many people, no change is noticed for a while.   Their ear continues to hear, or cling to hearing, a major triad – one albeit that is “out of tune” but still clearly intended to be a major triad.  The ear does not accept that it is perceiving a microtonal tonal triad that is neither major nor minor.   The microtonal change is considered an imperfection in the intonation.  There is no recognition of the triad as being of a new aesthetic species – neither major or minor.

Then a sudden switch occurs.   At a certain point in the migration downwards of the third of the triad, most interestingly a point that is closer to the eventual minor chord and further from the initial major chord, the sound, almost instantly, changes in the listener’s ear from being heard as an out of tune major triad to an out of tune minor triad.

This “inaccurate” minor triad persists until the third is close to its final value, at which point the sensation the minor chord at last is getting more and more “in tune”, until at the end it sounds very in tune.

The most interesting part of this sound experiment is that when the third starts traveling in the other direction, the location of the point where the ear ceases to hear the triad as an out of tune minor chord and flips over to hearing it as an out of tune major chord, does not occur at the same point as the similar position during the first phrase of the experiment.  This change in perception now occurs when the triad is closer to the final major chord and further from the minor triad.

2. A self-similar “fractal” chord:

I’ve made many experiments in discovering types of microtonal chords that have a distinct effect that is aesthetically interesting.

My aim was to create a microtonal analogy to a ‘self similar’ fractal design.   The results I got were extremely beautiful, and unlike in case number one, above, could not under any circumstances be heard as an ‘out of tune’ version of a more tonal chord.

I started with an arbitrary selection of a lowest and a highest pitch.  I then inserting a medium pitch that had the effect of dividing the overall range into two parts that bore a certain ratio (in my first experiment this ratio in pitch was 2 : 3).  I continued to divide up each of the smaller pitch intervals by the same ratio.  What started as just two pitches, became successively, hree pitches, five pitches, nine pitches, seventeen pitches, etc..*

*In computing the frequencies of the microtones I started with the unit of the “cent” (one hundredth of a half step) and then converted each cents value to a frequency.

3. Overtone series:

When an ear perceives a single tone or pitch from an orchestral instrument or the voice, an analysis of the sound vibration shows that there are actually a ‘chord’ of different pitches executing separate vibrations.  These additional tones are known as overtones.  If one could separate one overtone from the rest we would hear a sound at a different pitch from the one the ear first perceives.

One of the properties of the overtones is that they are the most spread out in pitch near the ‘fundamental frequency’ (the pitch that the ear perceives) and clump closer and closer together as they continue upwards in pitch.

There is a piece by Stockhausen called “Stimmung”* which has a group of singers each singling one of the upper overtones of a constant fundamental frequency.   A ‘range’ of overtones is chosen by the composer.  The fundamental is never sung, but a consecutive group of overtones is used.  A variable in this selection is what should the lowest pitched overtone in the overtone series that should be sounded and which is the highest pitched one, and how many overtones does that ‘interval’ contains.

In its application to microtonal music, such a group of overtones, can be used as a ‘scale’ of available pitches out of which the notes of the piece are formed.   However, one property of a scale is that it repeats over and over, usually at the octave.  We can make a series of overtones do this by taking just one octave of the overtone series and transposing its pitches up and down various numbers of octaves so as to form a continuous scale from bass to treble.

For most orchestral instruments the overtones are linear in frequency.  The first overtone is twice the fundamental frequency, the second overtone is three times the fundamental frequency, etc..   But the more three dimensional the instrument is the more it deviates from this simple linear pattern.  A bell, for instance, whose vibrating mechanism does not approximate a one dimensional line, has a different arrangement of overtones.

And if a four-dimensional creature were to suspend a four-dimensional bell from a string, and then set it into vibration, there would be an less linear overtone series.  It does not matter that we cannot construct such an instrument, for mathematics enables to predict what the overtones would be, and they can be reproduced exactly on an electronic synthesizer that is set up for microtones.   So we can form scales out of the overtone series for n-dimensional objects (where n goes beyond three).

Here is a list of sample possible constants for generating an ‘altered’ linear overtone series on a particular note:

In the following n is a whole number, and ff the fundamental frequency:

(pi) x (n) x (ff)

(e) x (n) x (ff)

Here are some other possibilities of generating a linear overtone series not based on multiplying the fundamental frequency by whole numbers.

1.1

2 to the 1/2 power

pi times e

sine of an angle

* There was work by Maurice Béjart’s modern ballet company which was set to the music of Stimmung which was sung on stage at Carnegie by the “Swingle Singers”.  Each singer intoned the pitch corresponding to one of the linear overtones of a single fundamental pitch.  So that the tones were not too widely separated pitch-wise, they used a part of the overtone series where there were approximately as many overtones within the scope of one octave as there are notes forming one octave of a more familiar scale.  For instance the following numbered overtones, in the fourth octave about the fundamental, span an octave and divide that octave into 8 parts: 7 8 9 10 11 12 13 14 15  

4. Graphing a mathematical function:

There is an aesthetic fallacy in trying to find a means of translation between something spatial (as a graph) and something temporal (as music).  However, if one is willing to experiment, one could try to derive the notes of microtonal chord from the y-values of some function f(x).  Each next note in the chord would be f(x) for each whole number value of x.  What would a parabola sound like?  A hyperbola?  A sine way?  We don’t know until we ‘hear it’.  We may stumble on a function whose sound as a chord is pleasing and unique aesthetically.

5. Expanding or compressing a tonal piece around a constant center of pitch:

This is more productive of interesting sounding tone groups.  Bach Chorales lend themselves nicely to this procedure.

Take each chord, translate it into cents, and then either increase or decrease each pitch in the chord relative to some stable frequency that is either be one of the pitches of the original chord or a pitch that is chosen randomly but which remains throughout the chorale as the center of expansion and/or contraction.   Or, another way would be to use the notes in one of the four voices as the “stable” pitch (even though it may change from beat to beat) and contract or expand the pitches of the other three voices relative to it.

P.S.

For those of you who dabble in microtones would you let me know what methods you use or whether any of the methods described above have proven useful.  Thanks, Joe

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