Sometimes, it Really Is Black and White

Key signatures remain a stumbling block for certain types of students.

We were reading the middle section of the Mozart “Rondo alla Turca” – the section with the seemingly endless running sixteenths in the right hand.

If I am reading a piece in G Major, when I come to a note in a measure that that is printed on the top line of treble clef it simply doesn’t “look like” an “F” to me.  It looks different, it “looks like” an “F#.”  I’m lucky that way.  For many students however F-s do not magically transform in appearance to F#-s.

I also carry around the inductive logic of the circle of fifths as a fixed and clear model in my mind.  There is no trouble in remembering that if there are three sharps in the key signature they will be F#, C# and G#.  I don’t have to examine the key signature to come to this conclusion.  For many, though, regardless of experience, they have to look at the sometimes dense group of sharps or flat signs at the beginning of each line, an decipher for which line or space each is centered on, then try to remember, each one separately, to go through a check list, as it were, for each note they encounter in the piece to figure out of it is a natural or not.

These students have difficulty every developing more than a rudimentary sense of what a “key” is.  They are apt to forget each time, for instance, that if there are three sharps in the key signature, they are always the same  sharps, and that these F#, C#, G#.* Sometimes they will find it easier to they remember the three as C# F# G#, so at least they are sorted alphabetically.  A typical question from such a type of student is “how do you know if the piece is major or minor?”  “Can you tell from just looking at the notes at the beginning of the piece; or is it something to do with the sound?”   Attempting to explain the answer to this question in terms of there being certain statistical likelihoods for certain notes and chords to show up in the first measures of the piece, further complicates and mystifies.

The inductive logic of the circle of fifths doesn’t establish itself firmly in their minds.  They do not see an imaginary sharp or flat sign to the left of each note along a line of music, whose existence is confirms a sharp or flat that in the key signature at the beginning of the line.  And practicing scales until they become automatic in the fingers seems a daunting task, as difficult and time consuming as learning entire pieces.

For many years I stubbornly retained the simple logic of he circle of fifths as the only unambiguous way of clarifying key signatures to students for whom this posed an issue.  Logic, I felt, will always win out.  It took a while to mature out of this notion.

At today’s lesson I chose a less elegant, a less logical, but simpler expedient.  I told Rachael that my intuitive impression was that as she was reading the notes on the page it didn’t seem immediately clear to her whether the next note to play was a white note or black note.  I took the first measure of the passage, and I asked her to play the passage as slowly as she needed to in order for her to say for each next note that she read, “this is a black note”, or “this is a white note”.  How she determined this was unimportant, it was just the final experience of the hand on the keyboard that mattered.

This shifted the emphasis from remembering the key signature and how it applied within the measure, and raising to a higher level of conscious awareness the identity of that note as simply being a white note or a black note.  There was no more key signature present.  There was just the individual identity of each note as falling into the class black note or white note.  If it was a black note it didn’t matter if it was written as a sharp or as a flat.  Only key color mattered.  The same with regard to white notes,  whether their note names were naturals, or flats or sharps.

This first measure of eight sixteenth notes was just memorized as a sequence of words.  Just as a binary number is a series of zeros and ones in a certain order, so the measure was a series of the words ‘back’ and ‘white’.

At first she seemed skeptical that this could work, since it seemed to beg the question of needing to know and retain in her mind the key signature.  But it turned out otherwise.  Now that there was only one of two things to choose about each note, and after putting in the initial downloading time it took to put the measure into this on/off, zero/one, black/white form, her confidence level in playing the notes correctly rapidly increased.  She felt a certainty and a mastery over what to play.  There were no questions left.  No uncertainties.  Just the color of the notes. She bypassed any worry about applying a ‘template’ of white and black notes, first to the key signature, and relate things from there to the notes of a measure.

*Or furthermore that the first two of those sharps are always the same as the sharps that appear when there is only two sharps in the key signature.

A subliminal way of providing music theory information to the student

Today’s incarnation of “Irving”* is playing the C Major Prelude from book one of the W.T.C.  I’m bringing up the subject of chords probably for the first time.

The harmonic-rhythm of the piece (the rate at which the chords change) is slow and even paced; the chords change only when measure changes.  It leaves me ample time to say to him casually, as he playing: “this is now a C major chord”; “this is a now D Minor-7 chord”; this is a G Major Chord, etc..

I do not assume he will understand the bigger part of what I am saying, but it is more at creating a subliminal background to what he is  playing.  Much like those once fashionable “learn while you are sleeping” tapes.  So, even if all he gets are the things listed below, that is more than enough:  1) There is something called a chord and apparently I’m playing first one then another; 2) that these chords apparently come in a wide variety of types; 3) but one can identify these types based solely on the notes I am playing.  He is getting used to hearing the terms I am using, terms like “major”, “minor”, “7-chord”.

It can be an advantage that he does not have to stop the flow of his playing in order to try to understand what these terms mean.   He may know no more than that the terms change in a way that, at this point, almost seem to vary in a patterned way with the sounds he is making.  Each time I use them in the future there will be a growing sense on his part what they mean and how to use them.

* I promise to give Irving a new name one of these days.

 

Sound, Hearing, and the Brain

Spoiler Alert – this one is a bit dense and philosophical.

How do sound qualities arise?  And how do we hear music as pitch, tone color, harmony, and melody, when nothing like these things actually exist in nature?

Sound waves go through cycles, often countless times per second.  During each cycle the “amplitude” (the wave height) changes from one instant to instant.  The number of cycles per second correlates with the ‘pitch’ that we hear.  But in this conscious phenomenon there is no awareness at all of the loudness changing from instant to instant.  As long as the frequency of the wave holds constant, the sound that we hear prolongs itself constantly through duration in time.

Thus, perceiving a steady pitch at a steady loudness is due to something that in terms of what is going on physically in nature is quite discontinuous.  When the piano plays a Middle C, we do not hear a series of 261 sudden increases in loudness each second.  Nor do we hear 440 sudden increases in loudness when the oboe plays its A above middle C to tune the orchestra.  Something discontinuous, fitful and periodic in nature ends up as something continuous and steady in consciousness.  Only when the vibration rate drops below around 20 cycles per second do we begin to hear the separate puffs of air, but at the price that we no longer hear a pitch.

What if our consciousness could run at a ‘tempo’ that allowed us to hear these individual peaks in loudness?  Seconds would seem to take minutes, and small fractions of seconds would seem like seconds. The result is that the very nature of what we would ‘hear’ would be totally different: discontinuity in time would replace continuity.

This would be the equivalent in time of putting a specimen under a microscope and magnifying it in space.  The greater the magnification, the less the specimen looks as it did to the unaided eye. If we were not told that it was the same object in both cases, we would be hard put to realize its identity.

Conclusion One:

Pitch, the basic substrate of all our musical perception, would disappear, and be replaced with an effect somewhat like a ratchet, or a rapid series of metronome clicks with silence between successive clicks.  Gone would be the very building blocks out of which musical structure is created.

Sound: Instrumental Tone Quality versus a Chord of Pitches

Our experience of instrumental tone color (a clarinet’s sound versus a violin’s sound or versus the sound of a human voice) is, as with pitch, based on a fortunate illusion, a simplification and then recasting of sensations reaching our brain.

When an instrument, like a clarinet, plays what we perceive as a single pitch, a scientific examination of its wave form reveals something that resembles more a ‘chord’ of many pitches than what gives us the perception of a single pitch.

There is no ‘reason’ why, we might hear simply one chord versus another in the different instruments, minus any change in instrumental quality.  After all, chords are part of the normal conscious phenomena that we perceive about sound.  Why do we need something extra when we might content ourselves with just perceiving chords?

When we perceive what we term a chord, most often the various individual pitches in the chord are sounding with approximately the same loudness.  What if the different pitches in a chord all had different loudnesses.  This would add a serious level of complication.  It is this extra layer of complication that the brain “simplifies” for us.  What we hear is not different loudnesses among the different pitches in otherwise similar chords, but simply a different tone quality, or timbre, to the overall sound.  A French horn and a violin playing Middle C produce the same chord of pitches, but the relative loudness of one pitch to another is different.  How impoverished would our perception of sound be if it was bereft of this extra
parameter of tone quality.  Sound would “sound” like shades of grey without any other color.

Part of the ‘illusion’ of tone quality is that we hear one pitch instead of many, and our brain casts the lowest pitch in the chord as the pitch we associate with the note, and as for the rest of the notes in the chord, depending on their mutual loudness, the brain recasts the phenomenon of pitch as the phenomenon of tone quality.

What if our brain had the ability to resolve the single sound of an instrument, at a single pitch, into a chord of many different pitches? The answer is simple.  Gone would be melody and gone would be harmony.

Conclusion number two: This almost deceitful sleight of hand by the brain allows for the richness of musical structure.

P.S. Two other parameters of musical sounds, rhythm and duration, do not depend on sound to be perceivable.  Duration is simply the inner experience of time in consciousness, and needs nothing external to
mark its progress.  And rhythm, which in a way depends on duration, can be taught to a deaf person through a sense other than hearing: touch, for instance.

P.P.S. Of all the arts, music comes closest to being the simple conscious perception of time.

Riding the forward wave of time: catching the flow of a single note in our consciousness

Awareness of small and smaller subdivisions of time.

First, a bit of metaphysics, courtesy of the French philosopher Henri Bergson (you can skip this paragraph if you want).  He says that no matter how deeply we look into smaller and smaller durations of consciousness, we never stop experiencing time as something flowing.  It never stops.  If anything, the closer we approach what we think is a single instant of time, the more the intensity of its flow increases and immerses us.  An analogy might be the ceaseless activity on the atomic and subatomic scale that went by unnoticed until, in the twentieth century, scientists were able to take a closer look.

When we are playing piano, the very act of playing acts to distract us from the close observation of time.  Our awareness of time becomes synchronized with our depression of the keys, i.e. at the onsets only of the sounds.  As a result, we have a “stop frame” view of time, assuming time has flowed between one frame and the next.  This is the same effect as watching a film.  For all we know, between one note and the next, time itself has stopped, like the silence we hear between one click of the metronome and the next.  Time resumes for us only at the onset – the “attack” – of the next note.

The attack catches our awareness again.  It is suddenly louder than what is left of the sound which preceded it.  The attacks are like the excited gestures of parents attempting to catch the attention of their baby so they can take a photo.

Time is thus porous to us, it has no palpable taste to us if we are trying to eat just one of the holes in a piece of Swiss cheese.

This view of time as discontinuous, and having only an implied continuity, can lead to problems for the pianist when the tempo of the music is too slow or two fast.  If fast, we may not be used to paying full attention to the quality of every sound when the sounds occur in a rapid stream or spray.  At a very slow tempo we may have little idea what to do while waiting for the next note to start.  A whole note is a good time for a pianist to scratch an itch.

How can we ignore the “attack” sequence of time and have our consciousness penetrate into the hearts of the sounds, that is to say the portion of time after the attack during which the sound is enduring.  The only answer can be to listen, and re-listen, to the sound, as often as possible during career of a single note.  During the course of even a relatively short note, we can re-hear, or better, re-initiate our awareness of the sound, over and over.  Even the notion of a note as a single, “solid” thing will disappear under this type of conscious awareness.

Conscious awareness is like a spotlight shown upon an object.  It is like the yellow magic marker that we used in school to highlight text that we wanted to single out from the rest of the page.  Even when the note is long and we re-initiate our awareness of it after a second or two has gone by, there is this curious effect.  Though technically the note is getting softer and softer, at just that instant, the note seems to suddenly get a bit louder.  It didn’t objectively gain in amplitude, but it gained subjective loudness due to the act of attention.

Our moments of re-awareness during the course of a single note are like moments of blowing on a fire to rekindle its strength.

Summarizing:

Ultimately, it is not the vibration of the string that keeps the sound going through time, it is our awareness that keeps the sound alive.  It is this awareness, which isn’t getting less and less as the note acoustically fades away in intensity, that allows us to connect the end of one note to the beginning of the next note with a degree of fluidity that escapes our powers when we are just trying to match one attack with another.