# The Principle of Nested Parentheses

In simplifying algebraic expressions, one starts with the innermost
pair(s) of parentheses, simplifies and reduces it, then works
gradually outwards to the outermost parentheses, i.e. the full
expression.

Today, I want to advocate the opposite process for piano
practicing, one that begins, figuratively speaking, with the outermost
parentheses and works inwards until all the details are presented.

A.B. is playing a piece called “Orientale” by Albeniz. We set up our
first, our outermost parentheses, to surround 5, 6 and 7 of the piece.   We left the parentheses empty except for the first chord of measure five
and the first chord of measure seven. Everything in between was omitted. We tried to effect a connection between just these two chord/islands in time, a connection that was crafted to make those two chords in sequence sound musically self sufficient and meaningful. Bear in mind that, as with any good parenthetical statement, the words (notes) inside the curved brackets are of less importance than what lies outside the brackets.

We next subdivided the outermost parenthesis into two two nesting
parentheses. The first nesting parenthesis goes from the beginning of
the fifth measure to the beginning of the sixth measure, the second
from the latter to the beginning of the seventh measure.

Each of the new, nested parentheses is of less importance than the original, surrounding parentheses. Thus the chord at the beginning of measure six is of less importance than either the chord at the beginning of measure five or the chord at the beginning of measure seven. The presence of the sound of the chord at the beginning of measure six should in no way interfere with the way that the chord in measure five connects with the chord in measure seven. This inner chord is not quite trivial, but it is at a different order of magnitude than the other two. This difference in magnitude should be noticeable both in terms of the amount of physical action and exertion used to sound it and in terms of its musical importance.

We continued the process by further dividing each sub-parentheses into
more numerous shorter parentheses. This process continued until, at
the last stage, every note in the original passage is present and
sounding. Gradually all the chords and melody notes appear.* At each
stage the full, or final, picture becomes more and more fleshed
out. The new material added by way of detail is, as in the stage prior
to it, stepped down in terms of the magnitude of physical action and

In this system the final details, including all the individual notes
in the score which we insert at that last stage are, strangely
enough, the least important. At each stage we discover that we can
make a convincing musical phrase out of just the material constituting
that stage.* Though eventually there will be more notes present, the
notes that are there in each each level sound entire and musical, as
if nothing is being left out – no note or chord missing, each should
note in no way depends for its musical character on any implied notes
we will hear in the future.**

At the final stage, when all the notes are sounding, all the other steps which we have previously enunciated are still “there” in some sense, enriching the overall texture of the passage.

* In one possible stage, we discover, for instance, that playing just the first two of each group of right hand triplet notes, creates its own independent melody without requiring the third note.

** Generally speaking, it is too easy to make connections between two
things that come one right after the other in time. It is their very
proximity that calls our attention to the relation between them. But
who is to say that the current music note in time should not form a
relation with a note that occurs two or more notes later, or later
still. And if there are such medium and long distance relationships,
they are the building blocks of nascently growing organizational
units of the piece until the whole piece is interconnected. As these
units grow longer in time the beginning of the unit is only partially
retained in memory, first as an ‘after image’, and then deeper and
deeper in memory, until they back to mind if they are in some way
reiterated or altered.

# The Sad Decline of My Absolute Pitch

I have a love and hate relationship with my ear.

For a person with absolute pitch, it is often the case that each individual key (C Major, C Minor, C# Major, etc.) has its own special character and aesthetic, which strongly colors any music that I play or listen to.  What I don’t know is if others with perfect pitch experience the same thing, and perhaps more importantly, whether the character or aesthetic of a particular key matches those of mine.

I learned that I had absolute pitch in gradual stages.  When I was about three years old, I would listen to my older bother play pieces from “For Children” at his lessons.  I knew enough to know that there were qualities about each piece that didn’t vary from one time to another, and that these had to do more than with the particular notes and their sequence.

It was many years before I understood what absolute pitch was and that I possessed it.  Actually it was my friend Jeffrey Rothenberg who discovered it for me.  We were in Mme. F’s French class in our junior year at high school.  I remember two particular events in that class that year.  The first has nothing to do with absolute pitch but is just nice: in the middle of a class meeting, Jeffrey got up from his chair, said somewhat ecstatically “Spring is here, and the cherry trees are in blossom in the quadrangle”, at which point he drifted, almost floated, out of the classroom.

The other, was when my friend Jeffrey was trying to discover if he had perfect pitch.  He would lean over to Edward Goldstein on his right, sing a note into his ear, and ask him to sing it into my ear (I was to Edwards’s right) , and whisper into my ear: Jeffrey wants to know if you think this is an “A”.  The fact that I could do that somewhat surprised me.  I thought: so I guess I must have absolute pitch.

About one out of ten thousand people in the world have perfect pitch.  Most are not musicians and probably do not realize that they have perfect pitch.* I figure they just assume that everyone else in the world hears sound the way they do, and that includes a merger of the effect of the up and down-ness of pitch with the effect of a changing coloration to the sound.  Only if these people study music they will learn, perhaps to their surprise, that every time they hear a note, they are able to give it a name.

In  school I began a phase of showing off my absolute pitch.  I wasn’t good at sports, so this was my way of being “macho”.  For instance, I got a telephone call from my friend Linda who said.  She said: “Do you hear the piece I’m playing in the background, what is it,  I can’t identify it.”  I listened for a few moments.  I that point in my life I had never heard it before, but I knew it was by Bach, that it was a concerto, that there were two pianos playing,  and that it was in the key of C Minor.  So I said to Linda: Well I’ve never heard this before, but I would say it is the Bach Concerto for two pianos in C Minor, the first movement.  We hung up.  Ten minutes later, when they probably announced the piece over the radio, I get a call again from Linda.  She said, “show off!”.

One of my favorite spots during my High School years was the Brooklyn Botanic Gardens.  I probably spent more time there than in classes.  I even had one teacher who would ask one of the students: when you walk home would you look for Joe in the Botanic Gardens.  He is probably sitting by the stream.  If you find him, would you give him the homework assignment.

Yes, I was by the stream, bent over, listening intently to the gurgles of the water, and trying to figure out what the pitches were of this sound.  I never could get them right.  I would notate what was in effect a chord of many notes and would then try it out on the piano when I got home.  There was no similarity (even after allowing for the difference in the sound quality of a piano and a brook.   It wasn’t until another year or two that I learned what “white noise” was.   That the reason I could not notate the brook was because there were so many pitches, all at once, that there was no way for the ear to untangle them each from the other.  Additionally, at every moment the interval pitch make-up of the white noise would change slightly change, but in such tiny degrees that were measurable only in microtones.  Microtones are the unlimited number of pitches that exist, for instance, between a C and a C-Sharp – or a ‘distance’ called a half step or semi-tone.

My experiences at the brook awakened my interest in microtones and today I am using the computer to compose microtonal pieces.   I’ve even trained my ear to detect a difference of two hundredths of the distance between a C and C-Sharp.   But they had to be isolated tones and not in a mixture or hundreds or thousands of tones all closely ‘spaced’.

Which brings up the clarinet.   I had been playing the B-flat clarinet since the fourth grade.  The clarinet is a “transposing” instrument.  When it plays the note which the clarinetist identifies as  a C on the clarinet, it does not match the C on other instruments.   A C on the clarinet was a B-Flat on the piano.   Though I didn’t know it until I was a Junior or Senior in High School, I had developed unconsciously two separate but parallel senses of perfect pitch, one that names the notes as they were called on the piano, and one for the notes as they were called on the clarinet.

In my twenties and thirties, if I was scheduled to teach a lesson, and I felt like I was coming down with a cold, I would protect the student by sitting on the other end of the room from the student.  It somewhat freaked out the student when they noticed no difference in my interaction with them, as when I would say something like: “Irving” you just played an F natural instead of an F sharp” (yes Irving existed even back then).

So, everything was going along swell between me and my absolute pitch, until the  invasion of original instruments.   The difference is: why listen to a clarinet play, in tune, the solo in the slow of movement of Beethoven’s 3rd Symphony, when we could hear it played out of tune on an instrument created during the early 1800s.    I grant that this is just a humorous way to describe the early music movement, but there was something more sinister for people with perfect pitch.   The orchestra tunes the “A above middle C”.  That ‘A’ would vary in pitch through the centuries.  In Bach’s time, the A was almost a half step below normal today’s concert pitch.  Thus began a process that was sully my pristine world of pitch.

At the beginning, when I heard a performance on original instruments, I would say “this is a piece in B Major”.  The piece had all the aesthetic qualities of that were characteristic of the key of B Major.  At the end of the performance I was of confused to hear that it was a piece in “C” Major.  Sometimes it was even a piece I knew but which I suddenly could not identify because it was in a different key.  However the worst thing was that after decades of original instrument performances, my “B” started sounding like a C.   And I was too old apparently to develop a second sense of perfect pitch to go along the first.   Talk about being confused.  I could not really tell any more if the piece I was hearing was in C major, tuned down, or C as I grew up with it.

And so performances on original instruments spread like a virus over my entire nexus of absolute pitch.  This was the beginning of the sad decline of my perfect pitch.

But the next step in this sad story totally befuddled me.  I was in San Francisco giving a lesson over the phone to a student in Oregon.  I did a lot of long distance phone lessons in those days – now I use skype.  She was playing the C-sharp minor fugue from Book One of the Well Tempered Klavier.  I got tired of holding the phone to the same ear (my right ear), so I switched quickly to my left ear.  And lo,  the pitch of the piece dropped by about an eighth tone (25 cents).  At first I thought I was imagining the difference, but wasn’t, on further experimentation the difference persisted.

I wondered whether the ears, like the eyes, consist of a dominant one and non-dominant one. I knew that with my eyes, if I closed one eye and then the other, an object in the near ground or mid ground, would change its alignment with the objects in the far ground. When I used both eyes, what I saw was what I had seen through my dominant eye.   I splendid musician I know, Wendy Loder, has confirmed having the same experience, with an even larger pitch difference than I experience.

Now I was faced with something similar with my ears.  Two pitches, one in each ear, but the higher of those two pitches was the one I head when I was hearing with both ears.  In my case the pitch that I heard through my right ear alone was the same as the pitch I heard with both ears.  That was freaky because I wondered where did the other pitch go.  It must still be in my brain somewhere.

I was offered this explanations.  The cochlea, in the inner ear, shrinks as one ages.  The cochlea in both ears might be aging at different rates.  Analogous single nerve endings in the two cochlea, that had always responded to a middle C still, in a sense did so, but now responded to pitches near middle C, but not exactly at the same.

As I write this, I am seventy-one years of age.  My original perfect pitch has survived through the years in only one case: notes coming from the piano.  Only occasionally for the other instruments of the orchestra.  But at least I’m never off my more than a semitone.

So, things couldn’t get too much worse – right?

Recently, the next nail in the coffin of my absolute pitch occurred in the form of how I was hearing octaves.  I used to object to the “stretching” of octaves that many tuners did when tuning the higher range of the piano.  I used to hate tuners who would tune the high octaves sharper than the mid range octaves.  Suddenly, though, I was now experiencing a distortion in the pitch of the high notes of the piano that made me wish I could stretch the octaves.  If I played a lower C, in the octave of middle C or an octave lower, together with one of the highest C-s on the keyboard, the higher C sounds a half step lower than the lower C.  It was like hearing a C and a B.  To be honest, this phenomenon had been creeping up on my over the years.  At first it was a curiosity.  Now it was intolerable.  The string for the higher C would have to be stretched tighter, almost up to a C-sharp, for it to sound like the same note as the lower C.  Now i know why some tuners stretched octaves.**

To be honest, I would have much rather had my absolute pitch go away entirely rather than in agonizing stages.  But there was always enough left of the absolute to know that something was amiss in my perception.  It was a more benign form of when a patient is consciously able to trace the course of her illness.  Now I am starting crave the bliss of ignorance of not having absolute pitch at all.  I can sense that my ability at relative pitch is asserting itself in situations where absolute pitch made relative pitch unnecessary.

I can now sit and contemplate what might be the next stage in the sad decline of my absolute pitch.

* Research at the University of California in San Diego found that while many may be born with it, discovering the gift is likely more the result of nurture than nature.Sep 18, 2012 (from a Google search)

** About ten years earlier I was offered another more ‘scientific’ and objective reason for stretching octaves.  In physics the string is often considered as a one dimensional object.  This allows the math to be simpler.  But a string is three dimensional.  It has length, width in a horizontal plane, and width in a vertical plane.   There is a “nodal” point at the half way point along the string   which as result divides the string into two parts, each part sounding an octave above the string at full length.   A nodal point is a place along the string where, under certain circumstances no vibration takes place.   But if the nodal point is three dimensional, rather than a nodal ‘point’ we have a nodal ‘sphere’.   This causes each of the remaining, vibrating halves of the string to be slightly less than half the length of the full string, and thereby have a pitch that is slightly higher than one octave above the pitch of the string vibrating as a whole.