Connections between notes separated in time
Music and Memory: Connections between past and present.
Summary: The relationships that we notice most between notes are those between two consecutive notes in a melody or two notes sounding in the same chord. If one tries to notice the relationship, for example, between the first note of a melody, and the fourth note of the same melody, it isn’t as easy to hear or be aware of. In effect, we have to ignore the notes in between. The first note has already happened; it has largely slipped out of memory. To experience this relationship as sounds rather than merely as ideas requires that they be more proximate in time.
The most tangible form of connection in sound is that between two notes that come one right after the other in time, the second beginning as the first, ends. In such a case the presence of the first note is still viscerally present in the finger and hand as the second note begins. We feel and hear how the second note changes, continues, distorts, deforms the first note. These latter qualities are not exactly present in the sounds themselves, but hover as an emergent form just outside of the conscious embrace of the sounds.
In the space of a painting, two objects adjacent in space remain side by side regardless of when we choose to look at the painting. In music, time defeats, or abolishes, space, because one moment in time eclipses another. The longer we wait between starting the current note and the next note, the harder it becomes to make a tangible, felt, as well as audible, connection between the notes.
The relationship between two sounds is harder to grasp or feel when there is one or more additional notes in between the two sounds. Physically, it is hard to make a connection or relationship between two such separated notes in time.
A simple example of this is the first entrance of the fugue theme in the Bach Toccata and Fugue in D Minor (the one Disney used in the first “Fantasia” movie and not the “Dorian” Toccata). The sense of the melody “A G F E D C# D…” is present and clear although there an A is constantly being interpolated between each pair of melody notes: “a G a F a E a D a C# a D…”.
This is a case wherein it is relatively easy to connect the notes of the “hidden” or camouflaged melody, which our ear forges on the spot out of notes that are separated by the presence of other notes. In the case of the Bach, the interpolation of an A-natural.
If short term memory can create a tangible and sensual link between every other note in a passage, then why not between notes that are more remote from each other in time sequence.
A good friend or spouse may be currently wearing clothes of a particular color, when we next see them be wearing a different a color. When that happens, we know two things: 1) we are looking at the same person, and 2) the outward color is different than the last time.
It is the same with music. At a later time in a piece we can hear something that we immediately recognize or, intuitively sense, as being the same or related to something heard before. At that moment, the past is suddenly brought very close to the present. This effect is fundamental to the creating a structure of sounds that exist in time only without space.
The emotion within every chord
There is an emotion that can be unlocked by the sounds of every chord, in fact by any combination of tones.
It is for philosophers to argue whether this emotion is already in the soul waiting to be triggered by the sounds, or is a new ‘effect’ dependent on the presence of a ’cause’ that lies in the sounds. The important thing is that emotions can as varied in quality as there are ways of combining sounds, and our job as pianists is to search for that emotion.
Summary of what follows:
The type of emotion I am talking about isn’t the common type of emotion with reference to which saying someone is playing “with feeling” is at best a semi-compliment and at worst a put-down for one who indulges in bathos instead of pathos, melodrama instead of drama, or who uses too much schmaltz (excessive sentimentality).
Emotion of a single chord:
If our internal emotional resonators are sensitive enough, then every different version of a chord or every different type of chord will evoke a different shade of emotion. In the first case, every position or inversion, every registration (in what octaves the notes are sounding), every spacing of the chord (what are the intervals between adjacent notes in the chord) yields a different mood.
This next sentence needs to be long, so I give it first in its entirety and then parsed into parts.
Here is the sentence in one continuous glob of words:
Is it possible that the complex matrix made up of the many consonances and dissonances produced arising out of specific pairs of overtones* of the notes in a chord, being too complicated for consciousness to keep track of, combine and are unified in our affective system as a feeling or emotion generated by that chord instead of as an arrangement of pitches.
Here is the sentence parsed:
Is it possible that …
… the complex matrix
… made up of the many consonances and dissonances
… produced among specific pairs of overtones** …
… of the notes in a chord, …
… being too complicated for consciousness to keep track of …
… combine and are unified in our affective system …
… as a feeling or emotion generated by that chord.
… instead of as an arrangement of pitches.
Statistically, no two chords would have the same exact arrangement of internally generated consonances and dissonances (degrees of agreement and disagreement) among its overtones.
It is through this matrix of overtones of each different chord that, if we train our aesthetic sensitivity, we can become aware of a unique feeling-tone generated by the sound of that chord.
Taking the conclusions of a previous blog a step further:
In a previous blog entitled “Sound, Hearing, and the Brain“, I spoke of certain conscious illusions without which we would have no perception or awareness of music.
One illusion was that what we perceive as a steady and continuous pitch, is the result, in the physical world, of a rapid series of separate puffs of air.
A second illusion had to do with the fact that what we perceive as the tone quality of an instrument playing one steady pitch is in fact the result, in the physical world, of many different pitches sounding at once. Instead of hearing a chord, we hear a single note with a certain tone quality (clarinet, oboe, violin, voice, etc.).***
It would seem then that philosophically as well as musically, the illusion is far more important aesthetically than the objective reality. The sensations of the objective reality are related to discontinuous puffs of air, and different instruments all sounding to us the same. In contrast to the former, the latter seems impoverished of qualities (though replete with measurable quantities).
Is there also an emotion of how one chord changes to another chord:
In my book “The Spectrum of the Arts,”
I talk about the difference between the literal shape or form of a single and static image, and the more figurative ‘shape‘ or ‘form‘ that underlies or explains how a shape changes shape through time.****
A similar distinction can be made about chords. The feeling-tone of one chord is one thing, the feeling-of-the-progression from one chord to the next is another thing. We can be aware of one, or the other, or we can be aware of both. Both are there to attract our aesthetic souls. Regarding the more figurative usage of shape or form, here is an example: “How a C major chord changes to a G Major Chord” has a different aura of feeling about it than “How a C Major chord changes to an E Minor chord.” Progressively adding silence between the end of the first chord and the beginning of the second gradually diminishes and finally eliminates this aesthetic effect.
Here is another spatial analogy to this musical effect in time: putting a patch of blue next to a patch of green produces a different aesthetic effect as putting a patch of blue next to a patch of red.
*the different overtone pitches have to be related in a certain mathematical way
** Each musical tone, though recognized in consciousness as being what we call a ‘single’ pitch, is in fact the result of an amalgam of different ascending pitches or frequencies. These are called ‘partials’ of the sound. The first partial is called the ‘fundamental frequency’ and the others the ‘overtones’ of the fundamental frequency.
If two sounds are close to each other in pitch, they produce a noticeable dissonance, something we might call an aesthetic interference pattern. The intensity of this effect varies with how close or far apart the pitches are from each other. When we have a chord of notes sounding at the same time, each one produces its own overtone series. Any one of the overtones belonging to one note of the chord might be close in pitch an overtone of one of the other notes of the chord. If so, the result is dissonance. We are likely to find such dissonances between overtones even in the most ‘consonant’ sounding of chords (like a Major or Minor chord).
*** An “oscilloscope” is a device that depicts a sound as a wave shape in space. A clarinet playing middle C produces a wave of a certain shape on the oscilloscope. A bassoon playing middle C results in a wave of a certain, but differently shaped, wave on the oscilloscope.
Here is where it starts to get interesting. A clarinet and a bassoon both playing middle C results do not display on the oscilloscope two different wave shapes, but just one shape, one whose spatial appearance is different than that of the clarinet alone or the bassoon alone.
Something even more interesting occurs if we examine just the shape of the clarinet sound alone, as shown on the oscilloscope screen. We have already said that what we perceive as a single pitch on a single instrument is actually the result of many different pitches sounding all at once. Each pitch would produce its own wave shape on the oscilloscope, but the shape would be much simpler than that of the clarinet.
If we could sound each of these separate partial sounds, but cause them all to sound all at the same time, the result would once gain be the more complex shape of the clarinet’s wave on the oscilloscope.
Four clarinets playing four different pitches will result in our hearing a “chord”: the simultaneous presence in our consciousness of four different notes or pitches. In contrast to this, when we the clarinet produces the various, different component pitches within the sound of a single note, we will not hear a “chord”, instead we hear a single pitch or note – but, importantly – it will have a unique “tone quality”. We can change this tone quality by changing how “loud” each partial pitch is relative to the others. Make certain adjustments of this type and we may hear the same pitch but with a new tone color, for instance that of a violin, an oboe, or a human voice.
**** A triangle can gradually morph through time until it appears as a square. But it can do so in many different way. Perhaps a baby fourth side appears in one of the three sides of the triangle and then gets larger. Perhaps the triangle first morphs into a circle and then the circle gets pinched into a square.
Coaching an instrumentalist for an orchestra audition
In today’s incarnation, “Irving” is a bassoonist rather than a pianist. He is about to audition for a local orchestra. The required excerpt for the audition is the opening of the second movement of Scheherazade.
I listened to him play the solo through. The notes were there, but overall it lacked a sense of the presence in his imagination of the other instruments playing at the same time, and the effect that would have on how he sounded the passage.
He had played the same solo a year or so earlier in an orchestra. So I asked him “what instruments were accompanying you during the solo?”
He thought about and said “the woodwinds?”
I said, “No, it is actually four solo double basses.”*
He played the solo again, but this time I played on the piano the chords played by the four double basses. This caused a sudden change in his playing. One thing that happened was that he fine-tuned both the pitch and the feeling of his notes to better fit in with the chords. In tonal music, no note has a single, abstract, or ideal pitch. It varies in small amounts to best fit in with the harmonic context in the form of the chord that is sounding at that moment. Each chord in turn has a certain feeling, which if recognized and felt fine tunes the timbre or tone quality of the bassoonist’s note.
No longer was his playing an island to itself, it had a broader context. The trick, I said, is to make these modulations to the sounds even when you are playing by yourself without the other instruments, which can only be heard in your head. The person auditioning you is listening to see whether this broader musical context shines through the notes that you play.
“How do I do this,” he asked?
Let’s start with knowing when in the solo the chord in the basses changes. He didn’t know. I said: let’s play through it again, this time listening specifically for the changes in the chords. It shouldn’t be too difficult to do because, based on how he had played the passage when I played the chords at the piano, he was already subconsciously responding to them.
Next I asked him if the first chord in the basses seemed to last a surprisingly long time before changing. If so, what beneficial effect did that harmonic inflexibility have on the effect of the solo? He said that it made the bassoon solo seem more “frozen and static.” I agreed.
Was he, I asked, aware that this first chord contained only root notes and fifths and lacked the third of the chord, the note that which would determine whether the chord was a major chord or minor chord. It was incumbent on the bassoonist to make that choice clear to the listener, and to be especially aware of when the bassoon made up for the deficit of the third by momentarily playing the third himself.
Later in the session I wanted to demonstrate, in a more general way, how the ‘color’ of a note depends on the chord to which it belongs. And how this color could change, depending on whether he was playing the root, third, fifth or seventh of the chord.
I had him hold a single note for as long as he could, while I surrounded his chord with first one chord then another. I started with the three major chords and the three minor chords that contained the note he was holding. Then I went on to seven-chords that contained his note. Then I gradually shifted to chords that didn’t contain his note, which therefore caused his note to be dissonant – but always dissonant in a specific enough way to create a definite and peculiar color to the dissonance.
Though he held the bassoon’s pitch relatively constant, he instinctively changed the timbre and the intonation to reflect the way his note fit (or did not fit) in the chord.
* albeit an odd orchestration, but an inspired choice given the shape and mood of the solo.
The printed score and its limitations
A lesson with Irving on the Chopin: F Minor Nocturne
He is an intermediate level student, and has not had enough years of experience in reading scores to not be thrown off by ambiguities in the music notation. In particular the rhythmic counter-intuitiveness of even an unusually fine edition like “Henle.” Here are some of the issues we encountered.
Sometimes it is difficult to tell that a series of eighth notes in the right hand line up simultaneously with a series of eighth notes in the left hand. This is simply because of the optical illusion produced when the stems of the notes in one hand go up and the stems of the notes in the other hand go down. We tend to be less aware that the note centers are vertically aligned and more aware of the left-right offset of the stems.
The printed symbol for a whole note often takes up more horizontal space than that of a shorter note, for example a half note. If there is a whole note and a half note in the same chord played by the same hand, before we can interpret the rhythmic relation between the two notes, we have to first ‘translate’ the feeling of horizontal imbalance on the page into a more mathematical sense of the ratio of the durations of the notes.
In the edition of the Nocturne we are using, the first measure of the cadenza-like, cascading downward run in sixteenths, begins after a quarter note. The publisher has left very little horizontal space between the quarter note and the first of the sixteenth notes. The intuitive impression is that the sixteenth notes start sooner than they actually do. As a result we may find it harder than usual to play the simple rhythm of a quarter followed by four sixteenths.
The width of two measures containing the exactly the same number of notes and in the same rhythm, vary because of the extra horizontal room taken by accidental signs, especially the double flat sign.
Near the end of the piece there is a wonderfully chromatic and somewhat dissonant pair of voices converging in the right hand. The printed notes are already counter-intuitive because of a sort of staggered chromaticism between the two voices. This makes the notes even more difficult to read because the edition compresses the width of that particular measure to save room. The notes seem harder to read, not as much because of the composer’s unique choices of pitch, but because they are jammed together left and right.
One can adduce many more such examples.
In general, a publisher assumes that the exact rhythm of a passage can be gleaned from, or sometimes in spite of, the horizontal spacing of the notes on the page. That it is up to the pianist to “translate” the spatial information into a durational awareness of what the rhythm is. Only sometimes does the rhythm on the page “look like” what it “sounds like” through time.
We forget this because of years of unconsciously making this translation, but for the less experienced pianist it helps to point out the when the appearance of the notes on the page make the rhythm even more ambiguous than usual to discern.
In Irving’s case we discovered just how strongly his subconscious brain rebelled against all of the above types of visual incongruities on the page. And since this was occurring on a subconscious level, he did not stop to make himself aware of the cause of his discomfort. He assumed that he somehow was doing something badly, or was having more trouble than other pianists learning the piece. But once he became conscious of these ambiguities, he was able to stop blaming himself for the results of those ambiguities. Irving could feel himself in the privileged position of a critic who is looking down upon the spatial appearance of the rhythms, but who out of kindness will correc in his mind the incongruities so that the rhythm sounds as the composer intended.
Singers have a particular issue with one aspect of the printed display of rhythms. It results from which notes are beamed together with others notes as against a note having its own self-standing flag. The publisher is more interested in showing where the last note of one syllable changes to the first note of the next syllable and does so by not beaming together those two notes. They have prioritized syllabification over a clear portrayal of rhythm. The result of seeing all the resulting isolated stems is to confuse the eye so that we cannot divine even simplest of rhythms, as when a quarter note divided into four sixteenth notes.
A new rule for Irving about sight reading
Irving* plays at an advanced technical level, but has significant difficulty sight reading at an intermediate level. We practice sight reading at every lesson.
There is a predictable sequence of events when something goes amiss as he is sight reading:
1) He comes to a stop.
2) He gets frustrated and angry (but not angry at anything in particular).
3) He voices his frustration long and loud, expressing an existential angst about what is happening to the flow of the music.
4) As quickly as possible he tries to figure out what went wrong, as if it counted (I.E. made up for things) just how fast he could make the correction.
5) He resumes playing the piece from exactly the same location where he left off.
This is not a very fruitful pattern of behavior for him, in fact it seems to me to guarantee the likelihood of making more mistakes.
A week ago, at his previous lesson, we agreed that for step 3 (voicing his frustration in a long string of words), he could substitute just a single word, “Darn.” I suggested that he say the word with an affected, theatrical accent. No matter what the problem – rhythm, hand coordination, notes, etc., the response had to be always the same and always said with the same accent.
At today’s lesson I wanted to go further and try to modify the entire cycle. I thought the best way to do this was in “real time” – i.e. as each step was happening.
To create the right circumstances to make this modification, I suggested that instead of reading a solo work we sight read four-hand works together.
With much good humor and mutual supportiveness, we agreed to a new rule which would (except for making a mistake in the first place) would replace all five steps:
It’s fine to make mistakes, but don’t allow yourself to pause. Keep the flow of the piece going in your head and try to re-synchronize with your four-hand partner.
This means having to deny yourself the negative pleasure of an emotional reaction to making the mistake. The latter takes too much time and makes it more difficult to jump ahead and try to re-synchronize with his partner.
Whether you stop because of a rhythm issue, a pitch issue, or just simply that the spot is too difficult to sight read, part of you has to keep advancing in the time of the piece. No matter how many beats, or measures, or even lines, pass by with only the other person continuing to play, try, and if necessary try again, to re-synchronize.
I stressed that the ability to do this is separate from, and has no relation to either whether the mistake happens or whether he tries to make a correction if there is a mistake.
At first it was very hard for him to follow this rule. But gradually he got better at it. A new habit was being born. He began to use his ear and his musical intuition to locate a place in the score that meant to sound together with what I might be playing at that moment.
The reason we had to agree beforehand to this rule, was that if a teacher ignored him and kept playing on when he had to stop, it would characterize the teacher has being mean, intolerant, and unbending, and other not nice things.
Thus we have taken the first steps to incorporating into the definition of sight reading: never stopping the pulse. And if playing with another, don’t expect the other person to be a nice guy and adapt to him.** Rather, mimic the more professional situation where sight reading with others depends on continuing on ahead regardless of what happens, and depending on the ability to re-synchronize.
*Irving, by the way, is my default pseudonym for any of my students, male or female.
** Adapting to the other person is something so easy for me to do by default because of my professional experience over decades as an accompanist.