More Beautiful Sounding Octaves: for the Medium-Size Hand
When I play octaves, there is a tendency, at least in my-sized hand, to have the pinkie and the thumb move towards each other when contact the keys. But it is worth sometimes practicing in way so that the tip of the pinkie as well as that of the thumb should move in a line along the longitude of their key. This requires my attention, because the hand is already spread for the octave, and the first and fifth fingers moving slightly towards each other happens naturally. Especially for the thumb it is a more natural movement. So, just once in a while, practice octaves so that those fingers move in a plane so that they go directly and horizontally towards the body in an extension of the longitude of their keys.
The muscles needed to move the thumb and pinkie in this direction move in these constrained directions require first, in the case of the right pinkie, an extreme flexion of the third knuckle, down and aimed to the right as it moves in the direction of the body, aided also somewhat by a flexion in the right side of the wrist. In the case of the right thumb it should practice its motion by slowly tracing over an imaginary straight line extending beyond the lip the key aimed towards the body. The third knuckle, where it attaches to the wrist, is prominent in keeping the thumb congruent with this line. As the motion is made the thumb is always compensating for the desire to move outwards and away from the second finger.
Poetry and Emotion
Mozart: The C Minor Fantasie (K. 475):
-the piece in general:
The piece as a whole is very cohesive and organic n spite of being made up of many small parts, parts that are very different from each other musically, tempo-wise, rhythmically, and most of concern to the piano, requiring very different technical masteries.
Some of the contrasts in the piece are vividly displayed in a way that suggests an almost tangible sense of change of orchestration, as if referencing a full orchestra, sometimes strings, or strings deepened by the sonority of french horns, sometimes winds, sometime voices.
-the opening measures:
Of all the ways I’ve tried to start this with piece so as to achieve a sonorous, commanding sound (similar to the C-s played by the piano alone at the very beginning of Brahms Third Piano Quartet) these have worked, albeit not consistently and not every time I try them.
Practice elevating the arms quite high, and then, very slowly, then lowering them back down. Keep lowering them. past the key slip until the arms and hands are lower than the keyboard. To transfer this feeling into actually playing the opening c-s, subjectively feel the arms descending very slowly, and be un-conscious of where, in the arms’ downward course through space, the notes start sounding. We simply notice unexpectedly that the notes have begun to sound. We just don’t know why. “Somewhere” in the slow descent of the arms. the sounds just begin, but we are unaware of where that happens, and when it happens. Somehow, at some point, the fingers have depressed the keys. We’re not even sure how fast the fingers moved to depress the keys.
If we want to know for certain whether the first note of the piece is resonant enough, it is not what we hear at the onset of the sound that provides an adequate way of determining this. It is more at being what we hear at the end of the sound or, perhaps more useful still, what we would still hear of it if it continued to sound indefinitely, with a next note happening. It is only by delaying our appraisal of the sound of the c-s, that we can first know whether the sound had begun resonantly enough. We are trying to make the ‘decay’ curve of the sounds occur as slowly as possible.
Unconsciousness of how we start the first sound plus waiting at least a second or two before fully listening to the sound. How strange! We control best the present tense by the future tense, at a point in time when arguably we should have no control of how the notes started. This is one of the paradoxes of time that occur in many hidden aspects of music and the performance of music.
She tried first to control the sound at its onset, and then, after a pause, she tried to ‘control’ the first sound after it was already attacked. Comparing the second try to the first, in the second the first instant of her sound was less ‘brash’ and ‘angry’ but the decay curve was slowed down, with the result that the duration of the sound was, as a whole, more resonant than the first time.
The first measure in general.
Let us make in our body’s imagination, a subjective analogy between pitches ascending along the keyboard (I.E. movement horizontally to the right) and the pitches somehow moving upwards a vertical direction, higher and higher off the keyboard. C is now “ground level.” The more the pitches rise through the measure, the stronger the build up of potential energy to return the notes to the ground (C).
As the pitches travel (vertically) “UP” from the C, it is as if we are trying to stretch a very strong spring, and the more we stretch it (as we go through Eb F# G and Af) the greater the resistance of the spring and the harder it is to raise the pitch any further. When we have reached the A-flat we have exhausted our strength, and sink back down to C. We are so exhausted that even C-natural does not stop things but we slide to new ‘ground level’ a half step below C (namely B-Natural).
Measure two. The sixteenth note followed by the sixteenth rest.
possibly Mozart’s way of insuring that the emphasis goes on preceding eighth note chord, which represents distress and tension, and not on the chord which follows it, which represents a letting go, a surcease. an emotional giving in.
-the left hand starting measure 5
So here’s the deal: you are only allowed to play one note at a time, but you must get, starting with the first left hand note, the effect of all four notes sounding together. These ‘sustaining’ chords assimilated from the sixteenths in the bass fructify and enrich the glow of the sound of the melody notes in the right hand. The left hand is not simply an Alberti Bass, it generates warmth that baths the right hand.
-starting measure 10
how to control the repeated thirds in sixteenth notes in the right hand:
Sometimes the ultimate form of control to get each third balanced with the next, and each balanced internally between its two notes, is the most passive method.. Sometimes when playing this passage I simply look at the notes going down and then back up. Nothing more than to look carefully at the keyboard and witness the specific keys in each third going down and then back up. For many of us, just watching the keys move vertically allows the body with its many subsets of muscles to perfectly coordinate among each other and achieve the desired quality, evenness, and balance among the sounds.
In your imagination add a vibrato on each and every note as if the thirds were being played by the first and second violinist of a string quartet. There is nothing you can do physically to create the effect this vibrato, a vibrato that seems to crescendo and decrescendo in warmth within the small compass of time of each sixteenth note.*
The fortes in the left hand at the beginning of the measures, can suggest added warmth and emphasis more than sudden, sheer loudness. It is the effect we get in orchestration when we double an instrument in the bass range with another instrument an octave lower.
-measure 16 and 17
…squeeze “the universe into a ball”…To roll it toward some overwhelming question,” (T.S. Elliot)/
“To see a World in a Grain of Sand” (William Blake)
Such are the microcosms formed by the first two sixteenth notes of each quarter note beat. Within each two notes one runs the gamut of human emotions.
-measure 17 going into 18
The last three notes of measure 17 are d4-s and they sound inside a B-Minor chord (as the third of the chord). Then, suddenly, at the beginning of the next measure, through the d4-s continue to sound, they now appear in the setting of a G-Major chord (as the fifth of the chord). This is no mild switch of mood. The entire meaning and sound quality changes. I make this contrast of chord quality as extreme as possible. Enough that the listener truly thinks the note they are now hearing is not the same note (d4) as the note they were hearing just before.
-measure 25 going into 26
If there is a more extreme example of the last item, it is here. Can we, in our musical imagination, hear the D major chord sounding before completing the fourth, even before completing the third, of the four repeated fs4-s that sound with the F-sharp major chord in measure. So, when it changes to an fs4 in a new chord, a D Major chord, in one way we are very surprised (like a new day has dawned, the sun has just risen and bathed the landscape,but in another feel) but in another, harder to figure way, that somehow we had received an adumbration of that D Major chord.**
J.M said something very nice at the end of the lesson: sometimes my experience with you at lesson is more that of a master class .
* Some string players who also play piano can be seen using a finger on the piano keyboard making the same gesture as on the violin when creating a vibrato.
** A thanks to David Garner at the S.F. Conservatory of Music who, when coaching recitatives at the Bay Area Summer Opera Institute (many years ago), told the singers that when singing the last few notes that are under the control of the current chord from the harpsichord or piano, they should already be hearing those notes as if sounding together with the next chord to come. Thank you David… : https://en.wikipedia.org/wiki/David_Garner_(composer).
Creating Harmonic Clarity
Bach: C Major Prelude, Book I, Well Tempered Klavier
Part of A.B.’s quest is to play the notes of this prelude “evenly”. Achieving this has to do with the chord outlined by the notes of each measure, and the balance of the notes in the chords in creating a clear impression of that chord as a whole. To make this chord more obvious to the ear, the player, when practicing, can “densify” each chord: if there are openings between adjacent written notes in the chord to squeeze in additional notes from the same chord, add those notes in. For instance in measure 2, there is room for an f4 between the d4 and a4. If we add in that f4, we create the denser five-note chord: c4 d4 f4 a4 d5. We can take that chord a step forward and add a c5 between the a4 and the d4, forming a six-note chord. The chord has been a D Minor-7 chord the entire time, but the additional chord tones just make it stand out more clearly to the ear what chord it is. Do this for every chord in the Prelude when Bach’s written notes allow for such additions.
An equally valid technique to add density to the character of a chord is add in chord tones in lower and/or higher octaves not used in the printed chord. In this form a chord could contain 8 – 10 notes, or by adding the pedal, larger numbers of notes, spanning the low bass to high treble. In this form, the “quality” of the chord reveals itself at its most obvious. This technique, helps “set” the sonority of the written chord inside a larger entity to which it in turns belongs.
Whatever are the sound characteristics and the mood characteristics of the individual chord, they become in this manner magnified to the ear. From this form of the chord we can then re-compress the chord (through the aesthetic equivalent of a ‘trash compactor’) without losing any of the sound ‘material’ present in the larger version of the chord: the larger instance of the chord being condensed into a smaller chord without losing any of the fullness or meaning of the uncompressed version of the chord.
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.
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).