# The Technique of “Isolating” Variables

Isolating Variables.

Whenever a passage involves an intricate balance between two concerns, such as rhythm and pitch, pitch and fingering, etc., there is a method by which one of the two can be “held constant” while allowing only the other one to change.*

In the following examples we separate apart two intertwined issues, putting emphasis first on one and then the other, by holding the other one constant.  Each is mastered singly before putting them back together again.

1.

If rhythm and pitch are changing at the same time:

Make all the pitches just one and the same pitch, and play that note in the rhythm of the passage.

or –

Play the sequence of pitches as written but do so in a “neutral” rhythm, (for instance giving each note the same duration).

2.

If loudness and pitch are changing at the same time:

hold the loudness constant and let only the pitch vary.

or –

hold all the pitches to one repeating note, and only let the loudness vary.

3.

If an intricate series of notes also requires a difficult pattern of fingering:

Play every note with one and the same finger.

or –

Stay on one note, but use the fingers in the order that they will need to be used when playing the passage in its normal form.

or –

‘bunch’ up the finger tips and use them as a single unit on just one note and play the rhythm of the passage.

4.

If the two hands are doing things that are quite different from one another and, thus, hand coordination becomes an issue:

Have both hands play the right hand’s notes, but in two different octaves.  Then reverse the procedure, and have both hands lay the left hand’s notes in two different octaves.

5.

If a melodic line involves sudden changes of register (octave).

Put all the notes of the melody into one and the same octave (a perfect example is Brahms: Op 117 No. 3, the middle section).

6.

If it is difficult to play a melody in octaves in one hand. Use the pinkie to play just the pinkie notes.  Then use the thumb to play just the lower notes.

7.

If there is a variety of articulation marks within a small group of notes.

Play it all very legato; then all very staccato; then all accented; then all sotto voce.

Then add back the articulation.  By this time you will be practiced in executing each type of articulation.

8.

If it is difficult to play something slowly (or rapidly) enough:

Play it first at the opposite extreme of tempo.  This procedure is especially useful for learning to sustain a long phrase or melody, that evolves over many measures.  First play it extremely rapidly.

You will get a sense of the main outlines and directions in the phrase.  Then slow it back down, and you will notice that the way the notes adhered to each other in the fast tempo is preserved into the slower tempo.

Mention is also made of these types of procedures in the blog:

* In mathematics, when there are several different ‘variables’, all intermixing and interacting with each other in a single equation, mathematicians, in order to gain understanding of how the equation behaves as a whole, use a procedure in which they treat all of the variables except one as if they were no longer capable of varying but were held constant.  Then, one can go through each of the original variables in turn, each time making it, for the nonce, the only one varying.  This is called partial differentiation.

# Some Unpublished Odds and Ends

14 short entries:

1. the Chopin Barcarolle.    2. downwards is often the least useful direction of motion.    3. where legato is harder to achieve.    4. altering what the listener thinks just happened.    5. Rachael found her sound.    6.  Applied dominants.  7.  A dotted eighth followed by a sixteenth.    8.  Changing from eighths to sixteenths.     9. Repeating chords.    10. Things not to think about.     11. restoring mobility to the body while playing.     12. music and language come from a common source.    13. phrases within phrases.    14.  is repeating something four times in music too many times.

1:

The Chopin Barcarolle:

In the opening phrase the notes in the left hand connect one to the next in one way, and the notes of the right connect each to each in a substantially different way.  The goal here is to bring the two hands more into sonic accord.

Though the opening passage is beamed as repeating groups of three notes.  Practice it first as in groups of two notes, and hold the second of each two notes longer than the first.

Why?  Sometimes distorting a phrase leads to bringing out the undistorted shape better than if one just practiced it in the undistorted form.

More generally, sometimes the best route to something is to go the opposite first.  From that position it will seem easier to get to the originally intended form.

2:

For the opening note or chord of a piece, motion downwards in the arms is often the least useful direction to go.

3:

A singing legato line is often broken at a point in a phrase where a relatively longer note is followed by relatively shorter note.  We

simply forget the longer by the time it ends.  To solve this, when you start the longer note, pose the question to yourself: how do I want this note be sounding shortly before it ends.  Then, when a moment or two later, you near that end, focus your ear carefully on the remains of that sound, and connect as legato you can, that softer end of the note to the sound of the next note.  Legato must take place between the end of one note and the beginning of the next, not from one attack to the next attack.  The latter may seem easier at first, but ultimately the attack becomes a distraction to the flow of the notes between attacks.  The point is that, in spite of the difference in the loudness of the end of one note, and loudness of the next note when it begins, we can still make a bridge to connect the sound, so sound flows through from one to the other.

4:

How you play the next note, or part of a piece, can transform how the listener thinks you played the previous note or part.  The listener always searches for an antecedent that makes sense as being the most logical thing to precede the new part.  If there is a crescendo written during the duration of a single note (which is acoustically impossible) play the next note with the loudness that you think the previous note would have achieved by its end, if it were crescendo-ing the whole time.

The performer has to be a magician of time.

5:

Rachael found her “sound” at the piano today.  It had been a long

search.  I celebrated for Rachael.  Plus it provided me the joy of

being reminded that the piano can be a beautiful sounding instrument and not percussive instrument of stops and starts.  Such a reminder is a useful thing for us to have once in a while.

6:

Explaining “applied dominants” to a scientist.

Bob is a 16-year old math prodigy who is already conversant with Complex Variables in mathematics.  Thus my explanation was couched in terms from quantum physics.

Bob, think of it this way: it doesn’t violate the continuity of the key of C major if, just for a “trillionth” (sic) of a second, we think of ourselves as being in the key of G Major – which turns the previous chord, a D7 chord, into a V7 of G.  If we stay with harmonic notation then then G itself the V (of C), and D7 is V7 of V.

Think of the momentary presence of the key G Major as a “virtual particle” whose existence is so short that it doesn’t violate the principles of quantum mechanics.

He got it.

7:

When there is a dotted eighth and a sixteenth, sometimes it helps to feel like the latter can take up a bit more time than it should mathematically, let it flow by languorously.  But in other situations one wants the opposite, we dispose of the short note in a brief burst.

8:

When shifting from, for example, eighths to sixteenths in the middle of the passage, the primary feeling in the body and the mind should be that the speed did of the notes never not change; that only the outward perception of the speed changes.

9:

While playing a series of rapidly repeating identical chords, raise the question in your mind, over and over, as you go from one iteration of the chord to the next: is there any finger that is not partaking of the energy coming down the arm.  You may have time only to check one or two fingers at a time, but with new iteration of the chord you can check another one or two fingers.  By “check” I mean searching for the internal sensation of the finger connecting with the arm and the shoulder.  This is done by tracing the sensation either from the shoulder to the finger or from the finger to the shoulder.

10:

It is sometimes more important what not to think about than what to think about.  For instance, instead of the horizontal plane of the keyboard think of the third dimension in space (the vertical).

11:

While sitting on the piano bench, raise you arms up and move them around freely in space.  Or swing your arms at your sides.  Or get up and walk around and see how your arms want to move naturally.

12:

Sometimes you have to say nonsense syllables along with the, either out loud or internally to our self, in order to get the phrase to come into shape and say something meaningful.  Phrases ‘speak’ in a verbally inarticulate language that like normal spoken language has ups and downs, cadence and flow.  Perhaps there was a pre-historic time when there not yet any difference between proto-music and proto-language.

13.

While playing the current phrase of music, know that it is part of a larger phrase, which is part of an even larger phrase … all the way until you can contemplate the entire movement (even the entire piece) as being one phrase, whose architecture never lets go of the notes as they pass by one by one.  However large a phrase you wish to contemplate, never loose sight while playing of where in that phrase you are. Slowly proceed through time from its beginning to its end, always having a sense of how much you traveled since the beginning and how much you still have to travel to get to its end.*

* When I used to go through the Lincoln Tunnel from “the city” to “Jersey”, after I lost site of the daylight behind me, the only real way I could tell how far I had gone in the tunnel so far,  was through an internal sense of the passage of time.  It became spatial again when I could the daylight ahead of me at the end of the tunnel.

14.

How many times should a composer repeat a figure identically?

When Bruckner, as he so often does, repeats a phrase identically four times in a row, one after the other, I have two very different reactions, sometimes one sometimes the other.  I oscillate between being bored by repeat 3 and 4,  and being swept into a relentless vortex.  What I am conjuring with is my personal balance between sometimes hearing more each time the phrase repeats, and the inuring effect of doing something over and over again.  Mozart made it simpler.  For special effects, he would repeat three times.  Of course three is a prime, and a “mystical” number, though four has its many philosophical and psychological proponents.