# Sight Singing Exercises for the Obsessive: Singing Between Notes

Here is a statistically based method for practicing sight-singing.  It is based less on musical, harmonic or diatonic context and more on the mathematical permutations that can occur between any notes.

Exercise one.  To be done over one or more days or weeks.

Choose a scale.  Choose a note from the scale.  Let us say as an example you choose the C Major scale and the note E which is the third step of the scale.Sing from the E to each of the other notes in the scale:

thus: E C  E D  E E  E F  E G  E A  E B  E C

E C  E D (downwards motion)

E E  (no motion)

E F  E G  E A  E B  E C (upwards motion).

Sixteen notes in all, in eighth pairs.

What was just done for the C Major scale starting always on E, can be done for the same scale starting on any of the other notes in the scale.

If you want to do this in an systematic start with lower C as the first note for a set of sixteen notes, then start with D for another sixteen notes, then E, etc..  until you start with the higher C.

C D  C E  C F  C G  C A  C B  C C

D C  D D  D E  D F  D G  D A  D B  D C

etc..

Having exhausted the links between two notes of the C major, one can use the Harmonic and the Melodic minor scales in C.

The entire process outlined above can be done for other possible tonics.

Tonic C# / Db

If you sing the name of each note that you sing, then there would be an advantage in doing C-Sharp major and D-Flat major as two separate exercises.

Then proceed with tonics D, D#/Eb … B

Exercise two.

Same general principle as exercise one, but based on the notes of a chromatic scale.

Find the lowest pitch you sing easily; the same for the highest pitch you sing easily..  An example might be from Middle-C up to the second G above Middle-C.   Or, a more expansive example, might be from a low A up to the second A above that A.

The idea is to sing from one note chosen from that range up to, or down to, every other note in that range.  Let us use a somewhat simple example: a lower C to the second E above that.

The first series of notes to sing would be:

c c#  c d  c d#  c e  c f  c f#  c g  c g#  c a  c a#  c b  c C*  c C#  c D  c D# c E  c F    c F#  c G

* lowercase letters indicates a note in a lower octave, and   UPPERCASE a note in the higher octave.

As with exercise 1, you can repeat the exercise starting on first one and then another step of the chromatic scale.

Her e is the beginning of the example of starting on “g”.

g c  g c#  g d  g e#  g e  g f   g f#  . . .

If you choose to sing the names of the notes you are singing then sometimes use sharp names and sometimes use flat names.

Exercise Three.

Mathematical permutation of a chosen number of notes in a scale.

Consider spreading this exercise out over  months to a year, so that you don’t have to spend too much time on it on any day.

3A: Choosing 3 different steps:

A good beginning would to choose just three notes from a single scale, later going on to four steps, five, etc..

The simplest choice of three scale steps would be the first three steps of a scale.  In what follows we will use the numbers (1, 2 ..) and not letters of the musical alphabet. so that the examples below can be used for any scale with any tonic.

There are only six permutations of the first three steps of any scale:

123   132   213   231   312   321.

Or, three scale steps, using scale steps 1, 2, and 4.

Here are the six permutations:

124   142   214   241   412   421.

Or, three steps:  2 5 and 7:

257   275   527   572   725   752.

3B:  Choosing 4 different steps:

By moving from three to four notes chosen from a scale. we significantly enlarge the number of possible “permutations”.

Here is full list of the 24 permutations of the scale steps 1 – 4:

1234  1243  1324  1342  1423  1432

2134  2143  2314  2341  2413  2431

3124  3142  3214  3241  3412  3421

4123  4132  4213  4231  4312  4321

Or, the 24 permutations of the four steps: 1 2 5 and 7

1257  1275  1527  1572  1725  1752

2157  2175  2517  2571  2715  2751

5127  5172  5217  5271  5712  5721

7125  7152  7215  7251  7512  7521

3C: Choosing additional number of  steps:

Adding the number of steps chosen from the scale rapidly increases the number of permutations.  Choosing 5 different steps leads to 120 different permutations.   If you pick the first five steps of the scale you would get 120 permutations starting with 12345 and ending with 54321.

It doesn’t make much sense to go much beyond five steps.  By the time you have considered an ample number of different groups of five steps you will have pretty much created singable phrases covering every note of the scale.

3C:  Changing the step numbers of the scale into printed notes on the staff:

If I get enough requests, I am willing to create a “Finale 25” file that would flesh out all the exercise sets using each tonic and scale type.  Hey, it will take a long time, but why not.

I recommend reading the blog entry “Singing in Tune” published on July 14, 2018.   There it is suggested that:

…learn to play the chord that is present in the accompaniment when you are singing a single note, and learn to tune you note into the chord.  Learn to do this also if the note sung is not a chord tone but a tone of embellishment.

…when you are sight reading a passage whose notes all belong to a common scale, make a cluster out of all the notes of the scale played simultaneously, and learn out to single out each note with the voice.

Get used to hearing two notes played simultaneously and learning to sing the lower note then the higher pitch (and if you want the lower pitch again).

Same as the above but hearing three notes played simultaneously, and learning to sing the bottom, middle, top, middle bottom.

Also learn to play a note in any range on the piano, especially the very low or high range, and transpose the note up or down one or more octaves until it lies within the normal range of your singing voice.

Pantomiming:

People seem to use two opposite strategies for trilling.  Either, use excess physical effort to try to maintain the trill going on and on, or use as little physical effort as possible as a way to keep the trill from stalling or changing and maintain its ease and flow.  I subscribe to the later method.

The limiting case for a least-effort-possible while trying to play is to pantomime.  Execute the trill like a “mime,” barely touching or tapping the keys (but in the correct order and speed).  Doing this teaches the body just how effortless a trill can feel when there is no overuse of energy.  The effort is so little that any conscious amount of energy we apply is already too much.

Once you have pantomimed the trill, say to yourself: “what is the absolute least amount of any additional effort or energy I can give in order to make the notes of the trill start sounding.”  Even if only some of the notes end up sounding, just add a bit more energy and leverage than before when you first went from silence to sound.  In making this difference in energy, less is more.

A variation on this technique is to sound and hold down the lower note of a trill while repeatedly tapping and releasing the upper note (either making a sound each time or making no sound – both are effective procedures).

Coming out of a trill

Many of us have difficulty with the last few notes of a trill.  It doesn’t matter how long the trill is, how many beats it is, we’re just fine until we are within a split second of needing to stop the trill.  This last moment is a confusing moment for the hand.  No matter when you think about the trill ending, just by thinking about it – such as the thought “gee, I guess it’s time to end the trill,” you transmit something to your body that gums up the end of the trill.  The last few notes of the trill will not flow smoothly.  It is better for the body, if possible, to remain “ignorant” of when it is time to stop the trill, and then suddenly, without warning, stopping,

Evenness counts for as much or more than speed

It is more satisfactory to the listener if you play a trill slower but evenly than to try to play it faster but and fail to maintain evenness.

It is the body as a whole that does the trill

A trill would seem to be an action limited to the neighborhood of the fingers.  It seems at first sight to be so precise a motion.

Here is a procedure to make the trill a part of a motion of the entire body.  I did this many years ago with my student Rachael:

We stood up.  We started wiggling the tips of our fingers, then spread the motion so it included our hands, then wrists…  At this point, our fingers, hands, and wrists were all moving at the same time in a random fashion.   Developing this idea further, we began randomly moving our forearms, then added our elbows, then our upper arms.  We looked pretty silly at this point.  Finally we added our torsos and eventually our legs.  I said: now you’re ready to play the trill.  Wiggle (or gyrate) your way to the piano, and don’t stop moving all the parts of your body until after you are seated at the piano bench and have started the trill.  The trill came out marvelously.  Unfettered, free, even, fast; as if it could go on forever.

The point was not to move the body like this every time we need to play a trill, but that doing so brings alive all the connections in the body so that any motion is possible, including going back and forth between two keys on the piano.

There is no formula for this procedure.  Nothing is gained by knowing which muscles you are moving or by how much.  The point is simply to bring alive all the parts of the body.

Turning any passage into a continuous trill

Take any melody in a score and create a trill on every note, at least for the duration of that note, if not a good deal longer.  The goal of this process is to make the passage sound like a continuous trill.  In doing so, you are imbuing the passage with the aesthetic qualities of a trill: great continuity, maximum flexibility and sense of motion, sinuosity, élan, continuous change and aliveness…   These are all qualities that you can then preserve into the normal execution of the passage.  All the qualities just mentioned retreat inside the heart of each note as the notes succeed each other.  If we liken a melody to an artery then the trill is like the blood itself flowing through the artery.

A long trill

A long trill can be concatenated out of numerous smaller trills that are stitched together.  Most of us can sustain a trill for a short duration of time but have difficulty if the trill is meant to go on for a long time.  Just knowing in advance that it will be long affects how we start the trill.

Here is a solution.  Start the trill as always, but after a short while, well before we would normally tire out, send a new wave of energy or pulsation down the arm from the shoulder as if to start a new trill.  The important thing lies in the timing of when to initiate the pulse of energy.   It must start out before the current group of trill notes has completed – it needs time to travel down to the fingers.*

Repeat this process as many times as necessary to complete the printed duration of the trill.  At first there might be pauses between the end of group of continuous trill notes and the beginning of the next.  After a while, though, the chunks of the overall trill will be linked seamlessly together.

When I do this, I can go on trilling indefinitely, without any loss of vivacity.  Sometimes I do this to show off for a student, saying as I’m doing it: see, I can go on, and on … and on …  Just by renewing the trill and starting it over fresh each time.

Changing the character within a long trill

Sometimes a long trill can be made to be more expressive if it changes speed in specific ways at specific moments during its course.  It gives the overall trill an architecture, and overcomes any monotony that might otherwise ensue.

A rarer but more extreme version of this would be to apply a ritard and/or accelerando within various portions of the trill.  This requires a fine degree of control so that the trill doesn’t stall out or get tied up in knots.

Special anchor spot in the forearm

There is a spot on the forearm, not far from the elbow, nearer the crease of the elbow than the point of the elbow, that is an effective point from which to experience the motions the muscles that are activated when playing a trill.

Take one of the fingers of the hand that is not doing the trill, place it on the spot described above, and push down on the skin, just until the finger feels something moving underneath the skin while playing the trill.

This is an ideal point from which to experience the reciprocal motion involved in the trill.  You will ensure greater evenness in the trill if instead of focusing on the fingers you focus on what is going on in this spot on the forearm.

An “inductive” approach to a trill

Begin with a single note.  Pose the question to yourself: can I play a single note with great rapidity?  Playing a short staccato is the answer.

Next append a second note to the previous note.  Pose the question: how fast can I play one note and then another?  Answer: I just have to treat the first note as if it is a fast grace note to a longer second note.

We proceed one more note at a time.  We trill three notes, as fast as we can, maybe using our voice to lead the fingers by saying something like “go-ing-THERE.”

Continue the process for four notes of a trill.  How fast can I execute them?  I just need to think of the first three notes as a group of grace notes leading to a the fourth, longer sound.  One can steer it by saying: I’m-go-ing-THERE.   Or thinking of the opening of Beethoven’s Fifth done at an extremely fast tempo.

And so on.  A five note trill.  A six note trill.  At some point we reach a number of notes so that continuing the trill is no problem: the trill has ignited.

I  wish you a trilling experience.

* The experience is not that different than repeating the same note legato a series of times.  Before, and not at the same time as, the key has come up all the way to the level of the other keys a stronger arm pulse is already making its way down the arm to overwhelm the upwards motion of letting go of the key.

# Two or more notes from one physical gesture, case 1: the ratchet

The principle of the ratchet.

There is a general category of motions that is capable of producing a series of sounds from one and the same continuous gesture.   This is of special advantage when playing very fast.

One example of this group is when a motion, though single and complete, occurs in small segments.

We start with a gradual and uninterrupted forearm rotation.  This motion is then broken up into parts by suddenly forcing the motion of the arm to come to a temporary and brief stop.  The result of this stopping is that the inertia of the rotation,  like water accumulating behind a dam, increases rather than decreases the force bent on continuing the motion.

At each such stop, one note is sounded, and then the rotation is permitted to continue.   This sequence of stopping the motion and then quickly continuing it, continues until the full course of the rotation is covered.  Depending on how one divides up the motion, the overall rotation will produce a series of notes ranging from a minimum of 2 to 3 notes to a maximum 8 to 12 notes.

The virtue of this procedure is that instead of making one motion per note, we have something that is more like one continuous motion that we attempt to resist.*

Each time the overall course of such a motion is temporarily arrested, the forward momentum that has built up until that point is first diverted into the production of a new note or sound.  Once that note has begun to sound, there is no longer any need for the restraint of the continuation of the overall rotation.  The note itself has acted like a brake or stoppage of the motion.  The more this stoppage persists the more a force builds up, like water behind a dam, until the motion forces itself to spill over the blockage (the note) and continue.

I call this type of overall motion that is broken down into a series of interruptions a “ratchet” like effect, after the rapidly repeated sounds made by the percussion instrument of the same name.

In future blogs I want to discuss many other types of motions that fall into the more general category of obtaining a series of sounds from the application of one motion (a motion that is sometimes interrupted as in today’s example, and sometimes flows continuously).

If you would like a preview list of all these motions, just let me know and I’ll post them.

* Like “pumping” the brakes of the car instead of jamming the brakes to the floor.  Or like the escapement of a Swiss watch that temporarily stops the main spring from unwinding, creating the sound of a “tick” or a “tock” and then lets the unwinding of the spring continue.

# Changing Fingering

Changing Fingering.  Changing any habit at the keyboard.

B. has been  working on the Italian Concerto.

He has discovered places where the fingering he is using is not serving him well, and thus wants to change the current fingering to a fingering that is more ergonomically efficient for his hand.   He says that he is OK at figuring out what the better fingering would be,  but the problem is that he can’t get his hand to accept the new fingering.  Trying to do so simply leads to confusion.

My suggestion: if one wants to change the fingering in a passage from what it has been before, instead of trying out the old fingering abruptly in favor to the new one, it is easier first to go into an in between state: a neutral state, in which the old fingering can go to rest and the new fingering can appear at the door to request admission.*

The neutral state that I suggested was to play every note with the same (sic) finger.  Ordinarily, which finger and which note are merged together in the mind.  However, playing all the notes with the same finger makes the mind  more aware of the identity of the notes apart from the fingers to play them.  This frees yourself from dependence on any one particular fingering and opens the door to return from the neutral state into another fingering rather than the wanted one.

*I had the same problem with introducing my old cat to my new cat.

# Sometimes Geometry Helps

How to get from one place to another on the keyboard.

First of two entries:

The line “subtended” by a small angle can be very long.

The two-dimensionality of the keyboard discourages us from thinking in three dimensions instead of two.  Getting from one location to another on the keyboard requires a motion that is as much up and down as it is side to side.

First, a geometrical digression.

An isosceles triangle is one in which two of the sides are equal in length.  There is no limit to how long or short the two equal sides can be.

Imagine an isosceles triangle in which the angle at the top is  where the two equal sides meet.  Imagine that the top angle being very small.  No matter how small this angle is, if you make the two equal sides long enough, the distance between those two sides will grow larger and larger.  And if the two equal sides are long enough, the horizontal base at the bottom of the triangle can be as wide as you want. For instance, several octaves on a piano keyboard.

If I need to displace my hand from where it is on the keyboard to a position on the keyboard remote from it, I try to be conscious less on a left to right motion and more of an up and down motion in the ‘third’ dimension.

My hand travels upwards first, rather than right or left, until it reaches the imaginary vertex at the top of an imaginary isosceles triangle.  Once at the vertex, I start to come back down, but on the other of the two equal sides.  At the vertex I make a very small and subtle change of angle.  It almost seems as if I am coming down the way I came up, but as I get closer and closer to the keyboard (the horizontal base of the triangle), I find that I am going to land in place on the keyboard a sizable distance from where I started.   This has been accomplished without almost any conscious sense of sideways displacement.

In a previous blog I spoke of imaginary motion versus actual motion.  Mirror neurons allow us to feel as if we are making a motion even when to the outside world we seem to remain motionless or nearly motionless.  The motion upwards to the vertex angle in the isosceles triangle can feel as if you have traveled upwards quite high with your arms before starting to descend – only the outside observer will not see much motion.  Your muscles however will be engaging as if doing the larger motion.

Sometimes it is necessary to escape into a third dimension, so that when you return just to the two-dimensional horizontal plane of the keyboard, it is “pregnant” with the mobility of having been in three dimensions.

This motion is an example of a more general heading of motions that help break out of the two dimensional confines of the keyboard.

Item Two:

The principle of the lighthouse.

Think of the beam from a lighthouse sweeping the horizon as the light rotates on a vertical axis.  While the part of the physical light itself that happens to be furthest from its axis describes a circle around the axis which is measurable in feet, maybe yards, the result of this limited motion allows the beam to travel across miles of distance along the horizon line.

Now, substitute the torso of the body for the light in the lighthouse, and the extremities of the arm as a horizon.  Rotational motion of the torso, measurable in inches, can cause the arms to travel along the keyboard a distance measurable in feet.

For any motion while playing, it is always best to find the point in the body that moves the least, but causes a motion of the hands that moves the most.  I learned this from my second teacher, Edwine Behre, who in turn learned it from Abby Whiteside.