Musical Pieces (Weblog)

May 13, 2016

A new (to me) student has been asking a lot of questions about scale and arpeggio fingerings, and I have decided this would be a good resource for students, so, without further ado:


Every scale can be assigned to one of three fingering rules:

    “C” Fingerings
    Fingers Together
    Thumb Rule

“C” fingering scales are the scales that are fingered the same as C Major/minor, namely: C/c, G/g, D/d, A/a, and E/e. The governing “rule” is that we want to play the 4th finger before or after we would play the pinkie — so on the 2nd scale degree in the left hand and the 7th in the right. If we put finger 4 in the right place, everything else is logical.

Fingers together scales are easiest to see if you start with the three keys that use all five black keys: F#/Gb Major, Db Major, and B Major. It is clear in these three scales that we must put fingers 2-3-4 and 4-3-2 on the sets of three black keys, and 2-3/3-2 on the sets of two black keys, and the thumbs on the only two white keys in each octave, so that our fingers are always working “together”. These same fingering rules apply to the relative minors of F#/Gb and Db, and the natural minor form of G#. And, because of the vagaries of certain black key placements, the same rule applies to both F scales and B minor.

In simpler form: BM/Bm, F#M/D#m and the enharmonics, DbM/Bbm, FM/Fm

These fingerings are so clear to the eye and logical to the hand that I actually teach BM, F#M and DbM scales to students before I teach the C fingering scales.

 Perhaps the most difficult scales to teach are the scales I call “thumb rule” scales: Ab, Eb, Bb Major, and F#, C#, and G# minor. I have run across various ways of teaching these, including the 3-2-1, 4-3-2-1 pattern in the LH of each of the major scales and that the RH 4th finger always plays the Bb, but I have always found that teaching the principles of the fingerings and requiring the student to work out the specifics, and then play them WITHOUT LOOKING AT THEM WRITTEN ON A SCORE, is the best way for them to attain complete understanding and mastery.

So, how does the “thumb rule” work?

September 7, 2015



           The difficulties of learning, memorizing, and performing Bach’s music — always exquisitely crafted, often thorny with technical and interpretive difficulties — are familiar to any accomplished musician. I have found the type of analysis outlined below, one which was basically stumbled upon while working through this piece with an advanced student a couple of years ago, to be particularly helpful. 

            It is not clear whether Bach intended the “Four Duets,” included in the third volume of the Clavier-Übung (1793), to be performed on the organ or the harpsichord, but they all lie within a fairly narrow range compared to works he was writing at that time for harpsichord, causing some to guess that they were intended for the organ.  There was some debate at the time over whether it was possible to write “artful” counterpoint for only two voices; some suppose that this might be Bach’s subtle answer to that question (they were not listed on the title page of the original publication), given their more complicated forms and a more highly evolved contrapuntal style well beyond that of the two-part inventions. Despite the nomenclature, they are, in fact, pieces for solo keyboard. The term “duet” refers to the fact that they are all, in fact, double fugues.

            My map for the first duet is presented as an animation in Figure 1. 

This browser cannot play the embedded video file.

Figure 1: Map, Duet BWV 802

            What does this map show?

            In general terms, it shows Subject statements (blue bubbles), key areas(1), and the overall form of the piece. More specifically, it shows the palindromic nature of the key structure – tonic (E minor, dark blue) – dominant (B minor, medium blue) – relative major (G Major, aqua) – dominant – tonic, and the relative length in actual time of each key area. Even more specifically, the pink bubbles represent the pillar-like scale passage Bach uses to introduce the subject(2) in each new key area; and markers show the occurrence of sequences which will be discussed later in this paper.

            How does mapping help the pianist learn and perform the piece more securely and musically? Identifying subject appearances and episodes, and recognizing how the key area of each section of the piece relates to the key area of the section before and after will surely allow for a more comprehensive and secure performance. Even at the most basic level, merely recognizing the relationship between the opening scale passage (seen in Figure 2 below) and the Subject helps the performer orient him/herself in the proper key, and being aware of the progression of keys will help keep the performer on the right track.

But let’s look more closely at this scale passage. Bach’s varying use of it (indicated by the pink bubbles in the map above in Figure 1), counterpointed only ever with itself, is indicative of the tonal significance of the passage it introduces. Bach inserts these scales as tonal pillars in an otherwise extremely chromatic piece of music. Each of the first two statements is in a single voice, one measure long, and introduces a completely expected key area: first i, (Figure 2), and then v. The third occurrence follows the expansion of the consequent/Answer phrase discussed below and demonstrated in Figure 8, reestablishes tonic, and is four measures long. Three of these four measures use the scale in an out-of phase parallelism in both voices (Figure 3).  To lead to subject statements in the relative Major (G) and V of the relative Major (D), Bach again uses a single statement of the scale, although now both times in both voices.

It is the penultimate use of this scale passage that is of particular interest. It is the only one which Bach places in dovetailed fashion, it is significantly longer in duration than the others, and it is the only one that modulates. What was this:  ,

Figure 2: Opening scale “pillar”

and then this:

            Figure 3: Scale “pillar” in out-of-phase parallelism, measures 19-21

becomes this:

            Figure 4: Scale “pillars” in retransition, measures 57-62

            In addition to the length, variety, presentation, and harmonic interest of this set of scale passages is the fact that these appearances of the scale passage are the only ones that include any leaps. Each of these factors contributes to our recognizing the importance of this passage, lending it particular musical significance that should be brought out by the performer.

            Now let’s study a few things in greater detail. One of the difficulties for a musician when performing Bach is making a long musical line out of short, rhythmically discrete melodic motions. Figure 5 below shows the Subject statement as it first appears, from measure 2 to measure 7:

            Figure 5a: First Subject statement, meas. 2-7.

            It is very easy to become beguiled by each independent gesture, resulting in a performance that sounds as fragmentary as it looks:

            Figure 5b: First Subject statement, broken into discrete gestural/rhythmic groups

            One can make a musical connection across these individual groupings (separated by contour and/or by rests) by observing the descending, mostly-chromatic motion outlined from scale degree 6 (c-natural) through tonic to flat 7 (d natural) in measure 7.

            Figure 6: First Subject statement, chromatic motion

            This structure can be shown in a simple Schenker-type sketch, which also shows the descending chromatic tetrachord in the bass voice counter-subject:

            Figure 7: Sketch of Opening Descending Motion

            Awareness of this line should help the performer perform with direction and purpose from the first rhythmic gesture of the Subject to the last sixteenth in measure 7.

            One of the most interesting things revealed by this type of analysis is how Bach extends the consequent phrase in measure 13 by moving chromatically to C-natural at the point where, if he were going to imitate the motion of the Subject, he would have moved to B and been near the resolution of the phrase. Instead, the C-natural propels yet another descending, now diatonic, motion, from scale degree 5 to scale degree 1 and the reestablishment of tonic. Recognizing this helps the performer understand that the melodic motion begun with the answer in measure 8 extends all the way to measure 18 – five measures longer than the Subject statement/antecedent phrase. The appearance of the C-natural in measure 13 is not only not the end of the phrase, but is the beginning of an expansion, making what follows not an episode, but a continuation; this passage must be performed in such a way as to make this clear to the listener.

            Figure 8: Sketch of Answer Descending Motion and Expansion

(In the sketch in Figure 8 I have reversed the voices to make a clearer comparison with the sketch of the Subject above; the Answer to the first subject and its chromatic/expansion/diatonic descent from G5 all the way to E4, from measure 8 to measure 18, is, actually, in the lower voice.)

            I found that, once we had identified these extended motions, my student’s sense of musical line and phrasing evolved from micro-managing discrete musical fragments to an expressive, artistic performance that articulated a real sense of direction and line. I believe analysis and mapping also helps the student better comprehend how Bach’s musical lines work as a whole rather than getting distracted or muddled by individual figurations. The teacher should help the student hear these lines and connections by playing just these structural notes above the line (on a separate keyboard, or an octave or two higher) as the student performs the passage.  Finding and playing these structural lines (as shown in the top line in Figure 9) helps in many of Bach’s pieces, even in the simplest two-part inventions.

            Figure 9; structural realization of the first 8 measures of Bach’s Invention #1

            Realization of long-term melodic motions can also help make musical sense of episodic, sequential passages, especially those governed by compound lines, such as those found in the modulation from tonic to the relative major in measures 22-29 (the beginning of which is marked as Sequence A in the timeline in Figure 1), in the modulation from V of the relative major back to the dominant in measures 39-46 (marked as Sequence B in the timeline in Figure 1), and leading into the dovetailed modulating scale passages previously outlined in Figure 4 (marked as Sequence C in the timeline in Figure 1).

            Simply put, a compound line is one which, on the surface, appears to be one melodic voice, but which, with more careful study, is revealed to be several voices operating according to simple voice-leading rulesrules. An obvious example is the reduction of the sixteenth notes from Prelude #1 in C Major from the Well-Tempered Clavier, Book 1.  Figure 10a shows the first four measures of the piece, Figure 11 its reduction:

            Figure 10: Prelude #1 from WTC 1; measures 1-4

            Figure 11: Prelude #1 from WTC 1; measures 1-4, voice leading reduction

            Sorting out the compound lines and long-term melodic motions of, for example, Sequence A, is demonstrated in the following series of examples. Figure 12 shows the passage as written:

            Figure 12: Sequence A, measures 25-28

            Figure 13 shows the passage, divided into two voices (shown by direction of the stems), and showing the stepwise motion between measure 25 and measure 27, and between measure 26 and measure 28:

            Figure 13: Sequence A, two voices, two stages

            A performer may want to articulate these two different voice levels in performance by playing measures 1 and 3 of the 4-measure sequence with a different tone color and/or dynamic than the 2nd and 4th measures of the sequence.

            Further investigation of this passage also reveals a deeper voice leading structure. For example, Figure 14 show the alignment of the F# at the end of measure 25 and the E at the end of measure 27 with the notes of its upper “voice”:

            Figure 14: further voicing realizations

            And by now, you’ve probably realized that some of notes in the middle are actually part of yet another voice.  Rather than muddling up the waters even further, lets reduce this compound line into a three-voice voice-leading realization(3):

            Figure 15: voice leading realization

            You now see that Bach is still writing descending, mostly-chromatic lines(4), which extend across all four of the measures.

            We could also, or rather, reduce the sequence to its fundamental harmonic progression – a descending second sequence, manifested through a series of descending-by-fifths dominant-7ths, which Bach uses to modulate to the key of the relative major(5). This is shown in Figure 16.

            Figure 16: Descending 5ths progression, Sequence A.

            What seemed a jumble of disjunct melodic motions and random chromaticism reveals itself to be a simple, ordered descending melodic line outlining a descending- fifths harmonic progression.  Recognizing this can only help the performer to produce a phrase with both melodic and harmonic purpose and direction.

            Even more simply, one can merely track the melodic relationships between the two hands in Sequence B shown in Figure 17. 

            Figure 17: Sequence B, meas. 40-45.

            Another pairing of contrasting tone colors, this time with the 1st and 2nd statements contrasting in sound with the 3rd and 4th, may help bring these connections out to the listener.

            I have found that these types of analysis – mapping of form and key area; identification of subject statements and the use of subject fragments in episodic passages; and the tracking of long term melodic motions across connected, shorter melodic ideas – applies in almost any of Bach’s compositions. I have also found that this kind of awareness helps the student learn the piece more accurately, memorize it more securely, and perform it with more coherence and musical effectiveness. Finally, I think that this type of analysis becomes more and more important as we guide students through pieces of higher musical complexity and/or chromaticism. Bach’s highly chromatic music is structured the way highly turbulent water moves between pillars of a bridge. The pillars here are represented both by the scalar passages which establish our new tonal center almost as anchors, and by highly chromatic passages filling out tonal, discrete tetrachords. Understanding these pillars, and recognizing the tonal tetrachords, are crucial to being able to keep our place, both in terms of memory, and musically.

These types of analysis do not necessarily help to make some of the performance practice decisions mentioned at the start of this paper: to pedal or not, to use graduated dynamics or not, the use of subtle rubato to emphasize important melodic or harmonic moments, etc. While important and necessary considerations, these are, in fact, questions of a different sort, and perhaps require a paper all their own.  Analysis, however, provides much useful information in terms of short- and long-term melodic structures and voicing. If we understand the harmonic basis of the work and the way the subject statements, key areas, and sequences function structurally, discrete, intricate gestures and chromaticism become less of a “problem” both in terms of accurate note-learning and in our ability to memorize securely. If we know where we are within the context of the phrase, and within the context of the piece as a whole, we are better able to generate musical direction and shape, and communicate the logic of the piece better to the listener – the goal of every performer, and every performance.  


(1) A “I” in a bubble under a “III” in a larger bubble indicates the tonic of the III as relates to the original key; that is, a G Major triad in a section of music “in” the key of G.

(2)Some might argue that this scale passage is, in fact, the beginning of the subject that first appears in the upper voice. As this scale passage is only ever counterpointed with itself, though, I am identifying it as a pillar, almost a bookend, before the subject statement that begins in the upper voice in measure 2 and before ALL such subject statements throughout the piece.

(3)A Schenkerian scholar would probably realize this as a 4- or 5-voice line, with a more detailed sketch showing neighbor tone motions and accounting for every pitch in the melody. I am merely trying to present the general idea of the ongoing descending motions, and providing what is perhaps as much information/detail as appropriate for high-schoolers or undergraduates studying this piece.

(4)Another area that warrants attention and analysis can be the searching out and identifying Bach’s use of ideas presented initially as “kernels” – the head of the subject, for example, or a chromatically-filed-in tetrachord – and then developed as the basis for episodes or a modulating bass line. The macrocosm from the microcosm, if you will.

(5)Sequence C behaves in quite a similar matter, but in this case moving us into the retransition passage discussed earlier around Figure 4

September 28, 2014

I have been working with several students in the past few weeks on trying to increase the speed and fluency of their scales, which requires some improvement in the speed and flexibility of, believe it or not, their thumbs. I thought it might be helpful to put a series of videos up for consultation.

In the first clip, I’m demonstrating how a relaxed and collapsible thumb actually makes fingers crossing “over” the thumb essentially a horizontal motion. And the more efficient a move, the faster and more fluent.

This next clip shows the motion I’ve been working with the students on. There are two important things to remember as we move away from finger 1  (ascending in the right hand, descending in the left):  1) as soon as finger 2 plays, the thumb cross quickly beneath the fingers; and 2) as soon as the thumb plays, the rest of the fingers move quickly to the next set of keys. As we move towards the thumb (that is, descending in the right hand, ascending in the left), it is important that as soon as the thumb plays, fingers 2-3 or fingers 2-3-4 (depending on where they are in the scale) cross quickly across the thumb and rest on the 2 or 3 notes in the next group, and as soon as finger 4 or 3 plays, the thumb should “shoot” out to rest on its next note.

The last clip shows the relative stability of the forearm during the playing of arpeggios, as well as the loose, flexible thumb crosses, and the suppleness of the wrist. Hope these help.

March 31, 2014

Being "Good" is Great; Working Hard is Better

She calls it "Grit."

Speaking of "Grit":

Yuja Wang playing Prokofiev's Tarantella Op. 11

Am betting she was born naturally talented. Am also betting she has worked pretty darn hard.

March 27, 2014

Pamela Frank, on how long should someone practice:

Pam Frank on practicing

To paraphrase the best part: Focus on quality over quantity…one hour of productive, HONEST (emphasis mine) practice is worth 8 hours of undisciplined practice. Practice only what you don't do well, which is really hard on your ego, but after a couple of weeks you'll really see a difference and then you'll feel better. If you can't improve something in an hour or two than you're not focusing on the right things. . . Practice less and think more.

January 20, 2014

Bruce Berr writes what is called an "ad lib" article every month for American Music Teacher magazine. A few months ago he submitted a graphic that he uses, showing his students how short ideas (maybe even only a few beats long) join together into what I call phrase parts (2 bars? 4?) which join together into phrases; phrases into phrase periods, periods into sections, etc. 

It looks like this:

Copyright 2013 Music Teachers National Association. Reprinted from American Music Teacher, Volume 62, No. 6, June/July 2013, with permission of Music Teachers National Association.

It is easiest to either play at the smallest level (the red bubbles on Bruce's graph correspond to my red bubbles below, the green to the green, etc.), attending to the nuance of individual gestures or motives; or at the largest (the orange, or even above that level), where we have decided on and maybe even achieved a particular dynamic level or even a mood or character, but fail to listen to how all of the nuanced gestures shape into phrases, etc. 

As musicians, we must "play," and therefore attend to, all of the "bubbles" all of the time. Listen, follow the cursor, and see if you see what I mean.

November 22, 2013

As I was cleaning up/out my various desks and piles, I ran across this article I had clipped from a magazine many many months ago. EVERY MUSICIAN AND PERFORMER should read it. 

The author writes "in praise of flubs," and I agree: it's not about "perfection," but about spontaneity, and expression, and being human, which means that sometimes there will be mistakes.

Let's take the pressure off of ourselves, our students, our peers. Recordings are great, but they generate an unrealistic expectation for live performance, and not even always in a good way. I read once about the days and days and days Jeremy Denk spent in the studio recording an one of the notoriously difficult Ives Sonatas -- a testimony to hard work, and discipline, and an effort to produce the best possible recording of a titanic work. But even he didn't know what the recording was going to sound like until the recording engineer "finished with it" and sent it to him.

Is that a "performance" of the piece? Or is it, as I think, something else?

Room in our world for both, but lets not mistake one for the other. 

August 21, 2013

I have a couple of spaces open for my Piano Pedagogy/Music Moves for Piano Workshop that I'm offering this fall. Six, 2-hour sessions, Friday afternoons September and October. $300. Please register by September 1. Just use the contact form to email me and I'll tell you what to do.

Materials needed: 
Eric Bluestine's The Way Children Learn Music,
Marilyn Lowe's Music Moves for Piano Teacher's Guide for the Preparatory Book, Rhythm and Tonal Patterns CD,  Rhythm and Tonal Patterns from the CD book, and one level of Music Moves for Piano: Preparatory, Level 1, or Level 2.  
All available through

June 2, 2013

I often tell students, when they have made the same mistake two times in a row, that they "can't make that mistake again" or it will become a habit.

I follow "Morgan Freeman" on twitter, who/which I realized recently may or may not actually be Morgan Freeman, but whoever "he" is posts many good and inspirational quotes, so I'm just going with it.

A paraphrase from one of his yesterday: You don't make the same mistake twice. The second time it's a choice. Choose differently.

May 4, 2013

In recognition of the centennial of the premiere of Stravinsky's Rite of Spring, Stephen Malinowski and Jay Bacal have created an animated graphical representation of the music, shown in real time with a performance. You can see it here:

I think this is a wonderful visual representation -- where the motivic layers, sequences, and repetitions and Stravinsky's ingenious use of texture are beautifully portrayed graphically. 

It also demonstrates the ingenious-ness of musical notation -- it really does look exactly like it sounds.

April 23, 2013

The April 8 issue of the New Yorker contains n excellent article by Jeremy Denk, subtitled "A Life in Piano Lessons." 

From the last paragraph: . . .Leland [an early teacher] had been right to remind me that there was no end to the details one could strive for, but Sebök [his last teacher, at Indiana] was also right--the desire for perfection could be a deadly weakness. Living comfortably in that paradox, without even knowing it, is part of being a musician. There's a labyrinth of voices inside your head, a counterpoint of self-awareness and the remembered sayings of your guides and mentors, who don't always agree. Sometimes you wish you could go back and ask your teachers again to guide you; but up there onstage, exactly where they always wanted you to be, you must simply find your way. They have given all the help they can; the only person who can solve the labyrinth of yourself is you.  

You can read the whole article here

April 19, 2013

Bobby McFerrin: Beatboxing, the amazing-ness of the human voice, and the musical nature of language

updated 9/7/2018