Resources For Composers: Violin Pedagogy

I’m writing a string quartet and have been reviewing violin technique. I though it would be helpful to compile a list of the classics of violin pedagogy: method books, treatises, exercises and so forth. Here’s the list, which I will continue to update. I’ll link to IMSLP files when they’re available. Please let me know if I’ve missed anything you consider essential.

Auer, Leopold (1845-1930)

Bang, Maia (1877-1940)

Casorti, August (1830-1867)

Flesch, Carl (1873-1944)

Galamian, Ivan (1903-1981)

  • Principles of Violin Playing and Teaching (1962)
  • Contemporary Violin Technique (1962)

Hřímalý, Jan (1844-1915)

Kreutzer, Rodolphe (1766-1831)

Paganini, Niccolò (1782-1840)

Schradieck, Henry (1846-1918)

Ševčík, Otakar (1852-1934)

Spohr, Louis (1784-1859)

A busy week in jazz, and writing!

I had a busy week in NYC seeing great jazz and then writing about it in a new blog that Nora Maynard and I are launching called cultured nyc.

First off, I caught two nights of the legendary Barry Harris at the Village Vanguard. Then, I saw the amazing hard-bop sextet One For All at Dizzy’s, in honor of Art Blakey’s centenary. Finally, I saw Dave Stryker with his organ trio at the Bar Next Door. All in all, a great week!

Altered Scale Minor 3rd Transpositions

A guitarist on the forum of Dave Stryker’s class at Artistworks recently asked an interesting question that really piqued my interest. The question is, can you transpose the altered scale in minor thirds, the same way you can transpose the diminished scale? I’ve been thinking for a while about how the diminished, altered, and whole-tone scales are related, so let’s treat this as a prelude to that topic.

The altered scale differs from the diminished scale in two ways. First, the altered scale is a seven-note scale and the diminished is an eight-note scale, so the altered will always have one note missing compared to the diminished. Second, the altered scale has one note different, it has a b13 (or #5), where the diminished scale has a natural 13. So, to sum up, one note missing, one note different. You can see this in the first figure.

Comparison of the altered scale and the diminished scale
Figure 1. Diminished Scale vs. Altered Scale

(Note: in the figure above, the Arabic numbers in the second row are called pitch classes. If you are not familiar with them, for now, you can assume 0=C, 1=Db, 2=D, and so on. It is much easier to think about transpositions, inversions, and symmetry when you consider pitches this way.)

Now lets see what happens as we start transposing at minor 3rds. For the altered scale, as we already know, every time we transpose a minor 3rd, we end up with the same collection of pitch classes, so essentially the same chord and the same extensions. Check out what happens with the altered scale. For each transposition, we have one note missing (the last column) and one note different (highlighted in yellow).

Comparison of the altered scale and the diminished scale, showing transpositions at the minor third.
Figure 2. Diminished Scale vs. Altered Scale m3 Transpositions.

Of all the transpositions of the altered scale, the one at the tritone makes the most sense; it’s easy to see it as a dominant 13 #11 chord. The other two minor 3rd transpositions are maybe a little trickier, since one lacks the major 3 and the other lacks the seventh. But I would wager that one could make convincing use of all of the transpositions, and maybe sound a little bit outside.

Here’s the same figure with pitch notation rather than pitch-class notation.

Comparison of the altered scale and the diminished scale, showing transpositions at the minor third.
Figure 2. Diminished Scale vs. Altered Scale m3 Transpositions (with traditional pitch notation).

One more thing I’ll point out, and this is admittedly getting into theory-geek territory. Since the diminished scale is an eight-note scale, it has four notes missing with respect to the twelve-note chromatic scale. In the language pitch-class set theory, those four notes together form the complement of the diminished scale; diminished plus complement equals chromatic. You will notice that the highlighted different notes in the altered scale, taken together, for the complement of the diminished scale. I’m not sure if that is a useful observation in jazz, but if Anton Webern played jazz, he would probably have figured out how to use it.


Earlier this month, the Pulitzer prizes were announced. As stated by the Pulizter organization, the music prize is awarded

For distinguished musical composition by an American that has had its first performance or recording in the United States during the year, Fifteen thousand dollars ($15,000).

The music prize was first awarded in 1943 to William Schuman for Secular Cantata No. 2 A Free Song, which had been premiered by the Boston Symphony Orchestra the previous year. The later recipients were, for the most part, well-known composers of contemporary concert music, or what some people term contemporary classical music. The winners were all men until 1983, when Ellen Taffe Zwilich won for Symphony No. I (Three Movements for Orchestra). In 1999, Melinda Wagner won for Concerto for Flute, Strings and Percussion. Since 2000, women have won more frequently, including Jennifer Hidgon (2010), Caroline Shaw (2013), Julia Wolfe (2016), and Du Yun (2017). In terms of genre, the prize had always gone to contemporary concert music, with the exceptions of 1997 when Wynton Marsalis won, and 2007, when Ornette Coleman won.

On April 16, 2018, it was announced that Kendrick Lamar had won the prize for DAMN.,

a virtuosic song collection unified by its vernacular authenticity and rhythmic dynamism that offers affecting vignettes capturing the complexity of modern African-American life.

This was the first time the prize had been awarded to a piece in the genre of Hip-Hop. Depending on whether your definition of popular music includes jazz or not, this was the first award to a piece of pop music. Several people, including straight up Internet trolls and probably some who should better, were upset enough by this award to take to social media to voice their displeasure. The Twitter account @NewMusicDrama collected the worst of these, conducted a poll, and announced the winner:

Seeing the invitation to conduct a dramatic reading, while enjoying a leisurely Saturday afternoon, I leapt at the opportunity. I now present the finished piece, NEUROLIGICALLY DIVERGENT

Early Beethoven

I’m only 21 pieces in so far, so I will need to pick up the pace to make it through all 194 pieces with opus number this year. Right now, I’m listening to the Violin Sonata No. 1 in D Major, Op. 12 number 1, and just came across my first “favorite moment” in these early pieces. It’s a cadential figure that happens in the first movement, at the end of the second theme.

Excerpt from Beethoven's Violin Sonata No. 1 in D Major, Op. 12 number 1.
Beethoven Violin Sonata No. 1 in D Major, Op. 12 number 1

From what I can recall, I first heard this piece in a performance in von Kuster Hall at UWO, around 1987 or 1988. This moment is striking, and you can hear why it would appeal to someone who has played rock guitar. Even better than a power chord!

Was Brahms Quoting Beethoven?

I was listening to the WQXR broadcast of the Vienna Philharmonic at Carnegie Hall last night. It was an all Brahms program: The Academic Festival Overture, The Haydn Variations, and the first symphony. I grabbed my trusty old Dover score and followed along for the performance of the symphony. I was not paying too close attention, but even so, something leaped out at me at the start of the second movement. The opening theme begins with a striking similarity to the first theme of Beethoven’s sixth symphony. I grabbed my Beethoven score, and sure enough, the first seven notes of both themes are the same. The Brahms is in E Major, the Beethoven is in F major, so the Brahms is naturally written a semitone lower. Both themes are given to the first violins. The rhythms and tempo are different.

Comparing the opening of Brahms' Symphony No. 1, Second Movement with the opening of Beethoven's Symphony No. 6, First Movement.
Brahms Symphony No. 1 vs Beethoven Symphony #6.

I’m wondering if this was a purposeful quote, or just a coincidence. Also makes me wonder if there are any other Easter eggs in “Beethoven’s 10th?”

Beethoven Listening Project

Nothing like a new year to start a new project! One of mine for 2018 is to listen to all of the works of Ludwig van Beethoven, from start to finish. How would you like to join me? We’re just getting started with the Piano Trio in Eb Major, Op. 1 No. 1.


Just watched Moonlight, and, happily, it’s great. Need to watch it again on short order. Don’t know if composer Nicholas Britell truly had Vaughan Williams’ Fantasia on a Theme by Thomas Tallis in his ear as he wrote the score, but I had to listen to that piece right away on finishing the film. It fit right in.

Drop-2 Chord Fun Facts

FF#1: Outer Limits

We’re going to talk a bit about seventh chord and four-part harmony here, so to keep things consistent, I’m going to refer to SATB for voicing, and keep pitch and string sets ordered from higher pitch to lower pitch.

Drop-2 seventh chords are formed by starting with a close position seventh chord and dropping the second note from the top (in SATB, the A) one octave. In the original close position chord, S and A are adjacent chord members. Now, however, S and B are adjacent chord members. So, we end up with SB pairs of {R,7}, {3,R}, {5,3}, {7,5}. In other words, between the outer voices of a drop-2 seventh chord, you always have some type of 10th or 9th.

Interesting. So, if that is going on between the outer voices, SB, what is going on between the inner voices, AT?

FF#2: Dyad Pairs

Now that we know what is always going on between the outer voices, what else can we say about how these chords are constructed? In the original close position voicing, adjacent voices, e.g., {T,B} are always adjacent chord memebers, e.g., {3,R}. But in drop-2, because of that octave displacement, adjacent voices are adjacent chord members + 1, e.g., {T,B} is now {5,R}. That means that {S,A} must be {3,7}. Well, with the knowledge of this FF and also FF#1 up above, these chords are now very easy to spell. In all four inversions, they are:
{R,5} {3,7}
{3,7} {5,R}
{5,R} {7,3}
{7,3} {R,5}

In drop-2 chords, root and fifth always go together, third and seventh always go together. This is worth memorizing.

FF#3: A Chain of Double Appogiaturas

Occasionally in jazz and popular music, we see harmonic motion by descending diatonic 5th, e.g., ii-V-I, or vi-ii-V-I, or I-IV-vii-iii-vi-ii-V-I. In four-part harmony with seventh chords, between adjacent chords we can say the following: two notes are common, the other two notes will descend a diatonic second. In fact, you can think of each of these chord pairs as double 4-3, 2-1 appogiaturas on the resolving chord. Think of the ii-V progression in Satin Doll for a good example of this.

To see how this plays out with drop-2 chords, let’s do the following. We’re going to play I-IV-vii-iii-vi-ii-V-I in F major, on the {2,3,4,5} string set, starting with the {3,7} {5,R} dyad pair. In the first progression, the common tones are between the outer voices SB, and the appogiatura happens on the inner voices AT. Next progression, the inner voices AT have the common tones and the outer voices SB have the appogiatura. From there, the cycle repeats.

FF#4: Those Dyads Again!

Let’s think about what just happened. We started with a I chord with the R member in the B voice. When we moved to the IV chord, the B voice became 5. The we moved to vii and B became R again. Wait, {R,5}, where have we seen this before?

What if we play the same sequence, I-IV-vii-iii-vi-ii-V-I, this time in Db major, same string set, but this time starting with {5,R} {7,3}. So we start with the I chord with 3 in the B voice, and next chord, the B voice becomes 7 of the IV chord. Wow, really? so now the B notes will alternate on the {3,7} dyad.

So, it looks like in a progression between any drop-2 seventh chords descending by diatonic 5th on the same string set, we have the following transformation R->5, 5->R, 7->3, 3->7. If you want to keep in simple, just remember that in the bass, {R,5} will alternate and {3,7} will alternate, depending on where you start.

FF Bonus Round:

Take any drop-2 seventh chord on the string set {1,2,3,4}. Drop the S on 1 two octaves, so that it becomes the B on 6, on the resulting string set {2,3,4,6}. What have we here?