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.
(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).
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.
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:
And the Official Winner of New Music Drama's ULTIMATE PULITZER BAD TAKE is……………….
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.
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!
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.
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?”