The Well-Tempered (and not-so-well-tempered) Clavier

Bach wrote The Well-Tempered Clavier as a showcase for a new tuning system that could play in all twelve major and all twelve minor keys. Up until that point, the various European tuning systems only worked for some keys, not all of them. If you were in or near the key of C, you were usually okay, but as you moved further out on the circle of fifths, things got ugly fast. So this new tuning system that actually sounded good in all the keys was an exciting development.

However… no one knows what tuning system Bach used. All we know is that it wasn’t twelve-tone equal temperament, the one we all use now. There were many systems in circulation at the time that people called “well temperament.” Was Bach using Werckmeister? Kirnberger? Kellner? Some idiosyncratic system of his own invention? No one knows. This video sums up the situation well:

Until this gets resolved, at least technology makes it easy to hear these different systems for yourself. I used Oddsound MTS-ESP to run some of the Well-Tempered Clavier preludes through various historical tuning systems. Here’s what I got:

Continue reading “The Well-Tempered (and not-so-well-tempered) Clavier”

Teaching statement

I am finishing my dissertation soon and am applying for full-time academic jobs. Here’s my teaching statement. It’s adapted from the first two chapters of Electronic Music School: a Contemporary Approach to Teaching Musical Creativity. Also see my research statement.

I have taught as an adjunct at New York University’s Steinhardt School, The New School’s Eugene Lang College, and Montclair State University’s Cali School of Music. At NYU, I have taught the Technology Practicum for Music Education for the past seven years. I designed this course and am its sole instructor. This past year, I also began co-teaching the Popular Music Practicum for Music Education, which I worked to overhaul extensively. This spring, I will be taking over an existing graduate course, Technology Trends in Music Education. At the New School, I have taught Fundamentals of Western Music, an existing course that I had broad latitude to remake. At Montclair State University, I teach Introduction to Music Technology, another existing course that I  modified and updated. I have also taught Electronic Music Composition and Cultural Significance of Rap and Rock, both of which I solely designed. Continue reading “Teaching statement”

Just intonation and key changes

Western people like two things in harmony: intervals derived from the natural overtone series, and the ability to play in multiple keys. Unfortunately, it’s not possible to do both of these things within the same tuning system. If you want to use just intonation intervals derived from harmonics, then they will not work in every key. So we as a civilization have decided to use a tuning system that enables you to play in lots of different keys, even though it means that all of the keys are slightly out of tune. Fortunately, the computer makes it easy to explore alternative tuning systems. I have been experimenting with this cool tuning plugin called MTS-ESP.

I have struggled my whole life to understand how tuning works, so I made a track to demonstrate to myself how just intonation sounds when you use it in all twelve keys.

What you are hearing in my track is a tuning system that is “perfect” in C major, but not so perfect in other keys, and very not perfect in a few of them. Let’s figure out why!

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The three diminished chords: blues, jazz and classical

Diminished seventh chords are strange creatures: a cliche for Dracula’s castle, but also a cornerstone of the blues. They are also difficult to understand. The good news is that in any given key, there are only three possible diminished seventh chords: the one whose root is the tonic of the key, the one whose root is a half step below the tonic, and the one whose root is a half step above the tonic. In the key of C, these are C°7, B°7, and C#°7 respectively. There are no other possible diminished seventh chords!

  • C°7 is made of the same notes as D#°7/Eb°7, F#°7/Gb°7, and A°7.
  • B°7 is made of the same notes as D°7, F°7, and G#°7/Ab°7.
  • C#°7 (or Db°7) is made of the same notes as E°7, G°7, and A#°7/Bb°7.

There are many arcane and unmemorable names for these three chords. I like to think of them as the blues diminished chord, the classical diminished chord, and the jazz diminished chord. Here they are on the chromatic circle against a C root.

You can see how simple and symmetrical these chords are: just stacks of minor thirds. But this simple structure hides a lot of harmonic intrigue. Let’s dig in! Continue reading “The three diminished chords: blues, jazz and classical”

The Kronos Quartet play Jimi Hendrix

I have mixed feelings about the Kronos Quartet arrangement of “Purple Haze” by Jimi Hendrix. On the one hand, it’s cool that they even attempted it. On the other hand, is the attempt successful?

It’s great that they’re taking advantage of the violin’s pitch continuum to do all the blue notes and guitaristic bends and slides and such. I’d love to hear more of that in string quartet writing. Continue reading “The Kronos Quartet play Jimi Hendrix”

Defining key centers with rhythm

Let’s say you have two chords, G7 and C. According to Western classical theory, these two chords establish that you are in the key of C. The G7 is tense and unresolved, and it makes you yearn for the calm stability of C. Music theory resources are full of language about how dominant seventh chords are always dissonant and always need to be resolved. For example…

  • Wikipedia: “Dominant seventh chords contain a strong dissonance, a tritone between the chord’s third and seventh.”
  • Andre Mount: “Whereas a triad may be consonant, a seventh chord is inherently dissonant.”
  • Jason Solomon: “The chord progression I-V-I is the essence of tonal harmony. The framing tonic chords serve as stable points of departure and return. The dominant destabilizes the tonic to set up its eventual return.”
  • Alfred Blatter: “Seventh chords by virtue of their more dissonant (unstable) nature create a strong harmonic drive toward a resolution. The strongest and most familiar of these is the dominant seventh chord, which almost compels the arrival of the implied tonic chord.”

Even jazz resources use this language.

  • The Jazz Piano Site: “The Dominant chord is an inherently dissonant chord because it has a tritone interval between its 3rd and 7th, and as such it wants to resolve towards the consonant Tonic chord.”
  • Dariusz Terefenko: “The dominant is an antithesis of the tonic in every conceivable way: it is highly unstable, represents chords on the move, accumulates harmonic tension, and does not rest until it reaches a local or structural tonic.”

Yeah, but the thing is, this is not true! Dominant seventh chords are dissonant only in particular stylistic contexts, namely, Western European folk and classical and the musics that descend from them. In blues, rock, jazz, and lots of pop music, dominant seventh chords can be tonic chords too, and they can sound perfectly resolved. The G7 and C chords might actually be defining the key of G, not C.

This is not just music theory arcana! If you want to play the blues on a C harmonica, you need to take an instrument that was designed to play G7 and C in the key of C major, and play it backwards so that you think of it as being G7 and C in the key of G blues. Continue reading “Defining key centers with rhythm”

Music Theory Songs

Ashanti Mills from my Patreon had a brilliant idea. He said, hey, you know how you combined interviews with Toni Blackman with hip-hop songs to explain hip-hop pedagogy? You should do that with music theory: have songs that explain their musical content to you. This is one of those ideas that seems obvious as soon as I hear it, but it took Ashanti suggesting it to make me realize that. So: here is my first batch!

The whole thing came together very quickly. In some cases, I took teaching materials I already developed in Noteflight, exported the MIDI, dropped it into Ableton, added beats, and went from there. In other cases, the idea existed in my head and just needed some a little trial and error to realize it.

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Chords and modal interchange

One of the most powerful music theory concepts you can learn is how to make chords from scales. If you learn a few scales, then you get a whole bunch of chords for free. The specifics of all the chord names can be complicated and daunting. But the concept of constructing them is very simple. Take a seven-note scale, like, for example, C major.

Start on any note. That’s your chord root. Go around the scale clockwise, skipping the next scale degree to land on the following one. That’s your third. Go around clockwise and skip the next scale degree to land on the following one. That’s your fifth. Do the same thing to find the seventh. (You can also keep going to get the ninth, the eleventh, and the thirteenth. Then you will have used all the notes in the scale.) Any seven note scale will produce seven different chords, and they will all sound good together in any order and any combination.

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Waiting For Benny

The Genius of the Electric Guitar is an aptly-named compilation of studio recordings that Charlie Christian made with Benny Goodman between 1939 and 1941. The album includes a couple of informal studio jams recorded while Goodman’s band was waiting for their leader to show up. Both jams have self-explanatory titles: “Blues in B” and “Waiting For Benny.” The latter one is where the real magic happens.

After a minute and a half of jamming in the key of A, Charlie Christian suddenly cues the band into a tune. Its key is ambiguous at first, but once the piano comes in, it quickly reveals itself to be F. I had always known this tune simply as “Waiting For Benny,” as do many other jazz fans. However, Benny Goodman later recorded it under the title “A Smo-o-o-oth One.” Apparently this recording was made at the same session as “Waiting For Benny”, though the documentation is unclear. Continue reading “Waiting For Benny”

The politics is in the drums: Producing and composing in the music classroom

This post was published in the Journal of Popular Music Education!

Pierre Schaeffer and DJ Premier

Introduction

Digital audio workstation software, recording equipment and MIDI controllers have become steadily less expensive and easier to learn over the past two decades. As a result, it has become possible for schools at all levels to offer “an art class for music” (Kuhn & Hein, 2021) in which students learn to write and produce original songs. However, music teachers in the United States usually find themselves unprepared to teach such a class. University music education programs focus on the performance and history of Western art music to the near exclusion of all else. When these programs address electronic music, it is usually in the context of “art” music. It is extremely rare for a preservice music teacher to learn to produce dance music or hip-hop.

As I write this, music technology courses are becoming more the norm than the exception in American university music programs, at least as electives, and are spreading rapidly throughout secondary schools as well. The coronavirus pandemic has driven a rapid adoption of technology-driven instruction out of necessity. The curriculum standards, subject matter and classroom practices of school music technology courses are still very much in flux. The music education field therefore has a unique opportunity to shape and define music technology as a subject before it becomes fully standardized. I will argue that it is not enough to teach preservice music teachers the skills needed to create electronic musics. Music educators must also engage with aesthetics and cultural contexts. It is particularly important that they critically examine the racialized divide between “art” and “popular” music.

Continue reading “The politics is in the drums: Producing and composing in the music classroom”