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Vi Hart, a mathemusician (cool eh!) at the Khan Academy posted an excellent video explaining 12 Tone music. She first explains the rules thus:

  1. You have to use all twelve chromatic pitches in some order and
  2. You go through them one-by-one.
  3. You can add some creativity by choosing the note length, what octave it's in, add rests, and
  4. You can repeat the current note or you can
  5. Switch back and forth between adjacent notes

8 minutes and 54 seconds into the video she composes a twelve-tone version of Twinkle Twinkle Little Star. It is remarkably tuneful (and funny!) but I was left wondering if the tunfulness came from the left hand harmonization which may have implied a series of keys. Is that the case? If it is then how is she doing that?

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(N.B. Thanks for adding a serial tag Andrew and adding it to the question.) –  dumbledad Jul 3 '13 at 6:17
I didn't know she was a musician also, this is awesome. –  Matthew Read Jul 3 '13 at 19:27

2 Answers 2

up vote 8 down vote accepted

As she explains later in the video, she's being extremely contrary to the basic ideas of serialism by implying tonality in the first place. The point of 12-tone serialism as it was designed was to treat each pitch equally so as to not create tonal function by emphasizing one pitch over another.

Even if you are operating within these rules, it's possible to imply tonality just by making use of the tone row in a clever way--if you try hard enough, ANY ordering of pitches can imply tonality.

And to the tonal ear, it's almost harder to construct music that -isn't- tonal than music that is, simply because what you improvise is going to be more in line with the music you frequently listen to.

In Vi Hart's case with this example, she's leaving the left hand unconstrained by the 12-tone principles, so it is VERY easy for her to give the tone row a tonal context. The simple fact that she's using triads, let alone tonal chord progressions, is enough to contextualize the serial melody line in tonality.

Essentially, all she's doing to deal with notes that are "out of key" is to find the closest related key where they do fit, and then execute that key change (or secondary tonicization, technically) compositionally in the left hand.

So, the short answer is YES, the left hand contributes to the tonality of the serial tone row, but it's not the only way to do so--it's simply the most basic and obvious way to do so within the constraints she was using.

Far more impressive, in my opinion, is the later example of "Mary Had a Little Lamb", in a 12-tone arrangement for vocal quartet. This time, ALL of her voices are constrained by the 12-tone rules, but she still managed to compose tonal music! It's certainly not "common practice" tonality, and it might still be a little jarring if you're not used to listening to extended tonality and new music, but it is very much tonal! (And in fact, I've had it stuck in my head for the past few days.)

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Can you tell what the progression of "closest related key where they do fit" is? It would be interesting to look at the chord/triad progression to see how she has fitted seemingly unrelated notes into a chord that still feels related to 'home' –  dumbledad Jul 3 '13 at 6:14
The chords are extremely tonal. You don't have to stray very far to hit all 12 semitones: C - F - C - Fmin - C - F#dim7 - G - Gmin - G7. It's not common practice, obviously (perhaps what I'd call "mode mixture") and the weirdest notes, F# and D#, are handled easily with that F#dim7 -- essentially a viio7/V since she resolves it to G. –  NReilingh Jul 3 '13 at 8:04
Oh, and the way she's constructed the last note is meant to be more of a musical joke than to fit in the same tonal context, so I didn't include it above. If you wanted, you could think of it as resolving down by half step to the tonic (C) that begins the next phrase. –  NReilingh Jul 3 '13 at 8:09

Her twinkle little star is entirely explained using typical, basic diatonic reharmonization techniques, like dominant chords and substitutes. And yes, it's all tonal in the key of Cmajor.

Start out on Cmaj. Move to Fmaj. Back to Cmaj. (I IV cadence)

Then move to Fm. A common trick because the #v (g#) has a dominant role, so you often see Fm, Dm7b5, Abmaj, Caug as part of a cadence in C, because each of those chords contain the g# and resolve back to (reinforce tonality of) Cmajor.

Back to Cmajor. Then Cdim (Idim). Again a common device in jazz and standards. This resolves to Gmaj (because the bottom two tones move down chromatically).

From Gmajor, she goes to Gm/Gm7. Three possible explanations, equally valid, seen many, many times in popular tunes:

(a) A typical key modulation, where the Cmajor chord becomes the dominant for the key of F, and hence the use of the IIm (Gm) as part of a IIm-V cadence in the new key.

(b) Bb major chord that is part of a modulation to the key of Ab (Ab has a dominant function in the key of C)

(c) key modulation from Cmajor down a whole step to Bbmajor. This sets the stage to come back chromatically to Cmajor as follows: Bbmajor > Bdim > Cmajor. (Bdim is a dominant chord in the key of C)

After Gm (Bbmaj), a dominant (G7 or Bdim).

And then back to C .... ? but wait, at this point, she does a fakeout. Instead of back to C, she chooses a random tone (C#) making it the only "atonal" tone in the song. And she does not harmonize the tone either, therefore truly making it random (and meaningless.)

Apart from this last tone, the rest of the song are cadences and substitutions that reinforce tonality in C major. Very typical chords you see over and over in many songs. Dating back decades if not hundreds of years. Just thumb through the Real Book.

If you harmonize the last tone as bII7alt (Db7alt) then you've got another typical dominant chord substitution in the key of C major.

Yes, she's using 12-tones, but it's all standard diatonic type of stuff. If you want a simple way to hear it, just play the block chords in the LH:

I IV I IV I IVm I Idim Idim V Vm V Vm V7


now if you eliminate the LH chords, and just play the melody, the tonality is still present, because the sequence of tones continues to establish the C major chord. The departures from the key (d#, f#, g#), are followed immediately by returns to harmonically neutral tones in the key (d, e, g) and the sequence in which they are played helps to "arpeggiate" the standard IV V I chord progression we are accustomed to hearing in C major.

Therefore, to answer the thread question, the supporting chords reinforce, but are not necessary for the tonality. Her melody by itself does it (the sequence of melody tones allows you to infer the underlying chord.)

It's not the "12-tone" music you normally associate with people like Shoenberg. And in my opinion rather misleading to imply that it's something "novel."

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Good answer – analyzing the chords like that is helpful – but I disagree that Hart was misleading. She was quite plainly subverting 12-tone music to make it less novel and more familiar. –  Bradd Szonye May 14 at 2:13

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