Matt Van  Brink, composer, pianist, accordionist

December 25, 2015

Scrap Happy

Each Scrap Happy is a collection of 100 old gems, new favorites, oddball ephemera, and the occasional earworm. Collected every December from my ears to yours.

Scrap Happy 2016 ==> LINK
Scrap Happy 2015 ==> LINK
Scrap Happy 2014 No Scrap Happy
Scrap Happy 2013 ==> LINK
Scrap Happy 2012 ==> LINK
Scrap Happy 2011 ==> LINK
Scrap Happy 2010 ==> LINK
Scrap Happy 2009 ==> LINK
Scrap Happy 2008 ==> LINK

December 25, 2014

Articles

"Teaching Improvisation"
Improv Insights, December 2014
A field report from Concordia Conservatory's Summer Composition & Songwriting Intensive

"Writing Over"
NewMusicBox, May 2012
Reporting on The Intimacy Of Creativity workshops

"Striking a Balance"
"Writing to Stereotype"
"That Eight-Minute Threshold"

NewMusicBox, May 2008
Three reports for NewMusicBox from VocalEssence's "Essentially Choral" workshops.

"Zappaesque"
Relix, April/May 2006
In collaboration with Jesse Jarnow, a short analysis of "Inca Roads."

January 3, 2007

A Sonnet about the Pythagorean Comma

In 1998 I experienced a geometric conversion. We students in Douglas Hofstadter's cognitive science course '"Circles and Triangles: Diamonds of Geometry (Cat:DoG)" at Indiana University were encouraged to explain complex concepts in simple ways, as well as simple concepts in complex ways. One of Hofstadter's favorite devices was to write a geometric proof in the form of a sonnet. Whittle the concept down to 14 rhymed lines, with a punchline at the end, and you've got a slam-dunk in the elegance department. Geometric proofs became objets d'art.

Later, as a graduate student at Boston University, in wrapping my brain around the Pythagorean comma, for Jeremy Yudkin's History of Music Theory course, I resorted to the same literary device.

Why Six Tones Make an Octave and a Comma
And Why it is the Same Comma as between Three Tones and a Fifth
A Sonnet after Boethius

A fourth makes two tones and a semitone,
Aristoxenus told us this much.
Three tones and semitone renders in stone A fifth. . .
Our own logic tells us as such.

A tone to splice, and our being precise,
Two semitones make not quite a full one.
A semitone twice and a comma suffice
To fill it, but we’ve only just begun!

Now as we look ’twixt a fourth and a fifth,
Three tones make semitone, comma and fourth.
Two fourths and a tone make an octave ’s width,
And six tones are double of three, of courthe!

Algebra decrees how six tones exceed
Of an octave. Indeed it ’s QED’d.

In the spirit of elegance, calcuations with large orders of magnitude are unnecessary. Armed with the knowledge that two semitones fall short of a whole tone, the following proof unfolds easily, and hopefully, obviously as well:

1 octave =? 6 tones
(1 fourth) + (1 fifth) =? 6 tones
(2 tones + 1 semitone) + (3 tones + 1 semitone) =? 6 tones
5 tones + 2 semitones =? 6 tones
2 semitones 1 tone

And why to two semitones fall short of a whole tone? Well, we'll need a bit of calculation just to prove this chunk of information. Using the elegant Pythagorean ratios, a fourth is 4/3 and a full tone is 9/8. The difference between two tones and a fourth is a diatonic semitone, which is a very inelegant number, 256/243

1 fourth = 2 tones + 1 semitone
4/3 = 9/8 * 9/8 * 1 semitone
4/3 = 81/64 * 1 semitone
256/243 = 1 semitone

From here it is obvious that two of these monstrosities are not going to add up to the lovely 9/8, and in fact they come up short:

2 semitones + 1 comma = 1 tone
256/243 * 1 comma = 9/8
1 comma = 2187/2048

Now that we know the comma exists, no more heavy calculations are needed, and we can get back to poetry. Eat your heart out, Quadrivium.