Wasatch Front

for Woodwind Quintet

About this song

This is a piece based on a chord progression taken from the Partch Tonality Diamond. Here is a picture of the diamond, with the note names I use:

This is the same as the Harry Partch diamond from Genesis of a Music, except my base note is C and Partch used G.

The green numbers are the degree of a major scale moving from the lower left to the upper right. The blue numbers indicate a minor scale moving from lower right to upper left. For example, C major is C D+ E F++ G A++ C, or 8:8 9:8 10:8 11:8 12:8 14:8 16:8. This can be reduced to 8:9:10:11:12:14:16.It is the 8th through 16th overtones (except 13 & 15) of C. A C minor scale can be derived by taking C D-- E-- F G A+ C, or 12:12 12:11 12:10 12:9 12:8 12:7 12:6, which can be reduced to 1/(12:11:10:9:8:7:6). These are the "undertones" of G. The inversions are what make the diamond work.

Wasatch Front is created from a chord progression derived from the diamond. The chords are:

C minor
D# minor
G minor
A# major
D++ major
F minor
Ab major
C minor

To hear this in its basic form, click here. Using LilyPond, I created a notated version of this chord progression:

Unfortunately, LilyPond does not really support microtonal accidentals. I had to convert the ones I use, namely b, --, -, natural, +,++, and # into the ones LilyPond makes available: flatflat with a line, flat, backwards flat, natural, half sharp, sharp, and double sharp. I really need to spend some more time on this, to understand how to notate more accurately. LilyPond produces such visually attractive notation, it is such a shame that it is wrong.

One of the most interesting parts of the progression is the microtonal intervals moving from one chord to another. For example, consider the third staff in the above notation fragment. Eb moves to D double sharp. In my notation, those notes are E-- to D#, or in ratios, 6:5 to 7:6. To calculate this motion, the arithmetic takes the first ratio, inverts it, and multiplies it by the second ratio: 5/6 * 7/6 = 35/36, or 35:36. This is equivalent to about 48 cents, or half a semitone. It would be like moving from the Eb on the keyboard to a note between the Eb and D. The second staff has a G (3:2) moving to a F## (7:5). This is a movement of 14:15, or 119 cents, just over a semitone. The top staff moves from C (1:1) to A# (or A++) (7:8). This is a drop of 7:8.or 231 cents. Again, this is not an interval available in the 12 tone scale. So with the first chord movement we have three different notes that are non-twelve in nature. But as I listen to them, they sound very natural and not at all unusual.

Csound, the tool I use to create the music, is very flexible about pitches. One technique I like to use is a glissando from one pitch to another using a microtonal interval. Listen to the flute in the following fragment, which moves by 36:35 in a glissando. I use the function table shown at left (F367) to move the pitch while it is played:

Csound generates this function with the following statement:

f367 0 256 -7 1 64 1 128 0.9722222 64 0.9722222 ; g66 35:36

Then during the performance, I tell the orchestra to apply this function to a note, and the result is a glissando down. The same method can be used for an upward glissando. Consider the following Csound statement:


f361 0 256 -7 1 64 1 128 1.0285714 64 1.0285714 ; g60 36:35

This produces an upward glissando as in the graph at left (F361):

This raises a pitch by 36:35 during the note performance. Listen to the flute in the following fragment. I combine the pitch movement with envelopes that make the instrument get either louder or software to simulate movement towards or away from the listener. The result sounds like the doppler shift experienced when a sound source moves towards or away from the listener. Try it with headphones to get a more effective result. I use two envelopes for each note, one for the left and another for the right channel. The result is a sound that starts right inside the listener's head and moves away towards the right or left.

I first heard this effect in a piece by John Chowning in 1972, in his piece called.Turenas I (described here). I was very impressed by the effect, but never found a reason to use it, until I played around with some of these microtonal intervals, where the shift was so small that it almost became inaudible. The introduction of envelopes that simulate movement made the pitch sound movements more understandable. Maybe they weren't pitch changes, but rather location changes.

In the following fragement, the clarinet moves from an F# (7:5), which is the 6th degree of the Ab major scale, down by a 20:21 to an F at 4:3, which is the fourth degree of the C minor scale. The French Horn moves from a D- (11:10), the 4th degree of the Ab major scale, down by a 120:121 (14 cents) to the D--, the second degree of the C minor scale. The bassoon moves from the Ab (8:5) up by a 5:4 (386 cents) to the 1:1 at C. With all three movements at the same time, things get a bit complicated. The result is a resolution of the Ab major to C minor. The fragment can be heard here. Listen the bassonist; sounds like he is leaning his bell into the microphone. Its all simulated, but it sounds real.

There are four envelopes I use, two for a sound moving away, left and right channels:

These are created with the following two Csound statements:

f292 0 1025 6 0 1 0.50 1 1.00 447 0.60 447 0.20 32 0.21 32 0.22 32 0.11 32 0.00 ; e6 channel one moving away slowly 
f291 0 1025 6 0 1 0.50 1 1.00 100 0.53 100 0.05 205 0.06 205 0.06 206 0.03 206 0.00 ; e7 channel two moving away faster

And two for a sound moving towards the listener, left and right channels:

The following Csound creates functions F264 and F365:

f265 0 1025 6 0 32 0.20 32 0.40 32 0.30 32 0.20 432 0.60 432 1.00 16 0.50 16 0.00 ; e33 channel one moving in gradually 
f264 0 1025 6 0 206 0.03 206 0.06 205 0.06 205 0.05 85 0.53 85 1.00 16 0.50 16 0.00 ; e34 channel 2 moving in at the end

The use of different envelopes for right and left channels is a simple solution to the complex problem of having a sound appear to move relative to the listener. With these four functions I can move the sound in from the left or right, or out towards the right or left, by varying the functions for the right and left channels. I don't have the mathematical chops to ensure that the movement is at the same perceived speed as a doppler shift of these ratios would dictate, but it gives a good first approximation, and has the added advantage of being musically significant.

Trills are another feature that Csound makes possible. The following function table trills up by the ratio of 12:11, which is the distance between the first and second degrees of the minor scale I use: C at 1:1 to D-- at 12:11.

This is generated by the following Csound statement:

f368 0 256 -7 1 16 1 0 1.09091 16 1.09091 0 1 16 1 0 1.09091 16 1.09091 
 0 1 16 1 0 1.09091 16 1.09091 0 1 16 1 0 1.09091 16 1.09091 
 0 1 16 1 0 1.09091 16 1.09091 0 1 16 1 0 1.09091 16 1.09091 
 0 1 16 1 0 1.09091 16 1.09091 0 1 16 1 0 1.09091 16 1.09091
 ; g67 trill 12:11 min1 to 2 or maj4 to 5

Additional trills include an 12:11 and 8:7 in the flute, with a 10:9 and a 12:11 in the oboe, and a 7:6 in the bassoon. This result can be heard in fragment here.

The final technique that Csound allows is the creation of a chain of glissandi from notes in one chord to the next to the next. The sound at the beginning of Wasatch Front is made by having each instrument move from one note of a chord to another note of the next in the chord progression. For example, at the intro the oboe moves from the 3rd degree of D++ major, which is G+ (10:7), to the 1st degree of F minor which is F (4:3) a drop of 14:15. It then continues without pause to the 5th degree of Ab major, on E-- (6:5), a drop of 9:10, and stays there since that note is the 3rd degree of the C minor scale.

f392 0 1024 -7 1.428571 224 1.428571 32 1.333333 224 1.333333 32 1.2 224 1.2 32 1.2 256 1.2 ; g91

This is shown in graph F392:

For each note in this opening chord, and the final one at the end of the piece, there is a function table that traces its movement from note to note in the chord progression. For each note there is a long envelope that allows me to accent certain notes over others to highlight sections of the changes.

The first few dozen measures can be seen notated using LilyPond in a PDF file.

The Csound macro preprocessor source code is here. Graphs of all the function tables are here.

The overall sound is of a typical woodwind quintet in the style of Darius Milhad or Hindemith. I used to play in a woodwind quintet in college, and we always enjoyed the music of those composers. I can't say that this is on that level, but it does have a nice sonority to it. It is dedicated to the members of our quintet: Dan, Dominic, Roger, Maria, and me on clarinet. To hear the whole thing, go to Soundclick.com and select Wasatch Front.

Completed 6/1/04