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The subminor scale is my name for a minor scale built from overtones, but with the root of the scale starting on the 3:2 instead of the 1:1. For example, consider an overtone series on F. The 3:2 above F is C. If the scale is based on a mode starting on C, as shown in the graph above, you have the subminor scale.

As with all overtone series, a cluster of notes above a certain pitch will always generate a difference tone. But even though the scale designed to favor the root at C, the difference tone will always be F. I will have to take that into consideration when I add low notes. They will have to resolve that F to C, and choose notes carefully to minimize the difference tone prominence.

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Listen to the difference tones move around in this set of changes.

• B 16/9 major
• D 12/11 sub minor
• G 3/2 sub minor
• C 1/1 minor
• F 4/3 major
• B 16/9 major

In this case, major is an otonality based 4:5:6 triad. Sub minor is otonality based also, but on the 6:7:9 overtones. Think of a G minor using G Bbb D. Minor is utonality minor 6/6:5:4. When I slide from one chord to another, the difference tones go in strange directions. They will probably disappear as I add more instruments to the mix. Today is sounds like a nice barbershop harmony tune that could have been taken from a hymnal.

Does this look right? It is supposed to show the steps of 72 Equal Divisions of the Octave in the Saggital font. I seem to remember I had the wrong accidentals a while back. Click on the image to see full size.

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This version includes several mirror functions. Where earlier sections used predominantly the utonality triad 5/(4:5:6), which is a standard just minor chord in A, there are now complementary sections that use 10/(7:9:11), higher up the utonality diamond.

The overtone series can be thought of as overtones 4:5:6 making up a major chord, and higher up overtones 7:9:11 extending that out. The undertone series is the opposite of overtone series. Other mirror functions have the choice of notes to play proceed sequentially, then backwards.

The piece is scored for sine waves. This is the first time I haven’t used orchestral samples in a piece. No more jokes about fake but accurate. The intonation is 53 tone equal divisions of the octave approximating just.

Source Code

Csound Score
Macro Preprocessor Source Code
Pascal Source code

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The lower reaches of the Hoh have dense vegetation on both sides of the river. This section gets upwards of 240 inches of rain a year. Every storm that hits the Northwest passes over this region, dropping moisture by the bucketful. Cool, damp, quiet, and relentlessly moving towards the ocean to start the cycle again.

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45 seconds into the work, we have some changes on the way.

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Tobiah wrote on the Csound mailing list a challenge to write a score for a very simple Csound orchestra file.

I have an idea for a brief informal contest. Given a simple,
one-oscillator orchestra, provide a score which produces the
most beautiful piece.

I offer an orchestra that I crafted for the purpose
of this event. One can make use of very limited
envelope an pan controls. Obviously, the craft will
be in the score generation program (although one is
welcome to hand edit her entry!).

If there is interest, I suggest a seven day window
for this challenge. Only the scores should be
submitted at first. We can look at source code
later. For large scores, a URL might be best. I can host
scores if you send them to me in an archive format.

Thanks,

Toby

sr = 44100
ksmps = 1
nchnls = 2

giSineFunc ftgen 1, 0, 65536, 10, 1

instr 1

;***** INIT SECTION *****
iDur init p3
iVol init p4
iStartPitch init p5
iEndPitch init p6

iAttack init p7
iDecay init iDur – iAttack

iPanStart init p8
iPanEnd init p9

;***** SYNTH SECTION *****
kEnv linseg 0, iAttack, iVol, iDecay, 0
kPitch expseg iStartPitch, iDur, iEndPitch
aSig oscili kEnv, kPitch, giSineFunc

kPan linseg iPanStart, iDur, iPanEnd

aLeft = aSig * kPan
aRight = aSig * (1 – kPan)

outs aLeft, aRight

endin

Never one to shirk a contest, I made some modifications to my Csound preprocessor to write the fields that his orchestra expects, and the results sounded kind of like all my other music made with my Csound preprocessor. The input to the preprocessor is here, and the Csound score is here. There are lots of debugging messages in the score as comments. When I’ve had more time to work on it, I’ll remove them. I had to make one modification to the sine wave generator function. I replaced giSineFunc ftgen 1, 0, 65536, 10, 1 with an equivalent ftable entry f1 0 65536 10 1 .

My version of Csound is 4.19, which is many levels back from the current version. It doesn’t support giSineFunc. But since I wrote the preprocessor in Turbo Pascal, which is still running today with a last touched date of May 2, 1989, I can’t complain. Software currency is for losers.

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There was an earlier Slow Dance that took two otonality triads and slid them in opposite directions, so I thought it would be useful to do the same with two utonality triads. The original took a chord of 8:10:12 and slid it up to 9:11:14, while sliding a 9:11:14 triad down to 8:10:12. This one takes the 12:(12,10,8) up to 12:(11,9,14) and visa versa. There is a point in the middle of the slide when a minor chord can be heard, midway between the two. The utonality triads are much less settled than the otonality ones.

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It sometimes takes the guys a few tries before they get it right. And no, there really isn’t a middle fork of the Hoh River in Washington. There’s a south fork, but that doesn’t sound right for a song title.

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This piece rapidly changes pace from fast to slow, alternative the finger piano, marmiba, and slide vibraphone parts from sixteenth notes to eighth notes, with several 3 against 4 against 6 against 8 rhythms. The tempo also shifts, very gradually, from one tempo to another, by about 30% up and down. It ends about 60% slower than it started.

The pitch also shifts. It starts in the key of A minor, but drops by one 53-TET step every 30-60 seconds. The shifts are difficult to perceive. It’s as if you suddenly notice that you are not where you thought you were. Over the course of the ten minutes the tonality drops by 22 steps, to a fourth below A, ending at E.

The tonality is the utonality to the 15 limit. In ratios, they are 24/(16,20,24,14,15,18).

The vibraphone, marimba, and finger pianos play repetitive rhythmic patterns,
while the french horn, clarinet, and oboe play a descending melody, answered by a inverse melody later in the piece.

The overall theme is of descending a river, with fast and slow sections, some complex, some serene, but always moving downhill.