The Science Behind the Story
A Sound Basis for Misunderstanding (with Sound)
(To cut directly to the chase and listen to the music Roger created with his drilled bassoon in the story, click HERE.)
Words and 'Music'
Some time ago, I found that I'd spent all my free time for a number of
months programming (in C++) a snazzy music synthesizer. Afterward, naturally
enough, I wanted to do things with it. One of the first things I did,
was to write another program that would 'translate' part of the fruit
fly genome to a musical score (it seemed like a good idea at the time).
Then I fed the score into my synth program and, untouched by human hands,
music came out. I was astounded by it. I wish I could say I composed it
myself (I wonder who owns the copyright). In any case, I e-mailed the
.wav file of the music to Stan Schmidt. He too thought it sounded like
music. Of course, I had to write a story based on it (The
Fruitcake Genome) and Stan bought it. When the story came
out, the music was put on the Analog site in an earlier 'Science Behind
the Story' article.
You can find the explanation how the translating was done HERE.
The story is HERE.
And can find the fruit fly 'music' HERE.
Or you can go to the Analog site and
click on the first 'Science Behind the Story' article.
The fruit fly music on the Analog site was popular. But due to Boing Boing (a popular blog), it was too popular, causing the Analog website (along with the Asimov site and a few others) to crash from overload.
A Sound Basis for Misunderstanding was spawned
by another music idea (a question actually), this one not as sexy as genome
translation. But just in case this gets Boing-Boinged as well, I've put
it (optionally) on my own site which, I hope, is more immune to bandwidth
saturation problems.
The question, basically, is: can a musical composition containing only
tones between the notes 'a' and 'b' sound, well, musical. Now, on a piano,
there is only one pitch, a-sharp (a#), between 'a' and 'b'. But could
there be more? We're now in the realm of microtonal music.
The A B Cs (and D E F Gs as well)
First, a little music theory. Here's a section of a piano keyboard.
The white keys are 'natural' notes, meaning not a sharp or a flat note.
The black keys are sharps (or equivalently, flats. Note, for example that
c-sharp is the same tone as d-flat).
The natural notes on the keyboard are a, b, c, d, e, f, g, and then it
starts all over again, an octave higher, a, b, c, d, e, f, g, etc. Notice
that there's a sharp note between every natural note EXCEPT in two cases:
b and c, e and f.
If we have a musical note, 'a' for instance, then to get the 'a' an octave
higher, we double the frequency of the first 'a'. So, for example, the
'a' just below middle c has a frequency of 220 Hertz. The 'a of the next
higher octave is therefore 440 Hertz.
So there are twelve pitches in an octave (usually one starts from 'c',
but we'll we start from 'a'): a, a#, b, c, c#, d, d#, e, f, f#, g, g#.
Each pitch is (by definition) one semi-tone higher then the previous one.
So the pitch separation between, for example, the natural notes 'a' and
'b' is two semi-tones. And the separation between b and c (or e and f)
is one semi-tone.
Since to go from one octave to the next, we double the frequency and there
are 12 semi-tones in an octave, then to go from a semi-tone to the next
higher semi-tone, we multiply the first frequency by the twelfth root
of two, or 1.05946. This is for a 'tempered' scale (The piano uses a tempered
scale). There are other scales, for instance the Pythagorean scale (which
string players often unconsciously use because it sounds better) where
going from one semi-tone to the next is slightly off from the 1.05946
multiplier. The Pythagorean and Tempered scales are pretty close and it
takes a trained ear to tell them apart.
Cents and Sensibility
Musical acousticians break the semi-tones into smaller divisions called
(rather unimaginatively) cents. There are 100 cents to a semi-tone. So
an octave contains 1200 semitones.
Following the above example with semi-tones, to go in frequency from a
particular pitch to another one cent higher, you just multiply the frequency
of the first pitch by the twelve-hundredth root of two, or 1.00057779
roughly.
A good ear can distinguish tones that are three cents apart. So, for example,
a frequency of 500Hz and 501Hz are different by about a tad over three
cents. A good ear (with a human attached) can distinguish these pitches
from one another.
Click HERE to hear alternations between 500 and 501
Hz sounds.
Now, the question is: Can we use a separation between musical sounds
of less than one hundred cents, and still have something that might be
called music.
Let's experiment.
All of our experiments will be played on a synthetic bassoon (with vibrato
suppressed).
HERE is a common tune, Twinkle, twinkle
little star with the normal 100 cents between sounds .
HERE it is with 50 cents between sounds.
And HERE with 25 cents between sounds.
And finally HERE it is with 12.5 cents between sounds.
Are any of the above microtonal examples music? I can't tell anymore.
To avoid the bias of using a familiar melody, let's try something a little less familiar--The Martian National Anthem, Mars of our Fathers.
