[Playing notes on a piano] One... Two... Three... Four... Five... Six... Seven... Eight... Nine... Ten... Eleven... Twelve...

12 different pitches, and then back to where we began. Incredible! Fantastic! The mystical number 12. There are 12 hours in the A.M. and 12 hours in the P.M. The new day begins at 12 midnight. There are 12 months in a year. Both the Western and Chinese Zodiac have 12 signs. Further, the Chinese use a 12-year cycle for reckoning time. There are 12 eggs in a dozen. 12 dozen in a gross, and 12 ounces in a troy pound. There were 12 tribes in ancient Israel. Jesus had 12 apostles. There are 12 days of Christmas. My friends, Eastern Orthodoxy observes 12 great feasts. In Shia Islam there are 12 Imams. In Ancient Greece the principle gods of the Pantheon were the 12 Olympians. There are 12 ribs in the human body. 12 labors of Hercules, and, in the United States, 12 people on a jury.

The five new pitches were added as the black keys on the keyboard, and there you have it, neat as a pin. A closed, 12-pitch Universe generated through a circle of fifths!

Except... Oh I just hate having to be the killjoy here, but there is one little problem. Isn't there always one little problem? You see, if we move upwards, through this circle of perfect fifths of three to two sonic ratios, when we get to the 13th pitch, we get to a pitch that's actually about an eigth of a tone sharper than the one on which we began. Oh! So close!

Well, the promise of an octave divided into 12 different pitches a semitone apart was too good so the solution to this little tuning problem was to temper or shrink all or some of these fifths so that the 13th pitch would indeed be the same as the first.

The fact is that there are few more 'popular' subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity.

Before MIDI, a musical note was a bottomless idea that transcended absolute definition. It was a way for a musician to think, or a way to teach and document music. It was a mental tool distinguishable from the music itself. Different people could make transcriptions of the same musical recording, for instance, and come up with slightly different scores.

After MIDI, a musical note was no longer just an idea, but a rigid, mandatory structure you couldn’t avoid in the aspects of life that had gone digital. The process of lock-in is like a wave gradually washing over the rulebook of life, culling the ambiguities of flexible thoughts as more and more thought structures are solidified into effectively permanent reality.

One of the more startling findings about early enrichment is the effect of music. You can hardly pick up a newspaper without seeing some kind of reference to how Mozart makes people smarter. The governor of Georgia recently proposed spending $105,000 of state money to provide every newborn baby with a compact disc of classical music, citing its positive effects on brain development and spatial and mathematical skills. What is it about classical music that is so good for mental function, and are children particularly susceptible to its magic?

Almost all the research on this subject has been performed by one group of neuroscientists from the University of California at Irvine. They were struck by the observation that people who are musically talented are often also talented at skills involving spatial-temporal integration, such as mathematics, chess, and engineering. Perhaps, they argued, music directly activates the same patterns of spatial-temporal activity in the brain areas involved in these forms of reasoning. Of course, music itself has no spatial component, but recall that pitch is converted into a spatial map by the inner ear. Our brains, then, experience music as simultaneous patterns in both space and time, perhaps not unlike the kind of mental patterning required to plot a chess strategy, a geometry proof, or a building's construction. According to this view, certain types of music should be better than others at promoting spatial-temporal reasoning, which is the hypothesis these researchers set out to test.

They began with a bunch of willing college students. One group of undergraduates spent ten minutes listening to a Mozart piano sonata, a second group listened to a relaxation tape, and a third group sat in silence for the ten minutes. Immediately afterward, all three groups were tested using a series of spatial reasoning tasks, such as figuring out the pattern in a series of figures, or what a piece of paper would look like after going through a sequence of mental folding and cutting. The results were quite striking; the Mozart group scored some nine points higher in spatial IQ than the relaxation and silence groups. In a follow-up study, the researchers added the repetitive, minimalist music of Philip Glass to the comparison. Again, only the group who listened to Mozart showed significant improvement on the folding-and-cutting task, and none of the groups differed on a test of short-term memory. So it does look as though certain fairly complex types of music do specifically enhance spatial-temporal reasoning, perhaps by exercising optimal patterns of neural activity in the right hemisphere.