Aspects of Music

VARIOUS ASPECTS OF MUSIC:  Here are just a few interesting things I found about music:

  a)  I was amazed at how ignorant I was of the mathematics of beautiful music.  While I had had an engineering training, I was relatively clueless about the easy-to-understand (and familiar) mathematics behind what makes music "beautiful" and why.  For instance, what--mathematically--makes a chord sound pleasing?  One very important element is the degree and richness of shared harmonic frequencies associated with chords, note progressions and even timbre.  There is a mathematical elegance and beauty in this.  (Of course, this is still only part of the story, as there are other aspects such as rhythm, percussion, mode/scale, style, etc.)  If you are interested in this subject, see here0 and here1 and here2 and here3 and here4 and here5 and here6, etc.

   b)  The pentatonic and diatonic scale were used long before Pythagorus, but he sought to understand it (as  did later the father of Galileo) and introduced the "circle of 5ths" tuning.  Somehow, it seems appropriate that Pythagorus dabbled in this, he being the same man who formulated his famous Pythagorean theorem that's indirectly related to a sine wave formulation.  The sine wave is ubiquitous in nature--it is seen in geometry and in nearly every branch of physics.  Even string theory evokes the idea of an oscillating wave, or a vibrating string.  A special case of the hauntingly mysterious Euler formula  e^(ix) = cos(x)+ i sin(x) , when looking at the special case where x = pi, reduces to e^(i pi) +1 = 0 (also called the Euler identity) and thus unites the constants 0, 1, i, e and pi using one addition, one multiplication and one exponent.  This is not only an example of mathematical simplicity and beauty, but Euler's formula is actually a useful tool in trigonometry as well as waveform calculations.  Perhaps the complex acoustic waveform harmonics in music are fascinating and beautiful to us because they are reminiscent of the structure of nature itself, including the stuff we are made of.  (I wax philosophical here ;-)

    c)  The 5-note major and minor pentatonic scale is interesting, in that it's impossible to create a really bad sounding chord with these notes--perfect for wind chimes.  Rock music, jazz, blues as well as traditional music from around the world is often limited to the pentatonic scale.  Archaeological finds indicate that music based on both the pentatonic and the 7-note diatonic scales has been around since the beginning of civilization.  The 12-note chromatic scale represented a logical further step that made it easy to play in both the major and minor modes, as well as in different keys.

   d)  Speaking of ancient music, Suzanne Haik-Vantoura claims to have deciphered heretofore mysterious markings in the original old testament texts and claims they are musical notation.  Her work is still controversial, but interesting.  Some of the resulting music is rather good.

   e)  The bible (especially the Old Testament) is full of references to music and musical instruments.  David surely must have invented and played a variety of musical instruments.  (Amos 6:5, 1 Chr 23:5, Neh 12:36, 2 Chr 29:26-27, 2 Chr 7:6)

   f)  So why a 5-note pentatonic scale, 7-note diatonic scale and 12 note chromatic scale?  Why not a 10 note, or 27 note scale?  (Other scale sizes do exist in a few isolated parts of the world.)   Again, there are good mathematical arguments for preferring this choice, which appeal to our desire for a maximum number of nice-sounding chord possibilities while at the same time minimizing the number of bad-sounding (or dissonant) chord combinations.

   g)  The equal tempered chromatic scale is often presented as a "compromise" between pleasing sounding chords and key-hopping utility.  I am beginning to doubt this, though.  I believe there may be a mathematical argument supporting the equal tempered chromatic scale as "sounding the best", when we look at all the possible "good" chord harmonics, even discounting the need for key-hopping.  I might be wrong, and this subject is too involved to discuss here...

   h)  Music can help to relieve pain, relax the body, speed stroke recovery, boost immunity, improve memory performance, concentration and ability to learn, improve athletic performance, improve productivity, reduce negative emotions, improve one's mood, and reduce fatigue.  It is even used in such diverse endeavors as therapy for autistic children and stimulation of plant growth.

   i)  Music can evoke emotion, and can amplify emotions we are already feeling.  This is not overlooked by the advertising industry.  Here's a simulation of dynamic emotional and neural responses to some music.

   j)  Music, like language, seems particularly unique to humans and has been engaged in and innovated by humans since the beginning of civilization.

   k)  So can computers make music?  Well, sort of.  Not exactly Beethoven, though.

   l)  Do violins sound better with age?  There is a lack of good evidence for this.  It might be a myth.

   m)  Even music is capable of being politicized or "culturized."  Here's is an example that's admittedly a bit patronizing.  On the other hand, here's an example of an attempt to rationalize "bad" music.  Theoretically, we can all learn to like hip hop and acid rock, right?  Perhaps our brain adapts to prefer a particular type of music after long listening?  Or does it require and/or create a certain mindset before compatibility is achieved?

   n)  Accomplished musicians of many years experience have certain parts of their brain areas enlarged.  This sort of begs a more general question:  Do our thoughts, experiences and actions affect our physical brain just as much as our brain affects our thoughts and actions?  The old nature/nurture question...