Music Theory (Scoggin) today is a set of rules that were reverse-engineered from existing music. It is detailed and complex, and is very useful for musicians. It is an established field of music and is outside the scope of this book. Here, we address the question of why the brain follows these musical rules, specifically for the piano. There are studies on related subjects; see Patel, Aniruddh D.,.
The brain automatically processes all sensory inputs. It commits them to memory
for later use and processing, uses them to figure out if anything dangerous or interesting is about to happen, where sound is coming from, etc.; innumerable actions so automatic that, for the vast majority of them, we are not even aware of what the brain is doing.
Recognition of music is the result of such automatic brain actions; but, what are they? The (76) Chromatic Scale is logarithmic("log") and the auditory system operates on a log frequency system so that both the cochlea, where the frequencies are detected, and the brain, where they are analyzed, have log structures. Unlike the eye, where the optical frequencies are calibrated on an absolute scale using quantum mechanical transitions (so that everybody sees the same colors), the auditory frequency scale is uncalibrated. Therefore, the only way for the brain to process auditory information is to calculate ratios between frequencies. On a log scale, ratios are easily recognized because ratios are distances on the log scale — that's the principle behind the slide rule. (On a log- linear plot, ratios are fixed distances.) That is why intervals are important in music and explains why the brain likes harmony — because the brain can recognize frequencies that are harmoniously related. Each harmony is a fixed type of sound and does not produce time dependent beats as do dissonant sounds.
The fact that harmonies are recognized by the brain indicates that the brain works with frequency ratios. The chromatic scale contains all the important harmonic intervals (fifths, fourths, etc.) and has the same log structure as the auditory system, allowing the brain to process music written using it; thus the chromatic scale is a functional replica of the cochlea. The piano is a replica of the cochlea which is copied into the brain and enables the brain to compute ratios of frequencies using logarithms as is done with slide rules. The piano is just a slide rule that enables the brain to compute ratios of frequencies that harmonize!
The infinite number of notes of the chromatic scale is particularly simple in log space because any note in that infinity can be reached by using only the twelve notes of the octave. Thus it is the simple and tractable nature of processing music in the brain
that distinguishes music written in the chromatic scale from other sources of sound.
By using a logarithmic scale and a system of recognizable harmonies, we have reduced an intractable set of the infinity of notes into an easily tractable twelve notes of the octave! However, it produces only a subset of music because music can be produced by banging a stick on a hollow log.
Harmonic music is a product of the attempt by the brain to keep track of frequencies by computing ratios of frequencies in logarithmic space. If the brain can not keep track of frequencies, it has no way of processing frequency information except by memorizing huge amounts of auditory inputs. We now have an explanation of why harmonic music is so special to the brain — it can memorize and process frequencies in music with a
minimum of effort by using log computations.
Thus our ability to enjoy music is inborn. The chromatic scale, although a purely human invention, turns out to be a functional replica of the log nature of the auditory system. This gives rise to the theory that the brain prefers the simplest inputs that it can handle, which can explain many properties of music that previously had no clear explanations and provides new insights into what music is:
(1) harmonies are ratios of frequencies that are easily recognized and computed in log space,
(2) repetitions of motifs are special, because of their simplicity, (3) the most popular melodies are also the simplest,
(4) repetitive rhythms simplify the memory process,
(5) music using the chromatic scale is an acquired taste, but is readily acquired because both the chromatic scale and the auditory systems are logarithmic,
(6) chord progressions are the simplest relationships between scales in log space; the progression creates tension because, with each progression, the brain must keep track of an additional tonic,
(7) returning to the starting tonic is satisfying because it frees the brain from having to remember the tonic changes,
(8) dissonances are unpleasant because the brain has no way of processing them, (9) music appreciation is partly inborn because it is part of the automatic brain processing of audio inputs,
etc.
This theory does not explain why we enjoy music. A possible explanation is that any auditory input is automatically processed by the brain as good or bad. Suppose that 90% is interpreted as bad and 10% as good; the composer simply chooses the good 10% to compose his music. Once the good ones are identified, it should be possible to find out why they are good. Of course there is nothing stopping composers from using the "bad" sound combinations and still write music, just as hot peppers and bitter melons are eaten by humans.
Everybody agrees that music is a language. The alphabet of musical language contains such components as the chromatic scale, loud, soft, fast, slow, legato, staccato, etc.. But these are not single letters as in the language alphabet, but are entire spaces of their own. Every space has its own set of symmetries, and that explains why symmetry transformations are important in music, and why Beethoven used group theory and its symmetry transformations, to compose [(67) Mozart's Formula, Beethoven and Group Theory]. Because the piano can reach the largest volume of this language space, it is the most dominating instrument in the musical universe.
A chord is a group of intervals with the same tonic; this makes the tonic a special frequency and explains why music follows chord progressions: chord progressions are the simplest ways with which the brain can keep track of frequencies, by remembering the tonics. When plotted on log-linear plots, the chromatic scale forms a straight line, and all harmonizing intervals appear at fixed distances from the tonic, making it easy for the brain to recognize intervals (harmonies) no matter where they appear on this straight line (relative pitch). This explains why anyone who appreciates music can easily learn relative pitch.
progression must return to the originating chord for the music to end; otherwise, the brain feels that something is incomplete: it has to remember both the starting and ending tonics, whereas if the music returns to the original chord, it has to remember only one tonic, or even none at all, depending on how it is keeping track of tonics.
Conclusion: a theory based on the logarithmic structure of the cochlea and brain, and automatic brain computations in log space using ratios, can explain many major characteristics of music, such as why harmonies are pleasant and why dissonances are not, and the chord progression rules.
As with learning to read, it is a good idea to learn as much theory (Scoggin, Nancy,,) as possible with each piece of music you learn. Teachers must pay special attention to theory lessons contained in every lesson piece because this is the best way to teach theory so that the lessons will be retained for life -- students are automatically reminded of the theory every time they play the piece.
Solfege is mainly for singers and composers. It consists of increasingly complex
series of exercises involving different scales, intervals, time signatures, rhythms,
accidentals, etc, for voice/music training. It also covers pitch recognition and dictation. It teaches universal music lessons, that are indispensable for advanced pianists, such as scale structures, learning absolute pitch [(17) Absolute Pitch, Relative Pitch], dictation, etc. Without solfege, budding pianists who feel the urge to compose will be handicapped, unable to figure out where to start, how to write it all down. There is no shortage of books and internet sites that can get you started, such as: http://www.vocalist.org.uk/ books_for_singers.html . Solfege books are available in stores or over the internet and is best started in a group class environment.