Music Theory

This is the beginning of an open source project to create an introduction to music theory book.

=Introduction=

Music are sounds you can remember in your mind.

Musicians craft sounds in order to trigger some feelings and/or thoughts in the listener.

With that definition of music, noise is not music and music is not noise, and it's a listener-based property of a sound signal: As in signal treatment, 'noise' means a random sound, and 'random' means 'unpredictable by the observer'. It's 'random', as the result of flipping of a coin is 'random' to an observer lacking proper measurements of the movement of the coin (prior to showing if it landed heads or tails), but not to one that has the whole measurements information.

So, if the listener is not accustomed to some sound, it will certainly be noise to him/her, even though it can be music (not noise) for a different listener. The listener won't be able to remember noise, because it is unpredictable for him/her, and it won't be music.

With that definition, too, you can make music while you sleep: Since it doesn't need any actual vibration of eardrums, as long as it is a rememberable sound to you (you can simply imagine it), it will be music. There is an awful lot of evidence that musicians crafted music while they were asleep (ex : riff from 'Satisfaction' by The Rolling Stones )

=History Of Music=

Some lifeforms started making sounds banging stuff, and decided consciously to make it sound in some way more than other. The rest just builds up on that.

The Grand Staff
=Basics Of Music Notation=

A 'note' means a fundamental frequency of a certain sound. (Fourier theory basics is a must for truly understanding this statement).

The custom in the 'Western world' popular music is to use sounds which notes belong to the Equal temperament tuning system. Apart from that, the frequency of a note called 'A3' is defined to be 440Hz (this note is called '69' in MIDI notation).

The rest of the notes are given as follows, 't' being the semitone difference from that A5 to the note we want (a semitone is the difference between two adjacent notes - in MIDI notation, it's the difference between note numbers):

$$f=440Hz*2^(t/12)$$

The names of the notes, going up in frequency from A one semitone at a time, go like

A, A#, B, C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C, ...

We add a number at the right whic is called the 'octave' number (when you go up in frequency 12 semitones from A(n), you get another A which frequency is the double of A(n), and it will be called A(n+1) - it's just a naming convension, don't sweat it - ). The names of the notes are that ones ( D, D#, E, F, F#, ... ) for obsolete reasons for this tuning (the # -sharp- notes had different frequencies and sounded 'bad' in older temperament systems).

Staff
\relative c' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn s1 }

The fundamental latticework of music notation, upon which symbols are placed. The five stave lines and four intervening spaces correspond to pitches of the diatonic scale - which pitch is meant by a given line or space is defined by the clef. With treble clef, the bottom staff line is assigned to E above middle C (E4 in note-octave notation); the space above it is F4, and so on. The grand staff combines bass and treble staffs into one system joined by a brace. It is used for keyboard and harp music. The lines on a basic five-line staff are designated a number from one to five, the bottom line being the first one and the top line being the fifth. The spaces between the lines are, in the same fashion, numbered from one to four. In music education, for the Treble Clef, the mnemonic "Every Good Boy Does Fine" (or "Every Good Boy Deserves Fudge") is used to remember the value of each line from bottom to top. The interstitial spaces are often remembered as spelling the word "face" (notes F-A-C-E)

Bars
\relative c { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f s1 \mark "↓" s } A Bar Line is used to separate measures. Bar lines are extended to connect the upper and lower staffs of a grand staff.

Clefs
A clef is a musical symbol used to indicate the pitch of written notes. Placed on one of the lines at the beginning of the staff, it indicates the name and pitch of the notes on that line. This line serves as a reference point by which the names of the notes on any other line or space of the staff may be determined.

\relative c' { \override Staff.TimeSignature #'stencil = ##f \cadenzaOn c4 d e f g a b c } \addlyrics { C4 D E F G A B C }

When the G-clef is placed on the second line of the staff, it is called the treble clef. This is the most common clef used today, and the only G-clef still in use. For this reason, the terms G-clef and treble clef are often seen as synonymous. It was formerly also known as the violin clef. The treble clef was historically used to mark a treble, or pre-pubescent, voice part.

\relative c { \clef bass \override Staff.TimeSignature #'stencil = ##f \cadenzaOn c4 d e f g a b c } \addlyrics { C4 D E F G A B C }

When the F-clef is placed on the fourth line, it is called the bass clef. This is the only F-clef used today, so that the terms "F-clef" and "bass clef" are often regarded as synonymous.

Time Signature
\relative c' { \override Score.Clef #'stencil = ##f \override Staff.TimeSignature #'style = #' \cadenzaOn s1 }

Time signatures define the meter of the music. Music is "marked off" in uniform sections called bars or measures, and time signatures establish the number of beats in each. This is not necessarily intended to indicate which beats are emphasized, however. A time signature that conveys information about the way the piece actually sounds is thus chosen. Time signatures tend to suggest, but only suggest, prevailing groupings of beats or pulses.

Rhythm
\relative c' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn c'\breve r c1 r c2 r c4 r c8 r c16 r c32 r c64 r } \addlyrics { \override Lyrics.LyricSpace #'minimum-distance = #2.0 Double-Whole Whole1 Half2 Quarter4 "8th"8 "16th"16 "32nd"32 "64th"64 }

Accidentals
\relative c'' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn ais4 bes cisis deses }

Enharmonic Equivalents
\relative c'' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn cis4 des }

Key Signature
\relative c'' { \key ces \major \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f s1 }

\relative c'' { \key cis \major \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f s1 }

Intervals
\relative c' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn c1 cis d dis e f fis g gis a ais b c } \addlyrics { \override Lyrics.LyricSpace #'minimum-distance = #2.0 Root1 minor Major minor Major Perfect Tritone Perfect minor Major minor Major Octave } \addlyrics { I1 II II III III IV - V VI VI VII VII "8" }

=Chordal Theory=

Triads
\relative c' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn 1     }

Major
\relative c' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn 1 }

Minor
\relative c' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn 1 }

Diminished
\relative c' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn 1 }

Augmented
\relative c' { \override Staff.TimeSignature #'stencil = ##f \override Score.Clef #'stencil = ##f \cadenzaOn 1 }