Western Music Theory ... A Mystery No More!

 

GREEK MUSIC HISTORY

[Music interlude playing a Tetrachord derived progression:  "The Chordinator presents music theory with roots in Ancient Greece arts and science."]

In the spectrum of vibrations that make up the natural world as we perceive it, sound has always been an essential element for communicating information, ideas, and emotions.  The artistic and scientific manifestation of sound being music,  Western rhythm and melody can be traced back to Ancient Greece, where Pythagoras became acquainted with the underlying quantitative relationships reflected in the sounds created by the vibration of a single stringed instrument.  The most far reaching discovery was the melodic proportion between one musical note and a second musical note a descending 4th interval away, which is the same as a second note an ascending 5th away.  

[Show ratios 4th= 4:3, 5th = 3:2, Octave = 2:1, then descending 4th and ascending 5th on piano, then Tetrachord disk]

The Ancient Greeks divided the descending 4th interval into various 4 note combinations called the tetrachord which was not a chord but a scale.  The 4th and 5th being the most significant intervals, the distance between them became known as a whole step.  The finalized melodic intervals within a tetrachord were called diatonic which consisted of a whole step, a whole step, and a half step.  When an additional whole step is used to join two tetrachords it resulted in a descending scale pattern that completed an octave.

[Show disk with 2 tetrachords and then overlay Phrygian mode over it]

The original ancient Ancient Greek modes differed in concept from the modern day modes somewhat in that they were static. But notice the full octave scale created by two tetrachords connected with a whole step is actually the Phrygian mode of today.

[Flip the disk over it over to show major scale in C]

Eventually this pattern of intervals was inverted to be ascending rather than descending and the scale became what we call today the Major Scale.  The series of 2 whole steps 1 half step, 3 whole steps and 1 half step,  That equates to 12 half steps.  The series of 12 half steps is called the Chromatic Scale.

[Show Chromatic disk]

THE MAJOR SCALE AND HARMONIZING THE MAJOR SCALE

The Major Scale is always the same pattern of 7 intervals superimposed over the 12 notes of the Chromatic scale.  Each degree of the Major Scale is represented by a number.  The 1 is the root.  The 2 is a whole step up.  The 3 is a whole step up.  The 4 is a half step up.  The 5 is a whole step up.  The 6 is a whole step up.  The 7 is a whole step up, and a half step up is the root, or octave.

[Music interlude: "The Chordinator presents all keys of the Major Scale which is the most fundamental scale in music theory.]

In exploring the 12 keys of the Major Scale, notice that each letter is only used once and that determines whether a note is flatted or sharped.  Also notice that by listing the Major Scales in ascending 4th order flats increase by one in each flat scale and sharps decrease by one in each sharp scale.  That succession of keys is the cycle of 4ths.  Similarly, by listing the Major Scales in ascending 5th order sharps increase by one in each sharp scale and flats decrease by one in each flat scale.  That succession of keys is the cycle of 5ths.     

[Music interlude "The Chordinator presents the Harmonized Major Scale."]

While philosophers of Ancient Greece helped provide a basis for melody with scales, clergy in the churches of the Roman Empire helped provide a basis for harmony with the advent of chords.  Chords are defined by formulas and are usually created by combining ascending diatonic 3rds, or every other note in a scale.  The main chord families that result are major 1-3-5, minor 1-b3-5, and dominant 7 1-3-5-b7.  Although there is no distinction verbally, Roman numerals are the written representation of chords in the same way Arabic numerals are the written representation of notes.  By stacking 4 diatonic 3rds starting on each degree of the Major Scale, a Harmonized Major Scale is created resulting in 7 chords.  No matter what the key, the Harmonized Major Scale chords are always the same series of Maj7 (I), min7 (ii), min7 (iii), Maj7 (IV), Dom7 (V), min7 (vi), min7(b5) (vii*) and  written using uppercase Roman numerals for chords with major 3rds and lowercase Roman numerals for chords with minor or flat 3rds.  To Harmonize C Major, the 1st degree of the scale results in 1-3-5-7, CEGB or CMaj7, the I chord.  The 2nd degree results in 1-b3-5-b7, DFAC or Dm7, the ii chord.  The 3rd degree results in 1-b3-5-b7, EGBD or Em7, the iii chord.  The 4th degree results in 1-3-5-7, FACE or FMaj7, the IV chord.  The 5th degree results in 1-3-5-b7, GBDF or G7, the V chord.  The 6th degree results in 1-b3-5-b7, ACEG or Am7, the vi chord.  The 7th degree results in 1-b3-b5-b7, BDFA or Bm7(b5), the vii* chord.  

MODES OF THE MAJOR SCALE

[Music interlude: "The Chordinator presents the modes of the Major Scale.]

Modes of the Major Scale are simply the diatonic scales that begin and end on each degree of the Major Scale.  The modes can be viewed as inversions of the Major Scale which take the notes of the underlying Major Scale but start on a different degree of the scale and make that note the new root.  Modes can also be viewed as distinct scales independent from the Major Scale from which they are derived.  The names of the modes are a tribute to the various regions in Ancient Greece.  Notice that each number is only used once in each scale,  The 1st degree of the Major Scale is Ionian 1 2 3 4 5 6 7, exactly the same as the Major Scale.  The 2nd degree is Dorian 1 2 b3 4 5 6 b7.  The 3rd degree is Phrygian 1 b2 b3 4 5 b6 b7.  The 4th degree is Lydian 1 2 3 #4 5 6 7.  The 5th degree is Mixolydian 1 2 3 4 5 6 b7.  The 6th degree is Aeolian 1 2 b3 4 5 b6 b7.  The 7th degree is Locrian 1 b2 b3 4 b5 b6 b7.  A basic approach to improvisation using modes as inversions of the Major Scale is to address each chord in the progression in the context of the harmonized major scale from which they are derived.  In the key of C, a ii-V7 progression is a Dm7 and a G7.  The relevant modes are D Dorian over the ii and G Mixolydian over the V7.  Notice both modes share the exact same notes as C Major, but the starting and stopping points are different. Notice also additional patterns of diatonic notes can be extracted such as pentatonics, arpeggios, triads, and intervals.  For example, a 4 note F Lydian arpeggio creates a Dmin9 sound over the Dm and a G13 sound over the G7.

[Music interlude "The Chordinator provides info that make it easy to map out notes and chords on fretboards and keyboards."]

[Music interlude "The Chordinator also helps find typos in published music instructional books."]