-music theory-

“the ‘first’ is what is otherwise called ‘rudiments’, currently taught as the elements of ‘notation’, of ‘key signatures’, of ‘time signatures’, of ‘rhythmic notation’, and so on. […]”

“the ‘second’ is the study of ‘writings’ about ‘music’ from ‘ancient times’ onwards. […]“

“the ‘third’ is an area of current ‘musicological study’ that seeks to define ‘processes’ and ‘general principles’ in ‘music’ — a ‘sphere of research’ that can be distinguished from ‘analysis’ in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built”

(“music theory” is frequently concerned with describing how ‘musicians’ and ‘composers’ make music, including ‘tuning systems’ and ‘composition methods’ among other ‘topics’)

(because of the ever-expanding conception of what constitutes ‘music’ (see “definition of music”), a ‘more inclusive definition’ could be that ‘music theory’ is the consideration of any ‘sonic phenomena’, including ‘silence’, as they relate to ‘music’)

(this is not an ‘absolute guideline’; for example, the study of “music” in the quadrivium ‘liberal arts university curriculum’ that was common in ‘medieval europe’ was an ‘abstract system’ of ‘proportions’ that was carefully studied at a distance from actual ‘musical practice’)

(however, this ‘medieval discipline’ became the basis for ‘tuning systems’ in later centuries, and it is generally included in ‘modern scholarship’ on the history of ‘music theory’)

(‘music theory’ as a ‘practical discipline’ encompasses the ‘methods’ and ‘concepts’ that ‘composers’ and other ‘musicians’ use in creating ‘music’)

(the ‘development’, ‘preservation’, and ‘transmission’ of ‘music theory’ in this sense may be found in ‘oral’ and ‘written’ music-making ‘traditions’, ‘musical instruments’, and other ‘artifacts’)

(for example, ‘ancient instruments’ from ‘mesopotamia’, ‘china’, and ‘prehistoric sites’ around the world reveal details about the ‘music’ they produced and potentially something of the ‘musical theory’ that might have been used by their makers)

(see “history of music” and “musical instrument”)

(in ‘ancient’ and ‘living’ cultures around the ‘world’, the deep and long roots of ‘music theory’ are clearly visible in ‘instruments’, ‘oral traditions’, and current ‘music-making’)

(many ‘cultures’, at least as far back as ‘ancient mesopotamia’ and ‘ancient china’, have also considered ‘music theory’ in more formal ways such as ‘written treatises’ and ‘music notation’)

(‘practical’ and ‘scholarly’ traditions overlap, as many practical ‘treatises’ about ‘music’ place themselves within a ‘tradition’ of other ‘treatises’, which are cited regularly just as ‘scholarly writing’ cites earlier ‘research’)

(in ‘modern academia’, ‘music theory’ is a subfield of ‘musicology’, the wider study of musical ‘cultures’ and ‘history’)

(etymologically, music theory is an act of contemplation of ‘music’, from the greek θεωρία, a ‘looking at’, ‘viewing’, ‘contemplation’, ‘speculation’, and ‘theory’)

(also a ‘sight’, a ‘spectacle’)

(as such, it is often concerned with ‘abstract musical aspects’ such as ‘tuning’ and ‘tonal systems’, ‘scales’, ‘consonance’, and ‘dissonance’, and ‘rhythmic relationships’, but there is also a ‘body of theory’ concerning ‘practical aspects’, such as the ‘creation’ or the ‘performance’ of ‘music’, ‘orchestration’, ‘ornamentation’, ‘improvisation’, and ‘electronic sound production’)

(a person who ‘researches’, ‘teaches’, or ‘writes’ articles about ‘music theory’ is a ‘music theorist’)

(‘university study’ (typically to the M.A. or Ph.D level) is required to teach as a ‘tenure-track music theorist’ in an ‘american’ or ‘canadian’ university)

(methods of analysis include ‘mathematics’, ‘graphic analysis’, and especially ‘analysis’ enabled by ‘western music notation’)

(‘comparative’, ‘descriptive’, ‘statistical’, and other methods are also used)

(‘music theory textbooks’, especially in the ‘united states of america’, often include elements of ‘musical acoustics’, considerations of ‘musical notation’, and techniques of ‘tonal composition’ (‘harmony’ and ‘counterpoint’), among other topics)

—

the Cmajor diatonic scale consists of 7 notes (starting with C as the root)

a “whole step” is a movement of two notes “up the ladder”
(a “half step” is a movement of one note “up the ladder”)

so the Cmajor scale goes:

whole step
whole step
half step
whole step
whole step
whole step
half step

(to return to C at the next highest octave)

this means the Cmajor diatonic scale is:

C D E F G A B C

the Aminor scale goes:

whole step
half step
whole step
whole step
half step
whole step
whole step

(to return to A at the next highest octave)

this means the Aminor diatonic scale is:

A B C D E F G

to create a diatonic scale for any other root note, use these same patterns for both the major and minor variants

for each root note, all other notes have a relative name…

for C…

C (root)
C# (minor second)
D (major second)
D# (minor third)
E (major third)
F (fourth)
F# (minor fifth)
G (major fifth)
G# (minor sixth)
A (major sixth)
A# (minor seventh)
B (major seventh)

to construct a “major chord”, combine:

root / major third / major fifth

(so a Cmajor chord is C E G)

to construct a “minor chord”, combine:

root / minor third / major fifth

(so a Cminor chord is C D# G)

for all other “extended chords”, one simply adds another note to the minor / major triad…

a “Csus2” would add the major second to a Cmajor chord:

(C E G D)

a “Csus4” would add the major fourth to a Cmajor chord:

(C E G F)

a “C6” would add the major sixth to a Cmajor chord:

(C E G A)

a “C7” would add the minor seventh to a Cmajor chord:

(C E G A#)

a “Cmaj7” would add the major seventh to a Cmajor chord:

(C E G B)

a “C-5” chord has a minor fifth (instead of major fifth):

(C E F#)

a “Cdim” chord has a minor fifth, major sixth, minor third:

(C D# F# A)

a “Caug” chord has a minor sixth (instead of major fifth):

(C E G#)

similarly, one can extend this pattern to the next octave. in the next octave…

C (“eighth” or root note at next octave)
C# (minor ninth)
D (major ninth)
D# (minor tenth)
E (major tenth)
F (eleventh)
F# (minor twelfth)
G (major twelfth)
G# (minor thirteenth)
A (major thirteenth)
A# (minor fourteenth)
B (major fourteenth)
C (fifthteenth)

and so on…

a “C9” chord includes both the minor 7th and major ninth…

(C E G A# D)

a “Cmaj9” chord includes both the major 7th and major ninth…

(C E G B D)

a “C11” chord includes both the minor 7th and eleventh…

(C E G A# F)

a “Cmaj11” chord includes both the major 7th and eleventh…

(C E G B F)

a “C13” chord includes the minor 7th, major ninth, and major thirteenth:

(C E G A# D A)

a “Cmaj13” includes the major 7th, major ninth, and major thirteenth:

(C E G B D A)

when improvising over a song in a certain key, you can utilize a number of scales…

the most common scale in Cmajor is the diatonic scale (that is the 7 notes C D E F G A B C played over the chord progression)…this is referred to as the “ionian” mode…

the 7 other common “modes” are simply the diatonic pattern with a different root position…

the “dorian” mode uses the major second as the root:
(key of Dminor)

(D E F G A B C D)

(in other words, simply shift the diatonic scale 2 and a half steps)

the “phyrgian” mode uses the major third as the root:
(key of Eminor)

(E F G A B C D E)

in other words, simply shift the diatonic scale down 3 and a half steps

the “lydian” mode uses the major fourth as the root:
(key of Fmajor)

(F G A B C D E F)

in other words, simply shift the diatonic scale down 2 and a half steps

the “mixolydian” mode uses the major fifth as the root:
(key of Gmajor)

(G A B C D E F G)

in other words, shift diatonic scale down 3 and a half steps

the “aeolian” mode uses the major sixth as the root:
(aka the “natural minor scale”)
(Aminor)

(A B C D E F G A)

the “locrian” mode uses the major seventh as the root:
(key of Bdim)

(B C D E F G A B)

(shift the Bmajor scale up one half step)

a “blues scale” consists of a non-diatonic pattern of:

one-and-a-half step
whole step
half step
half step
one-and-a-half step
whole step

so a “Cblues” is:

(C D# F F# G A#)

the diatonic scale can be combined with a blues scale to create a hybrid scale:

(C D D# E F F# G A# B C)

when playing in a minor key, one can alter the scale to create new minor scales:

“harmonic minor”

whole step
half step
whole step
whole step
half step
one and half step
half step

so A harmonic minor scale is:

(A B C D E F G#)

the “melodic minor scale” follows this pattern:

whole step
half step
whole step
whole step
whole step
whole step
half step

so A melodic minor is:

(A B C D E F# G#)

diminished scale:

whole step

half step

whole step

one and a half step

half step

whole step

half step

(C D D# F G# A B C)

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