Music theory - Scales and Chords

Temperament:

• adjustment in tuning of musical intervals away from 'natural' scale such that pairs of notes (B# & C, or C# & Db), are combined instead of being treated individually. This leaves neither note accurate but sufficiently so for the ear to accept it.
• in keyboard instruments, this avoids unmanageable number of finger keys
  • equal-tempered:
    • introduced to pianoforte in 1846, where each semitone is made an equal interval, making it easy to play in any key & to modulate
  • older systems of temperament:
    • mean-tone temperament:
      • commonest system prior to equal-temperament
      • left certain keys tolerable, others less so, and some unusable
  • untempered scale:
    • known as just intonation
• instruments such as violin family can have no system of temperament, the player determining the pitch and checking it by ear
• electronic instruments allow selection of smaller intervals than a semitone thus allowing microtonal scales

Modes:

• sequences of 7 intervals that make up a scale, with each interval being either a semitone or a tone
  • NB. Western music generally uses a music system of 12 notes to an octave
• the modes that became accepted in ancient Greek days of Pythagoras were those which nowadays can be conveniently represented by the white keys of a piano (albeit with slight differences in tuning)
• in the 5thC AD, 4 modes were adopted (authentic modes):
  • the 5th note (the dominant) was much used as a reciting-note in plainsong, anf the first note, as a cadence note to close the passage
    • where the 5th note was a B, the dominant was changed to C which was more suitable
  • the 4 authentic modes may be recreated by playing an octave scale of white notes on the piano, beginning respectively on D, E, F & G.
• in the 6thC AD, Pope Gregory added 4 more modes (plagal modes) derived from these 4 authentic modes
  • these plagal modes started on the dominant note of its related authentic mode, but in order to avoid having the reciting note at the very top or bottom of the series of notes, a new one was chosen, lying 3 notes below the original authentic dominant
• in 1547AD, Henry of Glarus (Henricus Glareanus), a Swiss monk brought forth, in a book called Dodecachordon, a theory that there should be 12 modes instead of 8, so added modes on A & C with their plagal forms, and named all 12 modes by what he thought (incorrectly) were their ancient Greek names, which have become adopted
  • 2 of these new modes were more suited to harmonising than the others and so these were adopted and now are our major & minor scales, whilst the others are now rarely used (apart from in some folk songs, and by Vaughan Williams, Bartok, Kodaly)

• Mode	Starting note	Dominant Note	Sequence (S=semitone; T=tone;)
  I (A) Dorian	D	A	T-S-T-T-T-S-T
  II (P) Hypodorian	A	F
  III (A) Phrygian	E	C*	S-T-T-T-S-T-T
  IV (P)	B	A
  V (A) Lydian	F	C	T-T-T-S-T-T-S
  VI (P)	C	A
  VII (A) Mixolydian	G	D	T-T-S-T-T-S-T-T
  VIII (P)	D	C*
  IX (A) Aeolian [minor]	A	E	T-S-T-T-S-T-T
  X (P)	E	C
  XI (A) Ionian [major]	C	G	T-T-S-T-T-T-S
  XII (P)	G	E

Modern scales:

• major scale:
  • uses the sequence as for mode XI
• minor scales:
  • the 'natural' minor scale uses the sequence as for mode IX
  • the 'harmonic' minor scale is formed by raising the 7th note of mode IX so it includes tones contained in the principal harmonics of the minor key, thus the sequence is T-S-T-T-S-1.5T-S
  • the 'melodic' minor scale is in 2 parts:
    • ascending part is formed by raising the 6th & 7th tones of mode IX, thus T-S-T-T-T-T-S
    • descending part is same as 'natural' minor
• pentatonic scale:
  • consists of a major triad, together with the 6th & 9th of the scale
  • for variety, the scale may be varied (eg. raise the 2nd tone and lower the 6th)
  • often used as a melodic improvisation run
• key signatures:
  • each major scale has its own key signature and its related minor scale with the same key signature
  • can determine the key signatures using the circle of 5ths and starting with Cmajor or A minor:
    • sequentially go up by a fifth adding a sharp to key signature each time:
      • Cmaj - Gmaj - Dmaj - Amaj - Emaj - Bmaj - F#maj - C#maj
      • Amin - Emin - Bmin, etc
    • sequentially go down by a fifth adding a flat to key signature each time:
      • Cmaj - Fmaj - Bbmaj - Ebmaj - Abmaj - Dbmaj - Gbmaj - Cbmaj
      • Amin - Dmin - Gmin - Cmin, etc
    • NB. the key signatures pairs are enharmonic ie. sound the same:
      • Bmaj (5 sharps) = Cbmaj (7 flats)
      • F#maj (6 sharps) = Gbmaj (6 flats)
      • C#maj (7 sharps) = Dbmaj (5 flats)

Chords:

• diatonic chords:
  • chords built upon tones of the major scales
• chromatic chords:
  • altered diatonic chords
• triad:
  • a chord consisting of 3 notes:
    • root note (fundamental)
    • 3rd tone from root
    • 5th tone from root
  • there are 3 main chords for a scale:
    • tonic chord where root = tonic (ie. 1st) note of the scale
    • dominant chord where root = dominant (ie. 5th) note of the scale
    • subdominant chord where root = subdominant (ie. 4th) note of the scale
  • a triad chord can be played in 3 main inversions:
    • lowest note is the root (root position)
    • lowest note is the 3rd tone from the root (1st inversion)
    • lowest note is the 5th tone from the root (2nd inversion)
  • chord patterns:
    • major chord = maj 3rd interval (ie. 4 semitones between root and 3rd tone) + min 3rd interval (ie. 3 semitones between 3rd tone and 5th tone)
    • minor chord = min 3rd + maj 3rd  (ie. 3rd tone lowered a semitone)
    • augmented chord = maj 3rd + maj 3rd  (ie. 5th tone raised a semitone)
      • has an unusual nostalgic or haunted sound
    • diminished chord = min 3rd + min 3rd (ie. 3rd & 5th tones lowered a semitone)
• 4 note chords:
  • 7th chords:
    • a 7th note from root is added to a triad
    • chord patterns:
      • dominant 7th chord = maj3rd + min3rd + min3rd
      • diminished 7th chord = min 3rd + min3rd + min3rd
      • minor 7th chord = min3rd + maj3rd + min3rd
      • major 7th chord = maj3rd + min3rd + maj3rd
    • the 5th of any 7th chord may be flatted for a more dissonant effect & is used with minor 7th chords
  • 9th chords:
  • 11th chords:
  • 6th chords:
    • produces a more modern sound by adding a 6th note from root to the triad

Chord progressions:

• cadences:
  • authentic cadence: tonic chord - dominant chord - tonic chord
  • plagal cadence: tonic chord - subdominant chord - tonic chord
  • mixed cadence: tonic chord - subdominant chord - (tonic chord) - dominant chord - tonic chord
• diatonic progressions:
  • usual progressions: vi-ii-V-I-IV-V-I (eg. Am-Dm-G-C-F-G-C)
  • circle of fifths:
    • allows the use of 3 or more consecutive progressions in 5ths to take us out of the tonality of the original key (ie. modulation)
• 12 bar blues:
  • 12 bar progression: I-I-I-I7-IV-IV-I-I-V7-V7-I-I

Modulation:

• term used for a change of key within a composition
• often used to change the mood and to avoid monotony
• a modulation is effected and the new key established when the dominant of the new key is followed by its tonic
• a transient modulation is one in which the new key is maintained only for a short time before being abandoned for another key

Transposition:

• process of playing or writing a composition in a key different from the original key
• music remains the same except for change in overall pitch
• basic rules for transposition from one key to another by sight:
  • determine the new key by the distance you wish to transpose up or down
    • eg. if you wish to transpose up a Perfect 4th, the new key will be one that is Perfect 4th higher eg. C to F
  • transpose the 1st note up by the chosen distance
  • transpose each successive note in new key by its relationship to the preceding note, moving horizontally
  • notes having accidentals in old key will have equivalent accidentals in new key