STRUCTURE AND INTERPRETATION OF MUSIC CONCEPTS ______________________________________________ ============================================== CLASS 11.1: =========== Tonal Music -- Scales, Chords, Harmonic functions, Harmonic progressions. _________________________________________________________________________ ========================================================================= SCALES: ~~~~~~~ * Scale-structure -- characterized by a list of tonal-interval-classes. * In tonal music: Major, minor -- 3 different kinds: Natural, Melodic, Harmonic. * Scale -- An "instantiation" of a Scale-structure by a tonal-pitch-class: C-Major, Db-Minor. Conventional notation: CM, Dbm. * Scale degrees are marked by Roman numerals: I II III IV V VI VII. * On each degree, chords are built using the THIRD tonal-interval-class that occurs in the scale. Degree: I II III IV V VI VII | | | | | | | Triad Chords: M m m M M m dim CHORDS ~~~~~~ ;;; -------- ---------- ;;; | CHORD-STRUCTURE | ;;; ------------------- ;;; ^ ;;; | ;;; | ;;; -------- ;;; ----------------------->|CHORD |<----------------------------------- ;;; | ^ -------- ^ ^ | ;;; | | | | | ;;; | | | | | ;;; | | --------- ------- --------- | ;;; ---------------- ------- |NINETH-| |REAL-| |SEVENTH| | ;;; |INTERVAL-CHORD| |TRIAD| | CHORD | |CHORD| |-CHORD | | ;;; ---------------- ------- --------- ------- --------- | ;;; ^ ^ | ;;; | | | ;;; | | | ;;; | | | ;;; ------------------>|<---------------------- | | ;;; ^ ^ ^ ^ | | ;;; | | | | | | ;;; -------- -------- ------------ ----------- | | ;;; |MAJOR-| |MINOR-| |AUGMENTED| |DIMINISHED| | | ;;; |TRIAD | |TRIAD | | -TRIAD | | -TRIAD | | | ;;; -------- -------- ----------- ------------ | | ;;; | | ;;; | | ;;; -------------------------------------------------------------->| | ;;; ^ ^ ^ ^ | ;;; | | | | | ;;; ---------- ---------- ---------- ------------ | ;;; | MAJOR- | | MINOR- | |DOMINANT| |DIMINISHED| | ;;; |SEVENTH | |SEVENTH | |-SEVENTH| |-SEVENTH | | ;;; ---------- ---------- ---------- ------------ | ;;; | ;;; | ;;; ---------------- | ;;; |INVERSE-CHORD |<-------------------------------- ;;; ---------------- ;;; ^ ;;; | ;;; | ;;; | ;;; ------------------------->|<--------------------- ;;; ^ ^ ^ ^ ^ ;;; | | | | | ;;; ------- ------- ------- ------- ------- ;;; | 6- | | 64- | | 65- | | 43- | | 2- | ;;; |CHORD| |CHORD| |CHORD| |CHORD| |CHORD| ;;; ------- ------- ------- ------- ------- Chords are characterized by their HARMONIC FUNCTION within a scale context. The harmonic function of a chord determines its interrelation with other chords, and its occurrences in chord progressions in a music piece. The vocabulary of chords in tonal music result from chords that are built on the DEGREES of the major and minor scales. The chords are different because the intervals in the scales are different. Yet the harmonic functions are the same in the major and minor scales. C major chords: Degree: I II III IV V(7) VI VII | | | | | | | Chords: C Dm Em F G(7) Am Bdim | | | Function: Tonic Sub- Dominant Dominant Chord names follow the convention of pop music lead sheets: A, C, etc for Major triads (3 notes chords), adding m to the chord means minor chord like Am Cm etc, "dim" and "aug" for diminished chord (2 small thirds) and augmented chord (2 large thirds). Adding number to a chord means adding a note or more. The main harmonic functions in a tonal music context are: TONIC, SUB-DOMINANT, DOMINANT. Each harmonic function has PRINCIPAL chord representative and secondary representatives. A principal representative provides a clear establishment of the harmonic function, while a secondary representative provides a weaker support. Representatives: HARMONIC-FUNCTION PRINCIPAL SECONDARY THIRD ----------------- --------- --------- ----- Tonic I Vi III Sub-dominant IV II VI Dominant V VII III Note that the principal representative of the harmonic functions in a major scale are the 3 degrees with major triads. Harmonic progressions are used for establishment of a scale context. There are some standard progressions. A "strong" progression would start and end with a principal Tonic representative, and would use a principal dominant representative on the way. Standard progressions are: T D T T SD D T Usually, harmonic progressions are combined in sequence. The strength of the progression is determined by its position in the sequence. A progression in the beginning or ending of a sequence (piece) tends to be stronger (represented by principal chords). A middle progression can be weaker. EXAMPLE 1 -- a strong progression in the beginning of a piece: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ First 10 measures of the 1st movement of "EINE KLEINE NACHMUSIK": Measures grouping 1-4, 5-10. Measures 1-10: Key G. Measure: 1 2 3 4; 5 6 7 8 9 10 | | ; | | | | | | Harmonic degree: I V7 ; I V7 I V7 I V7 I V7 I V7 I6 (rest) There are only 2 chords I [T] and V7 [D]. There is a strong accentuation of the tonality using the 2 stronger representatives of the harmonic degrees. The CADENCE (ending) in measure 10 is not a full cadence because the composition is in a move, and we are just in the beginning. The cadence progression ends with V7 in 3-4 (second) inversion (the fifth in the bass) and the I is in the first inversion (the third in the bass). The interesting thing here is that we have a 4 measure group, and a 6 measures group and not the usual 2, 4, 8 ... grouping. Harmonic-Rhythm: In the beginning it is very slow - a chord (and function) for every 2 measure; then a chord for every measure, and in the cadence it is very fast - a chord for a beat. Chord progression rhythm is relevant in melody composition. EXAMPLE 2 -- a strong progression in the ending of a piece: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Final full cadence harmonic progression -- in the end of the same movement: Measures. 127-137. Key G major Measure: 127 128 129 130 131 132 .......137 | | | | | | Harmonic degree: IV V7 I IV V7 I IV V7 I I...(V7)....I All chords in this full cadence progression are in the root position; there is no doubt about the key (scale) here. Examples (1) and (2) present two kinds of cadence progression - not final, using the [D] -> [T] functions but with chords that are not in the root position; and final cadence progression with the 3 harmonic functions [ST] -> [D] -> [T], and with root positions (the root notes appear in the bass). EXAMPLE 3 -- a common middle progression with a larger chord vocabulary: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Measures. 11-17. Key G major Measure: 11 12 13 14 ; 15 16 17 ;(18) | | | | ; | | | | Harmonic degree: I IV V7 VI II6 V7 I6 V7 I (rest); I IV V7 VI II6 V7 ; (I) Harm. Function: [T][SD][D][T] [SD][D] [T] [D] [T] The chords repertoire in the progression is richer, but the harmonic progression is as above. EXAMPLE 4 -- Harmonic nesting -- MODULATION: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Modulation is the "technique" of moving from one scale to another. The basic modulation technique is to use a chord that is part of the 2 scales as a pivot. Usually in the classic area the modulation is to a close key like the key of the dominant or the parallel minor. Measures 18-27 of this movement are transition to teh D scale. The transition (modulation) starts in the key of G-major and ends in the key of D-major. Sometime there is also a momentary transition that is even not considered as a modulation. In a modulation, the new key is established with a meaningful cadence in the new key. In a momentary accentuation of a scale degree, this is missing. The next passage demonstrates both. Measures 18-27: Keys G->D Measures: 18 19 20 21 22 23 24 25 26 27; | | | | | | | | | | Harmonic | | | | | | | | | | degree in | | | | | | | | | | G: I I I VII I V I | | | | | | Harmonic | | | | | | functions: [T] [D][T][D] | | | | | | in D: I IV VII6 I V7 I V7 I II7 II#37 V I V I V ; Harmonic functions: [T][SD][D][T][D][T][D] [T][SD][secondary D] (V7/V) The pivot chord is the dominant chord in G-major. In measure 21 it becomes the new tonic. This becaomes clear in measure 22. In measure 21 the V->I in G-major becomes I->IV in D-major. Measure 21 continues with the VII degree [D] - in D-major, and then the new [T] in measure 22. The progression from 21-22 is interpreted as a cadence in the new key: I IV VII I = [T][SD][D][T]. In measures 26-27 there is an HALF-CADENCE - in D-major. The half cadence creates a very defined articulation on the dominant degree (and a preparation to secondary Theme of the movement which is in the key of D-major). In measure 25 the II7 (Em7), which is a [SD] is followed by an E major chord which is not part of the D-major scale chords repertoire. It is the V7 Dominant-chord in the key of A-major (or minor). But since it is only a momentary change in scale it is not a Modulation. This phenomena is called secondary-dominant and it accentuate the degree it goes to. For a Modulation we need a confirmation, an establishment of the new key with a kind of a cadence that includes the main Harmonic functions in the progression - [SD]->[D]->[T]. EXAMPLE 5 -- Harmonic nesting -- MODULATION: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Based on the harmony of the first movement of Mozart's Piano Sonata no. 16 in C-major k.V 545 (do(2) mi sol, si (1 an a 1/2) do-re-do ...) I (I=I....) (V=I....) || C G Unstable area (V=Im, [D] [T] [D] [T] Gm (V=Im, [SD] [D] [T] [D] [T] Dm (V=Im, [SD][D][SD][T])) || Am Reprise (IV=I, [SD] [D] [T] [D] [T] [SD] [T]) (I=I ...........) F C