(Mira - I know that part of the things here were in class#9 but I think that I need to build the idea of harmonic function and the cadence again. Of course you can cut what ever you think, no offence.) CHORDS The properties of chords in the tonal world (environment), are not only the chord type, or the Pitch-classes that build the chord, or the inversion of the chord but also the function of the chord. By function we mean the interrelations of a chords and when and why it appears in the a chords progression in a music piece. The chords are part of the scale properties - the chords the we build on the major and minor scale degrees are different because the intervals in the scales are different. Yet the harmonic functions are the same in the major and minor scales. We'll demonstrate the harmonic functions on the on the C-major and C-minor scales. For the chords name we'll use 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. 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 The I IV and V degrees are the only three major chords in the major scale. This chords represent the 3 functions of chords and harmony as all in the roll of tonal melody and piece. The Tonic chord [T] - like the tonic degree is the most stable and will appear most of the time in the beginning of a piece and always in the end.. Sometimes the VI (and most rarely the III) appears in the function of T. The Dominant chord [D] usually as a 4 notes chord V7 (=dominant-seven) is the function that leads to the to the tonic in a full or authentic cadence (see later on). For example, the G7 chord in C-major scale is built out from the notes G-B-D-F. The dissonance interval in this chord, the triton F-B is very tense and the resolution of this dissonance is B->C F->E. The D and G notes usually goes to C too. The Bdim chord is functioning as [D] too. The SubDominant chord [SD] - IV - usually goes to a (D) function chord like V(7). The II degree chord is considered to be a very strong [SD] chord. Usually it is used as 4 note chord II7. For example, in the C-major scale Dm7 [SD] -> G7 [D] -> C [T]. The Dm7 chords has 3 notes in common with the F chord: F-A-C plus the D-note. Harmonic progressions including some CADENCEs Composing in a tonal world doesn't mean just to choose a scale as a reservoir of notes and chords. Usualy at least in the classic area, the composer establish the tonality using chord progressions based on [T] and [D] function chords, in the beginning. In the end of parts or units of a piece the chord progressions will form all kinds of cadence progressions depending on how much "ending" the composer want to emphasize in the cadence. A. Example 1 In the first 10 measures of the 1st movement of "EINE KLEINE NACHMUSIK" we can identify the measures grouping 1-4, 5-10. mm. 1-10 Key G. Measures: 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) As it looks there are only 2 chords I [T] and V7 [D] so there is a strong accentuation on the tonality using the 2 stronger functions and chords. Yet the cadence in m. 10 is not a full cadence because the composition is in a move we are just in the beginning, thus 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 measures group, and a 6 measures group and not the 2, 4, 8 ... grouping that we usually identify as "classic" (will see it in Dance like movements like the minuet in this work). Something else is the Harmonic-Rhythm: in the beginning it is very slow - a chord every 2 measure, then a chord for every measure, and in the cadence it is very fast - a chord for a beat. Planing a chord progression in a melody should consider this kind of key establishment. B. Example 2 An example of a final full cadence progression we can see in the end of the same movement. mm. 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 the chords in this full cadence progression are in the root position there is no doubt about the key here. To sum up examples 1. and 2. We could see 2 kinds of cadence progression - not final using the [D] -> [T] functions but the chords are not in the root position; and final cadence progression with the 3 harmonic functions [ST] -> [D] -> [T], and with the root notes in the bass. C. Example 3 To demonstrate a common progression in the classic style - without modulations - lets look at measures 11-17 in the same movement as above. (We would like to point out that the measure grouping here is 4+3 while measure 18 completes the Harmonic progression but start a new one in the same time (from the large structure point of view the transition part of the exposition of the music form called "Sonata Allegro" or "Sonata form" start here. In The end of the transition the key will be D major, the key of the dominant degree). mm. 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 ) Harmonic Function: [T][SD][D][T] [SD][D] [T] [D] [T] As we can see here the chords repertoire in the progression is richer, but their function is in the same manner. D. Example 4. The next example is of a simple modulation - moving from one key 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. The mm. 18-27 of this movement are transition part. It starts in the key of G-major and ends in a the key of D-major. As will see there is sometime there is a different between a modulation - where the new key is established with a meaningful cadence in the new key, and a momentary accentuation of aone of the scale degrees. We could identify both kinds in the next passage. mm.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 the D. As we can see in m.21 it becomes the new I. Of course we know it only when we look back from m.22. In m.21 the V->I in G-major becomes I-> IV in D-major. m.21 continue with the VII degree -[D] - in D-major and then The new [T] in m.22. In fact we interpret the progression from 21-22 as a cadence in the new key - we got I IV VII I = [T][SD][D][T]. In mm. 26-27 we can see- what is called 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 m.25 we can see the II7 (Em7) which is a [SD] then we got a E major chord which is not part of the D-major scale chords' repertoire, in fact 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. As we can see for a Modulation we need a confirmation, an establishment of the new key with a kind of a cadence that will include the Harmonic functions in the progression - used in a cadence - [SD]->[D]->[T], yet it is not suppose to be a full authentic cadence. SUMMERY In the examples above, we could see some harmonic characteristics in tonal music in the classic area and abour grouping. - All kind of cadences - full cadence, half cadence and some weaker progressions using the VII degree as [D], or using inversion chords in the cadence. - The consistent behavior of the harmonic functions in the progressions (cadences and others) - A full structured modulation. - A momentary deviation to another key like in secondary dominants. - Somthing about measue grouping which are not 2^2 (i'll look for examples of 3+3 units and 3+2 units there are aa lot of them in the classic music thou not in minuets or other dance style music). ************************ About the example you send me. Taking as a model the classic music area, I want to suggest some other possibilities. First, since there are, (1) establishment of tonality areas; (2) harmonic progression in a key sometimes with Secondary dominants; (3) modulations (in the classic area is usually to a to a close key) and (4) unstable harmonic areas - like in a development parts in sonata form. I want to suggest some different progression for the different possibilities. Establishing a key 1) I | I | V7 | V7| I | V7 | I II7| V7 I| (8 measures progression) 2) I | IV (or II(7))| V (and III)| VI | IV | II | V7 | I V7 I | (8 measures) using Secondary dominants: 3) I | II V/V | V V7 | I V/VI | VI V/II | II7 V | I V/IV IV VII | I V7 I| Modulation to the dominant key and back.No measures can be a scheme to a movement. 4) I I II V7 I (V=I, I V7 I II V7 I) (I=I, I V/V V III VI II7 V7 I) Exposition 5) I (I=I....) (V=I....) || C G Unstable area (V=Im, [D] [T] [D] [T] (V=Im, [SD] [D] [T] [D] [T](V=Im, [SD][D][SD][T])) || Gm Dm Am Reprise (IV=I, [SD] [D] [T] [D] [T] [SD] [T]) (I=I ...........) F C *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)