Harmonic Degrees and Harmonic functions (summery) ======================================= STRONG -->----->----->---->---->---->------> WEAK [T] I I6 VI6 VI III [D] V7 V V6 VII(7) III6 III [SD] IV/II5-6* IV II6 II VI *II5-6 The first inversion of II7. The notes of II5-6 are F-A-C-D. A. Harmonic Progressions =================== The main classic progression are: (1) I V7 I [T][D][T] (1a) [T][SD][T] (2) I IV V7 I [T][SD][D][T] = CADENCE (3) I IV V (I V) [T][SD][D] ([T] [D) = HALF CADENCE =(resting on the dominant usually the V not other function degrees like VII or III6 ) (3a) V I V = HALF CADENCE A well known progression in the baroque and classic area is the Falling Fifths*: (4) I IV VII III VI II V I [T][SD][D] [T] [T] [SD] [D][T] *(In the Modal area, we could find the "falling fourths" progressions such as: I V II VI III VII (down 4th )) B. Size and Proportions ================= (Very schematic but still follows the principles of classic music) GROUP SIZE - Usually I think that it is a good idea to stick to 2+2 bars, 3+3 bars, or 4+4 bars phrases (but 3+2 phrase is a possibility too). FUNCTION DUPLICATION - The appearance of the [T] and [D] functions in a phrase is equal more or less while The [SD] Function appears considerably less. Ex.1. Progression (1) in a 2+2 phrase === Bars: 1 2 3 4 | ...| ..|. ..| . . . I V V I Or I I V I The same proportions for Progression(1)can be used to the 4+4 phrase. Ex.2. Progression (1) in a 3+2 phrase === Bars: 1 2 3 4 5 |. ..|. .|. ..|. ..|... I I V V I Ex.3. Progression (2) in a 2+2 phrase === Bars: 1 2 3 4 |...|. .. | . .. |... I IV V I [T][SD][D] [T] (The same proportions for Progression(2) can be used to the 4+4 phrase.) Ex.4 Progression (3) in a 2+2 phrase === Bars: 1 2 3 4 | | | | I IV V I V [T] [SD] [D] [T][D] WHERE and WHEN to USE the Different Harmonic Degrees In the beginnings of pieces, movements or big parts the degrees that are used to feel the functions are strong ones but not necessarily the strongest ones. In endings the functions used are the strongest in the root positions. In the parts after the beginnings that are not endings, usually we can use the strong the medium and even the weak harmonic function degrees. Like in the next example. Ex.5. Progression (4)** in a 4+4 phrase === Bars: 1 2 3 4 5 6 7 8 | | | | | | | | I IV VII* III* VI*II* V* I [T] [SD][D] [T] [T] [SD] [D][T] (The same proportions for Progression(4) can be used to the 2+2 phrase.) * Degrees that can appear with the 7th added - VII7, III7, VI7, II7, V7; More interesting point is that those degrees can be turn to be secondary dominants. For example the pair VII --> III (Bdim --> Em in C-Major) can be changed to V/III (B--> Em); The VI-->II (Am-->Dm in C-Major) can be changed to V7/II --> II etc. ** There are many pop songs using this progression more or less such as: I Will Survive (MidiEx.1), Ho Baby It's a Wild World, Autumn Leaves... Interesting point is that all the examples I could think about, are in the minor scale. HARMONIC RHYTHM - Usually a chord per measure is a always expectable as we could see in most of the examples above. Yet in beginnings it can be slower - 2 measures per chord, while in endings of phrases, parts , movements it is always faster - a chord per half measure or even a chord per beat (like we saw in the examples from the first movement of EINE_KLEINENACHT). C. SEQUENENCING HARMONIC PROGRESSIONS ======================================== The safe thing to do while sequencing progressions is to use the 2+2 or 4+4 phrases. Ex.6. Progression(1)+Progression(1) in a 2+2 phrase === Bars: 1 2 3 4 | | | | I V I I V V I (The same proportions for Progression(1) can be used to the 4+4 phrase.) Ex.7. Progression(1)+Progression(2) in a 4+4 phrase === Bars: 1 2 3 4 5 6 7 8 | ...| ..|. ..| . |. ..|. .. | . .. |.... . I V V I I IV V I Ex.8. Progression(1)+(1) + Progression(2)+(3) in a (2+2)+(2+2) phrase ==== Bars: 1 2 3 4 5 6 7 8 | . .. | . .|. ..| . |. ..|. .. | . .. |.... . I V I* V I I IV V I V *The I degree is the ending of progression(1), and at the same time its beginning. Ex.9. Progressions (1)+ (3) + (2) in 4+4 phrase ==== Bars: 1 2 3; 4 5 6; 7 8; | | | | | | | | . . I V I* IV V I V I IV V I** V7 I [T] [D] [T][SD] [D][T] [D] [T}[SD][D] [T] [D] [I] * I* ending (1) starting (3) ** I** ending (2) starting (1) While Sequencing it is very common to use the alternative function degrees instead of using the strongest only - unless we are in the beginning or ending. The fact is that usually if we keep the CYCLE of the 3 HARMONIC FUNCTIONS and keep in mind to start and end with the strongest functions degrees we are always on the safe side. D. Nesting All the Harmonic Progressions suggested above can serve as a point of departure for a nested progression in the same key or in a related key. The technique to do it is prolongation of every function or degree in several ways.In fact this is a kind of top-down procedure which is the opposite to the reduction procedures used by Schenker or in GTTV. I suggest here 2 Points of view: 1. Looking at a Cadence as a FUNCTIONAL-CYCLE. In a part or phrase we got a Main CYCLE and - NESTED SECONDARY CYCLES. 2. Complimentary view using the prolongation procedure, (thou we can look at it as taken from progressions (1) and (1a)) is using a-b-a pattern/process without paying attention, for a moment, to the [SD}[D] [T] CYCLE. Thus to prolong every harmonic function or even harmonic degree we can had to it a another chord from the scale or from other scales. (FOR GROUP SIZE AND FUNCTION Duplications look at the examples above) Ex.10. PROLOGATION of THE Ist DEGREE using a-b-a pattern ==== I --> (I V I) or (I IV I) (I VII7/Im I) etc. Ex.11. ==== Taken Progression (1) as a MAIN CYCLE and prolonged it without modulation but with momentary deviations to other keys using secondary dominants. Every function will be substitute with a progression the [T] - can be substitute with progressions (1) or (1a) or (2) or (4), while the [D] can be substitute with progression (3) or (3a). Every Function or degree can be prolonged using a-b-a pattern. MAIN CYCLE - I V I (no modulations) (I V I) [T] [D] [T] ((I IV I){(1a) or a-b-a) (VII I V7) (I IV V7 I)) [T][SD][T] [D] [T][D] [T] [SD] [D] [T] (I II V I) (IV V7/IV IV II#3=V/V) etc. You can prolong Progression (1) endlessly. But we should have some useful constrains such as 1. To restrict the depth of nesting (main + 2 sub levels) 2. When implemented into real chords - restrict the amount of measures to 24 -32 measures. MAIN CYCLE - I V I with modulations (I V I) [T] [D] [T] ((I IV I){(1a) or a-b-a) (VII I V7) (I IV V7 I)) [T][SD][T] [D] [T][D] [T] [SD] [D] [T] {(I V I) (IV V IV) (I II VII III)} {(I II V V/V V=I (VII III VI II V7 I VII VI (I V7/IV IV=I)} {( I V I)... Main key: I New key:V Main key: I