5. Conclusions
Whilst the above root progression analysis is confined to a single piece of music, and demonstrates only three forms of the syntactic structure, similar results are confirmed by all other pieces analysed. Similar graphs can be seen for the pieces currently implemented on the progression database on this site. Please refer to: Comparative Root Progression Analysis. Whilst other researchers have proposed theories of root progressions and linguistic models of tonal music, what are new in this theory are the following:
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By systematically removing non-structural harmonies, the analysis of root progressions shows clearer patterns than in any previous hypothesis.
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Clustering of paired and non-paired progressions shows clearly the existence of two types of harmony: static harmony (chord oscillation) and dynamic harmony (root movement) (although this is anticipated by Schoenberg, La Rue etc.)
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The clustering of paired and non-paired progressions provides a mechanism for segmentation.
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This segmentation consistently relates to musical phrases.
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All harmonies can be explained and their function clearly related to their position in a musical phrase.
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By the identification of the role of structural and non-structural harmonies (including linear progressions) this analysis shows the nature of the relationship between vertical chords and contrapuntal melodic formations. (This point is not fully explained in this limited paper)
What is not covered by this limited analysis are the following:
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The historical way that these patterns have evolved
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The relationship between complete and incomplete phrase structures. (See book for this)
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A discussion of the possible extended phrase structures. (See book for this)
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Any variation in the patterns across different types or periods of music (vocal music, instrumental music, early music, folk music etc.)
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The existence or non-existence of these patterns in non-tonal, partly tonal, popular and 20th Century serious music, jazz etc.