Comparative Root Progression Analysis Technique
4.1.3. The Historical Process
You can read this section on its own or in conjunction with the interactive graphical tool which produces graphs of root progressions for pieces currently on the progression database.
If the graph is not already open, then press here: GRAPH to use the interactive graph for your self. You may wish to narrow this window in order to be able to read this window and view the graph at the same time.
Press here: HELP for help on how to use the graph then press Back to return to this page.
The purpose of this section is to show how the change in polarisation has historically come about. By comparing the polarisation graphs for compositions from 4 different periods of music: A pre-tonal piece by Lassus; a baroque movement by Bach; a classical piece by Mozart and a romantic piece by Brahms, we can see that whilst a pre-tonal piece shows some characteristics of the later progression patterns, the complete polarisation of chord progressions takes place on the transition from pre-tonal to tonal music.
Firstly, let's examine the use of chord progressions in the motet 'Tristis est anima mea' by Orlandus Lassus.
With no exclusion rules selected, this piece shows almost equally large proportions of rising and falling fourth progressions. Other progressions occur less frequently and in common with later pieces, the rising 3rd has the lowest of the counts. Consequently, the raw counts are not very dissimilar from the raw counts for later tonal pieces
LASSUS - ALL CHORDS INCLUDED
R4 = rising fourth (or alpha) progression
F3 = falling third (or beta) progression
R2 = rising second (or gamma) progression
Etc.
The polarisation is not dramatically affected if we exclude passing chords, appoggiatura chords and auxiliary chords as follows:
LASSUS - NON-FUNCTIONAL CHORDS EXCLUDED
Here, the numbers of Rising 4th and Falling 4th Progressions are reduced in proportion to the other progressions. However, the number of falling fourths is only slightly reduced in relation to the number of rising fourths. This results in a refined count that does not show the same polarisation pattern as is the case for later pieces.
In contrast, if we examine the refined counts for the Bach Brandenburg No 2 - Movement I we get:
BACH - NON-FUNCTIONAL CHORDS EXCLUDED
This shows a very high degree of polarisation in contrast to the Lassus.
This demonstrates how the polarisation of chord progressions occurs on
the change from pre-tonal to baroque music.
The polarisation is evident in the following example from the Mozart Piano Sonata in A minor KV 310:
MOZART - NON-FUNCTIONAL CHORDS EXCLUDED
Here the relative proportions of the stronger progressions are not exactly
as in the Bach example but what they do have in common is the fact that
the strong progressions (rising 4th, falling 3rd and rising 2nd progressions)
nevertheless occur to the almost total exclusion of the opposing weak
progress (the falling 4th, rising 3rd and falling 2nd).
In the Brahms Song 'Wehe, so willst du mich weider':
BRAHMS - NON-FUNCTIONAL CHORDS EXCLUDED
The polarisation of chord progressions for the refined count is again
evident as in the Bach and Mozart examples.
The graph tool can be used directly by the reader to test out different combinations of exclusion rules for all the pieces on the database. The number of examples on the database will be gradually increased over time.
Note: Pre-tonal pieces are not included in the 'All Tonal Pieces' graph but are included on the database in order to show the historic change in polarisation.
There is a more detailed discussion of chord progression for each of the above pieces in the section: Description of Pieces on the Database.
Comparative Root Progression Analysis Menu
2.4.1.