Description of Pieces

The following notes describe the graphs of the pieces currently on the progression database. These are not full analyses. They are just intended as commentaries on the graphs. One exception to this is the Mozart analysis. A full description of this is already provided within the Thesis at: Commentary on the Analysis and within the remainder of the Thesis section.

These analyses often highlight interesting style characteristics of the pieces. Where I've commented on these characteristics I've avoided attributing these more generally to period and/or type of music as larger samples are required to do this accurately. Clearly, there are more detailed style characteristics to be uncovered as further analyses are added to the database.

A general point which needs to be understood about the exclusion rules is this: when a chord is excluded, usually two progressions are removed and one progressions is added. This means that counts can go up as well as down. This also means that it is not possible to simply remove a progression 'just because it does not fit the theory'.

Even with no exclusion rules selected this piece shows a high degree of polarisation of progressions. The count of progressions is as follows:

The total absence of falling second and rising third progressions is mainly because there are no passing chords and no appoggiatura chords that give rise to these un-polarised progressions. This is evidence that these types of progressions arise mainly out of these types of non-functional chords.

Excluding passing chords produces the same figures as there are no passing chords to exclude. This is a style characteristic of this piece.

Excluding appoggiatura chords makes only a few changes to the figures due to the occurrence of only two brief cadential 6 4 chords in the piece. These are at bars: 8 and 118. There is an interesting diminished 7th appoggiatura chord at bar 112.

The additional exclusion of auxiliary chords has a more dramatic effect on the polarisation. The falling 4th progressions are now almost totally excluded as follows:

The one remaining falling fourth progression occurs at bars 14 to 15 where there is a sudden key change where the cadence in F at the end of the phrase is immediately followed by a C major entry of the main subject. It will be observed throughout these analyses that residual un-polarised progressions are normally associated with rapid modulations in this way or are associated with other phenomena such as chord sequences. This is evidence that residual un-polarised progressions are systematically selected rather than a random phenomenon. In these situations the composer appears to be using consciously learned processes which override the subconscious selection of polarised progressions.

A further point that is worth noting, in this particular piece, is that in the final graph, rising second (gamma) progressions are more common that falling third (beta) progressions. This deviates form the overall average on the database (where falling thirds are slightly more common than rising second progressions) and is a style characteristic of this piece.

Some other interesting points to look out for are: the dominant prolongations at bars 66 to 67 and bars 92 to 93.

I hope to provide further information about this analysis as more functions are implemented on the progression database.

Please note, this analysis was carried out on a version of the song in G minor. The original song is in B minor. I'm sorry if this causes any difficulty in following the discussion.

With no exclusion rules selected, this piece shows an unusual spread of chord progressions. In this piece, the falling fourth progression is the most common progression at least for this raw analysis. The numbers are as follows:

Rising fourth (alpha) Progressions	11
Falling third (beta) Progressions	8
Rising second (gamma) progressions	5
Falling second (gamma') progressions	9
Rising third (beta') progressions	4
Falling fourth (alpha') progressions	22

This is the most unusual of the raw counts on the database, so far, and demonstrates clearly that there is no common distribution of root progressions for a raw count of progressions. The relatively large number of falling second progressions is also unusual. What this distribution does have in common with other raw analyses is the fact that the rising third progression is the least frequent progression.

Excluding passing chords retains the unusual shape of the distribution; although rising seconds and rising thirds are reduce in numbers. There are 5 passing chords recorded on the database, for this piece. An example is the C# diminished 7th chord at bar 5.

Adding appoggiatura chords to the exclusion rules makes a significant change to the distribution. The number of rising fourth progressions has increased to 21 and the number of falling fourth progressions has reduced to 12. The effect is to produce a distribution which is now similar to that produced by other pieces at this stage of the analysis. The counts are as follows:

Rising fourth (alpha) Progressions	21
Falling third (beta) Progressions	8
Rising second (gamma) progressions	2
Falling second (gamma') progressions	1
Rising third (beta') progressions	1
Falling fourth (alpha') progressions	12

This change is because this piece is characterised by a large number of appoggiatura chords, in particular, chromatic appoggiatura chords. This analysis clearly demonstrates that a piece composed with an apparently confusing number of chromatic chords, in this case appoggiatura chords, once analysed carefully nevertheless demonstrates underlying structures which are similar to other pieces of tonal music. This supports the idea that some types of surface detail such as passing and appoggiatura chords merely decorated underlying familiar structural patterns and that these patterns are revealed by a root progression analysis.

Excluding all three types of non-structural (or non functional) chords has a further significant effect on the polarisation. The falling 4th and rising third progressions are now totally absent from the analysis as follows:

Rising fourth (alpha) Progressions	9
Falling third (beta) Progressions	7
Rising second (gamma) progressions	2
Falling second (gamma') progressions	1
Rising third (beta') progressions	0
Falling fourth (alpha') progressions	0

As is normally the case, in tonal music, this is due to the pairing of falling fourth progressions with the rising fourth progressions. The absence of rising third progressions is also due to pairing of progressions, in this case between rising and falling third progressions. An example of this is at bar 13 to 14 where the progression is: D7 - B7 - D7.

As is usual, at this stage in the analysis, this graph shows the characteristic "signature" for tonal music. i.e., once non-structural chords have been removed, there is a strong bias towards the use of the three strong progressions to the almost total exclusion of the three weak progressions. The paired falling and rising fourth progressions are highly clustered and create the segmentation into static harmony and dynamic harmony. See the discussion on this in the Thesis section Analysis of Root Progressions .

The one remaining falling second progression occurs at bars 20 to 21. As is usually the case, this is used to facilitate a modulation. It will be observed throughout these analyses that residual un-polarised progressions are normally associated with modulations or with other phenomena such as chord sequences. This is evidence that residual un-polarised progressions are systematically used rather than a random phenomenon. In these situations, the composer appears to be using consciously learned processes which override the subconscious selection of polarised progressions.

A further point that is worth noting, in this particular piece, is that in the final graph, the falling third (beta) progressions are more than three times as frequent as the rising second (gamma) progressions. This deviates form the overall average on the database, where falling thirds are only slightly more common than rising second progressions.

Some other interesting points to look out for are: the dominant prolongation at bars 6 to 8 and the static codas at bars 13 to 14 and at bar 27 to the end of the piece.

I hope to provide further information about this analysis as more functions are implemented on the progression database.

This piece has been included on the database as an example of a pre-tonal composition (Lassus lived 1532 -1594). This piece demonstrates that music prior to the tonal period does not show the same degree of polarisation of chord progressions as do pieces from the tonal period. In combination with other examples, this demonstrates that the change from music of the renaissance (mostly 'polyphonic') music to the music of the baroque (the first really 'tonal' music) is accompanied by a characteristic increase in the polarisation of chord progressions.

For this reason, this piece is not included in the 'All Tonal Pieces' graph (See Help on Using the graph) but is included on the database in order to show the historic process.

It is worth noting that as this piece is in 5 voices and the writing is highly triadic, the identification of chord roots is comparatively easy. However, it is not always easy to determine whether chords should be considered as passing, appoggiatura or auxiliary functions, as these designations do not necessarily always have the same meaning for this period of music. In order to be able to make a reasonable comparison with other pieces on the database, I've classified the chords by following the same rules of voice leading as for later pieces of music. Whether this is appropriate or accurate is not really important as the following comparisons show that the exclusion of such chords does not have the effect that it does for later tonal pieces.

With no exclusion rules selected, this piece shows almost equal 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 (bearing in mind that these do vary between pieces.) The raw counts are as follows:

The reader can use the graphical tool to try different combinations of exclusion rules but it turns out that polarisation is not dramatically different for any combination. Following are the counts for all exclusion rules selected:

Remember, when comparing the graphs, the scale changes to suit the largest numbers. With all exclusion rules selected, the proportions of rising 4th and falling 4th progressions are reduced. However, the number of falling fourths is nevertheless similar to the number of rising fourths. This results in a refined count that does not show the same degree of polarisation as for later tonal pieces.

See the historical process section for further comparisons or try out the graphical tool interactively for different combinations.

Some further details can be observed in the use of chord progressions as follows:

There is some pairing up of falling 4th progressions with rising 4th progressions. This accounts for the reduction in the final counts of rising 4th and falling 4th progressions. Examples of paired rising and falling 4ths are at bars 27 (last chord) to bar 30 (first chord) and bars 36 to 38 (excluding the last beat). However, this pairing does not occur to the same extent as in later tonal pieces. Consequently there is some segmentation into static and dynamic harmony but not to the same extent as in later music.

A detailed examination of cadential patterns in the piece also shows up some progressions that anticipate later procedures. These include the prolongation of dominant chords; the use of dominant pedals and what appear to be cadential 6 4 chords which appear in the analysis as appoggiatura chords. These factors contribute to the similarities in the progression graphs with later pieces of music.

As this example is the basis of the thesis on this site you will find more detailed analyses of this piece in the:Technique and Results section and the Thesis generally. There is a full commentary on this analysis at: Commentary on the Analysis. Following, is just a description of the progression counts as observed by using the graph tool.

With no exclusion rules selected, this piece shows a spread of chord progression that is only partially polarised. These are as follows:

The main points of interest in this graph are the facts that the rising and falling fourth progressions are the most common progressions whilst the rising third progression is relatively uncommon.

Excluding passing chords reduces the number of rising third progressions as two of these are due to passing chords. An example is the: A - C7 - F progression at bars 11 to 13. The C7 acts as a passing chord between A to F, the voice leading following the rules for passing chords exactly. However, there is only a small increase in the polarisation of the graph.

Adding appoggiatura chords to the exclusion rules reduces the number of falling second progressions as some of these are the result of cadential 6 4 appoggiatura chords. Again there is an increase in polarisation.

Excluding all three types of non-structural (or non functional) chords has a more dramatic effect on the polarisation. The falling 4th and rising third progressions are now totally excluded as follows:

As is normally the case, in tonal music, this is due to the pairing of falling fourth progressions with rising fourth progressions.

This graph shows the characteristic "signature" for tonal music. I.e. once non structural chords have been removed there is a very strong bias towards the use of the three strong progressions to the almost total exclusion of the three weak progressions. The paired falling and rising fourths progressions are highly clustered and create the segmentation into static harmony and dynamic harmony. See the discussion on this in the Thesis section Analysis of Root Progressions .

The reduction in the number of falling seconds counted is also due to auxiliary pairs made up of rising and falling second progressions. An example of this is the A - G# diminished 7th - A at bars 9 to 11. This progression is really the result of auxiliary movement in the voices rather than a clear root progression. This supports the way structural and non-structural chords are treated in these analyses. The one remaining falling second progression occurs at bars 56 to 58. As is usually the case, this is at a point of modulation. It will be observed throughout these analyses that residual un-polarised progressions are normally associated with rapid modulations in this way or are associated with other phenomena such as chord sequences. This is evidence that un-polarised residual progressions are systematically used rather than a random phenomenon. In these situations the composer appears to be using consciously learned processes which override the subconscious selection of polarised progressions.

A further point that is worth noting, in this piece, is that in the final graph, the falling third (beta) progressions are more than twice as frequent as the rising second (gamma) progressions. This deviates form the overall average on the database, where falling thirds are only slightly more common than rising second progressions. This is due to a large cluster of falling third progressions at bars 42 to 43 and bars 123 to 124.