In many years of teaching the harmonization of a chorale melody, if a student showed real ability, understood the variables of vertical and horizontal choice, I wanted to see how this achievement could be further refined. I was especially interested to see if it was possible to find in Bach any kind of preferences in the use of specific dissonances as a means of individualizing each chorale harmonization and from this introduce another pedagogical lens of selection. I therefore started to apply certain kinds of filters to Bach Chorales to see if there were any kinds of ratios of vertical occurrence that might indicate such preference. I did this without reference to text, which is of course a possible determinant for Bach’s choices, the widly different third and fourth strophes of Es ist genug being a famous example. Be that as it may, I was particularly interested in two aspects of Bach’s practice;
1) the ratio between triads and dissonant harmonies
2) the degree to which specific kinds of dissonance were emphasized in a chorale
I began with the first chorale in Remenschneider’s collection, Aus meines Herzens Grunde, which is particularly useful in that it contains only one accidental. I used Fortean PCS naming to make the tabulations. Here are some of the results of that analysis:
There are 80 verticals (icti).They are listed below in descending order of appearance. Triads are italicized .
Rank of occurrence/Number in chorale/PCS/# of occurrences/Common Name
1-1) 0,3,7 (49) Major/Minor Triad
2-6) 0,2,5,8 (6) Dominant/Half Diminished Seventh Chord
3-5) 0,3,5,8 (5) Minor Seventh Chord
4a-4) 0,3,6 (4) Diminished Triad
4b-7) 0,2,4,7 (4)
5-10) 0,2,7 (3)
6c-11 )0,2,6 (2)
7a-8) 0,2,3,5 (1)
7b-9) 0,2,5 (1)
7c-12) 0,2,4,6 (1)
The ratio of Triads (Major/Minor/Diminished) to dissonances is 53:27 or just about 2:1. This is towards the high end as is its ratio, 39:14 of Primary Triads (Major) to Secondary (Minor/Diminished) triads.
Of the dissonant verticals, the most common are 7th chords, Dominant and Minor.The ratio of these, including the Major 7th Chord, to other kinds of dissonances is 13:14 or nearly equal.
Of the 14 dissonances which are not 7th chords, the most common is 0,2,4,7 or what is numbered 7 in this chorale and occurs 4 times. This is the vertical which intrigues me the most in the harmonization. There are 5 possible transpositions in a Major scale of this PCS but Bach employs only one, G/A/B/D. Each one of its four appearances occurs in a different way, NT/PT/APT/SUS. Two have a unique voicing, the first and third and one is repeated, the second and fourth.
Further, two of the three note verticals, 0,2,5 and 0,2,7 are subsets of 0,2,4,8 and of the 4 occurrences of these two sets, two of them consist (9 and 10T1) of notes in the singular transposition of 0,2,4,8.
What is the significance of these observations?
Obviously, such a filtering of one chorale cannot predicate general principles. For example, O Mensch bewein dein Sünde gross has a ratio between triads and dissonances of 68:60 and, even more striking, a ration of 31:37 in the relation of Primary to Secondary Triads. Nevertheless, the emphasis on 0,2,4,7 in Aus meines Herzens Grunde suggests strongly to me that Bach articulates the individuality of this harmonization by the selectivity of the occurrence of this particular tetrachord in one particular transposition.
This kind of vertical emphasis assumes paramount importance beginning in the 20th C. with the breakdown of contrapuntal dissonance treatment.