# Harmony and Counterpoint Constrain One Another



## millionrainbows

From _A Geometry of Music, _Dmitri Tymoczko:
"Figure 1.3.4 shows that any two major chords can be connected by stepwise voice leading in which no voice moves by more than two semitones. This means that Lyrico can write a harmonic progression _without worrying about melody;_ that is, for any sequence of major chords, there is always some way to connect the notes so as to form stepwise melodies...
But what if Lyrico writes the chromatic cluster [B, C, Db] followed by [E, F, Gb], its transposition by ascending fourth? Here, none of the notes of the first 'chord' are within two semitones of any note in the second, and hence there is no way to combine a sequence of these chords so as to produce conjunct melodies (Figure 1.3.5). At the same time, however, the chromatic cluster can do things that the C major chord can't: Figure 1.3.6 shows that is possible to write contrapuntal music in which individual melodic lines move by short distances _within_ a single, unchanging harmony. Clearly, this is possible only because the chord's notes are all clustered together, ensuring that there is always a short path between any two of them." -p.13-14


----------



## millionrainbows

Torkelburger said:


> But doesn't he say "two major chords"? And "sequence of major chords"? B, C, Db and E, F, Gb are not major chord qualities *so would not apply to what he is talking about*.


You need to see what he is talking about first. He's comparing two different harmonic situations.

1.) Harmonic entities which divide the octave up relatively evenly, like major chords, are better suited for counterpoint in which harmonies change quickly.

2.) Clusters of closely-spaced notes are ideally suited for static music in which harmonies don't change.

This means that, with the "clusters" as our harmonic underpinning, "there is no way to combine a sequence of these chords so as to produce conjunct melodies." In this case, harmony has constrained counterpoint.

With major chords, one "can write a harmonic progression without worrying about melody; that is, for any sequence of major chords, there is always some way to connect the notes so as to form stepwise melodies." In this case, harmony has enabled counterpoint.
==========================================================

To understand the point, you have to also be flexible enough to consider the clusters as also being (non-triadic) _chords._

That is, once you understand that he is presenting a contrast, and accept the examples of clusters as being harmonically valid.

Then again, if you reject the idea of a cluster as a harmonic entity, and do not wish to venture outside of that box/paradigm of tonality, then there can be no discussion of this point.

WIK: A *chord, in music, is any harmonic set of pitches consisting of multiple notes(also called "pitches") that are heard as if sounding simultaneously.

In tonal Western classical music (music with a tonic key or "home key"), the most frequently encountered chords are triads, so called because they consist of three distinct notes: therootnote, and intervals of a third and a fifth above the root note. Chords with more than three notes include added tone chords, extended chords and tone clusters, which are used in contemporary classical music, jazz and other genres.
*


----------



## millionrainbows

What the above shows us is that CP classical music is a self-fulfilling system which is virtually 'automatic' in nature; a no-brainer for composers like Mozart, Handel, Vivaldi, and Haydn. The diatonic scale, which divides the octave up so evenly, and fits together in such a closely-related cookie cutter fashion, is an easy environment in which to do counterpoint and compose conjunct melodies for; they practically compose themselves. you can look in any direction and find a closely related chord or voice which is a member of a chord; do you want harmony A, B, or C? A harmonic buffet; whatever suits your fancy.


----------

