# Harmonic Function



## millionrainbows (Jun 23, 2012)

What I mean by tonal music being "visceral" or "of the senses" is because all its functions, even the "cerebral" ones (root movement, tension/resolution) are traced back to the ear/brain perception of vertical, instantaneous consonance/dissonance.

Sorry, but here's the long-winded explanation:
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Most dissonant intervals to most consonant intervals, within one octave:

1. minor seventh (C-Bb) 9:16
2. major seventh (C-B) 8:15
3. major second (C-D) 8:9
4. minor sixth (C-Ab) 5:8
5. minor third (C-Eb) 5:6
6. major third (C-E) 4:5
7. major sixth (C-A) 3:5
8. perfect fourth (C-F) 3:4
9. perfect fifth (C-G) 2:3
10. octave (C-C') 1:2
11. unison (C-C) 1:1

The steps of our scale, and the "functions" of the chords built thereon, are the direct result of interval ratios, all in relation to a "keynote" or unity of 1; the intervals not only have a dissonant/consonant quality determined by their ratio, but also are given a specific scale degree (function) and place in relation to "1" or the Tonic. This is where all "linear function" originated, and is still manifest as ratios (intervals), which are at the same time, physical harmonic phenomena.

One (1:1) is the ultimate consonance.

The interval ratios in the chart above, to the right, are just a way of expressing the relationship of two notes. For example, 2:1 is the octave, or doubling of frequency; conversely, 1:2 halves it.

In the key of C, a simple 1-3-5 G triad is not identical to the simple 1-3-5 C triad, because of its position (functioning as V) in relation to the root. The D, resolving down, now becomes root, as well as being the top of a fourth G-C, which is heard as root on top.

They are major triads and are equally dissonant. The functional difference is only apparent once tonic has been established. Tonic is established correctly once the listener has heard and connected (COGNITIVELY) the series of intervals that constitute the diatonic scale.

No chord exists in isolation, but all exist in relation to "1", unity, or tonic.

Implicit in any harmonic interval, whether it be 2:3 or 3:4, is an implicit relation, and specific note-position in the heirarchy, in relation to "1" or tonic, as well as its being more dissonant or more consonant in relation to "1" or the root.

Hearing harmonic (vertical) dissonance/consonance happens instantaneously, as the result of the ear/brain perceiving a harmonic relationship, or ratio (a ratio is not a fixed quantity, it is a relationship between two things).

But chord function (horizontal time-line) takes time to establish. This is cognitive, although it is based on visceral harmonic (vertical) "instant" recognition of the ear/brain to consonance/dissonance.

In the case of simple pop song progressions, using static chord exchanges of say, C-F, it might be ambiguous whether "C" is I and "F" is IV, or if "C" is V and "F" is I; in fact, many pop songs play on this ambiguity.

All chord functions relate to the Tonic, or unity. This is exactly the way interval ratios work, also.

From Harry Partch, "Genesis of a New Music:"

[A ratio represents a tone and an interval at one and the same time; in its capacity as the symbol of a tone it is the over number that is nominally representative (in the upward manner), but since the over number exists only in relation to the under number, the ratio acquits its second function, as representative of an interval;

...conventional musical example: 3/2 represents "D" in the "key of G" - upward from "G"; it is thus simultaneously a representative of a tone and an implicit relationship to a "keynote" - or unity.]

Thus, it is seen that the steps of our scale, and the "functions" of the chords built thereon, are the direct result of interval ratios, all in relation to a "keynote" or unity of 1; the intervals not only have a dissonant/consonant quality determined by its ratio, but also is given a place in relation to "1" or the Tonic. This is where all "linear function" originated, and is still manifest as...ratios.

[The scale of musical intervals begins with absolute consonance (1 to 1), and gradually progresses into an infinitude of dissonance, the consonance of the intervals decreasing as the odd numbers of their ratios increase.]

So, how does the "time line" figure into the cognition of "function" of chords? Cognition of harmonic function always involves hearing a sequence of events.


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