# Why atonal music is not harmonic, and tonality is



## millionrainbows (Jun 23, 2012)

I've never said that atonal music was "not harmonic" (whatever is meant by that); I say that atonal music is not based on a *harmonic model.*

Of course, all music using pitches is "harmonic" and has sonority.

In the case of 12-tone music, the original, retrograde, inversion, and retrograde inversion forms are well-suited for tone rows, because tone rows are *melodic* (not harmonic or vertical).

Try to apply this to tonality, and you can't, in this sense: a scale can't be "inverted" or "reversed" (this has no meaning) because it is only an _abstract index of notes, with no order. _Melodies can be inverted in tonality, but not scales.

Scales are conventionally_ depicted_ as a sequence of notes from low to high, as if they were "progressing" through time horizontally, but this is only a convention. Scales do not actually "exist" as realized musical entities; they are just an* index* of notes, with a starting point, which covers that octave.
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Tone rows are *melodic *musical entities, unlike scales, because they are horizontal, melodic entities (intervallic relations, regardless of pitch) with order, which must proceed in a sequence of time, like a melodic construct, in order to have meaning. The intervallic relations of a tone row are fixed, similar to a melody, but are really about interval relations.

These intervallic relations are _ordered,_ because it would make no sense to stack them vertically; they are not designed to be harmonically useful in that sense, since they contain all 12 notes, and register is not specified (in serial music, anyway): pitches, in the harmonic sense, are not the important thing in tone rows; _intervals are._

The idea of *melodic inversion, retrograde*, etc, is applicable to tonality, but _only in the melodic sense._ You can't "invert" a scale because it is not horizontal entity.

What are scales useful for, then? They are _unordered,_ so there are cross-relations between every note in the scale with every other note. What does this mean? It means that scales have a_ harmonic content,_ unlike tone rows.

What are harmonic content, and cross-relations in a scale? I means this: every note is related to every other note:

*C Major scale: C-C-E-F-G-A-B
*
Relations: First note, *C: *
C-D; C-E; C-F; C-G; C-A; C-B

Then, next note, *D: *
D-E; D-F; D-G; D-A; D-B

Then, next note, *E: *
E-F; E-G; E-A; E-B

Then, next note, *F: *
F-G; F-A; F-B

Then, next note, *G: *
G-A; G-B

Then, next note, *A:
*A-B

These intervals can be counted, to come up with a "harmonic content" of the scale: 
minor thirds: 2 (E-F, B-C)
major seconds: 5 (C-D, D-E, F-G, G-A, A-B)
minor thirds: 4: D-F, E-G, A-C, B-D)
major thirds: 3: C-E, F-A, G-B
fourths: 5: C-F, D-G, E-A, G-C, A-D
tritones: 1: (B-F)

20 relations; with 6 basic interval types (the rest are inversions): m2/M7, M2/m7, m3/M6, M3/m6, 4th/5th/, and tritone.

You can't do this with a tone-row, because the relations are restricted by ordering:
C-C#-D-D#-E-F-F#-G-G#-A-A#-B (chromatic set)

C-C#, C#-D, D-D#, D#-E, E-F, F-F#, F#-G, G-G#, G#-A, A-A#, A#-B, B-C

There a 12 interval relations. This is not a good row because the intervals are all the same, minor seconds.


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