Author Topic: Why tonality is harmonic, and serialism is not  (Read 591 times)


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Why tonality is harmonic, and serialism is not
« on: March 09, 2016, 03:31:05 PM »

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:

 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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