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Thread: ...How to Listen To and Understand Atonal Music?

  1. #61
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    Quote Originally Posted by Woodduck View Post
    I don't think my objection is misguided. The notion of "equal-interval chords" in which the intervals are in fact unequal except by a convention of notation (they're equidistant on the staff) seems to me no more than a physical description stating the obvious: that common practice tonality is based on triadic harmony and atonality is not. Perhaps that's all you meant to say?
    Triads and seventh chords are consistently made up of a succession of thirds. I think the word "succession" here is key. A triad is a succession of two thirds; a seventh is a succession of three thirds. When we say "succession of thirds", without specifying if it's a major or minor third, we are uniformly refering to one type of intervallic information. Tonality is here just a context that tells you whether it's a major or minor third. You can call it what you want, but I think my use of the term "equal-interval chord" as in the Wikipedia article on "Mixed-interval chord": "a mixed-interval chord is a chord not characterized by one consistent interval. Chords characterized by one consistent interval, or primarily but with alterations, are equal-interval chords. Mixed interval chords "lend themselves particularly" to atonal music since they tend to be dissonant."

    Perhaps I meant to conjecture, that even if tonal features such as partial major/minor chord progressions may be included in atonal music, there are strong reasons not to stack up multiple thirds. (Berg, for instance, explicitly puts up perfectly tonal harmonies, but often with only single third interval.)

  2. #62
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    Quote Originally Posted by Gargamel View Post
    Triads and seventh chords are consistently made up of a succession of thirds. I think the word "succession" here is key. A triad is a succession of two thirds; a seventh is a succession of three thirds. When we say "succession of thirds", without specifying if it's a major or minor third, we are uniformly refering to one type of intervallic information. Tonality is here just a context that tells you whether it's a major or minor third. You can call it what you want, but I think my use of the term "equal-interval chord" as in the Wikipedia article on "Mixed-interval chord": "a mixed-interval chord is a chord not characterized by one consistent interval. Chords characterized by one consistent interval, or primarily but with alterations, are equal-interval chords. Mixed interval chords "lend themselves particularly" to atonal music since they tend to be dissonant."

    Perhaps I meant to conjecture, that even if tonal features such as partial major/minor chord progressions may be included in atonal music, there are strong reasons not to stack up multiple thirds. (Berg, for instance, explicitly puts up perfectly tonal harmonies, but often with only single third interval.)
    Triad is a succession of thirds only in a scale where these thirds belong to the same interval class. So, not in 12 equal where step 3 and 4 don't belong to the same interval class - so, your remark about stacking thirds makes no sense (in theory only: in practice I doubt that most listeners won't hear in more than 9 different note melodies alterations of pitches instead of unique "scale degrees").
    Still, if you want to compose dodecaphonic music, you have to think in 12 equal logic, not in 7 (in 7 equal major and minor "thirds" are mapped to the same step, so 7-tone music can be triadic - or tetradic, because 7/6 is mapped also to the same degree as 5/4 and 6/5; in 12 equal 7/6 is mapped to 6/5 => so seventh chords of jazz and romantic music can be interpreted as septimal consonances, for example the dominant seventh can be thought as 4:5:6:7 = 1-5/4-3/2-7/4 and the whole 12 equal as kind of scale, equivalent to diatonic one, but heavily tempered; if we want more accuracy - 7/6 and minor third being different pitches, we can extend to septimal meantone ((31 equal is perfect)) or two other 12 tone scales in 22 or 27 equal.)
    Honestly, it's pretty hard to make real atonal music, because every possible progression has some harmonical interpretations.

  3. #63
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    Quote Originally Posted by Gargamel View Post
    Triads and seventh chords are consistently made up of a succession of thirds. I think the word "succession" here is key. A triad is a succession of two thirds; a seventh is a succession of three thirds. When we say "succession of thirds", without specifying if it's a major or minor third, we are uniformly refering to one type of intervallic information. Tonality is here just a context that tells you whether it's a major or minor third. You can call it what you want, but I think my use of the term "equal-interval chord" as in the Wikipedia article on "Mixed-interval chord": "a mixed-interval chord is a chord not characterized by one consistent interval. Chords characterized by one consistent interval, or primarily but with alterations, are equal-interval chords. Mixed interval chords "lend themselves particularly" to atonal music since they tend to be dissonant."

    Perhaps I meant to conjecture, that even if tonal features such as partial major/minor chord progressions may be included in atonal music, there are strong reasons not to stack up multiple thirds. (Berg, for instance, explicitly puts up perfectly tonal harmonies, but often with only single third interval.)
    I'd use the term "tertian."
    https://en.wikipedia.org/wiki/Tertian
    Last edited by millionrainbows; Feb-08-2021 at 14:16.

  4. #64
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    Quote Originally Posted by BabyGiraffe View Post
    Triad is a succession of thirds only in a scale where these thirds belong to the same interval class. So, not in 12 equal where step 3 and 4 don't belong to the same interval class - so, your remark about stacking thirds makes no sense (in theory only: in practice I doubt that most listeners won't hear in more than 9 different note melodies alterations of pitches instead of unique "scale degrees").
    Still, if you want to compose dodecaphonic music, you have to think in 12 equal logic, not in 7 (in 7 equal major and minor "thirds" are mapped to the same step, so 7-tone music can be triadic - or tetradic, because 7/6 is mapped also to the same degree as 5/4 and 6/5; in 12 equal 7/6 is mapped to 6/5 => so seventh chords of jazz and romantic music can be interpreted as septimal consonances, for example the dominant seventh can be thought as 4:5:6:7 = 1-5/4-3/2-7/4 and the whole 12 equal as kind of scale, equivalent to diatonic one, but heavily tempered; if we want more accuracy - 7/6 and minor third being different pitches, we can extend to septimal meantone ((31 equal is perfect)) or two other 12 tone scales in 22 or 27 equal.)
    Honestly, it's pretty hard to make real atonal music, because every possible progression has some harmonical interpretations.
    .....Harmonical?

  5. #65
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    Beethoven used root movement by thirds, as in the transitions in the Ninth. This kind of root movement is doubly interesting because not only does it move to distant key areas quickly, it also has the effect of "outlining triads" with the roots. Like, if you moved chords from Cmaj-Amin-Fmaj-Dmin. This has the effect of outlining a Dmin7 chord, D-F-A-C.

    In terms of their "cycling" properties, minor thirds have a value of 3 (semitones) and cycle within the octave as 3X4=12, and major thirds are a value of 4 semitones, so 4X3=12.

    In triadic terms, these are diminished seventh and augmented chords. The diminished seventh is so called because it "diminishes" the fifth of a triad, so it has an "inward-going" effect.
    The augmented chord has "augmented" or expanded the fifth, so it has an "outward-going" effect.

    These have corresponding effects on our perception of tonality. Holst's use of augmented triads has the effect of creating a sense of "harmonic vertigo," as if the tonality were expanding.

    Diminished structures will have the opposite effect, of a "shrinking" collapse of tonality, which will tend towards the chromatic, as the diminished scale is made of m3rds and semitones.

    Augmented structures 'expand' because the augmented scale can be mapped to the whole tone scale, and is a symmetrical construction of whole steps, which give a scale-like feeling of movement "away" from a note.

    Thirds can be considered n terms of root movement, or melodic implications.

    A third moving down is getting stronger or "ascending" in root feeling: we hear the second note as root, or resting point.

    A third up is getting weaker or "descending" in root feeling: we hear the first note as root, but we have moved away from it to a weaker note; thus, it is "descending" or weakening the sense of tonality.

    By 'weak' or 'strong' is meant simply either 'strengthening' and reinforcing a root or key center, or 'weakening' the root or key, and moving away from it, to perhaps another key.

    That's why Beethoven used root movement of chords by descending thirds, Cmaj-Amin-Fmaj-Dmin (in the transitions of the Ninth) because he was traveling to new root stations, and in downward-moving thirds we hear each succeeding root as stronger than the last.
    Last edited by millionrainbows; Feb-08-2021 at 15:33.

  6. #66
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    Quote Originally Posted by millionrainbows View Post
    .....Harmonical?
    Adj. 1. harmonical - involving or characterized by harmony
    (or an obsolete form of harmonic)

    Btw, your interpretations of harmony only in terms of 12 equal characteristics are too limited, my friend, you can play valid 5-limit temperaments in 9 to 19 notes per octave without problems (20 and 21 are probably too "enharmonic" for simple triadic harmony, but maybe even they can be used, if someone is careful). 22+ notes per octave is well tuned 7-limit (more dissonant harmonies can be found in bigger divisions).

  7. #67
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    Quote Originally Posted by BabyGiraffe View Post
    Adj. 1. harmonical - involving or characterized by harmony
    (or an obsolete form of harmonic)

    Btw, your interpretations of harmony only in terms of 12 equal characteristics are too limited, my friend, you can play valid 5-limit temperaments in 9 to 19 notes per octave without problems (20 and 21 are probably too "enharmonic" for simple triadic harmony, but maybe even they can be used, if someone is careful). 22+ notes per octave is well tuned 7-limit (more dissonant harmonies can be found in bigger divisions).
    You need to 'grok,' to begin with, why there are 12 notes, why they became equal, learn to generalize, and forget all this 5-limit stuff.

  8. #68
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    Why is all composition taught to consist of four parts? Although there is no need for resolution in atonal music, the idea of having four voices is persisent. Maybe it's just most practical to teach it that way, or if you need to sustain a sense of indeterminate root, the 4-part chord with the least possible transpositions would be the dim7 chord?

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