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Thread: Baroque "chord progressions"

  1. #151
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by Larkenfield View Post
    ‘The "diminished seventh" chord itself, supposedly built on the vii degree, is not really that at all: it's to be considered an incomplete G7 dominant (B-D-F), and should be resolved as that by assuming a G root, according to two respected sources: Walter Piston's Harmony and Schoenberg's Harmonielehre.’
    ——
    Add the A of the C-major scale to the B-D-F and you have the half-diminished chord that naturally resolves to the E minor chord of the scale. Mahler started off his Seventh Symphony with a half-diminished chord but did not resolve it to the tonic. B-D-F is part of the half-diminished and is much more than an incomplete dominant seventh because it has a different root than a dominant G chord.
    That makes perfect sense to me. I'd never thought of it that way.
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  2. #152
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    12 equal is not just a simplified representation of 5 or 3-limit (generated by perfect fitths) diatonic. Hexatonic, octatonic, various "blues/oriental/gypsy/ethnic" or symmetrical 9, 10, 11 (this one is the chromatic, skipping the tritone) notes scales exist in it and are better represented in bigger divisions of the octave (and lead to bigger "tonalities" that are not generated by stacking perfect fifths).
    I understand this, but it's the stacking of fifths that is the most important point. This has harmonic consequences. If you stack fifths C-G-D-A-E, stopping at five, you get the pentatonic scale C-D-E-G-A, which you will notice has no tritone and no fourth degree. This scale is therefore more consonant than the diatonic major scale, since it has no tritones.

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  4. #153
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    Quote Originally Posted by millionrainbows View Post
    I understand this, but it's the stacking of fifths that is the most important point. This has harmonic consequences. If you stack fifths C-G-D-A-E, stopping at five, you get the pentatonic scale C-D-E-G-A, which you will notice has no tritone and no fourth degree. This scale is therefore more consonant than the diatonic major scale, since it has no tritones.
    Pentatonic scale has only 5 degrees. You are trying to shove it into some heptatonic models. Many of your favourite atonal theorists and composers explored 5, 6 etc note scales as their own thing. It also sounds like its own unique tonality (after listening to just traditional Chinese/Japanese music for a few days, Western diatonic may sound "chromatic" for a short period of time).
    We have a "wolf" interval similar to the tritone in the black note pentatonic, it's 400 or its inversion - 800 cents, instead of 500/700 (when we stack fourths or fifths).

    I think hexatonics are the most important in 12 ET, because of the symmetry and complementarity in it.


    Of course, it's more consonant, the more intervals in the chord, more dissonance we get. Still, I don't listen to music that uses the whole diatonic as a chord...
    I'm not sure, if there is a objective measure about how consonant are the intervals in a melody.
    In general, smaller intervals around semitones are probably considered the most dissonant (way more dissonant than intervals around tritones ) and hard to distinguish or even play by amateurs (give a chromatic piece to a school brass band and just listen to the end result).
    Sometimes, small intervals can even sound wrong (like alterations, instead of new musical objects) when you play the chromatic scale - I guess it's something related to our pitch perception (some cognition "experts" have suggested melodies and scales with no more than 9 different notes) and psychological expectations; these two factors ruin many of theoretical musical resources like polytonality/non-octave divisions etc.
    Tritones can sound pretty "cool" and are staple in all the spy-thrillers and blues/jazz. The simplest consonant ratio is 7/5, I don't think it's that great, but it doesn't sound wrong.

  5. #154
    Senior Member millionrainbows's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    Pentatonic scale has only 5 degrees. You are trying to shove it into some heptatonic models. Many of your favourite atonal theorists and composers explored 5, 6 etc note scales as their own thing. It also sounds like its own unique tonality (after listening to just traditional Chinese/Japanese music for a few days, Western diatonic may sound "chromatic" for a short period of time).
    We have a "wolf" interval similar to the tritone in the black note pentatonic, it's 400 or its inversion - 800 cents, instead of 500/700 (when we stack fourths or fifths).
    With six-note scales, we get the most variety of intervals (Hanson) before redundancy sets in (i.e. repeats of intervals with no new interval introduced). The pentatonic doesn't have all six intervals; it is missing the tritone, so harmonically speaking, it is a very "consonant" i.e. tonic-reinforcing scale. 400 cents refers to the major third, and when you generate a scale from fifths, the thirds will suffer, but it is a less-important interval than the fifth, as far as harmonic stability over the entire range. That seems to be the difference in our thinking, I consider scales harmonically first and foremost.

    Of course, it's more consonant, the more intervals in the chord, more dissonance we get. Still, I don't listen to music that uses the whole diatonic as a chord...
    I was trying to say earlier that scales do have "harmonic content" because of the intervals which are generated by cross-relations, called "interval vectors." This is the way I've learned to think about unordered scales, so it might as well be a "chord".

    I'm not sure, if there is a objective measure about how consonant are the intervals in a melody.
    You could do a vector analysis of any melody, as I've demonstrated in my blog, with 12-tone rows. A tone row is an ordered set, like a melody, so its interval vector is much smaller than a scale. But any melody which is scale-derived (not a fixed ordered tone sequence) is better paired with the interval vector of the entire scale, since melodies are derived from an unordered set, called a scale.

    In general, smaller intervals around semitones are probably considered the most dissonant (way more dissonant than intervals around tritones ) and hard to distinguish or even play by amateurs (give a chromatic piece to a school brass band and just listen to the end result).
    Again, I don't look at notes individually; I put them in harmonic context, so a tritone is dissonant as an interval when we compare it to a fifth, and when one of those tritone's notes is the tonic, it destabilizes the tonic, which is a harmonic consequence. On the other hand, tritones sound more stable when they are the b7 and major third of a chord, but this also has to be put in harmonic context with a tonic on "1".

    Tritones can sound pretty "cool" and are staple in all the spy-thrillers and blues/jazz. The simplest consonant ratio is 7/5, I don't think it's that great, but it doesn't sound wrong.
    Again, this works in jazz as a tempered interval. to me, it's not necessary that it be a "just" ratio.
    Last edited by millionrainbows; Apr-03-2019 at 19:35.

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    Even in the introduction of the book "Essay on the True Art of Keyboard Playing" by C.P.E. Bach, the authors admit that Bach's thorough bass practice would become unwieldy as more chords were added to the harmonic collection. Rameau's 'root system' was far smaller and easier to work with.

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    During the early eighteenth century, Jean-Phillipe Rameau articulated the modern notion of a chord, classifying basic musical objects based on their pitch-class content rather than their order or registral arrangement. Rameau implicitly suggested that three basic operations preserve the "chordal" or "harmonic" identity of a musical object: octave shifts, permutation (or reordering), and cardinality change (or note duplication). For instance, one can transform (C4, E4 G4) by reordering its notes to produce (E4, G4, C4), transposing the second note up an octave to produce (C4, E5, G4), or duplicating the third note to produce (C4, E4, G4,G4) - all without changing its right to be called a "C major chord." Furthermore, these transformations can be combined to produce an endless collection of objects, all representing the same chord: (E4, G4, C5), (G3, G4, C5, E4), (E2, G3, C4, E4, E5), and so on. To be a C major chord is simply to belong to this equivalency class - or in other words, to contain all and only the three pitch-classes C, E, and G. We can therefore represent the C major chord as the unordered set of pitch classes {C, E, G}. -Tymoczko, p. 36

    I think figured bass is rather archaic unless one has an overview, and I think it's limited to that older style of music, and is really more of a "technique" which was used in lieu of harmonic/root thinking, which was not developed or accepted or used, whatever.

    This figured-bass thinking was perhaps a method which worked its way into the stylistic arsenal of composers, and yes, they had to be handled in specific ways, but the abstracted convenience of thinking harmonically is still in evidence to modern analysts. Figured-bass tends to get bogged-down in voice-leading details which ignore a purer, freer abstract distillation of harmonic considerations. And as harmony got more complex, what happened to figured bass thinking? It failed, or rejected more complex harmony. Figured bass is an ideological artifact of a bygone way of thinking. We have bigger, more complex fish to fry.

    A chord in all its inversions has the same root function (not bass note), and the same quality (major/minor).

    Maybe in earlier times, it is treated differently...

    In some convoluted sense, it could be said that since figured bass notation recognizes each inversion separately from a bass note (not a root function), that they are not "equivalent" in that sense.

    WIK:
    Figured-bass numerals express distinct intervals in a chord only as they relate to the bass note (not a root function). They make no reference to the key of the progression (unlike Roman-numeral harmonic analysis).

    Because that would be "harmonic thinking."
    Last edited by millionrainbows; Sep-11-2019 at 14:06.

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