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Thread: Ascending substitute dominants

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  1. #1
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    Ascending substitute dominants

    I can't find a definitive answer to this, so I thought I'd ask...

    If I use a substitute dominant ascending, should it be notated as a #?
    So, Dm7-Db7-CM7 is fine. Should the ascending form be spelled CM7-Db7-Dm7 or CM7-C#7-Dm7?

    If it were a 7 I would expect CM7-C#7-Dm7. But substitute dominants are defined by their expectation to resolve down a semitone. They are, in some way, inherently flat. Are they still flat when that expectation is confounded?
    Last edited by nuffink; 03-06-2018 at 01:09 PM.

  2. #2
    Registered User motherlode's Avatar
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    Should the ascending form be spelled ... CM7-C#7-Dm7?
    Yes.

  3. #3
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    Thanks, motherload.

  4. #4
    Registered User motherlode's Avatar
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    @nuffink

    In an old thread some months ago, you recommended an article on Pitch-Class Set Analysis. I downloaded it and went through it ... it's an excellent article!

    Last edited by motherlode; 03-17-2018 at 09:26 AM.

  5. #5
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    That would be this one... http://www.mta.ca/pc-set/pc-set_new/...ction/toc.html

    There's also a good calculator here... https://jeremiahgoyette.com/calc/set_class/ and the same site has a range of other calculators... https://jeremiahgoyette.com/calculators/

    and there used to be an excellent interactive table here... https://composertools.com/tools/ which has gone offline (I have a solution to it's loss which I'll PM you). The site still has an article that you may want to grab before it disappears... https://composertools.files.wordpres.../02/pcsets.pdf

    Finally a few observations about PCS theory -
    Forte's work, while groundbreaking, reveals the thinking of a mathematician rather than a musician. Specifically in its treatment of mirror sets (inversions) and its ordering.
    In Forte's work inversions are treated as identical. This leads to the situation that, for instance, the major and minor triads come from the same set (3-11) and the Harmonic minor and Harmonic major are both from (7-32). Later work has "corrected" this and now the inversions are separated, so the minor triad comes from 3-11a and the major from 3-11b. Likewise Harmonic minor is 7-32a, Harmonic major 7-32b.
    The other problem is that the sets are arranged into an order which makes little sense to a musician.
    The Diatonic scale is 7-35. Melodic minor is 7-34. 7-33 has no common name. 7-32a is Harmonic minor, 7-32b is Harmonic major. z-related sets can be miles apart in the lists.

    So I sorted them all by maximal evenness and, almost magically, the common sets float to the top. Not really magical, evenness is a powerful indicator of utility in both chords and scales.
    Here's the map... http://chordspace.com/images/jpegs/Map3.jpg

    I look forward to hearing what you come up with.
    Last edited by nuffink; 03-07-2018 at 02:57 PM.

  6. #6
    Registered User motherlode's Avatar
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    @nuffink

    Thank you for the additional information.
    Last edited by motherlode; 03-17-2018 at 09:25 AM.

  7. #7
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    I found Bruce Arnold's "Sonic Resource Guide" https://muse-eek.com/sonic-resource-guide/ to be a good book to understand PCS Theory as it is applied to improvisation. SRG is more of a reference book for looking up scales and seeing what chords you could apply it to. Also info on hexatonics which I found very useful.

    He has many other books applying PCS theory to all kinds of stuff like, arpeggios, sweeps, superimposition, ear training etc.. Quite a vast collection of courses. This page shows you some sweep ideas with various trichords: https://muse-eek.com/guitar-instrume...eep-arpeggios/

    I think the main thing I found with Mr. Arnold is he actually uses this stuff in his playing. Check out some of his recordings https://muse-eek.com/category/recordings he is all over the map using PCS to Jazz, Metal, Country, Blues and Classical music etc... Crazy interesting if you want to see/hear some applications.

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