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Thread: Ascending substitute dominants

  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 02:09 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 10:26 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 03:57 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 10:25 AM.

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    I'll be fascinated to hear it. As a software writer it informs everything I do. Other theorists have used it to good effect to interpret existing scores. What I haven't yet heard is much music which explicitly leverages it for composition.
    And I'm a great believer that "There's nothing as practical as a good theory".

  8. #8
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    One more curiosity, a standard tritone sub progression (IIm7-bII7-IM7)

    Key of Eb

    Fm7-E7-EbM7 or
    Fm7-Fb7-EbM7 ?

  9. #9
    Registered User motherlode's Avatar
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    (IIm7-bII7-IM7) = Fm7-E7-EbM7

  10. #10
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    Thanks again motherload. When using chord/lead sheet notation would you always spell the "difficult" roots (B#,Cb,E# and Fb) enharmonically?

  11. #11
    Registered User motherlode's Avatar
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    Yes.

  12. #12
    Registered User motherlode's Avatar
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    Nuffink wrote regarding PCS technique ...
    What I haven't yet heard is much music which explicitly leverages it for composition.
    Please refer to the Appendix for a two-page table of all possible prime forms of Pitch Class Sets. This table is an indispensable aid for composer
    Last edited by motherlode; 04-07-2018 at 06:37 PM.

  13. #13
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    I agree, this should be used for composition.

    "There are only (208) prime forms, I took two days and played everyone of 'em on the piano"

    Why? The prime forms are likely to be the least interesting rotations. I'd be playing the (to coin a phrase) Anti-primes - the least compact rotations.
    Locrian is the prime of the Diatonic, Lydian is the Anti-prime.

  14. #14
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    btw,

    Whilst from a maths point of view there are 208 prime forms, from a musicians point of view there are 352.
    Forte considered chiral sets to be equivalent, musicians don't.
    Put simply, for Forte Harmonic Minor and its inversion, Harmonic Major are the same set (7-32) with a prime form of {0,1,3,4,6,8,9}.
    For the rest of us these are 2 distinct sets 7-32a (Harmonic Minor, prime {0,1,3,4,6,8,9}) and 7-32b (Harmonic Major, prime {0,1,3,5,6,8,9}).

  15. #15
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    Quote Originally Posted by motherlode View Post
    [SIZE=4]It is my contention that without a fluent understanding of the prime form, much of what PCS has to offer is wasted.
    Ok, I accept your contention. After all, you've played them, I've only played with them on a spreadsheet. But, if it's true, it's a happy accident. Forte certainly gave the prime form no special place. He had to list them some way and the obvious choices are the most and least compact rotations. He chose the most compact as the prime.

    edit:

    Here's a little problem for the the idea of Forte primes as significant. The prime for the dominant 7 is [0,2,5,8]. No rotation of that makes a 7th.
    Last edited by nuffink; 03-19-2018 at 12:07 AM.

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