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Topic: Enharmonic Reintepretations...

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  1. #1

    Enharmonic Reintepretations...

    Hello all!

    I have a question about enharmonic reinterpretations to modulate to foreign keys. Now, I'm familiar with the four sonorities that can be reinterpreted:

    1. Mm 7---> Ger+6
    2. vii°7--> can be looked at as four different fully diminished 7th chords.
    3. Fr+6--> not too familiar with yet.
    4. Augmented chords---> not too familiar yet, either.

    I'm interested in how to easily remember the relationship of the four keys that share the enharmonic reinterpretation of the fully diminished 7th chord (vii°7.) I know that a fully diminished chord is composed of all minor thirds, which can make any of the four tones a leading tone. I've also discoved that each of the four keys are a 6th apart. I'm still not seeing an easy way to remember the relationships between these four keys (if there is one.) Any information is appreciated, thanks!
    http://www.jamesjumonville.com

    Captain Hook (if you see Pan let me know!)

  2. #2

    Re: Enharmonic Reintepretations...

    This might be even more complicated to you, but if it clicks, it will stick.

    Imagine the circle of fifths flattened out on a line:

    Cb-Gb-Db-Ab-Eb-Bb-F-C-G-D-A-E-B-F#-C#-G#-D#-A#
    <---- Flatter keys ---------------- Sharper keys ---->
    (extend as necessary)

    If a diminished 7th chord is properly spelled, the leading tone will be the note furthest to the right on this line (sharpest), and the key will be one half-step higher (naturally). The seventh will be furthest to the left (flattest).

    Let's take an example, and respell it for different minor keys, and two enharmonic equivalents:

    B, D, F, Ab:
    On our line, B is the furthest right, Ab is furthest left. B is therefore the leading tone, and the key must be c minor. The interval of a diminished 7th is formed between B and Ab. Notice that B-G# would actually be a major sixth.

    B, D, F, G#: key = a minor, 7th = G#-F
    B, C##, E#, G#: key = D# minor, 7th = C##-B
    Cb, D, F, Ab: key = Eb minor, 7th = D-Cb
    B, D, E#, G#: key = F# minor, 7th = E#-D
    Cb, Ebb, F, Ab: key = Gb minor, 7th = F-Ebb

    Notice that the tonics of the minor keys themselves form a diminished 7th chord, so that is a quick way to think of the keys once you have one of them.

    This is just a general guide. There are cases where the chord should be respelled due to ease of reading in individual melody lines which combine to form the chord.
    - Jamie Kowalski

    All Hands Music - Kowalski on the web
    The Ear Is Always Correct - Writings on composition

  3. #3

    Re: Enharmonic Reintepretations...

    Hey Jamie!

    Thanks for taking the time to explain all of this. It makes a litte sense, but the all the pieces haven't clicked into place yet. I'll have to read it a few more times and then maybe it will work out in my mind. Thanks again for the info and I'll write if any more questions arise.
    http://www.jamesjumonville.com

    Captain Hook (if you see Pan let me know!)

  4. #4

    Re: Enharmonic Reintepretations...

    Surely the "relationship" of the four keys is simply another diminished 7th chord a semitone higher?

    Terry

  5. #5
    Senior Member newmewzikboy's Avatar
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    Re: Enharmonic Reintepretations...

    I believe there are 8 not 4 enharmonic relationships for each dim7.

    One could also look at it as one of three tetrachords, any two of which make a octatonic scale.

    4-28*(3) 0369 004002 Diminished-seventh Chord

    Set 4-28; Inversionally symmetrical @ T2 and T6; 4 minor 3rds; 2 Tritones.

  6. #6

    Talking Re: Enharmonic Reintepretations...

    Here's a pdf with all enharmonic possibilities of Bdim7 chord.

    See chart!
    Sincerely,
    Falcon1


    icelandphotoblog.com
    my cafepress store
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    Please support your fellow musician from Iceland where the currency has fallen 70% against USD and 90% against EURO! Every dollar or euro counts!


  7. #7

    Re: Enharmonic Reintepretations...

    OK, I discussed this with my composition professor and basically he told me what Terry had said, simply look at that chord tone and go up a half step or semitone and that will be the new key. Now, each of the four reinterpretations will be in different inversions: vii°7, vii° 6 5, vii° 4 3, and vii° 4 2.

    Also, I've found that it is easy to see the common reinterpreatation of V7/IV as the Ger+6, the key would be either a minor 6th down/Major 3rd up OR look at the AUG 6th and discover the fifth that it is supposed to expand out to as an AUG 6th chord should in its common resolution.

    I don't yet understand how the Fr+6 or Augmented triads can act as reinterpretations. Thanks for all the help!
    http://www.jamesjumonville.com

    Captain Hook (if you see Pan let me know!)

  8. #8

    Re: Enharmonic Reintepretations...

    Quote Originally Posted by capt_hook
    OK, I discussed this with my composition professor and basically he told me what Terry had said, simply look at that chord tone and go up a half step or semitone and that will be the new key.
    Not to pick a nit, but I did mention that as well in my post. Sorry it was clouded by my denser observations.
    - Jamie Kowalski

    All Hands Music - Kowalski on the web
    The Ear Is Always Correct - Writings on composition

  9. #9

    Re: Enharmonic Reintepretations...

    Quote Originally Posted by Skysaw
    Not to pick a nit, but I did mention that as well in my post. Sorry it was clouded by my denser observations.
    I apologize Jaime, I do realize you had stated that in your explanation, but I think I overlooked that while being overwhelmed by the amount of info you gave I do greatly appreciate the time you took to explain it. I actually printed it out and read through it a few times. BTW, I like the music on your site! Thanks for the helpful chart Falcon1, I also printed it out to study when away from the computer.

    I usually don't get things at first sight, but when I work it out, take it apart, and learn it- it will be with me FOREVER I appreciate all the info that has been given in response to my question. I really love this site and I come here not only b/c I have GPO, but b/c all of you wonderful ppl willing to give a helping hand and are very understanding and courteous. Thank you all again very much.
    http://www.jamesjumonville.com

    Captain Hook (if you see Pan let me know!)

  10. #10

    Talking Re: Enharmonic Reintepretations...

    Quote Originally Posted by capt_hook
    I don't yet understand how the Fr+6 or Augmented triads can act as reinterpretations. Thanks for all the help!
    Here's a chart I did which, I hope, can help you:

    Sincerely,
    Falcon1


    icelandphotoblog.com
    my cafepress store
    my fine art print store
    my music store

    Please support your fellow musician from Iceland where the currency has fallen 70% against USD and 90% against EURO! Every dollar or euro counts!


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