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Thread: Geometric Voice Leading Presentation

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    Question Geometric Voice Leading Presentation

    Hello

    I'm coming from a non-academic background and just trying to understand the rules of voice leading for pursuing a future composing career. I've always found difficulties in understanding this topic in notation on paper.
    Only recently I've read an article about presenting the progress of scale degrees on both the Chromatic Circle and the Circle of Fifths as geometric shapes like triangles and trapezoid, and it really made a lot of sense to me (I'm a visual learner at heart).
    I started analyzing chord progressions on both circles and just noticed the differences between them in the way they represent the shapes. Now I have these questions:

    1- Is this a good way to understand the topic or not? If not, what's the best way?
    2- What's the best use of each circle in practice?


    Thanks
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    Senior Member millionrainbows's Avatar
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    Get "Geometry of Music" mentioned in the books thread, for a detailed explanation of what each kind of model is capable of.

    Remember that the circle model is based on recursive (repeating cyclically) pitch identity, so it has a "tonal" bias, in that "a G is a G" no matter in what range it occurs. That's because our ears hear pitches as being "octave equivalent." So the circle models will always be tonal, i.e. they are (by default) a model of octaves, and will therefore be "scale" biased. This won't show cycles of pitches which go outside the octave, like we see in Slonimsky's Thesaurus of Scales and Melodic Patterns.

    Remember that these models are just tools; they are limited in what they can show. Use them for their best purposes, but don't expect them to be everything you'll ever want.

    Also look into number lines, for what they can reveal.
    Last edited by millionrainbows; Oct-31-2018 at 23:06.
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    Senior Member Dimace's Avatar
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    Instead of looking these shapes, put your hands on the piano (or keyboard) and after everything will be much easier to you. Don't forget that 95% of composers, conductors and singers, they used it not only to create but also as a help in their training and as a learning method. The black and white sequence of the keys is very easy to learned and with it your questions to be answered.
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    Senior Member EdwardBast's Avatar
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    You need to learn about this "in notation on paper" and, as Dimace said, on a keyboard. Circle diagrams are just another step removed from the sound. You must be able to comprehend the symmetries and relations among notes aurally and in notation. Strangely enough, diagrams of the kind you posted, and more complex ones like toroids, are mostly the playthings of academics and theorists.

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    Quote Originally Posted by EdwardBast View Post
    You need to learn about this "in notation on paper" and, as Dimace said, on a keyboard. Circle diagrams are just another step removed from the sound. You must be able to comprehend the symmetries and relations among notes aurally and in notation. Strangely enough, diagrams of the kind you posted, and more complex ones like toroids, are mostly the playthings of academics and theorists.
    There are keyboards based on different symmetries... The only thing that is harder to play is chromatic scales. Real music is vibrations in the air and hardly follows the idealized and simplified Western notation (and theory). I can see how AI in the future can use analysis on audio files, learning more about music than any theoretical information. There are already such musical programs, but getting anything useful out of them for now is another topic. I've seen such papers on rhythms and tunings.

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    Senior Member EdwardBast's Avatar
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    Quote Originally Posted by BabyGiraffe View Post
    There are keyboards based on different symmetries... The only thing that is harder to play is chromatic scales. Real music is vibrations in the air and hardly follows the idealized and simplified Western notation (and theory). I can see how AI in the future can use analysis on audio files, learning more about music than any theoretical information. There are already such musical programs, but getting anything useful out of them for now is another topic. I've seen such papers on rhythms and tunings.
    The OP did not express an interest in different tunings or the other topics of central interest to you, ^ ^ ^ but in traditional harmony from a visual perspective.

    What greater comfort does time afford than the objects of terror re-encountered and their fraudulence exposed in the flash of reason?
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    Basil Valentine

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    Quote Originally Posted by Ehab View Post
    1- Is this a good way to understand the topic or not? If not, what's the best way?
    2- What's the best use of each circle in practice?


    Thanks
    Hello Ehab,

    1.) IMHO it's a very counter-intuitiv, unnatural and, as Edward already stated, pseudo-skilled approach. You might impress some "theoretical artists" with that, but in the real world it makes things just more complicated and I don't see any benefit in using this weird thinking style.

    2.) IMHO the best use of the circle of fifth is to learn the keys with 1b to 1# as a beginner - so C, F, G Major in classical thinking.
    Connect all major and minor chords with each other that are at least a third away. So in C/Am this would be C-Em, C-F, C-G, C-Am then Dm-F, Dm-G, Dm-Am and so on. The diminished chord is too special for the beginning and the very close chords require a different voice-leading then those at least a third apart. Go trough all possible voicings (e.g. 1,3,5 in the Soprano) and piano and choir style.

    For the beginning put the root note always in the bass and always think as following.
    1.) Which notes have which function ? So for C-F this would be "1/Root (C) in the Bass, 1 (C) in the Tenor, 3 (E) in the Alto and 5 (G) in the Soprano for the first chord C.
    2.) When going to F, which voices will stay (called "harmonisches Band" in german) and which will move and how will the functions change. So the Bass is 1 - 1 (C-F), the Tenor C stays but the function changes from 1 to 5, the Alto goes up from 3-1 (E to F) and the Soprano goes from 5 to 3 (G to A).

    This will take some time to get used to, but if you want to build high, you need a very stable fundament first. I promise you won't regret it.

    Extend when you're feeling comfortable in all previous keys with additional b and # till you have the full circle. And of course compose at least little exercises / harmonic models (including several variants of modulations between the keys - preferably good sounding ones - not just theoretical correct ones (what every computer program / chordgenerator today can do)). It's better to start with very easy pieces but do it perfectly, than to skip and later struggle all the time wondering, why progression stagnates since years.

    This way you will develop a REAL understanding of harmonic relationships, how music works naturally and how the different keys are related to each other instead of thinking different keys just as a transposition / shift of each other. After decades of work all keys will blend into each other and you will only be thinking in one big key, thinking keys like previously thinking chords within keys, and thinking chords like previously thinking single tones within chords ("the key of music" as I call it), flowing trough all harmonic regions and realize, how much there is still to explore in our 12 tone system.

    But don't forget, that harmonic understanding is just one part, a very important one, but still one part of many, that is needed for composition. Today there is a massive focus on the vertical aspect of music (showing in the increasing appearance of complicated frankenchords), but the horizontal aspect and most importantly the overall formal aspect (form, development, variation - the main parts of an overall dramaturgic emotional architecture of composed music) are getting lost more and more, resulting in music that just repeats little ideas endlessly or is merely a random chain of dissonant chords, that are just complicated (lots of unconnected notes), but not musically complex in any way (harmonical connections and relations between all notes in the piece - everything being connected with everything). Naturally we humans love complexity and not complicatedness - you can observe it in any other art and designs. Only as many notes as needed, not less, but also not more. After you reached a certain level of musical understanding, you will realize, that playing lots of stacked notes and frankenchords actually is way more easy, than playing just a few notes, but choosing those in a way, that just altering one note, will alter the whole harmonical context (W.A. Mozart being a perfect example for this). The real mastery lies in a complex and sophisticated yet simple and naturally flowing music.

    Actually rhythm is also very very powerful and highly interlocked with harmonic perception too and timbre-wise there was never so much to explore as today.

    Hope this gives you some food for thought and helps you on your artistic journey.


    Martin

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    Quote Originally Posted by EdwardBast View Post
    The OP did not express an interest in different tunings or the other topics of central interest to you, ^ ^ ^ but in traditional harmony from a visual perspective.
    This has nothing to do with different tunings (but someone can design such keyboard for any tuning system).

    https://en.wikipedia.org/wiki/Isomorphic_keyboard
    https://en.wikipedia.org/wiki/Jank%C3%B3_keyboard
    https://en.wikipedia.org/wiki/Generalized_keyboard

    (The only downside is that these types of keyboards are usually expensive.)
    Last edited by BabyGiraffe; Yesterday at 08:31.

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    Quote Originally Posted by EdwardBast View Post
    You need to learn about this "in notation on paper" and, as Dimace said, on a keyboard. Circle diagrams are just another step removed from the sound. You must be able to comprehend the symmetries and relations among notes aurally and in notation. Strangely enough, diagrams of the kind you posted, and more complex ones like toroids, are mostly the playthings of academics and theorists.
    That might be more true of pianists than it is of guitarists. Since the guitar neck is a self-similar succession of chromatic notes (no black keys), then many of these circular-derived models will transfer directly to the guitar fingerboard. Pat Martino sees these instances the "mechanisms" of the guitar which make it unique from the piano. The diminished chord repeats every three frets, and the augmented repeats every four.

    Yes, there does come a point, such as in jazz improvisation, where theory needs to "go out the window" because it distracts from playing by ear. As Baby Giraffe said, that's what music "is."
    Last edited by millionrainbows; Today at 20:55.
    "The way out is through the door. Why is it that no one will use this method?"
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    "In Spring! In the creation of art it must be as it is in Spring!" -Arnold Schoenberg

    "We only become what we are by the radical and deep-seated refusal of that which others have made us." -Jean-Paul Sartre

    "I am the spirit of dead zebras." - It came to me in a dream

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