# Geometric Voice Leading Presentation



## Ehab

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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## millionrainbows

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.


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## Dimace

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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## EdwardBast

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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## BabyGiraffe

EdwardBast said:


> 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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## EdwardBast

BabyGiraffe said:


> 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.


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## MartinAlexander

Ehab said:


> *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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## BabyGiraffe

EdwardBast said:


> 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/Jankó_keyboard
https://en.wikipedia.org/wiki/Generalized_keyboard

(The only downside is that these types of keyboards are usually expensive.)


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## millionrainbows

EdwardBast said:


> 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."


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## MartinAlexander

The point is, that the "logic" of music is best visualized on a keyboard. There's a huge range of pitches and every single one is there only once and the white/black coding interlocks with harmonic understanding, while e.g. on a guitar the range is limited, you have multiple ways of playing a note and no visualization of harmonic relationships. So from a didactic point it's definitely not even near as good suited as a keyboard (regardless of the soundgenerator attached to it) for voice-leading and harmonic understanding.

The point with notation is, that with notation you develope a pure thinking of music, detached from any instrument or genre. It's about learning music in it's purest form - not about a certain instrument, instrumentation or genre. Also voiceleading, so the horizontal aspect of music, is very good visualized.

I assume, if the threadstarter would like to just shift a few patterns in constant structure around the fretboard and play randomly scales over it, he wouldn't be too concerned about his voice-leading at all - he would just have thrown it out of the window ;-)


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## millionrainbows

MartinAlexander said:


> The point is, that the "logic" of music is best visualized on a keyboard. There's a huge range of pitches and every single one is there only once and the white/black coding interlocks with harmonic understanding, while e.g. on a guitar the range is limited, you have multiple ways of playing a note and no visualization of harmonic relationships. So from a didactic point it's definitely not even near as good suited as a keyboard (regardless of the soundgenerator attached to it) for voice-leading and harmonic understanding.


I see your points, but Western music as a whole is biased towards the keyboard and diatonic thinking, not chromatic. Of course, as guitarists and musicians, we all have to use these conventions, namely 7 letter-names (for the diatonic scale) and five "accidentals" or the left-over chromatic.

While it is true that on a keyboard "every note is there only once," it follows that each chord form is unique (in terms of black/white notes), so you have to learn 12 different forms for a major chord, not to mention inversions. On a guitar, the voicings can be moved up & down with only one form. That's an advantage.

To see the guitar as somehow inferior to the keyboard is a fallacy.



> The point with notation is, that with notation you develop a pure thinking of music, detached from any instrument or genre. It's about learning music in it's purest form - not about a certain instrument, instrumentation or genre. Also voiceleading, so the horizontal aspect of music, is very good visualized.


You seem to be blinded to the "givens" which all musicians have to learn. The fact is, the note names themselves are based on the diatonic scale. The keyboard did not"invent" this, but it is a direct reflection of it. As well, key signatures reflect this diatonic thinking. 
Many jazz tunes move through several key areas, such as "All the Things You Are." Using notation to score tunes such as this is a necessary inconvenience which chromatic thinkers must tolerate. True, the tune can be "crammed-in" to a key signature.

I'm not advocating another way of notation; I've already learned to use the present one. What I'm saying is that many academically trained musicians, mostly piano players, need to learn to "think outside the diatonic box" and stop criticizing the new thinking.

If you will examine the books, there are plenty of voice-leading principles which, incidentally, are most consonant and efficient, and are unrestricted by academic diatonic regulations; and this allows for a more chromatic and organic way of doing things.



> I assume, if the threadstarter would like to just shift a few patterns in constant structure around the fretboard and play randomly scales over it, he wouldn't be too concerned about his voice-leading at all - he would just have thrown it out of the window ;-)


No, that's condescending.


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## MartinAlexander

millionrainbows said:


> While it is true that on a keyboard "every note is there only once," it follows that each chord form is unique (in terms of black/white notes), so you have to learn 12 different forms for a major chord, not to mention inversions. On a guitar, the voicings can be moved up & down with only one form. That's an advantage.


If learning twelve different shapes is already such a burden for you, I totally understand where you're coming from. And all those difficult inversions...

You hear it Ehab - forget everything you learned about music - just buy an 1 octave digital keyboard, learn the C Major chord shape only and then use the transpose buttons to shift it around - that's really an advantage - you can't deny that !


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## millionrainbows

MartinAlexander said:


> If learning twelve different shapes is already such a burden for you, I totally understand where you're coming from. And all those difficult inversions...
> 
> You hear it Ehab - forget everything you learned about music - just buy an 1 octave digital keyboard, learn the C Major chord shape only and then use the transpose buttons to shift it around - that's really an advantage - you can't deny that !


No, you're distorting what I said about the advantages and disadvantages of keyboard vs. guitar.

I'm interested in telling people here about new ideas, not argumentation.


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## MartinAlexander

millionrainbows said:


> No, you're distorting what I said about the advantages and disadvantages of keyboard vs. guitar.


It's exactly the concept you described. Shifting one shape around is no new idea at all - regardless the instrument played on - and also has absolutely nothing to do with voice-leading at all.

So in which way am I distorting it ?


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## millionrainbows

This is the post that distorted it. Yes, pianos have twelve different unique shapes for each chord, but this is to be seen as one of the unique mechanical aspects of the keyboard. I am comparing this to the guitar's ability to move "one unique shape" up and down chromatically, covering all 12 key areas. 


MartinAlexander said:


> If learning twelve different shapes is already such a burden for you, I totally understand where you're coming from. And all those difficult inversions...





> You hear it Ehab - forget everything you learned about music - just buy an 1 octave digital keyboard, learn the C Major chord shape only and then use the transpose buttons to shift it around - that's really an advantage - you can't deny that !


Not better, just different. It's not to be seen as a burden for the lazy or an obstacle to the "retarded," and the solution is NOT to become a 21st-century musical illiterate who toys with Casio keyboards. That's condescending.


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## BabyGiraffe

millionrainbows said:


> This is the post that distorted it. Yes, pianos have twelve different unique shapes for each chord, but this is to be seen as one of the unique mechanical aspects of the keyboard. I am comparing this to the guitar's ability to move "one unique shape" up and down chromatically, covering all 12 key areas.
> 
> Not better, just different. It's not to be seen as a burden for the lazy or an obstacle to the "retarded," and the solution is NOT to become a 21st-century musical illiterate who toys with Casio keyboards. That's condescending.


Traditional keyboard design is hardly anything amazing or some of kind great engineering design. It's great for beginners that want to play in C major or some of the modes , other than that, I can't say a single good word for it... Here is a list of some modern keyboards with non-traditional designs: http://www.rogerlinndesign.com/other-tuned-instruments.html

I personally think that splitting the 12 keys into 2 whole tone scales - black and white keys is the best version of 12 note keyboard. It's not as easy as most of other variants, needs less keys, it's close to piano, but without the problems of it. 
I know some electronic producers and most of them stick to just white keys, then transpose in the computer software, haha...


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## millionrainbows

I knew a studio musician who had perfect pitch, and said he couldn't do the transpose thing, where you play in C and it's really G-sharp or something.. That sounds like an impediment to me.

I think if the piano was laid-out chromatically, in alternating white and black notes, it would work:

......B....B....B....B....B
...W...W...W...W....W 

Notice that this would fit together up thru the octaves. The notes would be (White: C-D-E-F#-G#-A#) and (Black: C#-D#-F-G-A). Hey, that's the same as your whole-tone scale layout!


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## mikeh375

Forumites, all this talk of new keyboard layouts buggers up my last 35 years of on/off practice!!!!

I knew a violinist with perfect pitch who could not read transposed scores because of the disparity between sight and sound - quite an impediment for a composer, but she wasn't too bothered.

Oh and what's the definition of perfect pitch?

Tossing a viola into the toilet and it not touching the sides.


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