Author Topic: Bartok And The Tritone  (Read 7777 times)

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winknotes

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Re: Bartok And The Tritone
« Reply #15 on: December 14, 2012, 11:52:38 AM »
This thread has really got me thinking and doing more reading about Cell-Z and Cell-Y.  While I don't understand 100% of what I'm reading in the sense that I wouldn't know exactly how to put it into practice, it is opening me up to new ways of looking at some material I'm currently using in a piece (I sense some re-writing coming up).  It also makes me realize that the idea of symmetrical motives or chords is something I've naturally gravitated to for quite some time now.  My struggle was always how best to fill in the missing notes. 

So much for the observations.  Now for a question.  How do you take these somewhat academic ideas and use them as a composer?  Right now I find myself grabbing onto the idea of looking at your "germ idea" in different inversions and relationships.  Inverting some of these smaller pitch sets can result in different 'key areas' which can help you form a large scale structure as well as thematic material. 
Steve Winkler
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winknotes

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Re: Bartok And The Tritone
« Reply #16 on: December 14, 2012, 12:10:07 PM »
Sorry but one more question.  I don't understand the numbering used in these discussions.  Like Z-1/7 Z-3/9, etc. 

« Last Edit: December 14, 2012, 12:11:43 PM by winknotes »
Steve Winkler
Finale 2011
Windows 7 64-bit
Garritan GPO4, JABB
VSL SE/SE+ Standard
Reaper (sometimes)

RJB54

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Re: Bartok And The Tritone
« Reply #17 on: December 14, 2012, 01:50:15 PM »
The Zn/n notation indicates the 'root' pitches of the cell using pitch numbers. There are two numbers because a Z-Cell has 2 axes of symmetry.

For example, the prime form of Cell-Z is C, F, F#, B which is symmetrical around the axis F/F#. The cell can also be voiced as F#, B, C, F which is symmetrical around the axis B/C.

The labels for these 2 different voicings of the cell are Z0/6 and Z6/0. Z0/6 indicates that the primary 'root' pitch of that configuration is 0 (thus indicating that the current axis of symmetry is F/F#) and the secondary 'root' pitch is 6. Z6/0 indicates that the primary pitch is 6 (thus indicating that the current axis of symmetry is B/C).

While the cell could also be voiced as B, C, F, F# or F, F#, B, C, for whatever reasons these voicings do not get their own labels.

By the way, don't forget about Cell-X!

Cell-Y is a four note subset of a wholetone scale while Cell-X is a four note subset of the semitonal scale.

For a superb example of how Bartok utilizes and expands upon these pitch cells see his 4th String Quartet. The base material of this piece are Cells X, Y, and Z. In this piece he has has devised myriad ways in which he uses these cells to generate motives/themes, expands upon them to generate new content (by, for example, expanding Cell-X with more tones from the semitonal scale, etc.), the way he uses the cells to establish/contrast 'areas of stability' (think key centers in diatonic music), and more.

When making use of these cells you don't have to be using these cells exclusively. As I said above 2 transpositions of Cell-Z make up an octatonic scale giving you a more free area to work in which is not necesserally constrained by the cells. Also, as I mentioned above Cell-Z allows you to 'modulate' between octatonic and wholetone environments. Cells X and Y being subsets of the semitonal and wholetone scales, respectively, also gives you the ability move from environment to environment.

Using these and other techiques Bartok's music can move between diatonic, modal, octatonic, wholetone, and atonal environments all within a given movement/composition without sounding chaotic, or to put it in a more postive way, all the while sounding logical and coherent.

In terms of 'filling in' the pitches of Cell-Z, as I mentioned above, Bartok tended to use semitones and wholetones often. Filling in a Z-Cell with semitones creates a pitch set related to Cell-X, while filling in with wholetones creates a pitch set related to Cell-Y. He would also use other pitch combinations to to create diatonic scales, modes, etc. from Cell-Z.

There are also other ways of expanding from these cells.

One of the things I've done is to create a cell I call Cell-V by expanding Cell-X to five pitches and dropping the middle pitch. For example. take cell X0 (C, C#, D, D#), add E to the cell and drop the D. You now have a pitch cell of C, C#, D#, E which is still a subset of the semitonal scale like Cell-X but its content is different. I do a similar thing with Cell-Y to generate a wholetone based cell type which which I call Cell-W.

The posibilities are boundless.
Information is not knowledge. Knowledge is not wisdom. Wisdom is not truth. Truth is not beauty. Beauty is not love. Love is not music. Music is THE BEST.
Frank Zappa

winknotes

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Re: Bartok And The Tritone
« Reply #18 on: December 15, 2012, 07:38:30 PM »
Thank you for that thoughtful and thorough reply.  The possibilities certainly are seemingly endless. 

I think it's time for me to force myself to write a short piece using some of these techniques.  It's clear that you can't approach these techniques with any traditional harmonic approaches, but in some ways you can.  I think there could still be the idea of a "tonic", "dominant" and "subdominant" with these.  Certainly the idea of a leading tone is there. 
Steve Winkler
Finale 2011
Windows 7 64-bit
Garritan GPO4, JABB
VSL SE/SE+ Standard
Reaper (sometimes)

winknotes

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Re: Bartok And The Tritone
« Reply #19 on: December 19, 2012, 05:21:00 PM »
I just have to say again I appreciate you all sharing this info about X, Y and Z cells.  It's really given me a nudge to get on with a scale I've started working with.  It will likely involve some re-writing of already written material, but such is life.   

Anyway I think this is going to be quite enjoyable.  Thanks again.
Steve Winkler
Finale 2011
Windows 7 64-bit
Garritan GPO4, JABB
VSL SE/SE+ Standard
Reaper (sometimes)

RJB54

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Re: Bartok And The Tritone
« Reply #20 on: December 19, 2012, 05:37:02 PM »
Your welcome Steve. Sorry I didn't reply sooner but I've been busy.
Information is not knowledge. Knowledge is not wisdom. Wisdom is not truth. Truth is not beauty. Beauty is not love. Love is not music. Music is THE BEST.
Frank Zappa