Author Topic: Bartok And The Tritone  (Read 7721 times)

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johnc

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Bartok And The Tritone
« on: August 18, 2011, 10:12:46 AM »
Hi,

Ran across this which I thought might be of interest.

http://www.philharmonia.co.uk/bartok/films/1/bartok_at_the_crossroads#wrap

Click on "Folk Inspiration".  At the end, the expert shows a folk melody Bartok wrote in his notebook, and put into one of his first pieces, the Sketches for Solo Piano Op. 9.   It is sketch # 5.  He notes the tritone A-D#.  I got the sketches, and there's also a C-F#.

I'm not sure what scale it it.

It's interesting to see the direct influence of folk songs on his music.  Like the ethnomusicologist says, he was probably drawn to the tritone's sound.

I like the piece and how percussive it is.  Played it over slowly at the piano.  Will try the others too.   Seems like there's a jazz piece in there somewhere.  I also like the unusual scale, and the unusual and dramatic chord changes.

John C

Michel.R.E

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Re: Bartok And The Tritone
« Reply #1 on: August 18, 2011, 10:30:50 AM »
it seems to be a Hungarian pentatonic scale.
without actually seeing the score or hearing more of the piece, it's difficult to tell.
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johnc

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Re: Bartok And The Tritone
« Reply #2 on: August 18, 2011, 10:47:06 AM »
Thanks Michel!

Think you're probably correct.  Will take another look at the piano.

I like this thing.  Will try and get it up to speed and with a decent rhythm at the piano.  Some of the stretches are too much.  I may leave out a note rather than roll the chord.  Thought this might have more of a percussive effect than breaking the rhythm with a roll.

John C

johnc

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Re: Bartok And The Tritone
« Reply #3 on: August 19, 2011, 11:36:11 AM »
Here's are a few recordings of the piece, and the sheet music.  (It's on page 9 of the sheet music.)  The piece is no. 5, "Romanian Folksong"

http://server3.pianosociety.com/protected/bartok-sevensketches-5-breemer.mp3

http://www.classicalarchives.com/work/3858.html

http://216.129.110.22/files/imglnks/usimg/7/7a/IMSLP12644-Bartok_op09b_7_Sketches.pdf

I found a Google Books entry where it has the key center as B.  That's the way I hear it at the piano.  Also, there is a perfect 5th between the B and F#, which emphasizes B as the tonic.

He seems to keep to the pentatonic scale for the melody, but use different notes in the harmony.   I think he might do this a lot, as I think I remember many of the pieces in his teaching work, The Mikrokosmos,  harmonized this way.  Maybe this gives it a little of a bitonal effect.

Anyway, sounds like jazz to me.  He, like Scriabin--- the unheralded founds of modern jazz harmony.  (Scriabin seemed to build the tritone into everything!)

Thanks,

John C

Michel.R.E

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Re: Bartok And The Tritone
« Reply #4 on: August 19, 2011, 12:47:21 PM »
ah, Skrjabin!

the creator of the octatonic scale! he superimposed two diminished 7th chords, and voila! 8-tone perfectly 4-way symmetrical scale.
used it extensively in his final works.
"Writing music to be revolutionary is like cooking to be famous: Music’s main function is not revolution. – Alan Belkin "

"Saying something new about something old is still saying something new. – Jamie Kowalski"

RJB54

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Re: Bartok And The Tritone
« Reply #5 on: December 11, 2012, 09:11:41 AM »
Another aspect of Bartok's compositional approach which emphasizes the tritone has to do with a subdivision of the octatonic scale other than into two diminished seventh chords as Michel mentioned above.

Bartok frequently made use of a 4 tone pitch set which is refered to in the Bartok literature as Cell-Z.

The prime form of Cell-Z comprises the pitches C, F, F#, B which can be viewed as 2 perfect 4ths/5ths a semitone apart, 2 semitones an augmented 4th apart, or 2 augmented 4ths a semitone apart.

The beauty of Cell-Z is that it has diatonic implications if you emphasize the perfect 4ths/5ths and non-diatonic implications if you emphasize the augmented 4ths.

Bartok frequently uses a Z Cell as a structural entity often in the voicings which place emphasis on the tritone.

One of the things Bartok does is to use a Z Cell to define boundry intervals for other pitch cells filling in the boundry tritones with semitones, wholetones, octatonic subsets, etc., thus generating new content.

He also often takes advantage of the fact that an octatonic scale can be divided into two Z Cells using a given Z Cell as a 'pivot' entity to 'modulate' between passages based upon the octatonic and wholetone scales.

The general process being to subdivide the current octatonic scale into 2 Z Cells voiced as 2 tritones, which is inherently wholetone in character in and of itself, then fill in the tritone with whole tones creating a 4 tone subset of a wholetone scale, then expand the 4 tone pitch cell with the remaining 2 tones of the appropriate whole tone scale and as simple as that you've logically moved from an octatonic environment to a wholetone environment. You can also follow the opposite process to move from a wholetone environment to an octatonic one.
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winknotes

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Re: Bartok And The Tritone
« Reply #6 on: December 11, 2012, 10:34:06 AM »

The general process being to subdivide the current octatonic scale into 2 Z Cells voiced as 2 tritones, which is inherently wholetone in character in and of itself, then fill in the tritone with whole tones creating a 4 tone subset of a wholetone scale, then expand the 4 tone pitch cell with the remaining 2 tones of the appropriate whole tone scale and as simple as that you've logically moved from an octatonic environment to a wholetone environment. You can also follow the opposite process to move from a wholetone environment to an octatonic one.

I'm not sure I understand this paragraph.  Do you have time/energy to post a manuscript example?  Very interesting.
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RJB54

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Re: Bartok And The Tritone
« Reply #7 on: December 11, 2012, 12:07:10 PM »
Here is some musical examples which I hope would be helpful.

Score=https://www.box.com/s/r2r7n1c6rfpao57atwc7

I'll start with a flowchart like illustration in the first staff.

You start with an octatonic scale at '1'.

The octatonic scale will be divided by emphazing one or the other (or both) of two Z-Cells which comprise that octatonic scale as at '2' and perferably voice the Z-Cell(s) as augmented 4ths as at '3'.

You then emphasize one of the augmented 4ths as at '4'.

You then fill in that augmented 4th with whole tones as at '5'.

You then add the 2 additional wholetones to the mix as at '6' and you end up with a wholetone scale.

In the quick and dirty musical example in staves 2 and 3:

'A' shows the presentation of an octatonic scale.

'B' extracts a Z-Cell (C#, F#, G, C) from that octatonic scale.

'C' extracts one of the tritones from that Z-Cell.

'D' fills in that tritone with wholetones resulting in a 4 pitch wholetone pitch set.

'E' (which overlaps with 'D') expands that pitch set into a wholetone scale and presents a wholetone motive which is related to the octatonic motive presented at the beginning.

In reviewing the musical example I realized that in the speed with which I created it I made a mistake and left out some of the pitches of the final wholetone scale in the last bar :o, but the idea being illustrated is still valid.
« Last Edit: December 11, 2012, 03:22:43 PM by RJB54 »
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winknotes

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Re: Bartok And The Tritone
« Reply #8 on: December 12, 2012, 06:41:42 PM »
Thank you so much for taking the time to explain.  It's clear to me now and quite interesting.  It gives me some ideas of another way to look at some scales I've been playing around with. 
Steve Winkler
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RJB54

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Re: Bartok And The Tritone
« Reply #9 on: December 13, 2012, 06:13:00 AM »
Your quite welcome.
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.
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Jamie Kowalski

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Re: Bartok And The Tritone
« Reply #10 on: December 13, 2012, 07:17:19 AM »
Thanks also from me. I didn't know about his Cell-Z, though it's a set of pitches I played with briefly as well when I was looking at symmetrical four-note sets. I used it briefly in a string quartet back in 1989, but a lot more focus was on a similar symmetrical set: B, C, E, F.

RJB54

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Re: Bartok And The Tritone
« Reply #11 on: December 13, 2012, 08:04:19 AM »
Your welcome Jamie.

Yes, your pitch cell, while similar, isn't a Z-Cell as it doesn't include 2 tritones. Changing the E to an F# would turn it into a Z-Cell (C, F, F#, B).

This pitch set was stumbled upon by multiple early post-diatonic composers, not just Bartok, and found to be quite useful for their varying compositional purposes.

For example, Webern used it in some compositions (where it is refered to in the Webern literature as Cell-W) and Berg used it as a significant pitch collection in Lulu (where George Perle refers to it as Basic Cell I).

Another aspect which I didn't bring up, but which you mentioned, is its symmetricality which is enhanced by the fact that it has two axes of symmetry not just one. Bartok also frequently made use of this aspect as well as he often established large scale forms/relationships via axes of symmetry.
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Jamie Kowalski

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Re: Bartok And The Tritone
« Reply #12 on: December 13, 2012, 08:18:37 AM »
I just remembered that I used BCEF even more extensively ten years later in my orchestral work "Equilibrium."

One interesting thing I was contemplating about mirror symmetry in pitch sets is whether there is a meaningful distinction between those whose mirror line lies on a given note (BCEF), and those where it lies in the crack between two notes (BCFF#). The first has D as its center, and the second has the note between D and D# as its center.

RJB54

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Re: Bartok And The Tritone
« Reply #13 on: December 13, 2012, 12:05:51 PM »
As far as I am aware in the case of Bartok's music (who, after all, is the subject of this thread) his concern regarding axes of symmetry between notes or on notes varied depending on the piece/context.

(Note that in the notational convention I use below C/C indicates an axis of symmetry on C, while C/D indicates an axis between C and D.)

Particulary in smaller contexts such as phrases, subphrases, etc., he mostly viewed axes of symmetry C/C and C/D as the same, although he occaisionally did differentiate.

In larger contexts such as sections, movements, etc., his concern basically depended on what he was doing in any given piece.

For example, posit a main axis of C/C.

Sometimes he would establish on the note symmetrical relationships to the main axis by having the axis of symmetry in subsequent passages follow a pattern such as: C/C, B/B, C#/C#. Bb/Bb, D/D.

Other times he would incorporate between the note patterns such as: C/C, B/C, C/C#, A#/B, C#/D, etc.

At other times he will have mixed pattern such as: C/C, B/B, C#/C#, A#/B, C#/D, D#/E, G#/A, G/G, E/E, etc.

As far as my personal view is concerned, if you are making axes of symmetry a significant structural principle of a composition, its up to you to make the decision as to differentiate between axes on and between pitches. Just be logical.

As an example, I am currently working a piece whose basic material is comprised of several symmetric pitch cells some of whose axes of symmetry are on and some are between. I'm trying to be structurally logical reguarding the relationships of the axes of symmetry between sections governed by each type of pitch cell so that axes follow a coherent axial pattern which allows for both on and between axes.
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.
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Jamie Kowalski

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Re: Bartok And The Tritone
« Reply #14 on: December 13, 2012, 01:43:22 PM »
I think I tend to be just a bit less logical for my own purposes, at least in the context of how the material should be developed. I'll sometimes start off with a concrete concept such as this and then systematically throw a bunch of unrelated ideas against it, and see what the interactions between the elements suggest to my ear.