THEORY 302a: Bartok - Mikrokosmos 141

The answers to some of the questions are on the bottom of this post. Italicized questions should get a short writing response (a sentence or two) along with the composition portion.
1. View the attached score and listen to a recording.
2. The first step when analyzing a piece is to discern its form. Attempt to discern the parts. Then, look for how many phrases are used in each section. What makes a section more similar or dissimilar to another?
3a. The whole step interval (G & A) bounced around the bottom of page two breaks the obvious pattern. Same with the final Piú mosso section. Why would he write it like this? Obviously it's not simply to sound "cool".
3b. Do the non-A sections have any relation to themselves? To the A sections? If so, what is it? If not, why would we write it like this?
4. In almost every section, the pitches do not fall into any pre-established scale. This is because this piece utilizes intervallic mirror technique, where the pitches are reflected exactly upon a tonic note. Your task is to find all the places where this reflection is either shifted or inexact in some way. Ponder why he would bother doing this. 
5. Write a short piece for solo piano using mirroring and a recurring A section with changes. Your piece should include a process, that is, a theme of continuously changing something in the piece by a some fixed amount, linear or exponential. 
 

2. Systems 1-3: A
Systems 3-4: B
Systems: 4-5: A
Systems 5-7: B'
Systems 7-8: A
System 9-10: B"
System: 10-11: C
Systems 11-13: A
Systems 13-15: D
(What's important here is that the A sections sound similar, but the other sections do not show any obvious similarities to considered like sections)

4. Mirror off an eighth note in second and third A.
The fourth A section gradually displaces the mirror by eighth note, and changes the intervals of the left hand several times, most noticeably the E natural in the beginning.
D uses a separate kind of thrown off mirror system.

Please use the shared score and not this one with audio. This video is just meant to be able to listen to the music.

• 3a. The whole step interval (G & A) bounced around the bottom of page two breaks the obvious pattern. Same with the final Piú mosso section. Why would he write it like this? Obviously it's not simply to sound "cool".

I find this question quite hard to answer, because I do not think I completely understand the question. Do you mean ''why do the notes look like they look now'' or ''why did Bartók choose these notes to bounce?'' I think you mean the beam of the notes, which go over the bar lines.
I think that Bartók wanted an almost 'free rhythmic' passage, because the accents move by altering the beaming.

• 3b. Do the non-A sections have any relation to themselves? To the A sections? If so, what is it? If not, why would we write it like this?

The form reminds me of a French rondo. All non-A sections are contrasting and very recognisable themes. The key of this 'rondo form' is that there is just enough contrast (non-A themes) and just enough repetition (A themes).

• 4. Ponder why he would bother doing this. 

One possible reason for inexact mirroring could be that Bartók wanted a certain chord / interval that was not possible with exact mirroring.

• 5. Write a short piece for solo piano using mirroring and a recurring A section with changes. Your piece should include a process, that is, a theme of continuously changing something in the piece by a some fixed amount, linear or exponential. 

I have doubts about the accidentals when mirroring. Do I need to keep the visual distance between the notes the same or do I need to adjust the distance so that a Gb can be a F#?
I am now writing the piece.

3a. The whole step interval (G & A) bounced around the bottom of page two breaks the obvious pattern. Same with the final Piú mosso section. Why would he write it like this? Obviously, it's not simply to sound "cool".

I observed that the chain of long notes for the whole piece is as follows: Bb - B - D - Eb - F# - G -Bb. To make the flow smoother, G-A chords are added so that it would be G - A - Bb, which are either half-step or whole-steps. Those 4 G-A chords also keep the rhythmic pattern as in all sections, of which first half always start in a downbeat while the second half starts with an upbeat.     

 
3b. Do the non-A sections have any relation to themselves? To the A sections? If so, what is it? If not, why would we write it like this?

In the non-A sections (and actually also A section) have left-hand parts mirror to the right-hand parts. In other words, when the right-hand part is going up, the left-hand part moves down with exactly the same intervals. I think Bartok may want to introduce subject and reflection together.  

In A-sections, the first bar of each section has a perfect 4th between the highest and lowest note. While in non-A sections, for example in B", it is also a perfect 4th in the main melody but it's mirrored from A. It is probably also a kind of reflection written to create contrasts. Since A and non-A sections are altered (in Rondo form), it can thus keep the momentum throughout the piece.  

4. Your task is to find all the places where this reflection is either shifted or inexact in some way. Ponder why he would bother doing this. 

Actually, those long notes are the origins of reflections for the left and right-hand parts of the same section. I guess Bartok write those long notes in octaves to hint such reflections. 

Other than melodic shifts, there are also rhythmic shifts.Starting from System 7, third A-section, the left and right-hand parts differ by a quaver. It makes the piece less monotonous as in the previous parts left and right-hand parts are already in sync rhythmically for so long.  

// I shall start writing the piece.

3 hours ago, Maarten Bauer said:

I find this question quite hard to answer, because I do not think I completely understand the question. Do you mean ''why do the notes look like they look now'' or ''why did Bartók choose these notes to bounce?'

Actually I meant, this section is so short, doesn't even follow the mirror, and is predicated on nothing we've seen before. Why would he do this?

3 hours ago, Maarten Bauer said:

I have doubts about the accidentals when mirroring. Do I need to keep the visual distance between the notes the same or do I need to adjust the distance so that a Gb can be a F#?

It's important to remember than a major second is not the same thing as a diminished third. Unless it's a conscious choice, try to keep these the same throughout.

45 minutes ago, HoYin Cheung said:

I observed that the chain of long notes for the whole piece is as follows: Bb - B - D - Eb - F# - G -Bb. To make the flow smoother, G-A chords are added so that it would be G - A - Bb, which are either half-step or whole-steps. Those 4 G-A chords also keep the rhythmic pattern as in all sections, of which first half always start in a downbeat while the second half starts with an upbeat.

This question was more referring to: "this section is so short, doesn't even follow the mirror, and is predicated on nothing we've seen before. Why would he do this?"

Here is my composition:

Here is my Etude:

My contribution is the "Allegro moderato".Allegro moderato.mp3

Finally, I found a free evening to compose. :) Here's my piece:

Sorry, wrong posting!