# Micromacrocosmic Structure

Discussion in 'Music' started by Mrs Music, Aug 11, 2011.

1. ### Mrs MusicNew commenter

Hi there. I'm planning my teaching of the A level set works for the coming year and just can't get my head around the structure in Cage's Sonatas! Can anyone please explain it to me (in stupid terms)?
It is going from points two and three below that I'm having a mental block:
o The length of each part relates to the number 7
o The basic unit of 7 is proportioned as follows:1¼ ¾ 1¼ ¾ 1½ 1½
o These proportions are initially seen in crotchet beats: 4 1 3; 4 1 3; 4 2; 4 2. .

2. ### Mrs MusicNew commenter

Apologies for the lack of paragraphs. The points above relate to Sonata 1 and the notes I'm looking at are online, by EDEXCEL.

3. ### silverfernNew commenter

I'll try my best!
Macro-structure: (Using a 'base unit' of 7-crotchet-beats):
- Bars 1-7 = 28 crotchet beats = 4 units of 7. So that's the '4'.
- Bar 8 = 7 crotchet beats = 1 unit of 7. So that's the '1'
- Bar 9-12 = 21 crotchet beats = 3 units of 7. So that's the '3'.
(These bars then repeat, creating 4 1 3; 4 1 3).
- Bars 13-19 = 28 crotchet beats = 4 units of 7. So that's the '4'.
- Bars 20-26 = 14 crotchet beats = 2 units of 7. So that's the '2'
(These bars then repeat, creating 4 2; 4 2).
(So for the whole 26 bars, you get 4 1 3; 4 1 3; 4 2; 4 2).
- - - - -
What really interesting is that these ratios are also used within Cage's macrostructure, to create a microstructure... (it helps to circle the following rhythmic groupings)...
Look at bars 1-7.
- Bar 1 contains a '4'-crotchet-beat figure. This is followed by a '1' beat rest. And is followed by a '3'-crotchet pattern. So, 4 1 3.
- Bars 3 and 4 are the same, 4 1 3.
- Bar 5 and 6 can be grouped as: '4' (the whole of bar 5), and '2' (the first half of bar 6)
- Bar 6 and 7 can be grouped as: '4' (second half of bar 6, and first half of bar 7) and '2' (second half of bar 7).
(So, for bars 1-7, you get 4 1 3; 4 1 3; 4 2; 4 2).
Sadly, nothing exciting in terms of 'microstructure' happens (unless anyone can enlighten me!) in bar 8, or 9-12.
But, the 4 1 3; 4 2 microstructure is used in bars 13-26:
- Bar 13 and 14 can be grouped as: 4 1 3 (put circles around the '4' crotchet beats in bar 13, then the first '1' beat of bar 14, then the remaining '3' beats of bar 14)
- Bar 15 and 16 can also be grouped 4 1 3.
- Bar 17-19 can be grouped: '4' (bar 17), '2' (first half of bar 18), '4' (overlap of bars 18-19) and '2' (second half of bar 19).
(So, for bars 13-19 you get 4 2; 4 2).
Cage then uses the rhythmic technique of diminution in bars 20-26. Instead of using crotchet beats, he halves the beats, to quaver beats. Now counting quaver beats, the ratio pattern can be seen:
- Bar 20-21: '4' quavers, '1' quaver (the tied note), '3' quavers (the dotted-crotchet).
- Bar 22-23: '4' quavers (the single quaver and dotted-crotchet), '1' quaver (the tied note), '3' quavers (the dotted-crotchet).
- Bar 24-25: '4' quavers (bar 24), '2' quavers (first half of bar 25)
- Bar 25-26: '4' quavers (overlap of bars 25-26), '2' quavers (second half of bar 26).
(So for bars 20-26, you get 4 1 3; 4 1 3; 4 2; 4 2).
Hope that helps. Sorry if it's a bit confusing!

4. ### florian gassmannStar commenter

I think the Rhinegold study guide explains it much better than Edexcel, but I think silverfern has trumped both!

5. ### Mrs MusicNew commenter

silverfern, thank you so so much! Very much appreciated