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Transformations At Level 0
1. Twinkle, Twinkle, Little Star
Footsies
All the levels being binary, thefootsiesare quite simple here.
(a) When we examined this song in the preceding section,
we could not produce ternary subdivision at the smaller levels (smaller thanLevel 0)
because we had only one small level (Level -1) and
we needed at least 2 of them (Level -2andLevel -1)
However, it is possible to produce ternary grouping usingLevel 0.
Let us start with a fusion of Level -1 and Level 0.
(b) The first complete bar of 4/2 atLevel 0
starts after the first 2 notes (between 2 solid bar-lines) and contains the required
4 notes.
As in 2. Polly, Put The Kettle On,
we will reduce by half the values of the first 2 beats of each 4/2 bar.
At the ternaryLevel -1 0, we now have bars of 3/2 meter
Footsies
At the smallest level (ternaryLevel -1 0), the feet start L(eft), T(ouch), R(ight) (4 cells).
At the next level (binaryLevel +1), the feet start L(eft) with 2 notes pickup (2 cells).
Let us now proceed to a fusion of Level 0 and Level +1.
(c) A complete bar of 4/1 atLevel +1
starts after the first 6 notes and contains the required 4 note values (7 notes
in all).
We will reduce by half the values of the first 2 beats of each 4/1 bar
(one 1/1 note and two 1/2 notes will become - one 1/2 note and two 1/4 notes).
The same note values will be attributed to the last note and to the first 2 notes.
At the ternaryLevel 0+1, we now have the original 2/2 bars, grouped by 3.
Footsies
At the smallest level (binaryLevel -1), the feet start L(eft) (6 cells).
At the next level (ternaryLevel 0+1), the feet start L(eft), T(ouch), R(ight)
with 2 notes pickup (2 cells).
At the next level (binaryLevel +2), the feet start L(eft) with 6 notes pickup (1 cell).
You might enjoy a littleaudio clipin which Twinkle is presented complete,
with bridge, in its ABA form.
In the 2 A sections, there is a fusion of ternaryLevel -1 0and
in the B section, there is a fusion of ternaryLevel 0+1.
And finally, a fusion of Level +1 and Level +2.
(d) The complete bar of 8/1 (2 bars of 4/1) atLevel +2
is best seen by placing the last note at the beginning.
We can now reduce by half the values of the first half of this large 8/1 bar (the
first 4/1 bar) -
the first six 1/2 notes of the piece will become 1/4 notes and
the last 1/1 note will become a 1/2 note.
At the ternaryLevel +1+2, we also have the original 2/2 bars, with 2 notes pickup,
grouped in 3 binary cells, (instead of the original 4),
You might enjoy another littleaudio clipin which Twinkle is presented complete,
with bridge, in its ABA form.
In the 2 A sections, there is a fusion of ternaryLevel 0+1and
in the B section, there is a fusion of ternaryLevel +1+2.
For all the other songs
These procedures of producing ternaryLevel -1 0,Level 0+1, and evenLevel +1+2
could be applied to the other songs.
Once again, the possibilities are almost endless.
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