# A Legacy From My Teenager Times

When I was in high school, I composed this for a music class. Since
I didn't know much about music theory at that time, I just did what
I wanted. But I occasionally remind it even now. I think it was
really good. Considering that it was composed by someone who don't
know much about music theory.


I tried to construct something like a topological space with a
motive I arbitrarily came up. To be a topology, there are some
conditions to meet. For example X, {} <- T. So this music starts
with X and {}.

But I wasn't restricted by those rules. Since {} = X^c, I also came
up inversion and treated it like complement. Retrograde too. And
I did the Inversion Retrograde as the intersection of the two.
Since finite intersections belong to T. Though I didn't know any
of those musical terms at that time.


Also I constructed the left hand part to make it like a fugue.
First it starts only with the right hand side. Then it repeats with
the left hand side. But I don't remember how it was exactly like.

All I remember is that I constructed it by applying some mathematical
rules to the right hand side. Much like how Bach did. But I didn't
think about Bach at that time.







## Construction

4/4. Every note has the same length. The left hand side was the
same.

' means an octave over. , means an octave under.

Note that I didn't use these terms at that time. This is just how
I remember it.



X (Motive) =

C   E- F  G  | A- G  F  A- | G  F  E- B- | A- B  B- D'
E'- B- B  A- | B- G- A- B- | A- G- F  G- | A- G- F  D


{} = X^c =

             |             |             |
             |             |             |


Inv X (X^-1) =

C'  A  G  G- | E  F  G  E  | F  G  A  D  | E  D- D  B-,
A,  D  D- E  | D  G- E  D  | E  G- G  G- | E  G- G  B-


Ret X (X^r) =

D   F  G- A- | G- F  G- A- | B- A- G- B- | A- B  B- E'-
D'  B- B  A- | B- E- F  G  | A- F  G  A- | G  F  E- C


InvRet X ((X^r)^-1) =

B-  G  G- E  | G- G  G- E  | D  E  G- D  | E  D- D  A,
B-, D  D- E  | D  A  G  F  | E  G  F  E  | F  G  A  C'

If I make it now, I would do Retrograde Inversion instead.


X again =

C   E- F  G  | A- G  F  A- | G  F  E- B- | A- B  B- D'
E'- B- B  A- | B- G- A- B- | A- G- F  G- | A- G- F  D







## Summary

C   E- F  G  | A- G  F  A- | G  F  E- B- | A- B  B- D'
E'- B- B  A- | B- G- A- B- | A- G- F  G- | A- G- F  D

C   E- F  G  | A- G  F  A- | G  F  E- B- | A- B  B- D'  (With the
E'- B- B  A- | B- G- A- B- | A- G- F  G- | A- G- F  D   left hand side)

             |             |             |
             |             |             |

             |             |             |              (With the empty
             |             |             |              left hand side)

C'  A  G  G- | E  F  G  E  | F  G  A  D  | E  D- D  B-,
A,  D  D- E  | D  G- E  D  | E  G- G  G- | E  G- G  B-

C'  A  G  G- | E  F  G  E  | F  G  A  D  | E  D- D  B-, (With the
A,  D  D- E  | D  G- E  D  | E  G- G  G- | E  G- G  B-  left hand side)

D   F  G- A- | G- F  G- A- | B- A- G- B- | A- B  B- E'-
D'  B- B  A- | B- E- F  G  | A- F  G  A- | G  F  E- C

D   F  G- A- | G- F  G- A- | B- A- G- B- | A- B  B- E'- (With the
D'  B- B  A- | B- E- F  G  | A- F  G  A- | G  F  E- C   left hand side)

B-  G  G- E  | G- G  G- E  | D  E  G- D  | E  D- D  A,
B-, D  D- E  | D  A  G  F  | E  G  F  E  | F  G  A  C'

B-  G  G- E  | G- G  G- E  | D  E  G- D  | E  D- D  A,  (With the
B-, D  D- E  | D  A  G  F  | E  G  F  E  | F  G  A  C'  left hand side)

C   E- F  G  | A- G  F  A- | G  F  E- B- | A- B  B- D'
E'- B- B  A- | B- G- A- B- | A- G- F  G- | A- G- F  D

C   E- F  G  | A- G  F  A- | G  F  E- B- | A- B  B- D'  (With the
E'- B- B  A- | B- G- A- B- | A- G- F  G- | A- G- F  D   left hand side)