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PROFESSOR: Well, now that we've
all turned in our proposals

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for repertories for
the second problem set,

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I want to go through some of
the problems that arise, even

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in Western notation and
even in classical music,

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that raise interesting
questions for representation.

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So we're looking here at a piano
trio, this by Clara Schumann,

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and it might look like
there's not too many problems

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to represent, but we'll
get back to it a little bit

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and look a little bit deeper.

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Here is a little piece from
Don Giovanni by Mozart.

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And you can see it's
not a high quality scan,

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but there's still
interesting things here.

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This is not actually
Don Giovanni.

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This is a piano reduction.

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So we have the
singer Donna Elvira

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and all the orchestra
reduced to two staves.

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Here is the similar passage,
the same passage actually,

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with different language-- we
have Italian and English before,

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and now Italian and German--

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but where we have the
full orchestral score out.

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And how do we represent the
differences and the connections

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between these two scores?

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This is already
difficult problem

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that hasn't been fully solved.

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But wait till we try
to represent, oh,

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how do the manuscript parts
for various pieces of relate?

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When we go into the 20th
century and 21st centuries,

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there are even more
complex problems.

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This is a late score by Igor
Stravinsky which is actually

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pretty standard in many ways, in
that it uses notes and things,

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but the clefs, if they
continue into the next staff,

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they're continued with lines.

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And probably most obviously
when an instrument doesn't play,

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its part is--

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its staff is removed.

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Or something like this--

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this is from one of my scores
when I was in college--

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where the staves are removed
when people don't play.

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But also, at various
points, the representation,

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the distances
between notes are not

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given with standard
noteheads but are

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given with time durations.

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And some of the notes,
such as these here

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that are accelerating,
aren't given in exact--

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they're not given exactly
between an eighth note or a 64th

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note but some
continuum in between.

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A lot of the greatest
music being written today,

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such as this piece
by Kate Soper,

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uses extended
notational techniques.

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So here, we have filled
in circles representing

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the closed mouth, and we
have open mouth signals,

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and we have symbols
for pure speech.

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And the violin
part, you might see,

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actually isn't in treble clef,
but it's in percussion clef

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with four lines, each
one representing just

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to play on that string.

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These aren't the notes.

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These are the strings
to be playing on.

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There are many pieces, such as
this piece by Brian Ferneyhough,

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Études transcendentales,
that require

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us to have notational formats
that go, again, beyond what we

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might think of as
common notation

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but only pursue it a
little bit further.

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Such as early on here,
we have a triplet

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in the place of 21 over 20
in the place of 7 over 4.

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Or at the end, we have
a measure whose time

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signature's denominator
is not a power of 2.

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How do we represent such things?

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We don't have to get into 20th
and 21st century music to run

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into problems like this.

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Here is another passage from
Mozart's Don Giovanni, where

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there are three different
orchestras playing

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on stage and in the pit, and
they are in three different time

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signatures representing the
different classes of people

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whose dances would
be represented

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in different tempos--

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in 3/8, 2/5, and 3/4 four.

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Measures do not
necessarily line up.

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How do we even count measures
in something like this?

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In an otherwise seemingly
normal passage by Debussy,

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we have this moment--

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and I thank Donald Byrd
for pointing this out--

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where we actually have
two different clefs active

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simultaneously on
the same staff.

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How does this get represented?

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If we go back to the Clara
Schumann example with which we

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began, we can see that
there are actually

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certain things
that are extremely

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difficult to represent.

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Why is this rest here, but
there's no rests before?

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What part of the
measure does this mean?

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Well, it's kind of obvious this
voice is moving up to here,

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but how is that
obvious for a computer?

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Or what parts exactly are these
notes that cross staves part of?

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How do we represent
cross-staff beaming?

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How do we represent some of
the time that would actually

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be used in a grace note?

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And when we go
earlier in time, there

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are problems that
expand even further.

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This is only a little bit
different from common Western

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music notation in this
example from, I believe,

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the 17th century
of church music.

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But we are using different
symbols for different notes

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and leaving out one
layer of the open notes.

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When we go very far back
in time, such as in this,

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I believe, ninth century chant
manuscript from the opening

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of the "Mass for Christmas," we
have symbols that just tell us

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the direction that notes
go, not their exact pitch.

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Do we want to be able to
encode things such as this?

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Here is a beautiful manuscript
from the beginning of the 15th

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century in the shape of a heart
because the composer's name,

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Baude Cordier,
"Cor" means heart.

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And do we want to represent
the graphical layout

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of the original score,
let alone these notes

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that are in red or
other unusual formats?

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And here's another example from
the same time period, where

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the harp strings
become the staff lines,

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but the notes only appear
on the staff lines.

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Therefore, all of the notation
is expanded into double size.

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What we want to do with this?

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What do we want to do with a
piece such as Cornelius Cardew's

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Treatise, where notational
symbols are used

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to give inspiration to the
performer, to the singers,

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and how to perform this.

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There is a score, but every
performance is different.

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Here's another score
for Earle Brown

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Folio from December of 1952.

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How do we interpret this?

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How do we store the
interpretations of this piece?

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I already mentioned in
class that non-western music

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and popular music have their
own difficulties as well,

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have their own problems,
and interesting points,

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as does machine music,
electronic music,

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or in this case a
piano player role,

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where exact, precise
differences, distances

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between notes, can be encoded.

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So I hope that this
gives some sense of some

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of the rich variety
of representation,

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and I'm looking
forward to seeing how

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your representations end up.

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