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MICHAEL SCOTT ASATO
CUTHBERT: Hello.

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As the last element
in our discussion

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of musical
representations, I want

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to talk about two
different fundamental ways

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that we can represent musical
scores, timewise and partwise.

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And these really
matter in anything

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that has more than one note or
more than one independent part

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going as once.

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And I want to acknowledge I'm
going to be using slides from

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a presentation called
"Notation as Composition"

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by William Andrew Burnson,
creator of the Belle, Bonne,

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Sage notation package.

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One of the ways that we can look
at musical notes is as-- musical

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scores is as a series of
containers so that we can think

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of--

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and part-based containers.

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So we have a score,
and within that score,

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as the first element, we
have two parts in this case.

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And within those parts,
we have measures.

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And we might even go further and
think that within those measures

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we have voices.

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But first, when we think about
dividing a score into parts,

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let's say it's the score of
a massive three-hour opera,

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well, you start with whatever
is at the top of the piccolo

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or something like
that, and you go

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with the piccolo
part from measure one

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all the way to the end
of the three hours.

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Then you go to the second
part, probably the flute,

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and you go all the way
from one to the end.

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And so on.

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And so you have
everything in one part

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from the beginning to the end.

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And it makes it very easy to
do the kinds of analyses that

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look at what happens in a part.

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The other principal way of
looking at musical notation

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representation is
you have a score.

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And within that, you
have all the things that

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happen at a certain moment.

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So at the beginning,
you might say, well,

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there's all the clefs.

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And if it's a 10-part score,
you might have treble, treble,

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treble, treble, treble, alto,
bass, bass, bass, bass, bass,

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so on.

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And then you have all the
key signatures, all the time

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signatures, and then every
note, everything that happens

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at the beginning of the piece.

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And then you have
everything that

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happens at the next
instant, the next time

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that something happens here.

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And in this
particular case, when

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we get to the third instant,
which is the E quarter

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note in the bass, and then
the C eighth note, and the E,

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there is something
that is happening

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in the top part, that
G half note, that

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is not represented
in that instant

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but is thought to be
continuing from before.

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And in the next instant,
there is just an eighth note

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with nothing else happening.

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And so this makes it
very nice to see what's

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happening at every attack.

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And you might be able to
programmatically go back and see

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what's happening
at every instant.

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But it makes it very hard
instead to figure out what's

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happening from one beginning
of the score to the end.

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By the way, we call
these instants instants

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or offset moments or cuts
through hierarchies, generally

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speaking.

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But often, we colloquially
call these salami slices

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and the process of creating
these things salami slicing.

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It's just kind of
something that's come out.

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In music21, we call this
process quartification.

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And so you'll see that
quartify happens a lot.

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So which is better,
part-based containers

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or time-based containers?

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Each of these formats has
their own positive things

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and drawbacks.

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As I said, part-based
containers make it very easy

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for us to follow an
entire part from beginning

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to end, an entire line
from beginning to end.

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Time-based containers
let us see what

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chords are happening
in a certain moment

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but very hard to follow melody.

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But each of them has certain
difficult-to-encode things,

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for instance, an ossia staff,
a staff where something

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optional is happening.

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Or you can do this
instead of something else.

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What part is that in?

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How do you encode that?

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Do you put a part
with hidden measures

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all the way up to this
moment and hidden measures

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all the way to the end?

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And how do we indicate that
the player could do this?

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So this is something
that's very hard

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to encode when we do
part-based representations.

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So instead, let's move to
time-based representations

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because it doesn't have this--
they don't have this problem.

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But instead, they
have other problems.

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Where do we put
these grace notes

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in encoding like this,
especially when we know

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that not all five
of those grace notes

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come after that last-- let's
assume it's treble and bass

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clef-- after that last B of the
septuplet within the triplet?

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Where do we go?

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How do we encode grace notes?

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Do they attach to the
note next to them or what?

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And both of the representations
have major problems

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when we want to
look at things that

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involve horizontal and
vertical at the same time,

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things like voice leading.

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Here's a common
voice leading error

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in very strict
traditional harmonic

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writing, where we have--

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and we have overlap
where the low G crosses

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the boundary
established by the B

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before and goes up
to the C above it.

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Which format makes
this possible?

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If you're just looking at
each part alone, you see,

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OK, there's a B going to an E.
Then we get to the next part.

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There's a G going
to a C. But you

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don't see that the
G going to the C

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overlap the B going to
an E. On the other hand,

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if we look at it in time-based,
we have a G and a B.

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And we look at that,
then the next chart, we

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see there's a C and an E,
but it's hard to tell, well,

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did the G go to the C?

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Did the G go to the E?

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What happened?

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How's the voice
leading happening?

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So these are the problems
in musical representations.

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And we'll quite
often find that we

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have to convert from
part-based representation

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to time-based
representation and back.

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Or in the case of a
voice leading moment,

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we have to keep both the
part and the time-based

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representations in our
head, in the musical memory,

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in the representation at
the same time in order

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to find these things.

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I find these problems really
cool and hope you guys do too.

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And solving them is another one
of the great joys of this class.

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