I'm about to show you something pretty
amazing I think it's the musical
equivalent of a fractal the mathematical
concept often represented in geometric
art that explores recursion and
self-reference
so this kind of crappy synth sound is
playing the first four measures of smash
mouths all stuff if we look at the piano
roll we see that it's actually made up
of MIDI data comprising sixteen thousand
five hundred and fifteen individual
notes whizzing by a thousands of notes
per second we can zoom in closer so to
speak using this feature in Ableton Live
which lets you have the tempo of a MIDI
clip so now let's listen to this but
exponentially slower every time
[Music]
[Laughter]
somebody once told me the world so yes
you heard that correctly this version of
smash mouths all-star yields smash
mouths all-star when it slowed down to
about 1000 times the original speed how
did I put this together and why does it
work well before we get into it I
strongly recommend that you watch this
video my video on harmonica pilot
rhythms in a nutshell that video argues
that one since notes in the major scale
relate to one another by simple pitch
frequency ratios too since Polly rhythms
are also measured in simple ratios 3
when you speed rhythm up you get pitches
for therefore notes and melodies are
just Polly rhythms sped up really really
quickly are you with me so far well
there's gonna be some math involved
explained by somebody who is not a
mathematician so you have been warned ok
so the first step here is the sequence
the first couple bars of all star in the
piano roll we will think of this full
clip of notes as our basic rhythmic
pulse
now we're gonna reference this chart
from Wikipedia of intervals and their
corresponding pitch ratios we'll use
these to mark up the sheet music of all
start as a reference so the first
interval as is related back to the root
is 1/5 so it has a ratio of 3 to 2 the
next interval is a major 3rd so add as a
ratio of 5 to 4 etc etc normally these
ratios describe pitch frequencies
measured in Hertz or cycles per second
today these ratios will describe all
star frequencies how many times your ear
will hear the first four measures of all
star by smashmouth per second yes this
is an actual thing that I spent a lot of
time on what am I doing with my life ok
let's do it we're gonna need to figure
out how many all-star clips we need to
cram in within a given amount of space
so that our ear will hear it as one
continuous note when we speed it up so
in order to do that we're going to need
to find whole number integers that
relate to one another by the ratios that
describe the frequencies that we
mentioned beforehand now I'm sure
there's some fancy math that we could do
to calculate those integers but the
Wikipedia list that we were referencing
earlier already has them 27 relates to
24 by a ratio of 9 to 8 30 relates to 24
by a ratio of 5 to 4 etc etc so what we
need to do now is lay out groups of all
star clips based upon the integer that
relates to each individual note from the
melody so the first note is the root so
it will get
24 all-star clips the next note is the
fifth so it will get 36 all-star clips
so in order for these to be ratios of
frequency they need to occur in the same
amount of time they have to have the
rhythmic ratio of 36 to 24 or 3 to 2
fortunately Ableton Live makes this
really easy to program it would be
fairly complicated otherwise all I have
to do is consolidate these clips using
ctrl J so let the notes using ctrl a and
then drag the notes over to fit 24 bars
this is 36 all-star clips being smushed
within the span of 24 so now the
rhythmic ratio is 3 to 2 if we listen to
the clip for the second note v we now
hear that the all-star melody is going a
little bit faster than the first one
if we were to write out this process in
standard notation it would look like
this which is fairly complicated but it
is possible to do this without Ableton
lives nifty feature so we're basically
going to go through this process with
every single individual note from all
star the next note is the third in the
key so it will get 30 all-star clips the
next note is the third again so let's
just copy and paste that
however it's twice the length of the
preceding notes it's a quarter note in
the melody so let's double the entire
thing so we'll take longer when we
actually speed it up we're basically
just gonna keep doing this
referencing back and forth to the table
and the sheet music is actually a really
straightforward process soon we'll have
fractal eyes the entire melody
let's listen to it and then let's start
slowly speeding it up so that we'll hear
it more and more as it pitch
[Music]
the ramifications of this I think are
pretty interesting because you could
conceivably make any melody by
sequencing versions of itself to
generate itself this sort of self
reference and recursion is explored
quite heavily in Douglas Hofstadter's
book
gödel Escher Bach and I really strongly
recommend that book if you found this
video at all interesting I got the idea
for this video from a reddit thread
where somebody suggested that this might
be possible like a musical Quine a coin
by the way is a bit of computer code
which generates its own source code as
is only output well turns out it is
possible and something that I think is
quite cool anyway guys thank you so much
for watching this video my name is Adam
Neely I have a new video coming out
every Monday so if you like what you're
watching here please consider commenting
liking and subscribing I view regular
Q&A videos so I do read through all the
comments and there's been a lot of
really awesome comments recently so
thank you so much for any every anybody
and everybody who has commented also
consider definitely clicking the ringy
button because I do occasionally post
videos throughout the week at different
times of event Monday like gig vlogs and
recently I posted a all-star meme shame
on me for that but yeah there we go if
you really like what I do please
consider joining my patreon because it's
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over on my patreon that I am able to do
these videos consistently week after
week and afford the time and energy to
put into all the research and all the
editing and all that stuff so thank you
very much
if you're like these awesome awesome
people or subscribing to my patreon
thank you so much for that anyway by the
way I've included the MIDI clip from
this video in the description just in
case anybody wants to I don't know check
if I was making this whole thing up you
just load it up into some sort of
digital audio workstation throw some
sort of synthesized or a piano patch on
there and then go to town and you'll see
for yourself that yes it does yield
all-star when it's sped up until next
time everybody
base all-star when it slowed down to
about 1000 times the original speed when
it slowed down to about 2000 times the
original speed when it slowed down to
about 4000 times the original speed
so I actually haven't done the
calculations yet so that just me just
doing that kind of sounds like joke from
Arrested Development to the four
thousand dollar suit is holding the
elevator but the guy doesn't make that
in three months when I just take a whiz
you this $5,000 suit
$6,300 suit come on all right
hopefully it's 1,000 2,000 4,000 we'll
find out