We're going to talk about turning numbers into notes.
So, there's some music in this session.
I'm very grateful that Pip Wilcox who is gonna be operating the end
of the laptop for the audio.
[LAUGH] Last Monday here in the Maths Institute,
we held a performance.
A second performance of Emily Howard's Ada sketches.
And that's gonna be one of the things we talk about today.
It's really about that.
But then there's a lot in there, and we've actually been thinking for
some time about exactly the thing on the slide.
Turning numbers into notes.
It's been a discussion that's been going on in anticipation of
this event over the last year in the digital musicology community, and
the computers and music community.
So, we're gonna bring those things together today.
I'm very pleased to have this opportunity to have a chat with Emily, and also
grateful to the people who are involved in putting on the event last Monday.
What you'll see on the slides are some stills that were taken and
some recordings that we made last week.
So, I'm gonna start by asking Emily to say a little bit about her
background as Nick mentioned [SOUND]. Emily comes with qualifications from Oxford.
>> Well, I was lucky enough to be brought up playing the cello, and
music was all around me.
And so, I did a lot of composing, very young.
And I also enjoyed studying science at school and mathematics, and I came here to
study mathematics and computer science, it was called computation in those days.
And I had a great time, had a great tutor, Richard Bird.
And yes, after that, there was something kind of missing maybe.
And I went back to studying composition.
I did a Masters in Composition at the Royal Northern College of Music, and
a PhD in Composition at Manchester University.
And I'm still based in Manchester at the Royal Northern College of Music.
>> So, we have mathematics, computer science, and music.
Very relevant today.
I think there are many people in the audience who will resonate with these
interests.
I want to say a little bit about this note, we've seen
footnotes already today, this one- >> [INAUDIBLE]
>> Oh, okay.
>> Yeah.
>> We can do that one as well, quickly.
>> Cheers.
>> Okay.
>> Okay, I'll pit a mic right next to my mic.
So, this is quite an important and well known quotation from Ada Lovelace.
Supposing, for instance,
that the fundamental relations of pitched sounds in the science of harmony and
of musical composition were susceptible of such expressions, which she was talking
about operations, and adaptations, the engine might compose elaborate and
scientific pieces of music of any degree of complexity or extent.
This is a very interesting statement, and
it's the one we've been discussing for some time.
I came to this, incidentally, thanks to Betty Toole in the front row.
Because five years ago I was moving to Oxford, and
I was giving a normal lecture, and my theme was to do with machines in music.
And I was at the Internet Archive in San Fransisco, where Ted Nelson,
the creator of hypertext, was presenting his autobiography.
I bumped into Betty and I said I was giving this talk, and Betty brought my
attention to this and gave me permission to use material from her book.
Thank you very much.
So, it started for me five years ago, this discussion.
Emily, how did you come to this?
>> I think I came to know about Ada Lovelace in about 2008.
And I was looking around for an opera subject.
And a good friend of mine, and colleague Laura Tunbridge who's here at Oxford now,
suggested Ada Lovelace to me.
And possibly, well probably because of the mathematic and
computing science background.
And I went away and I read this sketch of the analytical engine, and I looked,
I was particularly taken by this quote, and so, and
I wrote the Ada Sketches in 2011, and also two orchestral pieces.
A piece called Mesmorism, and a piece called Calculus of the Nervous System.
>> [LAUGH].
>> And we have a clip of Mesmorism a little bit later on.
>> So, of that trilogy,
this is Ada Sketches, this is a bit of the score,
could you tell us a little bit about how you came to do this particular piece?
>> Yeah, so Ada Sketches, well it's an opera sketch, so an opera,
I mean, it's an art form that comprises words, music, and drama.
And a sketch because, well apart from the pun, actually, it really is just a sketch.
It's not finished. It's about seven to eight minutes long and
I wanted to try out several of the ideas that I was thinking about from reading
about Ada and reading about her mathematics in particular.
So, the piece is based on a number of dramatic oppositions.
First of all, there's Ada Lovelace, played by a mezzo-soprano.
And there's the analytical engine, and that is actually an instrumental ensemble,
it's flute, clarinet and percussion.
And of course you've got the opposition kind of inside of Ada's head.
You've got her mother's influence, the mathematical, methodical and moral.
And her father's influence, famously mad, bad and dangerous to know.
And then, something that interested me deeply,
having read her notes, is a kind of representation in the piece of
creative processes and the moments of discovery, kind of breakthrough moments,
I find very interesting, whether they are original or not.
When you're solving a mathematical problem,
or indeed kind of working on a piece of music, and you have a click and
something happens and you think, that's exactly how it should go.
These moments interest me and I was thinking it would be very interesting
to try to put them into the music.
And so I have, in this sketch,
at the opening, Ada is literally working on an equation.
I was looking at the note B as well, and I chose,
I think it was 3 over 2 to the power of 36.
And 36, composers have to make some decisions.
36 because she died when she was 36.
And I worked through a kind of a text,
thinking about what she might say in a very formal kind of way.
As she worked on this equation, and as she tried to solve it in the way it might have
been solved if they could get the analytical engine to work.
So, that's what's happening at the beginning of this piece, and
I think you might hear part of it.
Just to say something about the instrumentalists. As she works, and
this might be in her head or it might not be, it's for
the audience to decide, kind of the machine Its beginning to work.
And so she's solving the equation and you hear,
at first you won't think of it as a traditional kind of music.
You kind of hear just the odd, the simple works, and then somehow they
sound very machine-like and very repetitive, algorithmic, and it really is.
Because I've actually taken what she's talking about, literally, and
I've used all of that mathematics in the music to create as algorithmic,
as non-personal, a piece of music as I possibly can for the analytical engine.
>> Thanks very much. And we're gonna hear a tip of that in
a second, just to give a history of the performance we had last week.
The format that Emily's now using isn't simply to
have a bunch of excellent musicians performing this work, but
it's actually to engage also a mathematician and the audience.
Okay, I want to say a little bit more about that in a second.
So, that format was first explored in the science museum a month or so ago.
Although there have been previous performances of this work.
And we brought it to Oxford, partly thanks to the support
of our sponsors, some music projects we have here.
We have some digital musicology projects
in particular one called Transforming Musicology.
We're very grateful to many sponsors here and to the Maths Institute and
the Bodleian Library, the Oxford Research Centre in the Humanities and
many others, for enabling us to put on the visit last weekend.
That project captured the content and
it captured the audience reaction to the performances.
And what we're exploring for example, is, did the audience receive,
did they interpret, did they understand the performance differently after
the mathematics had been explained to them?
So, look out for publications about this coming out.
And meanwhile, let's have a short clip, all the clips we have in this session
are just two or three minutes long, of the beginning of the operatic work.
This is Rosie, who's a spectacular singer.
Just to let you know we haven't tested the volume.
>> [LAUGH] >> I was responsible for recording this.
The dynamic range of this recording is extraordinary.
Rosie starts by speaking quietly.
I encourage everyone to read the libretto, it's really, really good.
And then sings quite loudly, just so you know.
[LAUGH] Pip, can we play the clip, please?
[MUSIC]
Thanks, Ben.
And so, you get the idea, it's just not very, very quietly,
the other pieces of music we have probably won't be as quiet as that was.
I'm sorry it took us a little while to work out how to turn the volume up.
These are the musicians and they were extremely impressive.
They made every note count.
If we're talking about computers for music.
But one of the things that is extremely clear is these musicians were excellent.
Do you want to say something about your excellent student?
>> I mean I wish you could have heard that a bit more clearly,
I mean you'll hear it later on, they really are excellent.
They worked very hard on performing it.
Rosie, the singer, is an alumna of the Royal Northern College of Music.
And then the other three are current students there.
>> We were very impressed.
During the evening, Emily got them to do some things,
which any musicians in the audience had to be seriously impressed by.
There was getting a [INAUDIBLE] to play in quarter tones and
getting two students to play six notes in one against seven from the other
without counting in. It was hugely impressive.
[LAUGH] They're excellent.
I, in particular, spent time with the percussionist.
I'll come back to that.
The- >> People are still having trouble
hearing your voice.
Do you want to unplug the microphone out of your pocket?
>> Yeah, I've got two microphones here.
[LAUGH] So the work is, in some ways about mathematical discovery.
And, and I like this quote I've taken from something you wrote Emily,
about, this is exploration of the musical solutions of computation,
for the hypothetical [INAUDIBLE] can you say something about that?
>> Yeah. So, following on from what I was saying
before, she's explaining, in the text, she worked on that mathematical discovery,
and the way I have represented that, not that you heard it,
she's speaking in this very formal way as she does the mathematics and
as she gets further into the equation, a solution, and she makes a discovery.
She goes into a much more typically operatic sounding voice that
you heard just there when she was singing to the power of five.
And later on, she has a similar moment when she starts to think about whether or
not the machine will be able to use notes instead of numbers.
So, this is her more visionary, like a cultural discovery.
So, I've represented them in the same way, vocally.
As the piece continues, there's a real sudden moment in the piece,
where always Ada has been speaking or
singing and the machine has kind of been developing very independently.
And then at one point the machine takes over, it is independent and
this is a really crucial moment for Ada because she kind of snaps out of
the very formal approach, because machine just goes.
And she has absolutely no effect on it.
And at that moment,
she's sort of thinking about, like a human versus machine kind of idea.
Where would I fit in?
What if the machine can compose the melodies?
What about me?
So, yeah.
>> We'll hear that clip. We're talking about a mathematical discovery,
one of the unusual things about this performance was we had a mathematician.
[LAUGH] So, what's it like gigging with a mathematician?
>> It's great, actually.
Cuz I've been working with Lasse, he's from the University of Liverpool.
And I've been actually doing a Leveshume artist-in-residency in
the Department of Mathematical Sciences for the last ten months.
And so I've been speaking regularly with Lasse in particular about his work
on dynamical systems.
So, when we were talking about him being involved in this Ada Sketches performance,
I spoke with him, and he was able to give really fantastic explanations of
the mathematics used in this.
So, for example, the idea of reducing the number of steps.
And he gave, I think he spoke about encryption today and
how this could work today.
And he also spoke about creative discoveries for
himself in his own mathematical research.
>> So, I have a clip now from a couple minutes further through the work where
the human, machine interaction, that tension is playing out.
>> I'll just say one last thing.
The machine here it sounds absolutely, completely otherworldly and
it's completely functionally derived.
And it's in combat, if you like, with Ada when she comes in and
this is her at her most lyrical.
[MUSIC]
>> When I was looking at that clip to include in the presentation.
It's very difficult to choose the beginning and
end points because the words through this part are fantastic.
And it ends with her saying will Ada resonate, and then she talks about [INAUDIBLE].
Earlier on, between the two clips you've heard, she talks about Fibonacci and
I'll come back to that.
So, thank you.
That gives you a good taste.
The whole piece is about seven or eight minutes long, and you've now heard
a couple of bits, one of them better than the other in terms of volume.
And I just want to show you a picture I took with my phone during the gig.
[LAUGH] So this is the percussion,
and yes it does feature flower pots and tin cans.
[LAUGH] You can see an excerpt from the score there with the instructions,
note the requirement for these to be tuned quarter-tone.
So, it's interesting aspect of this from a musical viewpoint, interesting challenge.
We had great fun raiding the music faculty
percussion store.
[LAUGH] But interesting that the use of quarter tones.
I want to ask Emily to say something about that because we
are just moving into the numbers to notes piece.
So, this is a relevant point.
>> So, to say something about the quarter tones.
Well I wanted to have quarter tones in the analytical engine part.
And actually the demonstration I did with the flautist was to have the flautist
play a major scale, which we're all happy with.
And then to play semitones, these are also steps that we're quite happy with.
And then she was able to demonstrate,
I didn't ask her to play a quarter tone scale, it was a bit unfair,
that she was able to demonstrate the note between semitone.
And so I use them quite frequently.
I'm not sure we managed to get it absolutely accurate for the percussion.
>> [LAUGH] That's probably true.
Thank you.
So, then we'll just talk about mapping numbers into notes.
And Emily, as you can see from the whiteboard here, is describing a mapping.
And what we did was then move into kind of a procreation
phase, so more hackathon than concert.
Because the audience members were then able
to do their own compositions by mapping numbers to notes.
They came up with numbers from the various sources and
we got the student musicians to play.
Which they did fantastically.
These are the worksheets that we were using and I just wonder if Emily could
describe something about the exercise there in mapping.
>> Yeah, so we just took the 12 semitones,
we didn't use quarter tones for this.
And we just assigned them, the 12 semitones, and assigned numbers to them.
I think we had started at 1, you could start at 0, you can do anything you like,
which is one of the joys.
But it's good.
You need to have some kind of rule to follow to begin with,
which you could then break.
And then, actually one of the first things I did was to ask the audience just to pick
some random numbers.
And we heard them.
Luckily the musicians were so fine that you knew we could do a quick mapping on
the board and then they are able to play them in lots of different ways.
And as you can see here,
their suggestions, you know, lots of general suggestions for whether you would.
Choose to have it high or low, or loud or soft, and
we could hear all of these versions.
We did a kind of Jeremy Corbyn-styled vote for whether we
would like this piece to be this way or that way, and then came up with all types.
So, we did this for each of the players,
and then I think the whole audience, the interactive audience, had a go themselves,
and we had performances of five or six pieces, I think.
>> Excellent, the machine expanded to include the people in the room.
This is the musicians playing one of the pieces by one of the tables,
you can tell by the expressions on their faces that it was quite challenging.
[LAUGH] We talked about Ada Sketches.
And I just want to emphasize this is not the only piece of work [LAUGH] by Emily.
And I wonder if you'd like to hear a little bit of Mesmerism.
See if you can't give us some context for this as part of the trilogy.
>> It's for solo piano and chamber orchestra.
And it was written for Alexandra Dariesku, a pianist, and
the Liverpool Mozart Orchestra for their 60th anniversary.
Now, the Liverpool Mozart Orchestra, I'm from Liverpool I know them all very well.
It's an amateur orchestra and in fact, Lasse Rempe-Gillen who's the mathematician who played in that orchestra,
plays the violin,
and so he played in the premiere of Mesmerism.
You're going to hear it now.
It's been recorded by the Royal Liverpool Philharmonic Orchestra who quite recently,
a couple months ago and also Alexandra Dariesku
with conductor Andrew Gourlay and
it's going to be released next year on NMC in a debut disc of mine.
[MUSIC]
>> Now, for something completely different [LAUGH] just to finish with.
I mentioned we've been discussing this for
a year in the digital musicology community.
And I've been doing a thought experiment with colleagues in that community.
One aspect of it is-- I don't know how many of you are Dr Who
viewers, but one aspect of it is going back in time.
So, it'd be a great episode to Babbage and
Ada Lovelace and do a sort of what happens next.
What happens if the machine had been built, what would Ada Lovelace have done?
And we've had quite a lot of thinking about that and
that really makes us get our head back to what the music was like then,
interesting music, what could you do with a machine?
And then the second part of the thought experiment is to say well,
what if you could put Ada Lovelace in the Tardis and
bring her to the present day, what would she make of computers today?
So, what we've been talking about at the moment has been quite historical,
we've been quite embedded in 200 years ago.
Just at the end here, I want to bring it forward.
So, first of all, I want to go back to that mention of Fibonacci,
it's in the libretto, it's a number sequence you'll all be familiar with.
I wanted to go through this process of what might have happened next.
Maybe Ada Lovelace and
Charles Babbage would have programmed the analytical engine to generate a sequence like this.
And one of the interesting properties of this sequence is, as many mathematicians
will know, is if you use modular arithmetic, and I'll use the example
here, where we're using modulus 35, so it's like clock arithmetic 35 instead of 12.
And the sequence that comes out is a repeating sequence.
It's a well-known mathematical property and you have depending on the modulus,
you have different to that repeating sequence.
So, we explored that.
And how do you do that?
Well, you find an emulator for the analytical engine.
And then this is an emulator within the programming language Java,
which some of you will know.
That is a piece of code that I wrote that generates two
Fibonacci numbers at a time,
I'd be very happy to discuss this with programmers in the room.
We could have a long discussion about whether is an emulator or
a simulator, cuz I'm not sure you can emulate something that's never been built.
That generates, oh there we go, there's the trace of it running.
You'll seem some words there, mill, card,
store, you've heard of all these things this morning.
That generates a sequence like this.
You'll recognize it starts with the Fibonacci numbers.
And then we have to do a mapping, and as Emily just described, in my mapping I have
to confess to an accidental creative moment here.
I mapped C, let's see, to number 1,
forgetting that I was in modular arithmetic, so I really meant B to 0.
That would have been a really good decision creatively, but
we'll come back to that [LAUGH].
Let me show you what it sounds like to play that piece of music,
and here's another error I make.
The first sound I used when I was exploring this was
a celeste, that hadn't existed until probably 70 years later,
I then used a harpsichord which is a much better choice.
I'd like to hear this and then.
You'll hear, if you listen to this, see if you can spot something melodic going on,
because I could hear that.
I've listened to this, I've walked to Cafe Nero.
And once I got to Cafe Nero, I had the melody in my head.
And I split the keyboard and then just to have the melody parts.
So, if we get Pip to play first of all everything for
a few bars, and then we just hear the upper part of it.
[MUSIC]
Can anyone hear [INAUDIBLE] at the top there?
Let's hear just the top part there, please.
[MUSIC]
[LAUGH] >> Okay,
so this is 200 years ago if we've managed to trustle the engine to harpsichord.
Perhaps that's what would have been generated. It's quite funky.
Bringing the next slide you'll see the Tardis.
So, if we come forward to today I like just brought us to somewhere I guess,
50's, 60's Bill Evans-style jazz.
What you're about to hear is what happened when I gave that theme to my jazz group.
What you have here is a five bar sequence.
You will hear the chord sequence and
then that thing you just heard will come in on the vibraphone.
Clara, would you play this please?
[LAUGH]
[MUSIC]
There we are.
So, I offer you that theme.
I'll put it on the web or something.
If anybody would like to perform it in different genres.
I think we should clip those in, it seems to be
we can discuss what creative decisions I made in getting there.
One of them was accidental that put us into mapping the [INAUDIBLE] B, maybe
it was a mixed idiom.
And then we, the second one was deliberate cuz I split the keyboard.
And in fact, I've got versions of this with different instruments and so on.
We'll close there, I hope you enjoyed that.
We can demonstrate this and play other genres on our little display
in the registration area if anyone's interested later on.
Hope this has been interesting, thank you very much.
>> [APPLAUSE]