1 00:00:14,860 --> 00:00:18,200 We're going to talk about turning numbers into notes. 2 00:00:18,200 --> 00:00:21,070 So, there's some music in this session. 3 00:00:21,070 --> 00:00:24,889 I'm very grateful that Pip Wilcox who is gonna be operating the end 4 00:00:24,889 --> 00:00:26,505 of the laptop for the audio. 5 00:00:26,505 --> 00:00:31,789 [LAUGH] Last Monday here in the Maths Institute, 6 00:00:31,789 --> 00:00:34,504 we held a performance. 7 00:00:34,504 --> 00:00:39,505 A second performance of Emily Howard's Ada sketches. 8 00:00:39,505 --> 00:00:42,504 And that's gonna be one of the things we talk about today. 9 00:00:42,504 --> 00:00:43,500 It's really about that. 10 00:00:43,500 --> 00:00:48,250 But then there's a lot in there, and we've actually been thinking for 11 00:00:48,250 --> 00:00:51,432 some time about exactly the thing on the slide. 12 00:00:51,432 --> 00:00:52,790 Turning numbers into notes. 13 00:00:52,790 --> 00:00:56,273 It's been a discussion that's been going on in anticipation of 14 00:00:56,273 --> 00:00:59,949 this event over the last year in the digital musicology community, and 15 00:00:59,949 --> 00:01:01,991 the computers and music community. 16 00:01:01,991 --> 00:01:03,680 So, we're gonna bring those things together today. 17 00:01:03,680 --> 00:01:08,070 I'm very pleased to have this opportunity to have a chat with Emily, and also 18 00:01:08,070 --> 00:01:13,090 grateful to the people who are involved in putting on the event last Monday. 19 00:01:13,090 --> 00:01:16,730 What you'll see on the slides are some stills that were taken and 20 00:01:16,730 --> 00:01:19,170 some recordings that we made last week. 21 00:01:19,170 --> 00:01:24,711 So, I'm gonna start by asking Emily to say a little bit about her 22 00:01:24,711 --> 00:01:31,504 background as Nick mentioned [SOUND]. Emily comes with qualifications from Oxford. 23 00:01:31,504 --> 00:01:36,187 >> Well, I was lucky enough to be brought up playing the cello, and 24 00:01:36,187 --> 00:01:38,510 music was all around me. 25 00:01:38,510 --> 00:01:43,504 And so, I did a lot of composing, very young. 26 00:01:43,504 --> 00:01:48,242 And I also enjoyed studying science at school and mathematics, and I came here to 27 00:01:48,242 --> 00:01:53,770 study mathematics and computer science, it was called computation in those days. 28 00:01:53,770 --> 00:01:58,490 And I had a great time, had a great tutor, Richard Bird. 29 00:01:58,490 --> 00:02:05,380 And yes, after that, there was something kind of missing maybe. 30 00:02:05,380 --> 00:02:09,650 And I went back to studying composition. 31 00:02:09,650 --> 00:02:14,560 I did a Masters in Composition at the Royal Northern College of Music, and 32 00:02:14,560 --> 00:02:16,840 a PhD in Composition at Manchester University. 33 00:02:16,840 --> 00:02:20,504 And I'm still based in Manchester at the Royal Northern College of Music. 34 00:02:20,504 --> 00:02:22,503 >> So, we have mathematics, computer science, and music. 35 00:02:22,503 --> 00:02:23,504 Very relevant today. 36 00:02:23,504 --> 00:02:27,733 I think there are many people in the audience who will resonate with these 37 00:02:27,733 --> 00:02:28,504 interests. 38 00:02:28,504 --> 00:02:31,061 I want to say a little bit about this note, we've seen 39 00:02:31,061 --> 00:02:35,504 footnotes already today, this one- >> [INAUDIBLE] 40 00:02:35,504 --> 00:02:36,504 >> Oh, okay. 41 00:02:36,504 --> 00:02:37,504 >> Yeah. 42 00:02:37,504 --> 00:02:38,504 >> We can do that one as well, quickly. 43 00:02:38,504 --> 00:02:39,504 >> Cheers. 44 00:02:39,504 --> 00:02:42,505 >> Okay. 45 00:02:42,505 --> 00:02:45,504 >> Okay, I'll pit a mic right next to my mic. 46 00:02:45,504 --> 00:02:51,505 So, this is quite an important and well known quotation from Ada Lovelace. 47 00:02:51,505 --> 00:02:52,995 Supposing, for instance, 48 00:02:52,995 --> 00:02:57,094 that the fundamental relations of pitched sounds in the science of harmony and 49 00:02:57,094 --> 00:03:01,628 of musical composition were susceptible of such expressions, which she was talking 50 00:03:01,628 --> 00:03:05,726 about operations, and adaptations, the engine might compose elaborate and 51 00:03:05,726 --> 00:03:09,860 scientific pieces of music of any degree of complexity or extent. 52 00:03:09,860 --> 00:03:11,497 This is a very interesting statement, and 53 00:03:11,497 --> 00:03:13,504 it's the one we've been discussing for some time. 54 00:03:13,504 --> 00:03:18,504 I came to this, incidentally, thanks to Betty Toole in the front row. 55 00:03:18,504 --> 00:03:22,085 Because five years ago I was moving to Oxford, and 56 00:03:22,085 --> 00:03:27,550 I was giving a normal lecture, and my theme was to do with machines in music. 57 00:03:27,550 --> 00:03:33,044 And I was at the Internet Archive in San Fransisco, where Ted Nelson, 58 00:03:33,044 --> 00:03:38,090 the creator of hypertext, was presenting his autobiography. 59 00:03:38,090 --> 00:03:41,323 I bumped into Betty and I said I was giving this talk, and Betty brought my 60 00:03:41,323 --> 00:03:44,505 attention to this and gave me permission to use material from her book. 61 00:03:44,505 --> 00:03:45,504 Thank you very much. 62 00:03:45,504 --> 00:03:48,504 So, it started for me five years ago, this discussion. 63 00:03:48,504 --> 00:03:50,503 Emily, how did you come to this? 64 00:03:50,503 --> 00:03:55,505 >> I think I came to know about Ada Lovelace in about 2008. 65 00:03:55,505 --> 00:03:58,450 And I was looking around for an opera subject. 66 00:03:58,450 --> 00:04:02,750 And a good friend of mine, and colleague Laura Tunbridge who's here at Oxford now, 67 00:04:02,750 --> 00:04:05,140 suggested Ada Lovelace to me. 68 00:04:05,140 --> 00:04:08,420 And possibly, well probably because of the mathematic and 69 00:04:08,420 --> 00:04:10,740 computing science background. 70 00:04:10,740 --> 00:04:15,727 And I went away and I read this sketch of the analytical engine, and I looked, 71 00:04:15,727 --> 00:04:19,103 I was particularly taken by this quote, and so, and 72 00:04:19,103 --> 00:04:23,750 I wrote the Ada Sketches in 2011, and also two orchestral pieces. 73 00:04:23,750 --> 00:04:26,504 A piece called Mesmorism, and a piece called Calculus of the Nervous System. 74 00:04:26,504 --> 00:04:28,504 >> [LAUGH]. 75 00:04:28,504 --> 00:04:33,504 >> And we have a clip of Mesmorism a little bit later on. 76 00:04:33,504 --> 00:04:34,882 >> So, of that trilogy, 77 00:04:34,882 --> 00:04:37,852 this is Ada Sketches, this is a bit of the score, 78 00:04:37,852 --> 00:04:42,503 could you tell us a little bit about how you came to do this particular piece? 79 00:04:42,503 --> 00:04:47,712 >> Yeah, so Ada Sketches, well it's an opera sketch, so an opera, 80 00:04:47,712 --> 00:04:53,580 I mean, it's an art form that comprises words, music, and drama. 81 00:04:53,580 --> 00:04:58,410 And a sketch because, well apart from the pun, actually, it really is just a sketch. 82 00:04:58,410 --> 00:05:01,036 It's not finished. It's about seven to eight minutes long and 83 00:05:01,036 --> 00:05:05,471 I wanted to try out several of the ideas that I was thinking about from reading 84 00:05:05,471 --> 00:05:09,580 about Ada and reading about her mathematics in particular. 85 00:05:09,580 --> 00:05:13,520 So, the piece is based on a number of dramatic oppositions. 86 00:05:13,520 --> 00:05:17,740 First of all, there's Ada Lovelace, played by a mezzo-soprano. 87 00:05:17,740 --> 00:05:21,770 And there's the analytical engine, and that is actually an instrumental ensemble, 88 00:05:21,770 --> 00:05:25,100 it's flute, clarinet and percussion. 89 00:05:25,100 --> 00:05:29,440 And of course you've got the opposition kind of inside of Ada's head. 90 00:05:29,440 --> 00:05:33,680 You've got her mother's influence, the mathematical, methodical and moral. 91 00:05:33,680 --> 00:05:38,750 And her father's influence, famously mad, bad and dangerous to know. 92 00:05:38,750 --> 00:05:43,090 And then, something that interested me deeply, 93 00:05:43,090 --> 00:05:48,450 having read her notes, is a kind of representation in the piece of 94 00:05:48,450 --> 00:05:53,020 creative processes and the moments of discovery, kind of breakthrough moments, 95 00:05:53,020 --> 00:05:56,480 I find very interesting, whether they are original or not. 96 00:05:56,480 --> 00:05:58,500 When you're solving a mathematical problem, 97 00:05:58,500 --> 00:06:02,510 or indeed kind of working on a piece of music, and you have a click and 98 00:06:02,510 --> 00:06:05,550 something happens and you think, that's exactly how it should go. 99 00:06:05,550 --> 00:06:08,410 These moments interest me and I was thinking it would be very interesting 100 00:06:08,410 --> 00:06:11,540 to try to put them into the music. 101 00:06:11,540 --> 00:06:15,370 And so I have, in this sketch, 102 00:06:15,370 --> 00:06:21,662 at the opening, Ada is literally working on an equation. 103 00:06:21,662 --> 00:06:25,208 I was looking at the note B as well, and I chose, 104 00:06:25,208 --> 00:06:28,504 I think it was 3 over 2 to the power of 36. 105 00:06:28,504 --> 00:06:32,506 And 36, composers have to make some decisions. 106 00:06:32,506 --> 00:06:33,504 36 because she died when she was 36. 107 00:06:33,504 --> 00:06:36,469 And I worked through a kind of a text, 108 00:06:36,469 --> 00:06:42,120 thinking about what she might say in a very formal kind of way. 109 00:06:42,120 --> 00:06:46,580 As she worked on this equation, and as she tried to solve it in the way it might have 110 00:06:46,580 --> 00:06:50,230 been solved if they could get the analytical engine to work. 111 00:06:50,230 --> 00:06:53,430 So, that's what's happening at the beginning of this piece, and 112 00:06:53,430 --> 00:06:55,300 I think you might hear part of it. 113 00:06:55,300 --> 00:07:00,200 Just to say something about the instrumentalists. As she works, and 114 00:07:00,200 --> 00:07:02,180 this might be in her head or it might not be, it's for 115 00:07:02,180 --> 00:07:07,130 the audience to decide, kind of the machine Its beginning to work. 116 00:07:07,130 --> 00:07:09,495 And so she's solving the equation and you hear, 117 00:07:09,495 --> 00:07:12,503 at first you won't think of it as a traditional kind of music. 118 00:07:12,503 --> 00:07:17,533 You kind of hear just the odd, the simple works, and then somehow they 119 00:07:17,533 --> 00:07:23,431 sound very machine-like and very repetitive, algorithmic, and it really is. 120 00:07:23,431 --> 00:07:28,259 Because I've actually taken what she's talking about, literally, and 121 00:07:28,259 --> 00:07:33,010 I've used all of that mathematics in the music to create as algorithmic, 122 00:07:33,010 --> 00:07:39,170 as non-personal, a piece of music as I possibly can for the analytical engine. 123 00:07:39,170 --> 00:07:41,681 >> Thanks very much. And we're gonna hear a tip of that in 124 00:07:41,681 --> 00:07:45,950 a second, just to give a history of the performance we had last week. 125 00:07:45,950 --> 00:07:50,170 The format that Emily's now using isn't simply to 126 00:07:50,170 --> 00:07:52,780 have a bunch of excellent musicians performing this work, but 127 00:07:52,780 --> 00:07:57,180 it's actually to engage also a mathematician and the audience. 128 00:07:57,180 --> 00:07:59,680 Okay, I want to say a little bit more about that in a second. 129 00:07:59,680 --> 00:08:06,520 So, that format was first explored in the science museum a month or so ago. 130 00:08:06,520 --> 00:08:10,504 Although there have been previous performances of this work. 131 00:08:10,504 --> 00:08:15,902 And we brought it to Oxford, partly thanks to the support 132 00:08:15,902 --> 00:08:20,630 of our sponsors, some music projects we have here. 133 00:08:20,630 --> 00:08:22,190 We have some digital musicology projects 134 00:08:22,190 --> 00:08:25,390 in particular one called Transforming Musicology. 135 00:08:25,390 --> 00:08:28,087 We're very grateful to many sponsors here and to the Maths Institute and 136 00:08:28,087 --> 00:08:30,976 the Bodleian Library, the Oxford Research Centre in the Humanities and 137 00:08:30,976 --> 00:08:33,504 many others, for enabling us to put on the visit last weekend. 138 00:08:33,504 --> 00:08:35,502 That project captured the content and 139 00:08:35,502 --> 00:08:38,505 it captured the audience reaction to the performances. 140 00:08:38,505 --> 00:08:42,212 And what we're exploring for example, is, did the audience receive, 141 00:08:42,212 --> 00:08:46,166 did they interpret, did they understand the performance differently after 142 00:08:46,166 --> 00:08:48,505 the mathematics had been explained to them? 143 00:08:48,505 --> 00:08:51,504 So, look out for publications about this coming out. 144 00:08:51,504 --> 00:08:57,064 And meanwhile, let's have a short clip, all the clips we have in this session 145 00:08:57,064 --> 00:09:02,640 are just two or three minutes long, of the beginning of the operatic work. 146 00:09:02,640 --> 00:09:06,504 This is Rosie, who's a spectacular singer. 147 00:09:06,504 --> 00:09:08,504 Just to let you know we haven't tested the volume. 148 00:09:08,504 --> 00:09:13,505 >> [LAUGH] >> I was responsible for recording this. 149 00:09:13,505 --> 00:09:17,504 The dynamic range of this recording is extraordinary. 150 00:09:17,504 --> 00:09:19,504 Rosie starts by speaking quietly. 151 00:09:19,504 --> 00:09:26,504 I encourage everyone to read the libretto, it's really, really good. 152 00:09:26,504 --> 00:09:29,504 And then sings quite loudly, just so you know. 153 00:09:29,504 --> 00:09:35,504 [LAUGH] Pip, can we play the clip, please? 154 00:09:35,504 --> 00:09:46,504 [MUSIC] 155 00:09:46,504 --> 00:09:47,505 Thanks, Ben. 156 00:09:47,505 --> 00:09:51,676 And so, you get the idea, it's just not very, very quietly, 157 00:09:51,676 --> 00:09:56,504 the other pieces of music we have probably won't be as quiet as that was. 158 00:09:56,504 --> 00:10:00,505 I'm sorry it took us a little while to work out how to turn the volume up. 159 00:10:00,505 --> 00:10:07,380 These are the musicians and they were extremely impressive. 160 00:10:07,380 --> 00:10:08,490 They made every note count. 161 00:10:08,490 --> 00:10:12,504 If we're talking about computers for music. 162 00:10:12,504 --> 00:10:18,504 But one of the things that is extremely clear is these musicians were excellent. 163 00:10:18,504 --> 00:10:21,505 Do you want to say something about your excellent student? 164 00:10:21,505 --> 00:10:24,406 >> I mean I wish you could have heard that a bit more clearly, 165 00:10:24,406 --> 00:10:27,503 I mean you'll hear it later on, they really are excellent. 166 00:10:27,503 --> 00:10:29,504 They worked very hard on performing it. 167 00:10:29,504 --> 00:10:34,504 Rosie, the singer, is an alumna of the Royal Northern College of Music. 168 00:10:34,504 --> 00:10:40,504 And then the other three are current students there. 169 00:10:40,504 --> 00:10:41,505 >> We were very impressed. 170 00:10:41,505 --> 00:10:45,586 During the evening, Emily got them to do some things, 171 00:10:45,586 --> 00:10:51,080 which any musicians in the audience had to be seriously impressed by. 172 00:10:51,080 --> 00:10:54,024 There was getting a [INAUDIBLE] to play in quarter tones and 173 00:10:54,024 --> 00:10:57,949 getting two students to play six notes in one against seven from the other 174 00:10:57,949 --> 00:11:00,503 without counting in. It was hugely impressive. 175 00:11:00,503 --> 00:11:02,503 [LAUGH] They're excellent. 176 00:11:02,503 --> 00:11:04,504 I, in particular, spent time with the percussionist. 177 00:11:04,504 --> 00:11:07,504 I'll come back to that. 178 00:11:07,504 --> 00:11:11,702 The- >> People are still having trouble 179 00:11:11,702 --> 00:11:12,504 hearing your voice. 180 00:11:12,504 --> 00:11:16,504 Do you want to unplug the microphone out of your pocket? 181 00:11:16,504 --> 00:11:18,505 >> Yeah, I've got two microphones here. 182 00:11:18,505 --> 00:11:26,250 [LAUGH] So the work is, in some ways about mathematical discovery. 183 00:11:26,250 --> 00:11:29,750 And, and I like this quote I've taken from something you wrote Emily, 184 00:11:29,750 --> 00:11:34,958 about, this is exploration of the musical solutions of computation, 185 00:11:34,958 --> 00:11:39,503 for the hypothetical [INAUDIBLE] can you say something about that? 186 00:11:39,503 --> 00:11:42,473 >> Yeah. So, following on from what I was saying 187 00:11:42,473 --> 00:11:49,049 before, she's explaining, in the text, she worked on that mathematical discovery, 188 00:11:49,049 --> 00:11:53,432 and the way I have represented that, not that you heard it, 189 00:11:53,432 --> 00:11:58,606 she's speaking in this very formal way as she does the mathematics and 190 00:11:58,606 --> 00:12:04,160 as she gets further into the equation, a solution, and she makes a discovery. 191 00:12:04,160 --> 00:12:09,142 She goes into a much more typically operatic sounding voice that 192 00:12:09,142 --> 00:12:13,950 you heard just there when she was singing to the power of five. 193 00:12:13,950 --> 00:12:20,328 And later on, she has a similar moment when she starts to think about whether or 194 00:12:20,328 --> 00:12:25,740 not the machine will be able to use notes instead of numbers. 195 00:12:25,740 --> 00:12:29,420 So, this is her more visionary, like a cultural discovery. 196 00:12:29,420 --> 00:12:32,745 So, I've represented them in the same way, vocally. 197 00:12:32,745 --> 00:12:38,438 As the piece continues, there's a real sudden moment in the piece, 198 00:12:38,438 --> 00:12:42,760 where always Ada has been speaking or 199 00:12:42,760 --> 00:12:46,990 singing and the machine has kind of been developing very independently. 200 00:12:46,990 --> 00:12:51,638 And then at one point the machine takes over, it is independent and 201 00:12:51,638 --> 00:12:56,452 this is a really crucial moment for Ada because she kind of snaps out of 202 00:12:56,452 --> 00:13:00,530 the very formal approach, because machine just goes. 203 00:13:00,530 --> 00:13:04,280 And she has absolutely no effect on it. 204 00:13:04,280 --> 00:13:05,050 And at that moment, 205 00:13:05,050 --> 00:13:09,000 she's sort of thinking about, like a human versus machine kind of idea. 206 00:13:09,000 --> 00:13:09,980 Where would I fit in? 207 00:13:09,980 --> 00:13:12,140 What if the machine can compose the melodies? 208 00:13:12,140 --> 00:13:13,380 What about me? 209 00:13:13,380 --> 00:13:15,140 So, yeah. 210 00:13:15,140 --> 00:13:18,830 >> We'll hear that clip. We're talking about a mathematical discovery, 211 00:13:18,830 --> 00:13:23,730 one of the unusual things about this performance was we had a mathematician. 212 00:13:23,730 --> 00:13:25,960 [LAUGH] So, what's it like gigging with a mathematician? 213 00:13:25,960 --> 00:13:27,800 >> It's great, actually. 214 00:13:27,800 --> 00:13:30,450 Cuz I've been working with Lasse, he's from the University of Liverpool. 215 00:13:30,450 --> 00:13:35,350 And I've been actually doing a Leveshume artist-in-residency in 216 00:13:35,350 --> 00:13:39,490 the Department of Mathematical Sciences for the last ten months. 217 00:13:39,490 --> 00:13:42,780 And so I've been speaking regularly with Lasse in particular about his work 218 00:13:42,780 --> 00:13:44,000 on dynamical systems. 219 00:13:44,000 --> 00:13:50,780 So, when we were talking about him being involved in this Ada Sketches performance, 220 00:13:50,780 --> 00:13:54,220 I spoke with him, and he was able to give really fantastic explanations of 221 00:13:54,220 --> 00:13:55,740 the mathematics used in this. 222 00:13:55,740 --> 00:13:59,360 So, for example, the idea of reducing the number of steps. 223 00:13:59,360 --> 00:14:02,480 And he gave, I think he spoke about encryption today and 224 00:14:02,480 --> 00:14:04,190 how this could work today. 225 00:14:04,190 --> 00:14:07,910 And he also spoke about creative discoveries for 226 00:14:07,910 --> 00:14:10,770 himself in his own mathematical research. 227 00:14:10,770 --> 00:14:15,837 >> So, I have a clip now from a couple minutes further through the work where 228 00:14:15,837 --> 00:14:20,504 the human, machine interaction, that tension is playing out. 229 00:14:20,504 --> 00:14:25,504 >> I'll just say one last thing. 230 00:14:25,504 --> 00:14:29,847 The machine here it sounds absolutely, completely otherworldly and 231 00:14:29,847 --> 00:14:32,505 it's completely functionally derived. 232 00:14:32,505 --> 00:14:37,139 And it's in combat, if you like, with Ada when she comes in and 233 00:14:37,139 --> 00:14:43,504 this is her at her most lyrical. 234 00:14:43,504 --> 00:15:13,504 [MUSIC] 235 00:15:13,504 --> 00:16:13,504 [MUSIC] 236 00:16:13,504 --> 00:16:17,504 >> When I was looking at that clip to include in the presentation. 237 00:16:17,504 --> 00:16:19,704 It's very difficult to choose the beginning and 238 00:16:19,704 --> 00:16:22,505 end points because the words through this part are fantastic. 239 00:16:22,505 --> 00:16:27,504 And it ends with her saying will Ada resonate, and then she talks about [INAUDIBLE]. 240 00:16:27,504 --> 00:16:32,080 Earlier on, between the two clips you've heard, she talks about Fibonacci and 241 00:16:32,080 --> 00:16:33,505 I'll come back to that. 242 00:16:33,505 --> 00:16:34,504 So, thank you. 243 00:16:34,504 --> 00:16:35,504 That gives you a good taste. 244 00:16:35,504 --> 00:16:40,049 The whole piece is about seven or eight minutes long, and you've now heard 245 00:16:40,049 --> 00:16:44,320 a couple of bits, one of them better than the other in terms of volume. 246 00:16:44,320 --> 00:16:48,595 And I just want to show you a picture I took with my phone during the gig. 247 00:16:48,595 --> 00:16:50,922 [LAUGH] So this is the percussion, 248 00:16:50,922 --> 00:16:54,505 and yes it does feature flower pots and tin cans. 249 00:16:54,505 --> 00:16:58,489 [LAUGH] You can see an excerpt from the score there with the instructions, 250 00:16:58,489 --> 00:17:01,503 note the requirement for these to be tuned quarter-tone. 251 00:17:01,503 --> 00:17:05,920 So, it's interesting aspect of this from a musical viewpoint, interesting challenge. 252 00:17:05,920 --> 00:17:07,708 We had great fun raiding the music faculty 253 00:17:07,708 --> 00:17:08,635 percussion store. 254 00:17:08,635 --> 00:17:12,530 [LAUGH] But interesting that the use of quarter tones. 255 00:17:12,530 --> 00:17:15,920 I want to ask Emily to say something about that because we 256 00:17:15,920 --> 00:17:18,940 are just moving into the numbers to notes piece. 257 00:17:18,940 --> 00:17:21,510 So, this is a relevant point. 258 00:17:21,510 --> 00:17:23,430 >> So, to say something about the quarter tones. 259 00:17:23,430 --> 00:17:28,910 Well I wanted to have quarter tones in the analytical engine part. 260 00:17:28,910 --> 00:17:34,680 And actually the demonstration I did with the flautist was to have the flautist 261 00:17:34,680 --> 00:17:37,330 play a major scale, which we're all happy with. 262 00:17:37,330 --> 00:17:41,480 And then to play semitones, these are also steps that we're quite happy with. 263 00:17:41,480 --> 00:17:42,890 And then she was able to demonstrate, 264 00:17:42,890 --> 00:17:45,480 I didn't ask her to play a quarter tone scale, it was a bit unfair, 265 00:17:45,480 --> 00:17:50,410 that she was able to demonstrate the note between semitone. 266 00:17:50,410 --> 00:17:52,810 And so I use them quite frequently. 267 00:17:52,810 --> 00:17:56,504 I'm not sure we managed to get it absolutely accurate for the percussion. 268 00:17:56,504 --> 00:17:57,503 >> [LAUGH] That's probably true. 269 00:17:57,503 --> 00:17:58,504 Thank you. 270 00:17:58,504 --> 00:18:01,770 So, then we'll just talk about mapping numbers into notes. 271 00:18:01,770 --> 00:18:08,760 And Emily, as you can see from the whiteboard here, is describing a mapping. 272 00:18:08,760 --> 00:18:11,900 And what we did was then move into kind of a procreation 273 00:18:11,900 --> 00:18:15,440 phase, so more hackathon than concert. 274 00:18:15,440 --> 00:18:18,100 Because the audience members were then able 275 00:18:18,100 --> 00:18:21,290 to do their own compositions by mapping numbers to notes. 276 00:18:21,290 --> 00:18:23,670 They came up with numbers from the various sources and 277 00:18:23,670 --> 00:18:26,890 we got the student musicians to play. 278 00:18:26,890 --> 00:18:28,420 Which they did fantastically. 279 00:18:28,420 --> 00:18:32,457 These are the worksheets that we were using and I just wonder if Emily could 280 00:18:32,457 --> 00:18:35,716 describe something about the exercise there in mapping. 281 00:18:35,716 --> 00:18:39,808 >> Yeah, so we just took the 12 semitones, 282 00:18:39,808 --> 00:18:43,905 we didn't use quarter tones for this. 283 00:18:43,905 --> 00:18:49,575 And we just assigned them, the 12 semitones, and assigned numbers to them. 284 00:18:49,575 --> 00:18:52,325 I think we had started at 1, you could start at 0, you can do anything you like, 285 00:18:52,325 --> 00:18:53,445 which is one of the joys. 286 00:18:53,445 --> 00:18:54,135 But it's good. 287 00:18:54,135 --> 00:18:56,713 You need to have some kind of rule to follow to begin with, 288 00:18:56,713 --> 00:18:58,012 which you could then break. 289 00:18:58,012 --> 00:19:01,531 And then, actually one of the first things I did was to ask the audience just to pick 290 00:19:01,531 --> 00:19:02,505 some random numbers. 291 00:19:02,505 --> 00:19:03,504 And we heard them. 292 00:19:03,504 --> 00:19:07,745 Luckily the musicians were so fine that you knew we could do a quick mapping on 293 00:19:07,745 --> 00:19:11,912 the board and then they are able to play them in lots of different ways. 294 00:19:11,912 --> 00:19:12,772 And as you can see here, 295 00:19:12,772 --> 00:19:16,780 their suggestions, you know, lots of general suggestions for whether you would. 296 00:19:16,780 --> 00:19:19,300 Choose to have it high or low, or loud or soft, and 297 00:19:19,300 --> 00:19:21,120 we could hear all of these versions. 298 00:19:21,120 --> 00:19:26,210 We did a kind of Jeremy Corbyn-styled vote for whether we 299 00:19:26,210 --> 00:19:29,220 would like this piece to be this way or that way, and then came up with all types. 300 00:19:29,220 --> 00:19:30,710 So, we did this for each of the players, 301 00:19:30,710 --> 00:19:35,610 and then I think the whole audience, the interactive audience, had a go themselves, 302 00:19:35,610 --> 00:19:39,070 and we had performances of five or six pieces, I think. 303 00:19:39,070 --> 00:19:45,860 >> Excellent, the machine expanded to include the people in the room. 304 00:19:45,860 --> 00:19:50,824 This is the musicians playing one of the pieces by one of the tables, 305 00:19:50,824 --> 00:19:56,504 you can tell by the expressions on their faces that it was quite challenging. 306 00:19:56,504 --> 00:19:58,505 [LAUGH] We talked about Ada Sketches. 307 00:19:58,505 --> 00:20:04,504 And I just want to emphasize this is not the only piece of work [LAUGH] by Emily. 308 00:20:04,504 --> 00:20:08,505 And I wonder if you'd like to hear a little bit of Mesmerism. 309 00:20:08,505 --> 00:20:10,504 See if you can't give us some context for this as part of the trilogy. 310 00:20:10,504 --> 00:20:14,504 >> It's for solo piano and chamber orchestra. 311 00:20:14,504 --> 00:20:18,680 And it was written for Alexandra Dariesku, a pianist, and 312 00:20:18,680 --> 00:20:23,730 the Liverpool Mozart Orchestra for their 60th anniversary. 313 00:20:23,730 --> 00:20:27,559 Now, the Liverpool Mozart Orchestra, I'm from Liverpool I know them all very well. 314 00:20:27,559 --> 00:20:32,480 It's an amateur orchestra and in fact, Lasse Rempe-Gillen who's the mathematician who played in that orchestra, 315 00:20:32,480 --> 00:20:33,930 plays the violin, 316 00:20:33,930 --> 00:20:36,330 and so he played in the premiere of Mesmerism. 317 00:20:36,330 --> 00:20:37,250 You're going to hear it now. 318 00:20:37,250 --> 00:20:41,225 It's been recorded by the Royal Liverpool Philharmonic Orchestra who quite recently, 319 00:20:41,225 --> 00:20:43,504 a couple months ago and also Alexandra Dariesku 320 00:20:43,504 --> 00:20:46,201 with conductor Andrew Gourlay and 321 00:20:46,201 --> 00:20:51,503 it's going to be released next year on NMC in a debut disc of mine. 322 00:20:51,503 --> 00:23:42,504 [MUSIC] 323 00:23:42,504 --> 00:23:47,503 >> Now, for something completely different [LAUGH] just to finish with. 324 00:23:47,503 --> 00:23:50,955 I mentioned we've been discussing this for 325 00:23:50,955 --> 00:23:54,503 a year in the digital musicology community. 326 00:23:54,503 --> 00:23:58,505 And I've been doing a thought experiment with colleagues in that community. 327 00:23:58,505 --> 00:24:00,836 One aspect of it is-- I don't know how many of you are Dr Who 328 00:24:00,836 --> 00:24:04,504 viewers, but one aspect of it is going back in time. 329 00:24:04,504 --> 00:24:07,338 So, it'd be a great episode to Babbage and 330 00:24:07,338 --> 00:24:10,504 Ada Lovelace and do a sort of what happens next. 331 00:24:10,504 --> 00:24:14,504 What happens if the machine had been built, what would Ada Lovelace have done? 332 00:24:14,504 --> 00:24:17,181 And we've had quite a lot of thinking about that and 333 00:24:17,181 --> 00:24:20,791 that really makes us get our head back to what the music was like then, 334 00:24:20,791 --> 00:24:24,860 interesting music, what could you do with a machine? 335 00:24:24,860 --> 00:24:27,170 And then the second part of the thought experiment is to say well, 336 00:24:27,170 --> 00:24:29,890 what if you could put Ada Lovelace in the Tardis and 337 00:24:29,890 --> 00:24:33,647 bring her to the present day, what would she make of computers today? 338 00:24:33,647 --> 00:24:36,003 So, what we've been talking about at the moment has been quite historical, 339 00:24:36,003 --> 00:24:37,505 we've been quite embedded in 200 years ago. 340 00:24:37,505 --> 00:24:39,504 Just at the end here, I want to bring it forward. 341 00:24:39,504 --> 00:24:43,164 So, first of all, I want to go back to that mention of Fibonacci, 342 00:24:43,164 --> 00:24:47,504 it's in the libretto, it's a number sequence you'll all be familiar with. 343 00:24:47,504 --> 00:24:53,504 I wanted to go through this process of what might have happened next. 344 00:24:53,504 --> 00:24:55,165 Maybe Ada Lovelace and 345 00:24:55,165 --> 00:25:00,504 Charles Babbage would have programmed the analytical engine to generate a sequence like this. 346 00:25:00,504 --> 00:25:05,141 And one of the interesting properties of this sequence is, as many mathematicians 347 00:25:05,141 --> 00:25:09,182 will know, is if you use modular arithmetic, and I'll use the example 348 00:25:09,182 --> 00:25:14,503 here, where we're using modulus 35, so it's like clock arithmetic 35 instead of 12. 349 00:25:14,503 --> 00:25:17,504 And the sequence that comes out is a repeating sequence. 350 00:25:17,504 --> 00:25:20,879 It's a well-known mathematical property and you have depending on the modulus, 351 00:25:20,879 --> 00:25:23,504 you have different to that repeating sequence. 352 00:25:23,504 --> 00:25:25,503 So, we explored that. 353 00:25:25,503 --> 00:25:26,504 And how do you do that? 354 00:25:26,504 --> 00:25:29,504 Well, you find an emulator for the analytical engine. 355 00:25:29,504 --> 00:25:32,919 And then this is an emulator within the programming language Java, 356 00:25:32,919 --> 00:25:34,503 which some of you will know. 357 00:25:34,503 --> 00:25:37,312 That is a piece of code that I wrote that generates two 358 00:25:37,312 --> 00:25:38,956 Fibonacci numbers at a time, 359 00:25:38,956 --> 00:25:42,450 I'd be very happy to discuss this with programmers in the room. 360 00:25:42,450 --> 00:25:45,741 We could have a long discussion about whether is an emulator or 361 00:25:45,741 --> 00:25:49,720 a simulator, cuz I'm not sure you can emulate something that's never been built. 362 00:25:49,720 --> 00:25:52,504 That generates, oh there we go, there's the trace of it running. 363 00:25:52,504 --> 00:25:54,106 You'll seem some words there, mill, card, 364 00:25:54,106 --> 00:25:57,020 store, you've heard of all these things this morning. 365 00:25:57,020 --> 00:25:58,610 That generates a sequence like this. 366 00:25:58,610 --> 00:26:01,340 You'll recognize it starts with the Fibonacci numbers. 367 00:26:01,340 --> 00:26:06,683 And then we have to do a mapping, and as Emily just described, in my mapping I have 368 00:26:06,683 --> 00:26:11,640 to confess to an accidental creative moment here. 369 00:26:11,640 --> 00:26:14,970 I mapped C, let's see, to number 1, 370 00:26:14,970 --> 00:26:17,885 forgetting that I was in modular arithmetic, so I really meant B to 0. 371 00:26:17,885 --> 00:26:21,152 That would have been a really good decision creatively, but 372 00:26:21,152 --> 00:26:22,895 we'll come back to that [LAUGH]. 373 00:26:22,895 --> 00:26:26,860 Let me show you what it sounds like to play that piece of music, 374 00:26:26,860 --> 00:26:28,950 and here's another error I make. 375 00:26:28,950 --> 00:26:32,511 The first sound I used when I was exploring this was 376 00:26:32,511 --> 00:26:35,927 a celeste, that hadn't existed until probably 70 years later, 377 00:26:35,927 --> 00:26:40,470 I then used a harpsichord which is a much better choice. 378 00:26:40,470 --> 00:26:42,503 I'd like to hear this and then. 379 00:26:42,503 --> 00:26:47,043 You'll hear, if you listen to this, see if you can spot something melodic going on, 380 00:26:47,043 --> 00:26:48,504 because I could hear that. 381 00:26:48,504 --> 00:26:50,434 I've listened to this, I've walked to Cafe Nero. 382 00:26:50,434 --> 00:26:52,504 And once I got to Cafe Nero, I had the melody in my head. 383 00:26:52,504 --> 00:26:55,504 And I split the keyboard and then just to have the melody parts. 384 00:26:55,504 --> 00:26:59,355 So, if we get Pip to play first of all everything for 385 00:26:59,355 --> 00:27:03,504 a few bars, and then we just hear the upper part of it. 386 00:27:03,504 --> 00:27:15,300 [MUSIC] 387 00:27:15,300 --> 00:27:19,504 Can anyone hear [INAUDIBLE] at the top there? 388 00:27:19,504 --> 00:27:22,504 Let's hear just the top part there, please. 389 00:27:22,504 --> 00:27:34,505 [MUSIC] 390 00:27:34,505 --> 00:27:39,933 [LAUGH] >> Okay, 391 00:27:39,933 --> 00:27:45,380 so this is 200 years ago if we've managed to trustle the engine to harpsichord. 392 00:27:45,380 --> 00:27:49,900 Perhaps that's what would have been generated. It's quite funky. 393 00:27:49,900 --> 00:27:52,504 Bringing the next slide you'll see the Tardis. 394 00:27:52,504 --> 00:27:58,363 So, if we come forward to today I like just brought us to somewhere I guess, 395 00:27:58,363 --> 00:28:00,880 50's, 60's Bill Evans-style jazz. 396 00:28:00,880 --> 00:28:06,200 What you're about to hear is what happened when I gave that theme to my jazz group. 397 00:28:06,200 --> 00:28:08,500 What you have here is a five bar sequence. 398 00:28:08,500 --> 00:28:10,870 You will hear the chord sequence and 399 00:28:10,870 --> 00:28:14,573 then that thing you just heard will come in on the vibraphone. 400 00:28:14,573 --> 00:28:17,504 Clara, would you play this please? 401 00:28:17,504 --> 00:28:23,505 [LAUGH] 402 00:28:23,505 --> 00:29:16,504 [MUSIC] 403 00:29:16,504 --> 00:29:17,504 There we are. 404 00:29:17,504 --> 00:29:18,504 So, I offer you that theme. 405 00:29:18,504 --> 00:29:19,504 I'll put it on the web or something. 406 00:29:19,504 --> 00:29:22,504 If anybody would like to perform it in different genres. 407 00:29:22,504 --> 00:29:25,122 I think we should clip those in, it seems to be 408 00:29:25,122 --> 00:29:29,504 we can discuss what creative decisions I made in getting there. 409 00:29:29,504 --> 00:29:34,018 One of them was accidental that put us into mapping the [INAUDIBLE] B, maybe 410 00:29:34,018 --> 00:29:35,504 it was a mixed idiom. 411 00:29:35,504 --> 00:29:39,504 And then we, the second one was deliberate cuz I split the keyboard. 412 00:29:39,504 --> 00:29:43,504 And in fact, I've got versions of this with different instruments and so on. 413 00:29:43,504 --> 00:29:46,504 We'll close there, I hope you enjoyed that. 414 00:29:46,504 --> 00:29:50,161 We can demonstrate this and play other genres on our little display 415 00:29:50,161 --> 00:29:53,504 in the registration area if anyone's interested later on. 416 00:29:53,504 --> 00:29:55,504 Hope this has been interesting, thank you very much. 417 00:29:55,504 --> 00:30:03,480 >> [APPLAUSE]