Musical Consonance and Dissonance: The Good, Bad and Beautifully Ugly - Milton Mermikides

They let me come up on my own. Now I've graduated. Thanks so much for coming. Thanks for watching online. You know the drill, there's the code here. You can scan that and ask me questions and tell me where, what I got wrong along the way. This codes are also in the leaflets in front of you, so let's get to it. What do we mean by music being good? Well, we could look externally and ask other people, critics even, and they might give us a league table. These are purely illustrative with high value and low value music. And then we can fill these in however we wish. Now we are all individuals, so we don't need to confer con conform to this. We can look internally and we, this motion is called a guilty pleasure. We shouldn't be guilty. It should be proud defiance, actually. But no one talks about the other end, which is the guilty displeasure. So one gives us the raised eyebrows, the other, the gasps. Why is this? Well, one reason is even dedicated musicians have a particular affinity to music they first heard in their mid-teens and around that area it's called the reminiscence bump. And I'm gonna name the other bit the grump slump <laugh>. It doesn't do it for you anymore. Now, even if we lived in the same time, we wouldn't hear the same, uh, music necessarily, but born at different ages, it means there's disparity here. You just don't get it between these two. There are other reasons. Music is an acquired taste. These are contemporaneous critiques of great composers. Look at the bottom left and get ready to gasp <laugh>. There you go. Nauseous clap trap from Gershwin. And if they say this about great composers, imagine progressive composers. Um, you might guess some of these Stravinsky. Anyone wants to guess this one? These three are my favorite, particularly the Irish potato under the influence of of powerful atomizer, which actually I want to hear now and just anybody can get these sort of critiques. Whoops. Okay.<laugh> beloved pop artists are under the same critiques. Oh my gosh, they told you about the gasps And even people who should know better. Great composers about great composers, Tchaikovsky called Rams, these lovely terms. And my new favorite insult, a gift list bastard <laugh>. So there's some thing with music is that we like the familiar and we like the novel, but it's a non-linear thing. You might be aware of this curve. It's called the uncanny valley. It's uh, usually in reference to animation or robotics where if we're trying to mimic a human, um, a human is the epitome of the target. But there's a cute area on the left. But as we get close to human but not close enough, there's this revulsion we have called the uncanny valley. These are to mannequins, ventriloquist dummies, and me with Madame two swords. I think there's a same with instrumental emulation also. We like synthesis eight bit, um, convincing sampled instruments. But there's this trough when we try to imitate an acoustic instrument, um, and don't quite make it<laugh>. So there's this element of being too close to comfort. You see, noise is okay and music and Harmon is wonderful, but somewhere in between has this revulsion and I love the zeer, but it has that, um, effect on people that it's a sort of musical charlatan. Let's compare it to a trumpet. It's got similar harmonics, but they go up just a little bit too high. And so we have this response to it. So we put it in a musical context and you'll find this uncanny response to it. You get the idea. In lecture one, we looked at reasons why we love music and it moves us. Um, it's a model called Bre vma. But there is a, we, we had a, um, a cuter acronym of ever beam, if you remember. But the same reason we don't, we love music. It is also reasons why we don't like it. Let's call it never beam. These are your responses from the survey. Survey. Episodic memory can remind us from a bad time. Brainstem reflex can be an irritating and annoying and even emotion. We can detect emotion, but, but be feel manipulated by it. These are all your responses here. This brings us to consonance and dissonance. See, if you look up dictionary definitions, there's this suggestion that dissonance is unpleasant. Unpleasant and consonance is pleasant, but music doesn't always need to be pleasant. Nice is a four letter word describing music. And you'll find there are positive and negative attributes given to both consonants and dissonance. So here's the paradox. Pleasantness doesn't mean musical enjoyment always, and dissonant doesn't mean it's unenjoyable. In fact, just like we need some seasoning on our food, their styles where some dissonance is baked in triads on the beat, don't do it for funk and blues. We need a little bit of dissonance with the seventh and we need some offbeat syncopation. And then that feels correct. You've got, We enjoy this giness. And there's these terms that have come up through the ages. It used to be called vigil, but now, um, zapper called it eyebrows. Um, the new one is stank face. And um, the word funk stems from the Latin word, meaning a smell. So it's as if the music is so flavorsome, it BLEs into other senses of taste and smell and touch. And when we hear descriptions of music that we enjoy, they're things like dirty and nasty and monstrous. I mean, if you pull this face eating a meal, it wouldn't not be a great, it would not be a great review. But for somehow with music, this is all, this is the aim to make people look disgusted. Now, I tend to pull this face and I'll try and minimize it during this uh, talk, but there's this beauty in the ugly Dissonance has many dimensions. Some of them are built in physiological, some are very cultural and learned. And you can think of as a group of, uh, dichotomies, a group of dichotomies like these. And these are all happening at once, pulling in different directions, which creates that rich experience. Can we find an objective measure of it? Well, this brings us to oiler who was a genius in many different fields and contributed much including these symbols in the middle here. But he also contributed a lot to music theory. And he came up with this beautiful concept, the greatest sua artist, the degree of sua of sweetness between two intervals. Now I see some people glazing over with this, so we'll, we'll get through it, I promise. But it's, here's the idea. Two notes are sort of in a frequency relationship with each other. One might be double the other three fifths of the other. And he, what he does, he does is assign a value to how far away away they are in terms of these numbers. If you double it, go up octaves, you get a point of sua and the same in the other direction. But there are other prime numbers and they have higher values of flavor in his system. Up the perfect fifth gives us three points and then additional points this way. And, and we can expand it out from any of these points here to we have this multidimensional grid of pleasantness, which I've laid out a part of it here. Now let's test it out. We'll go down from some consonance to some dissonant intervals. Seems to work. Whoop, that's just one square on this huge grid that we could theorize that comes out. Now there's a degree limit to our perception, but it's amazing how such a simple idea actually works. And leitz put it quite beautifully, it's that our soul makes these calculations and we don't know it's doing that. But um, there's a logic and inner logic that happens that we feel in music and in fact it's not just humans that feel consonants and dissonance. A study showed that infant chimpanzees can recognize consonants and dis dissonance and shows preference to each of these. So perhaps too they have a similar soul. How on earth does this work? Well, the Harmonic series is an off sighted explanation. So we're playing two notes against each other. They tend to each have their own harmonic pattern. And if we increase the frequency of one against the other, what you'll see is some alignments and misalignments. And it turns out that the octave has a many alignments. It's near equivalence, the fifth fewer number, but still consonant the major third fewer and then minus second. Um, takes a long time to wrap around. What's beautiful about this idea is that it doesn't just work on the pitch level, but if we turn it this way, we can think about the sweetness in terms of rhythm, how rhythms collide. So for example, the rhythmic octave is something two against one. So we'll hear it in this example, the clicks against the beats Consonant. What about this pattern? It's a sort of rhythmic perfect Fourth, it's the do WAPs that Ella Fitzgerald will sing. Oh, don't A thing if it ain't got that swing. Do I do? I do, I do, I do, I do, I do, I do, I do, I do. I oh, So I, I can't help the face. I'm so sorry. Let's increase the dial again. This beautiful tune has a guitar part that has a five, um, subdivision phrase against a normative four four. So you get this wonderful phasing that occurs a sort of rhythmic major. Third, Some people take this really far. Um, the metal bands masu are a genre called genre called math metal. I would say they are a level math metal. Um, what they like to do is uh, have segments of four, four good old fashioned rock, 4, 4, 8 bar phrases. But then run a very high primed number is 25 against 16, which would give us a sweetness rating of 13. Okay, so it's, you're gonna have eight bars of four four against this 25, 16 and then a three 16th gap before it comes in again. I will attempt to conduct eight bars of four, four and counter out against that. Here we go. 1, 2, 3, 2, 3, 4, 5, 6, 7, 8. Oh, So beautiful <laugh>. Oh, no, no, no. Okay. Yes. Okay, thank you very much. This also explains Tamra dissonance. This we can have harmonics above a single note, but if we start to move them around, there is a roughness and we are super sensitive to this roughness 'cause it's how we recognize words that they're spoken. For example, when I say a EI or you, what I'm doing is changing the intensity of two formants above those four, um, above the fundamental. And that's how you can understand what I'm saying hopefully. So what I'll do is generate those two formants just with an XY and you should hear things that sound like vowels. Now this is purely electronic and it'll sound a little uncanny perhaps, but you should recognize these sort of vowels emerge and musicians use this also. In fact, musicians are manipulating these dissonances on on multiple dimensions. Let's take Aretha Franklin. You'll hear inter valic dissonances with melody. You will hear her control of tamra. You'll see of the brightness of the higher harmonics come. There's rhythmics in caption and there's also bends and stability creating high um, order dissonances. This is just our isolated vocals. Um, I will get chills and probably make a face at one point just warning I psych take, Oh a modulation. But these can be done instrumentally also both with playing technique and signal processing. He is Jimi Hendrix's vocalizing through Wawa and his playing technique. I promised I wouldn't make that face. Okay, talking about Jimi Hendrix, it's not just the sound and the rhythmic quality, but the harmony, the chords intervals against each other. And speaking of the logic of the soul, when I first heard at that reminiscence bump Jimi Hendrix, I heard this one chord now called the Hendrix chord. Sometimes it's called dominant seven sharp nine. But it's really just four notes, not five. And somehow I knew it was special. It just cut in with this visceral directness. I didn't know why, but it just spoke to me immediately. Here it is. Let it hang there for a while. Why is it? What is that scrunch nest? Well, we can explain this complexity to some degree with very simple systems. Music's so complicated. Sometimes you need a simple inroad. And this is called pitch class, set theory. Um, so you wouldn't get it unless you were at university. But um, I'd like to teach it to you in 10 minutes rather than three years and 27,000 pounds <laugh>. So here's the idea. Let's make some simplifications. Let's assume there are only 12 notes for octave. And from lecture three, we know that's a simplification and we'll assume Octa equivalents, that means all a C wherever it is on the piano, it's still a C and we'll be neutral in terms of intervals, whether they go up or down. That's the concessions we make. And from that we get the idea that there are 12 pitch classes, the pitch class C, pitch class C sharp, and so on. And so we can put them on a clock face here. So let's hear some of them. I'll split the octaves and all of them. There you go. That was the first year <laugh>. But here's the interesting thing. We can think of intervals now as simply connections between those, um, positions on the clock, just bars that connect those points. These are called interval classes. They can either be the same or they can be one step apart, two step apart and so on. That's it. And they each have different qualities. I think of them as spices. The one on the far left is quite, um, spicy and as a bite to it as the sharpest dissonance. Um, then the next one is less dissonance and so on. I'll talk you through them as we go along the less dissonance interval. Class two. Now the sweeter intervals, the minor third, major third and their inversions, the major third and the very stable and consonants fifths and fourths. That formed a structure to a lot of music as we discovered last lecture. And finally, interval class six has a mystery restlessness about it perhaps. So every chord is built up of these interval classes. We'll go through them With Different levels of scrunch on my scrunch ter. So when we have a cord, I like to think of it as clinking glasses or fist bumping. So, um, imagine there's two people actually imagine there's one person. There's no clinks to be heard. So a OneNote has no intervals. But two, there's one clink, one interval, three people. There are three intervals, um, and so on. In fact, that is the uh, formula for working out. For example, the four intervals is four times three, which is 12, I'm told divided by two is six. Um, so um, you can tell I'm really fun at parties, but you can work out how many if we've completed all the glass clinking and here's how they go. So the more intervals, the more opportunity for scrunchies. And all you need to know for now is that there is the ends really matter. In fact, we discovered in that vulture bone flute that we avoided those uh, outer points. So we can measure scrunchies in some way to some degree by this profile, a flavor profile. Let's go through some. For example, if we want to have a perfect fifth, we can create the major and minor triad. We can make a sus chord that adds some dissonance. Or we can make the Maria triad chord Adding some scrunches. How about unstable tri chords? They do not have the fifth in them. And we can invent some of these or the most dissonant of this group. Ooh, Now you'll get a degree four note chords. I'll just play through some of these with increasing level of dissonance. They're familiar ones, but you can see their profiles spread to the sides. And let's compare two pentatonics, our vulture bone flute, the major pentatonic with that Japanese traditional scale, the URA pentatonic as it's sometimes called. And you'll see the URA has a little more bite to it. And the Sakura, there's a scale faded by de, which are six notes, evenly spaced the whole tone scale. And what you'll find is that in fact it avoids certain intervals. Not sure why I did that, but it shows that dissonance can actually happen from the avoidance of certain intervals. And because there's no fifth, there has this eccentricity that seems like there's no home, which is one of our dimensions of dissonance. Seven note scales. We can see these advance from the diatonic, the acoustic to the harmonic miner spreading outwards and the harmonic minor, which adds a few more dis How far does this go? Well, all 12 notes get ready for it and watch out for the scrunch ter, which will max out. But musicians use this dial of dissonance. Jazz musicians like to toy with it. For example, taking a standard 2 5 1 and pulling at certain points in it to add some dissonant expression. This is when it starts to lose people. That's okay still with us. No, and this wonderful one here.<laugh> And composers like the wonderful Taka mitsu who intuitively use dissonance as a expressive medium in chords that escape. Easy naming beautiful. But there's a way of making dissonance in an efficient manner. Remember the clinking glasses, if there's four people, there are six clinks. So six intervals. But there are six interval classes. And it's in fact possible to represent in every interval class with just four notes. It's a sort of efficient dissonance. They're called all interval tetra chords for obvious re reasons. And there are four of them. The lidian tetra cord, it's reflection, the frien tetra cord, the edgier onic tetra. And this last one, which may feel familiar, it is the Hendricks chord. So somehow I knew in my logical soul that this chord was special. And there it is. There are other ways for things to be dissonant beyond that roughness. It's around the idea of proxim proximity, what is close and far in terms of music. And that's again, a paradoxical continuum. For example, if we take C major and D minor, all the notes move. It has what's called a chromatic distance of five because that's the amount of notes that move semitone on the piano. Let's take one that's closer in this regard. C sharp minor, one of the notes. The same is the same. The others just move by a semitone. So surely the latter should feel closer. But when we hear that, we do not get that experience. So that's C to D minor. Now, C to C sharp minor. What? Why does that feel more distant? If we sit them on the chromatic circle, you can see that the blue and the red are close. But if we represent them in the circle of fifths, which there might be reason to relieve matters, suddenly it becomes clear. Even though they share a note, they are very far apart. We also have this amazing ability listening to music where we group things. They don't have to happen at the same time, we have this thing called macro harmonies. So collectively, C and D minor create that medieval hexa cord we heard last time. But these two chords make something altogether more mysterious. And this idea of home in a way is integral to common practice music making a minus seems to be close to other shared harmonies. And we can create sort of orbital structures that want to lead to these to get back home into this sort of network, a template for making music. And we intuitively know that even with single notes, we hear this happening. It seems so right. And again, oiler formalized a way of thinking about this idea of musical proximity. It's something called a tonics. And here's this diagram of it. It basically arranges the notes in closeness in terms of fifths, major thirds and minor thirds, which we see laid out here on the tonics fifths, major thirds and minor thirds. And in fact, if we travel this direction, we get this familiar feel of diatonic triads. But we can travel in different dimensions and create a more eerie collection of chords, the mysterious hx atonic and the gritty onic. Here's Brahms, that gift less bastard navigating along a hexa cycle really beautifully. What this creates is something that might be called cons. Contrastive valence. It's saying two things at the same time. And this is a very high level of dissonance, major and minor duality. The opening of right of spring features it with just two notes, C and C sharp, which are at contrast 'cause they suggest both a minor and a major at the same time. Here, Let's zoom in on that moment there. We'll just freeze on that moment. Just sit in that for a moment. Won't you pour coffee of extend it with full cords at the same time? A a minor major chord in this passage. It goes by quick, but let's hear it again. Oh, Sorry, sorry for making those noises. Tchaikovsky, who apparently wasn't a gift list bastard, I'm gonna say it three times now. Um, didn't superimpose them, but separated, um, chords by minor thirds in this passage, creating an otherness and not to be outdone, Stravinsky flat out put the most distant chords together, C major and F sharp major, the pro chord, which you can hear in this passage in the accompaniment meshed together. And then the melody switches between the two. And Piat solar in fact goes further by not just doing the two triads, but extends them into key areas of their own. You hear it split between the two guitars here. Beautiful. Now, we shouldn't assume that this is just a progression through the ages get to increasing dissonance. There are these moments, particularly in the renaissance of incredible, um, dissonance of this sort sometimes called false relations. And here you'll see d sharps and d naturals occurring with the grievous rhythm in this beautiful 16th century piece. Oh, that's so nice. There is also a dissonance to be had in waiting an anticipation. In fact, latest research shows that we gain pleasure by rewards, eating and other activities, but there are also opportunities for pleasure and mechanisms in the brain during the wanting phase where we're hunting or foraging for food or seeking something out. And music seems to tap into that, the enjoyment of waiting or searching and then being rewarded. And then this learning phrase, which helps us move on to the next cycle of Anticipation. This Japan piece is a case study in such anticipation. It's very simple, really. The, the first chord is a first inversion E minor, and it ends with the roots inversion, E minor this, and it ends with this. And the melody simply descends from B We all know somehow what the next note is without hearing it, so I won't play it. But what we'll do is jump to the end of the piece and see these, this pattern of anticipation. What happens is that we do eventually reach that root note, but what that hand gives literally the other takes away by not landing on the correct chord and a series of colora colorizations of that, uh, target note, until finally we reach the inevitable, tragic ending. There is a pleasure to be had in striving for something, um, a sort of meaningful pleasure that we have to earn. And music somehow represents that it needs both those dissonances and consonances. And we'll end with this final case study of a jazz guitarist called Pat Martino, who s sadly passed away recently. He was an astonishing human and player. And in fact, from the age of 16, he was touring professionally. Cut his first album as a side man. And, uh, his debut album, uh, won, uh, much acclaim. Uh, there's him with George Benson and um, he has this perfect mi mix of consonants and dissonance and all these dimensions. Uh, the jazz guitarist, my old Ja Taras Garrison Fuel said like a Philly cheese steak, which is apparently a type of food he's playing is, has sustenance with the perfect amount of grease. So let's listen to him as a young man, perfectly meet, meeting the harmonies, improvising through these harmonies, but the right level of delay in his playing and bluesy touch and attack. Just Wait, Sorry, I know I should stop. I can't help it. Park Martino was incredible player. He could memorize whole passages and produce these lines on the, on the guitar, on any instrument to produce these lines of that tempo. It's extraordinary at any age. Um, but over the years he had some issues and it turned out that his brain, there was this huge blood clot growing and I mean huge, that he had a neo fatal seizure in 1980 and a surgery which could have gone either way removed this huge clot from his brain. There's the whole of it on the right side image there. And when he came to, he had severe amnesia, so much so that he had to be reminded, in fact, convinced that he was a musician. And so someone showed his, his the record cover and he said, well, it looks like me, so maybe I play, I can, I can play. So he had to slowly relearn. The legend says he transcribed his own recordings to learn again. So he was described as the only jazz master who had to do it twice. Um, but he returned, uh, with an incredible resurgence. And within a few years he was playing as well as before and actually with a sort of maturity, which might have come anyway. But there was this sort, this added insight, almost like the logic of his soul was exposed, and he did these beautiful di diagrams and connections. He made the connection of the I Ching, which are six lines that can be broken unbroken to the idea of what you can play on the guitar, 64 ways of voicing something that you use directly. And you might recognize some of these diagrams from earlier that he had this insight on. His return album was absolutely wonderful. And in 2007 and eight, we, um, produced a documentary about his life and I had the privilege of working with him on the music and recording some music with him for the, for the score. And it was the time I was doing my PhD, so I was really interested in his playing and some of these dissonances that he was producing. For example, this is his playing on this beautiful piece he wrote called Welcome to Her Prayer. Now in Jazz, what you have is a lead sheet. It's a sort of, it shows the melody, but no one plays the melody like that. It's sort of this reference point and part of the expression is pulling away from that melody. And I was trying to show how he, um, modulated and pulled away always behind, actually behind the unheard melody, uh, in his, the internal melody. And so what this is Will, I'll, what I'll do is play the melody against his improvisation. And you can hear that internal conversation happening. That diagram shows the amount of pull in each phrase. So we will end this lecture, I think by listening to two minutes of him improvising on this piece. And I will bring up the various measures of dissonance that might be incurring in his soul. There's an ancient Greek concept of EU ammonia. It's a sort of pleasure, which I think of as a meaningful pleasure, a pleasure that's won through striving for something and through learning and music involves this cycle of anticipation, reward, and learning and makes us whole. Thank you so much. Thank Well, thank you so much to Milton for another wonderful lecture. Um, I am Dominic Broomfield ue, um, visiting professor of film and theater music. I'm particularly pleased that we got both Kaz and West Side story into that one. Um, as Milton said at the beginning, we have the special Slido, um, QR code so that you can ask questions. I did want to begin though, um, with a question about, um, gift Less Bastards. Do you want to name any of your own Gift Less Bastards? No. Like famous? Are there any famous Composers? Long? No. I mean, music is really, really hard and you're A diplomat. Oh My goodness. No, but I, I love every, I mean, I love everything, but I think we all have some of those, uh, exaggerated pleasures, this pleasure. And when people often ask me what my favorite thing is, and I refuse to ask apart answer apart from buck. Um, but, uh, something that kind of, uh, mm-hmm <affirmative> gets me is music where I'm req obliged to dance to. And it's a sort of music that doesn't have much Tamil change. And that is a sort of mediocre Eurovision Euro techno thing, which is about a certain tempo and it's very generic and it's a very particular type of, um, Why is it mediocre though? Uh, because there's no surprise and everything is, uh, binary. And so, but that said, I wrote an article about it and we, and we produced a song mimicking this, and now I kind of love it, <laugh>. I kind of love it. Gareth Malone saw it and called me a rap. God, I'm not a rap God <laugh>, but so everything is interesting. Okay. And some things I'm deeply moved by, and that's as far as I go. Okay. And can you tell us any more about oiler? I was obsessed with actually the images of him because he looked so kind of quirky as an individual. Yeah, he lost his, he lo he lived a long time. He lost his eyesight. It didn't seem to stop him. And his contributions to maths, I think he invented graph theory, those symbols, pie. That's his, the idea of a sum, the idea of a function. And in his spare time, he basically invented the tonics, which everyone thinks they invented on YouTube. And, um, and this measure of consonants and dissonance, kind of an extraordinary Newtonian figure. Really Fascinating. Okay, let's turn to the people's questions. Uh, someone says, going back to the start, would the Beatles hit a higher scrunchie meter reading than Bach? Oh, well, first of all, I should say that the scrunch on material is really silly because it's one dial which doesn't account for anything, but it does give some impression. Um, so, uh, let's think. I don't, uh, I'm trying to think of Beatles chords versus bar chords. I don't think so. It's hard, hard to generalize. I mean, if we, if we sing a number of notes and what the crunchiness happens, I think there is, um, I think there's probably more dissonance in terms of verticality in the polyphonic writing of bar. We, we sounds like a PhD though.<laugh>. Okay. Uh, I think you've sort of answered this near the beginning. Is our response to scary music innate or learned? Ditto, calm, sad, exciting, happy. So you, you talked a bit at the beginning about how music is socialized and how our, how some of these reactions are socialized and some of them are not So scary music. Uh, it's meant define terms. You mean some things that have what's called brainstem reflex, which we can't help respond to, which is probably the most culturally shared responsive, which are sharp sounds and low rumbles and those sort of things. And they're used overtly, uh, in terms of harmonic distances. It's, we should be careful not to generalize about any of these things. Um, but it does seem that in general as a theme, octaves and fifths are felt as more stable than minor seconds. Mm-Hmm.<affirmative>. That's not to say it's universal. Super. Uh, Helen asks, you have used music to help us hear and understand complex data more intuitively. How could we further use consonance and dissonance for that purpose? Oh, that's just a too beautiful question. I know I don't wanna spend too long here, but, um, you've, You've got an hour go<laugh>. So I'm very interested in the use of musical translation. Music is an incredible language that we innately learn. It's not good for certain symbolic things, but it's very good at appreciation of multiple dimensions. And there's a field data music sonification, which uses our hearing faculties in the representation of data. People who know me at all will know I'm deep into that world. So I've got a book coming out in a matter of weeks called Hidden Music, the Composer's Guides of Sonification, which is just that idea. So, wow. Um, next, actually year three, we'll have a lot of That. Year three. Oh, ooh, that's a very advanced trailer. Um, good. In regards to the Hendrix chord, um, anonymous says they didn't feel it when, when it was played on the demo keys as opposed to how they felt when Hendrix plays it. Why is this? Because of the harmonics produced by the distortion, basically. Mm-Hmm.<affirmative>. I wanted to hear it in a pure form and then see it in context. Mm-Hmm.<affirmative>. But yes, remember those harmonic series and what distortion does is brighten up those higher partials and so it exaggerates the, uh, rub the roughness of those Intervals. There. There is even a bit of that with the writer spring, isn't there? I was dismayed to see the piano score because when it's played, It's a different thing. Oh yeah. It's, Yeah. So it's score is a very impoverished view. It's a useful lens, but it does not capture the dimensionality of sound. And the next question, moving on very helpfully from that is how does seniority and tamra relate to how we experience consonance and dissonance? So, um, uh, so there's mappings of harmonics, but there are, it's very, it's very complex and a lot has been done on that. Um, I didn't have time for it. I had quite a few things in here. But there have been attempts to, to map not just intervals, but whole sounds against each other. There's a study of sinis, a former Gresham professor of music and, uh, the dimension, a dissonance dimension based on the sounds, not just the harmonic intervals. So it's complicated, but it can be done. And there are papers galore if anyone wants to, has the stomach for them. Mm-Hmm.<affirmative>. Um, and someone says with the general principles and ideas you've presented, also apply to music from other cultures which don't use the 12 tones we are used to. Yeah, that's, uh, a good point also. And these idea of proximity, also the tonics, does that, um, coincide A lot of these were admittedly overtly western ideas or common practice at least of these. Um, there's a, uh, paper I've cited in my accompanying essay, which looks more globally at these ideas. But I do think there are themes of anticipation and rhythmic complexity and um, Tamil effect, particularly when linked to language that are very, very common. But we should be careful about generalizing, about pitch relationships like that. Super. Well, I think that's a lovely place to stop, but you want to quickly tell us about the next lecture, the final one of your first year? I can't believe we're already there. Me neither. So May 16th. It's my final of the series and it's answers the question is music. Infinite? Will we run out of music? Uh, good music or any music? Um, I don't wanna give away, but it's an obvious answer.<laugh>, Next time. Brilliant. Well, you can sign Up. Don't come, but I have to find out Now. Yeah. Can we thank once again, Mel, please. Thank You so much. Thank you. Thank.