Gresham College Lectures

The Art and Science of Tuning - Milton Mermikides

January 29, 2024 Gresham College
Gresham College Lectures
The Art and Science of Tuning - Milton Mermikides
Show Notes Transcript

This lecture presents the rich history of musicians’ engagement with pitch.

From the tuning systems of Babylon, Pythagoras and Hindustani ragas, through the temperaments of the Baroque and Classical eras and arriving at contemporary electronic, blues, jazz and global practices, we explore how musicians have organised, sliced and manipulated the pitch continuum for expressive effect.

In so doing, we reveal the mechanics that determine the 12 notes of the piano keyboard and the beautiful spectrum of pitch colours between them.


This lecture was recorded by Milton Mermikides on 18th January 2024 at LSO, St Luke's Church, London

The transcript and downloadable versions of the lecture are available from the Gresham College website:
https://www.gresham.ac.uk/watch-now/art-tuning

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Um, as we all make another orbit of the sun, it's interesting to think that we actually live in this ocean of waves, um, from the motion of planets that give us our years, months, and days to our biological clocks of sleep, breath and heartbeats. And up into that ocean of electromagnetic radiation that's just getting deeper and deeper of 4G, 5G and then up to the visible spectrum, which gives us a window to the world. And right in the middle of it, we are gifted from 20 hertz to 20 kilohertz, more or less. This canvas for sound and music. All you need to know, uh, for this lecture is that low frequency means a long wavelength. So you can imagine a string that's very long and it, and it vibrates very slowly and that produces a low pitch. Conversely, a very short string, like when you're fretting high on the guitar, creates a high frequency and therefore a high pitch. So let's see where our audience's windows lie. What I'm gonna do is give a sweep from 20 Hertz, which you won't hear up to 20 kilohertz not too loud, but, um, and what I'd like you to do is just raise your hand when you can hear tone, not just noise, but a clear tone. And then drop it as soon as it disappears. Be honest. Ready? Here we go. The Gresham College lecture that you're listening to right now is giving you knowledge and insight from one of the world's leading academic experts making it takes a lot of time. But because we want to encourage a love of learning, we think it's well worth it. We never make you pay for lectures, although donations are needed. All we ask in return is this. Send a link to this lecture to someone you think would benefit. And if you haven't already, click the follow or subscribe button from wherever you are listening right now. Now let's get back to the lecture. Hello, I hope you're phrasing your hands. Now. Thank you for taking part in the Gresham College Age survey <laugh> that saves us a lot of time. So that window, whatever it is for all of you, is the canvas on which music is painted and musicians use all of it. This is the end orchestral chord of a day in the life beat the Beatles. And John Lennon requested a 15 kilohertz tone of squared in red here, reportedly to annoy the dog. It actually at 15 kilohertz. It also annoys cats, cows, Guinea pigs, bats, and anyone under the age of 18. So what I'm gonna do is play it for you. You'll hear the orchestral noise and then we'll play that tone and then I've transposed it down so eventually everyone can hear it. So I've basically scaled it down. Um, again, let's raise hands if we can hear it, not just the tape hiss, but it should be a pure tone. What Sickening isn't it? There it is.<laugh>. So below that is our audible spectrum where we find all our music. And I'm just gonna take you on a brief tour of it. We start in the high region from the top of the female vocals. So we'll hear the squeal of Mary Clayton, which we heard in lecture one down to the top F six of Queen of the Night, now to the mid, mid-high region of flutes, bassoons, and pianos. And right in the middle. Now let's move to the region of cellos, the bottom of male vocals. And then the lowest note in orchestra can play I the vines because you Are mine. Oh, I walk the line because you're mine. I walk the line. You don't get the melody yet. What we have to remember that this audible spectrum doesn't come with notes attached and grid lines. It's just this gradient. And the history of music shows that no one can decide what any of the notes are. This is a brief history of where concert A is over time. I've labeled a few of them here. Clearly 1759 Trinity College was the birth of dubstep<laugh>. And still now, although a four 40 is prevalent, um, we still find different standards, but an orchestra is slightly higher. Uh, in orchestras in Cuba apparently tune lower to save on strings 'cause they're hard to come by. And there's something else called the internet, which has decided that 432 hertz is the one true frequency and everything else is a form of mind control. Nevertheless, we're not really so interested in naming a particular frequency, but in how these frequencies fit together, what makes them in tune. And for that we turn to this mythical figure of Pythagoras. Here he is on what looks like an early Instagram account, having a fun day. And what you'll see is he's playing various instruments with these numbers attached to them. And instruments is the right word, because they're both musical instruments and scientific instruments to find about music and to find out about science at the same time. And he was fascinated by the concept that number connects to music, which is actually quite profound. For example, if we play halfway along with a string, uh, doubling its frequency, we get an octave, which sounds completely harmonious, almost equivalent to the note, which didn't have to be necessarily. And he felt this was the case because there was an order to the entire cosmos that governed the music of the, that governed the motion of the planets and our inner lives. And also music a universal music. The music of the spheres, you can see it depicted here. And these are orbiting planets actually spelling out notes along a mono chord. So it is in fact true, there is this deep connection between number and tuning. If you think of it this way, if we take a string, we can divide it up into even parts. And what happens when we get that is a fascinating series of intervals. This is known as the Harmonic series, and it's showing equal divisions of a string at, you'll see those nodal points and you can eek them out of any instrument actually. But a guitars need to represent you. See where those nodes occur, that's where they appear on the string. If you touch lightly, strangely, they go higher as you go lower, but there are many, many of them, and it's mirrored as well in a really beautiful fashion. So let's just take a brief tour of some of the lower end of this harmonic series. So the first thing we find between harmonic one and two is an interval known as an octave. And the octave say from low C to a C is so universal, nearly universal. I'd say that almost every music culture has the same note name for notes that are separated by an octave. They just keep repeating. They didn't have to do that. But it shows that there is some sort of equivalence that exists there. And so that means when we double the frequency or have a string, we will always go off an octave. So the second, uh, harmonic gives us an octave where with the next harmonic B uh, the next octave would be on fourth, eighth, and the 16th. So these octaves go on forever. Let's move to the next harmonic, which is the third harmonic that gives us an octave and a fifth. And the fifth again, is near universal building block of music. We heard it in lecture one many times over, which means if we triple a frequency, we get an octave and a fifth. So the third harmonic, and then the ninth is an octave of fifth above that. But here's the nice little trick we can do between the third and the second harmonic, because the second harmonic is an octave. The third is an octave, and a fifth is a gap of a fifth. So that ratio three against two gives us what we'll call a pure fifth, meaning it's sourced from the harmonic series. Going to the next prime number, we get this fifth harmonic, which gives us two octaves and the sweet, sweet major. Third. And again, we can use this trick, five against four gives us a major third and we'll call that a pure third. So that's all you need to know for this lecture really is these three, what we're presented with, what the cosmos sings to us is a major triad almost immediately. And we can generate it really easily. We can tell a computer to play a hundred hertz, 200 hertz, 300 hertz, and so on. And we get these sounds. You will note some sound a bit strange. The ones that sound strange are the prime ones, seven, 11, and 13. So these will keep continuing. We know that 'cause of a force known as mathematics, but these are sort of the ingredients of tuning. Um, but what's fascinating is that harmonics emerge naturally on almost every instrument, most stunningly in overtone singing, where a single singer sings a fundamental and then somehow eeks out harmonics so clearly that it sounds like whistling. So this is an incredible overtone singer now performing for you. Harmonics four through to 16, Listen Out for 11 and seven. And music naturally emerges from this harmonic series. Here's the first five with some orchestral compliment. And above that first triad, we get something that sounds like soul. Essentially. Again, this is a single singer. Mm, The inflections are incredible. The seventh, You'll notice at the bottom there's these numbers sense. What this describes is how these harmonic, these harmonics differ from equal temperament. That's what you'd find on a piano. So you'll notice when the numbers are big like that seventh there, it's minus 31, it's might be unfamiliar to you. So we'll call the interval source from the Harmonic series pure, and the other ones equal tempered. And what's interesting about these pure intervals is they fit perfectly well together. They lock in. So what I'm gonna play you is an equal tempered major triad, perfectly valid one that you'd find on the piano and then tweak it. So it fits with the harmonic series. And what you'll see and hear hopefully is the choppy waters of a major triad will go into this slow dance melting into each other. Quite astonishing. And so this is a good place to start if we're gonna start making things in tune and building melodies and um, scales and so on. And in fact, a Pythagorean approach is to take a piece of string and then simply divide it into even parts. Let's say you take, um, you divide it into ninths and you play eight ninths of it, and you'll get a harmonious tone. So you can construct these by making equal divisions of a string. And this was an approach used in ancient Greece. These are ancient Greek tetra chords where you have a perfect fourth and you simply divide it into even parts. There were various types, general of them, the diatonic at the bottom, the chromatic, and the very juicy and harmonic at the top. So what I'll do is animate this antique illustration so that we can hear them in place. And what's beautiful is that those two tetra chords could build a number of scales by stacking one on top of the other, making eight notes, the octave, that was the diatonic, the chromatic. Now, and the juicy one sounds so ancient, It's like going back in the midst of time. So that's one approach. Take a string and just divide it up. But we can be more thorough and comprehensive. Comprehensive and systematic. For example, we can just use the third harmonic and just use, which we'll call the pure fifth and keep going up and up and up. It'll get as high, but we can just use the law of octave equivalents to drag it down into the scale position. So we get threes and nines and 20 sevens, and we just bring them down octaves and gather them up. And these are the sort of bright notes from this upward trajectory of the fifth. But we can do the same backwards, take the top octave drop fifths and then gather them up. So what you have is a strata of major, bright, warm, uh, colors, and then, uh, some cold ones underneath. So here are the warm ones, colder ones, and a scale between the two. This brings us to perhaps the most beautiful example of harmonic tuning and that happens in Indian classical, north Indian classical music hindustani as whether other forms. But we'll focus on this one, which are 22 divisions of the octave. And I'll show how you, how they're built. So imagine we start with one note and we'll do the same trick. We go up fifths and down fifths to gather this pallet of notes, but this is what's called a five limits system, which means that we don't just use the third harmonic, but we go up to the fifth to get that sweet major sound into the ingredient. So for any one of these, we can go along the sweet third pathway up or down and create an array of these notes. These notes, I'm hearing a strange tone. Thank this is a beautiful array of notes that we can, we can organize. And we've got, what we get is this beautiful pattern where the root is fixed, the fifth is fixed. And then for every other chromatic note, there are two flavors, one slightly sharper than the other, always in the same distance. It's called the didian comma between the two of them. Now these you can find on the guitar here, but none of them fit exactly on the fret. They all fall either side of them. There two flavors of one note only the octaves are in. If I put it on a circle, you can see them here, the roots and the fifth fixed, and then the two intervals separated by this little comma. Let's hear them Now more than just a set of scale tones. These are really emotional resonances, so much so that they're often given names to depict their emotional range. And you'll see that the upper ones are more active than the lower ones. And we have sort of strong and confident and anxious and weak underneath it. And so we can build raagas by selecting from these. So for example, this beautiful raaga takes this selection and it's an early morning raaga. We know it's an early morning raaga because it has both moonlight and sunlight in it, and it represents what's called raha, which is this pain of being in love but not with a person that you love. This achingly beautiful emotion where you are warned by the love, but you are pained by the separation. And so we hear uncertainty and um, at peace and so on. So I'm gonna play you a a two minute extract of this wonderful singer performing, um, just the beginning part of this raga. And I've illustrated where they lie on this diagram here, just to let you know whenever she sings at peace, that note, I will be getting a chill over there, but they're wonderful. You'll also hear moonlight before you hear sunlight as the dawn breaks. So you could see why tunings the Hallmark series is so irresistible. And although we live in a 12 tone universe, there is, there have been through the ages a small but acutely dedicated series of musicians exploring this world From the fifth harmonic and way above it, the early electronic composers weren't gifted with, uh, software and keyboards that lined up with some equal tempered system. They had the obligation and opportunity to dial in tones wherever they could be. And so a lot of them reached back to the ancient past to build scales. Or in the case of Wendy Carlos invent new ones, the writings of prolific British musicologist, Kathleen Schlesinger, um, on the Greek Alice, the Greek flute, where she documented from illustrations all the whole positions and, um, con projected about the tuning systems there. This inspired, uh, composers like Harry Parch who didn't go up to the fifth harmonic or the seventh, but the 11th. It's a four more dimensional lattice that I can talk about later. But built 43 notes, of course, no normal instrument can play 43 notes. So he built these extraordinary ones, this just a fraction of them, you see that adapted guitar. And what's beautiful is he colored, coded the harmonics like I did. Here you'll see the 11th harmonic is purple. And the third and the fifth harmonic is uh, yellow. Uh, one of Schlesinger's friends and um, students was Elsie Hamilton, an Australian composer truly dedicated to this world. And she used to build scales from way up there from the 16th harmonic that she named after planets. So what I'll play you is her study on the Saturn scale from the 16th harmonic performed by the talented classical guitarist, Bridget Mur, no relation. Um, and what I will tell you before we start, uh, is that these higher harmonics or an acquired taste like anchovies, your first eight might first taste might be not be the best one. And it's very divisive. Some people can't, won't tell the difference between an outta tune guitar and a and a high level just intonation. But if you sit with it, you'll hear a real beauty, I hope, particularly in the lower over ringing resonances. I actually love it. But back to earth in the realm of making 12 notes. See, the issue with just nation intonation is that it's really beautiful, but it's based around one note. You heard in the, in the, in the Hindustani example, there was a drone and these notes resonated from it. The issue with that is that you can build as many as you like, but the view from one of these other notes is different from that one. If you wanted the same view, it'd have to build a whole orbiting planets around that one. And then further and further it's boundless. And some music really thrives on a closed system. And we know such a closed system known as the circle of fifths. So we go up fifths and we go back to where we started. We're happy and we can make music forever. So let's see what happens if we do that with a pure fifth three over two. We go round and let's hear it. It's out of tune. It should be this. But the top note is more like this. And we wanna tweak it down to this. This is known as a Pythagorean comma and what it creates is not a circle of fifths, but a spiral of fifths that never closes. Whoops. It's the difference between, um, 12 pure fifths and seven octaves. It's a maths problem and it's about a quarter of a semitone too high. It seems unfortunate, but it's in fact inevitable when we try and pair up prime numbers. This just is the nature of them. I'll explain it this way. Imagine a chromatic circle, C, C sharp D all the way back again, if we take a fifth up, we get to G here and it's even temperately marked. A D you can see is slightly sharp. And as we complete it to quell create a 12 point star, there's this gap at the top. So the fifth doesn't agree with the octave, it gets worse. The sweet major third is way short to complete an octave also. And the third and the fifth don't agree with each other either. These are known as commas from the ancient Greek to chop off. They're like the February 29th of tuning <laugh>. And so we have to sort of fudge the system if we're gonna close it. So any tuning system with 12 notes is somehow have to, has to somehow engage with these commas. Compromise. For example, if when Pythagorean tuning we might favor pure fifths, which means we could have a whole string of of fifths around the circle, but because they're slightly too sharp, one of them will be a wolf fifth, a little too narrow. Uh oh, what if we want pure thirds? Well, you see those yellow lines are creating pure thirds. So we get lovely creations like this. To achieve that, we need slightly narrow fifths, which leaves one crazy wide world. Fifth, Whoa. So you could play something like this in C major, but in D flat it's slight sounds very different. So it matters what key you play something in. Here's some Mozart and C major. And in D flat, There's no need, um, to be angry about this <laugh>. That's my one joke. I'm allowed <laugh>. What we have to do is temper those tunings so they fit together. And that's the history of, um, a large portion of western music is deciding how to balance, how to fudge that system. So the veloti system is known as sixth comma. We know what a comma is. It's that extra tuning stuff at the top. So if we divide it in six, we can make six of those fifths a little bit narrow and we've closed the circle. Why choose these ones here?'cause they'll give us sweeter thirds in the mo more common system. But there are other ways to do it, like work my state a quarter comma system and spread it out that way. And the one that's most known, and maybe only that it is for some people, it's equal temperament, which are the 12th comma system where every fifth is narrowed just by a little bit. And what that means is that the, um, fifths are almost pure, but none of the thirds are and they're way off. But what that allows is us to modulate and play chord together and transpose to any key. And that's useful, particularly if you wanna write something like this. Bass. Well-Tempered clavia are 24 pieces in every major and minor key. Now I note it's his well tempered clavia, not his equal tempered clavia. So he used a temperament which was adjusted to make each key sound slightly different to have a character about it. There's him with hi one of his puzzle cannons, which he adored puzzles we did not know for about 250 years what temperament he used. There were many prevailing at the time, so we're not sure exactly how he would have written this. But a researcher in 2005 came forward of this intriguing conjecture. And that is, if you look at the top of the is written autograph manuscript, you see that next to the sea of K clavia is another sea. What the hell is that doing there? And it connects us to the spiral, which just looks decorative, but if you look a little, a little closer and turn it the way it appears to have been written on the bottom of the page, not to smudge it, we get this sequence of loops, but they're not the same. Some have little knots in them and some are open or pure. And there's just enough of them for us to wrap it around and create a circle of fifths with C marked. And you'll see those open pure turns are pure fifths and then not show the number of fractions of a comma that exist. So we might have a clue of what he heard as he played. Let's compare the two. It's subtle, but you will hear it, I hope. So, a I'll play you anal temperament, A, uh, C major and then a, um, this swell tuning fraction seats a little bit more, which means that every key sounded different. So he wasn't just writing in those keys, he was writing for those keys. So I'm gonna play a fraction of prelude number three in equal temperament followed by the swirl tuning. Do you hear the difference in resonance? Maybe in this case it becomes more jangly with a swirl tuning. And so we might imagine bark enjoying the sweetest sororities of C major, which is the only pre where he lets notes really ring together. I must say that some scholars disagree with this, um, interpretation of the, of the, of layman's temperament, but I personally find it really compelling knowing vast love of puzzles. And it just seems so particular in that sea that's there and it's just delicious. The idea that the solution was hidden in plain sight for over 250 years of waiting to be discovered for you to see it. See 12 tones per octave is so established now that we kind of think that's what it is. It's anything else is the stuff of global music or historical practice. So it's quite surprising when you look at what these exemplars of classical music thoughts about that situation. This is Mozart's lesson notes to the English composer Thomas Atwood. Imagine being Mozart's student. It's terrifying. I mean, he was a fine composer, but um, Mozart wrote the musical joke based on his exercises, which couldn't have been for that comfortable to listen to on the premier. But here's his notes. And if we look at these, I'll interpret, interpret what you see here. He's showing the difference between major semitones and minus semitones. What the difference between E and F and F flat and f they're the same on the piano, they're the same on the guitar. What are you talking about? Here's what he was talking about. Let's imagine a series of pure thirds C to E and E to G sharp, which sound like this. Then if we go up to the C, it's very wide. You hear that there is a solution rather than shifting that G sharp, we can imagine that there is a third coming down from the sea to a new note that we'll call a flat, which means G sharp and a flat. Were not the same G sharp. What that means, we could split accidentals, which we could play rou triads in different keys. But that would mean having different notes for G sharp and A flat and F sharp and G flat, which seems ridiculous. It means you'd have all instruments and teaching would have to be completely different. Yes, it was. Here's a fingerboard diagram on the left showing the difference between G sharp and a flat split key keyboards, which allowed you to play those intervals in different contexts and scale. You're expected to practice your scales like this take much longer. We think of microtonal discussions as maybe being experimental or historical or interesting, but micro tonality is alive and well mainly in the western world through the blues, which just explores this whole gradient in beautiful ways. Here is a recording of Vera Hall. She was daughter, a daughter of a freed slave and a wonderful blues folk singer. This is a 1937 recording by Alan Lomax. And you can hear these in inflections in her beautiful voice. Oh Lord, trouble sohan trouble. So don't nobody know my trouble with God. Don't nobody know my trouble with God. And when we examine recordings like this in other seminal blues players, when we have an octave, we don't really have a scale. We have this landscape with clusters and ridges and planes. You'll see that we have roots and octave clusters, but between the minor and the major third, it's just this mountainous region. The minor third is associated with sadness, the major third with joy. But they explore this bittersweet continuum between them and we can come up with just harmonic close relations, which may be valid. But really a lot of the power comes between teasing between these landing points. We have the same at the flat and fifth and the and the seventh. And we could sometimes these are called neutral thirds, neutral fourths and sevenths. Not happy or sad, but this blend of bittersweet beauty. Here's an excerpt from the Tragically Short-lived Steve Ray Vaughan playing and really teasing out those minor major and other bittersweet tones Bird give. We started this lecture talking about Pythagoras and his idea of the music of the spheres and his conception of this ordered universe, which played beautiful music. But we now have the tools to know how those planets are rotating and to recreate those frequencies. So using the law of octave equivalents, what I've done for you is taken the planets and just taken them up 36 octaves. So we get a scale that you can hear. What's it gonna sound like? I give you the solar scale quite neatly. It is two tetra chords separated by the asteroid belt, kind of like those Greek tetra chords. Uh, have to invent some clefts here. So it's, it's 32 octaves below that note. Now, I've not finessed this for you, which many people do and do these sonification, they're gonna give you the frequencies pure and simple and it's gonna sound not as harmonious. And many might think I happen to love it. Um, but let's hear the solid planets and the gas planets and in one swell, The thing about music is that we are not just slaves to some mechanisms of there we can learn to appreciate tones and express ourselves within them. We are free agents essentially. And so I'm gonna let you sit just for two minutes with that scale I'm gonna curate to you. Um, and you'll hear what I've done is I've put the plants in one by one and you'll get the rhythm of the planets, which is 20 octaves above their actual spin rate. And then the harmony will emerge. It's two minutes and I'll join you at the end. Musicians use the full gradient of pitch to express themselves. Sometimes it's aiming for a harmonic purity, sometimes it's fighting against it and it's perhaps it's somewhere between this striving for perfection and an embrace of the perfectly imperfect that music and indeed happiness lives. Thank you so much Dominic. Thank you so much. Thank you. I'm afraid you get me emailed and hello everyone. I should say I'm Dominic Broomfield Mke visiting professor of music at Gresham. And um, I was asked to step in an hour ago because the, the people in charge were so stressed by how complicated and challenging this was going to be, thinking that I would be well placed to deal with it, which is absolutely hilarious from my point of view.'cause I know nothing about mathematics. Anyway, it is a great honor, uh, to lead the q and a. Thank you so much Milton for that. I was removed by your composition at the end. Oh, okay. I thought I'm never gonna be able to stand up there and ask any questions. Um, before we do the q and a, I wanted to remind everyone that the transcripts of the lectures are available online and in Milton's cases there are, there's lots more information available to download. So I really recommend looking at those. Now. Another, um, reminder that you can submit questions for this q and a by, um, using the QR code on the leaflets, which you should have on your chairs. And we do have a few questions, but I think you've already answered Oh, some of them. So let's see whether you agree that you've answered them. Okay. One of them is how exactly does a guitar tuned using harmonics, which are not tempered play in tune with a piano that is tempered. Okay, but you kind of, well, So Well you showed a great solution to that, which is change your piano <laugh>. Hang on. So a guitar is, uh, you mean an untempered, do they mean an untempered guitar?'cause a guitar is generally an even tempered guitar, which will marry with a even tempered piano. But the question really is how do people, let's say choir sing to a piano and what do they do and is it any different from when uh, they sing acapella and when they sing with a piano and they just, and you can answer that perhaps <laugh>, but the, um, when we, when we look at uh, um, ensembles that are, are unencumbered by fret and string placements, we find that they do merge towards those harmonic points. Not that they're better, but it seems to resonate. And I've talked to the s Swingle singers who I managed to play with once, and they talk about making these little changes from chord to chord. Much like the Mozart example where they tweak a G sharp to an a flat depend a flat depending on context. And with a piano, um, they wouldn't do that so much Mate that caused a lot of trouble in his 35 years, did he not? Yeah. Um, we have a, a question from Blake. Uh, is there a relationship between wavelengths of audio and the colors a person with synesthesia might see? That's a beautiful question. Yes. And actually a lecture for upcoming lecture called 22nd of February<laugh>. That's where, um, not next, next one, but an up one in the future that I hope to do exactly on that thing. Mm-Hmm, <affirmative>. Um, actually, you know, I'd like to say it'd be nice if it was, but it seems that cytes actually as varied as, um, you can imagine. So I saw this wonderful exhibition where a single note was played to a set of cytes and then they got animators to animate what they were hearing and you could tell each ide apart and there was no correlation at all. Um, so that's not the case, but it does seem that there's a preference to lower, reds tend to be lower. So Rabins and I think I believe had reds for his lower notes too. But I do you know how, how octave works? I think it, it really varies and what's really sweet is that the seven colors of the rainbow were made because, um, Newton wanted them to be seven notes and you know, various other reasons.'cause let's face it, indigo violet as a kind of a doggy area. And before that there were only three colors. So we kind of just, you could de market ever you, uh, however you want to. And it's almost an octave when you look at the visible spectrum in later lecture I'll bring down the light so we can hear that, but it's just short of an octave. So again, it's a strange order if there is order in the cosmos. Mm-Hmm,<affirmative> Super. Thank you. Uh, uh, how to figure out the, it says the plants sounds, I think that means planets does it or plants? Well it could mean either. Yeah and both. It is amazing. Love it. Is it about the speed that they move around? Okay, so the plan, the the last example, yeah, it's bit hard to explain. So imagine that the earth goes around the sun every year was easy to imagine that. And what we do is speed it up. So we make it go twice round or four and then 8, 16, 32. And when we do that fast enough, it starts to enter arrhythmic range. If you do it 20 odd times, you start to hear it, there's stick thick, thick. And then if you keep going opt octas, um, around 31 you'll start ending the pitch spectrum. And then at 36 op octas, it's a C sharp nine shop. Of course. Good <laugh>. Um, then No, no, no. Lucky I got it. But yeah. Um, to what extent do our modern brains, do we have modern brains? No, no I don't. Okay. Problematize the question. Hear music differently from our baroque Forbes. Oh, that's great. Yes. Tell me about modern brain rock brain. The thing Is, we can't, there's certain Pandora's boxes we can't close, for example, imagine only hearing music when it's live. You know, it's just a different context and different experience. Um, how brains have changed for that. It's hard to know. I mean, I I have a question which I shouldn't be asking the question, but, you know, perfect pitch. In that era, was it sort of a localized, perfect pitch and or was it less prevalent because people were using different, um, reference points? There was no unified reference point. Um, I I imagine it's quite profound, but I, but also the recent years, I mean the musical history is so short and compared to we've been making music for a long time. But in terms of, you know, music we share in that way in global, um, exchange is so recent that I don't think there's been a evolution. But it probably, um, primes triggers certain built-in aspects of our brains rather than change them. But I would imagine it's of a huge difference. Yeah. And, and you can't even imagine not hearing an instrument. So for example, imagine Deb Sea at the opening of the Eiffel Tower and what he hears grown up in western music and classical music is a gamma land ensemble. He wouldn't have heard a recording of it. They came over and he was transfixed and for and for hours he would transcribe it and write prose about how hauntingly beautiful. And I dunno if we can recreate those sort of schisms in our experience now. No, it's really hard to transport ourselves back to a time pre-internet, pre international travel being as it is now. I find it's so stressful on stressful but strange teaching students now who don't remember the pre-internet age, which I do. And I kind of think you can't really imagine what the world was like when we didn't interact with it in that way. So dealing with music back hundreds of years and imagining other brains is it's pure, it's fiction isn't it really? We, we have to sort of make it up. Exactly. Good. Uh, which one is higher? A flat or G sharp in the Mozart example. Okay, so nice Easy one. Yeah, that's, see which one is higher is the A flat, which is surprising because we, uh, expressive intonation tells us that sharp note should go higher. But what we can think of is the difference between what is a horizontal intonation. Imagine we're getting a leading turn to a note. Sometimes musicians tweak those sharper as getting sort of to that note, but as they sit together, G sharp will be lower than a flat. But you can think of it as the letter is lower, so go chee sharp and then a flat. Mm-Hmm.<affirmative>. Uh, could you talk about any cases where octaves are not in capital letters, universally heard and understood? Yeah, brilliant question. So I said near universal and there are a, a one culture, which I can't recall right now, where there's a different name at the octave above, but it's so rare that it's practically universal. However, the tuning of octaves is not even on pianos. You've heard of stretched octaves where to make the piano sing. They stretch out the chewing a little bit. It still sounds in tune, but it's tweaked higher. But probably the most interesting example is in fact Gamma Lan, where what they're looking for is a sort of bright shimmering tone as opposed to notes being in tune in that way with that fundamental because they're metallic, they have all sorts of over ringing harmonics that don't quite fit into that system. So it's a more Tamil organization in that way. Mm-Hmm.<affirmative>. And there's one ex, uh, paper that came out which showed that there was a, uh, a culture where when they, someone played the music, they played it back in a different key and not at octaves. When Did equal temperament become the norm? Oh, that's a good question. Well, really it's when, um, uh, it was pushed through for a couple of reasons. One, the music that was being made where you wanted the late romanticism, where you enjoyed the fact that a flat could be a G sharp 'cause it made for these magical changes. Um, and also, um, serialism and so on. Um, of course computer music where they treat them as a number, the same number G sharp and a flat where they have the same, uh, mid number. But it's also when music was came into the home and pianos and the simplicity of making them and teaching in that way, it became more communal music making. So, um, it was really the turn late 19th century into the 20th century where, and that's why most people don't even question the piano that they receive. Yeah, I really question the piano I receive all the time and this explains why. Um, uh, final question. Do you think advancements in music production software to make different tuning systems more accessible could change the sound of mainstream music? What does mainstream music mean? Well, okay, so uh, tuning so more accessible, you mean more prevalent sort of qual temperament, more prevalent. I think it's already doing that. Um, the mm-hmm <affirmative>, it's, it's done that for rhythm where this wonky rhythms has become a norm where the off-grid rhythms have become a norm in electronic music. And now you hear them in adverts and um, everywhere. Um, but software is actually amazing at doing that. There was a new, um, sort of protocol called MPE and MIDI 2.0, which allows you to, in the past you, when you bent a note on the piano, all the notes moved, but now you can bend them in, in individually and software like Ableton Live 12 now you can change the tuning of the entire system to anything that you invent. And, um, I predict that we will see a resurgence. I mean, it's always been there, but there's an embrace of the Microtonal universe. Super. Thank you so much. Can you remind us, um, when your next lecture is and what it's about? Uh, it's February 22nd. Am I right, Lucy? I hope that's the case. Sorry, I could look it Up. That was the hardest question of all of those. Okay. Okay. If you look in your leaflet,<laugh>, and I'll tell you the subject in the meantime, it's on scales and modes and how we put these notes together to evoke beautiful scales, melodies, and how different cultures around the world create this wonderful palette of colors. Super. And the tickets should go on sale next week. Well, thank you so much again to everyone for coming along, everyone for tuning in online. And can we thank once again, professor Milton? Thank you so much. Thank, thank you.