Exploring the Music Theory Iceberg

If you're not familiar with the iceberg meme, it's basically just a fun way to categorize a topic starting from the well-known and mainstream ideas at the top and then going progressively deeper into unusual and obscure ideas. And the great fun of these iceberg memes is seeing how weird it gets as you go down. So I thought I would create a music theory iceberg and today we're going to start above ground at the tip of the iceberg and work our way down into the murky weirdness below. So starting at the very top we've got A equals 440 hertz. This is what's called concert pitch, a standard universalized pitch that we tune A above middle C to, to allow all instruments to be in tune with each other without having to coordinate which note to tune to. Pretty much every piece of music you've ever listened to, particularly popular music, will be tuned to 440 hertz. We've also got some time signatures here, most prominently 4-4. As I'm sure you're aware, the vast majority of popular music is in the time signature of 4-4. But we do get some other time signatures sometimes and the two most common ones beyond 4-4 would be 3-4 and 6-8. Over here we've got 12 tone equal temperament. Pretty much every piece of music you've ever listened to will be in 12 tone equal temperament. Without going into too much depth, it's the way that we define how each note should be in tune with each other. All we have to do to tune something in 12 tone equal temperament is to tune all of the octaves first and then divide those octaves into 12 equally spaced pitches. Over here we've got our three standard accidentals, natural, sharp and flat. We've got the pentatonic scale, perhaps the most fundamental and straightforward scale in all of music. We've got our two most common clefs, the treble clef and the bass clef. Major and minor, which of course are the two overarching types of tonality in western music. And they've also snuck in power chords here which are chords that don't have a major or minor because they don't have a third, they're just a root and a fifth. Right, level two, so we still haven't gone below the surface yet but this is the tip of the iceberg with music theory. At the top here we've got harmonic minor. So harmonic minor is a variation on the typical minor scale, on the natural minor scale, where we make one modification, we raise the seventh note. and this makes the scale more appropriate for writing harmony in the minor key. We've got a few more chord types here, chord types beyond major and minor. We've got diminished, augmented, seventh chords, inversions and suspended chords. And although these chord types are certainly less common than major and minor, these will still turn up in a wide breadth of music in all styles. Over here we've got the blues scale which is exactly the same as the minor pentatonic scale but with one additional note that we could call the blue note. the flat fifth. Now quite an important concept in this tier is circle of fifths. The circle of fifths is sort of a universal tool that ties together various concepts in western music. On the most basic level it's a way of working out which sharps and flats are in each key, or in a more advanced usage you could use the circle of fifths to conceptualize how different key changes might feel brighter or darker. Sequence is a very fundamental element of melody writing. It's basically when you take a phrase and then you immediately repeat that phrase but now at a either higher or lower pitch. And the last thing we've got on this tier is cadences. A cadence is basically just a short chord progression, a short chord movement that resolves a passage. The two main types of cadence that you'll hear used time and time again are the Perfect cadence, also known as the authentic cadence, which is 5 to 1. Or the plagal cadence, sometimes referred to as the Amen cadence, that resolves from 4 to 1. And now we enter the water. And starting us off we've got this selection of odd time signatures. As the name would suggest, these time signatures are odd, they're unusual. But because of that, they have a really intriguing quality, a really unusual sound to the Western listener. Diatonic modes is what you'll think of as just modes. Mixolydian, Dorian, Lydian, all of those common modes you hear about. A mode is when you take the notes of a scale, but then you treat a different note as the root point, as the starting point. So for example, G Mixolydian is C major but treating G as the root note. They're called diatonic modes here because they're referring to the modes of the major scale. Modal interchange is obviously related to modes, it's when in a piece of music you might switch between using different parallel modes. So one part of the music might be in E Mixolydian and another might be in E Dorian. Here we've got some different accidental marks, we've got double accidentals. This is a double flat and this is a double sharp. For example, A double flat would be the note G natural because we've flattened A twice and the note A double sharp would be the note B because we've sharpened A twice. There's various instances where you might need to use a double sharp or double flat when writing something down on sheet music. Down here we have the whole tone scale. This is a very easy scale to remember because it's literally just whole tones, tones going up. Now we mentioned these odd time signatures or what we might call odd meters, but here we have mixed meter. Mixed meter is when a piece of music switches between different time signatures regularly, mixing different meters together. For example, Good Morning Good Morning by The Beatles keeps switching time signatures, resulting in what you would call a mixed meter. Now earlier we had the harmonic minor, here we've got the melodic minor. The melodic minor is another variation on the minor scale. This is the natural minor scale, the harmonic minor scale raises the seventh degree and the melodic minor then raises the sixth degree as well, effectively to bridge the gap that was created when we raised the seventh degree. Upper chord extensions is basically any time you have a 9th, 11th or 13th in a chord and it could be a flat 9 or a sharp 9 or it could even be an add 9 or an add 11, that sort of thing. Anytime you have a chord like that it's referred to as an upper chord extension. And this funny symbol here is another type of clef. We already had the treble clef and the bass clef. This is what would usually be called the alto clef and is nowadays only really used for the viola. Now although normally when you see this symbol it will be an alto clef, this symbol in its most basic form is what we actually call a C clef. The symbol is a stylized C and it works that whatever line you put the C on is the C line. So in a standard autoclef we put it so the middle line is passing through the middle of the C, so the middle line is C. This is actually the case with all clefs. A treble clef is what's called a G clef. So although we almost always place it on the second line up like this, making this line the G line, we could place it on a different line, changing where the note G is. And same for the bass clef, this is the F clef. The idea is whatever line passes through these two dots is F. In basic terms, a Neapolitan chord is a major chord built on the flat second degree of the scale. However, it comes with some context as well. A true Neapolitan chord will be voiced like this in the first inversion and will resolve onto the fifth chord of the key. And in Roman numeral analysis, we can even label the Neapolitan chord with its own unique symbol, a capital N. The augmented sixth is a similar type of chord where you have to use it in a particular context. In basic terms it's a dominant seventh chord built on the sixth degree of the minor scale, so for example in the key of A minor it would be an F7 chord. But the way we use an augmented sixth chord is that our F7 here needs to now move to the fifth chord of the key, in this instance E major, and the voice leading has to be done in a particular way. The F at the bottom of the chord needs to resolve down onto E, and the E flat at the top of the F7 chord needs to resolve up onto E. And this is why it's called an augmented 6th chord. Because here we've got Eb resolving onto E, we actually instead label this as a D sharp. Because this not only shows the player that this note is a leading note resolving up onto the E, but it also avoids a bit of an awkward accidental. And because we've labelled this Eb note as a D sharp, It's changed the interval of the chord from a dominant 7th, a minor 7th, into an augmented 6th, F to D sharp. And the last thing to remember with augmented 6th chords is there's actually three different types of voicing for them, each named after a different nationality. Another type of chord, this time from rock music rather than classical music, is the Hendrix chord. The Hendrix chord is just another name for a sharp 9 chord, a 7 chord with a sharp 9 added on top. So for example we could have E7 sharp 9. This is our Hendrix chord. As the name suggests, Hendrix was quite a fan of this chord. For example, we can see it here in Purple Haze. And what makes it so distinctive is that we simultaneously have the major third here, the G sharp, and we also have the minor third here, the G natural. Although the most accurate way to notate this would be with an F double sharp. Now of course this chord got its name by being used significantly by Jimi Hendrix, but we can also see it in other songs like here in Michelle. A picardy third is when a passage of music in the minor key resolves onto the major chord. For example, this passage of music is in the key of B minor but resolves with a B major chord, giving it a grand and complete ending. An altered chord is an idea from jazz where the dominant chord of the key, the 5th chord of the key, has its 5th either flattened or sharpened and or could have its 9th flattened or sharpened. I say and or because if a chord chart says G-Alt for example, It's not specifying a particular type of altered chord, it's just telling the player that they need to play a G dominant 7 chord but with some alteration made to the 5th and or the 9th. The alterations made to the dominant chord will add extra tension to the chord meaning it will have a sweeter resolution when it reaches back to the tonic chord. Polyrhythm is when we have more than one consistent pulse playing at the same time. So for example a very common polyrhythm is 3 against 2. two consistent pulses in the same time as three consistent pulses. A tritone substitution is an idea from jazz music where we substitute a dominant chord with the dominant chord a tritone away from it. This is most commonly done with the fifth chord of the key so for example in the key of C major we would be substituting our G7 chord for a Db7 chord. And what allows this to work is that both those chords G7 and Db7 both contain the same tritone, so they both have the same effective resolution back to the tonic chord. Quartal harmony is harmony built from stacks of fourths. So most of the harmony we deal with is what we would call tertiary harmony, harmony built from thirds. All our common chord types, major, minor, diminished, seventh, ninth, anything like that is built by stacking thirds up. But alternatively we could make chords by stacking different intervals like fourths. For example in Tarkus by Emerson, Lake and Palmer, these arpeggiated chords played on the organ are all built by stacking fourths up. And as you can see from the chord labels, because our chord labelling system is built around tertiary harmony, when we're dealing with quartal harmony the names can get a little bit odd. You'll see a lot of sus4 for example. And the last thing we've got in this tier is minor scale modes. So earlier we mentioned diatonic modes, these are modes of the major scale, where we've taken the major scale but we've started on a different degree resulting in a new scale like Mixolydian, Dorian etc. Minor scale modes are when we make modes from a minor scale. So for example we might take the melodic minor scale and by starting on a different scale degree we generate a new alternative scale. For example, the fourth mode of the melodic minor scale is what we would call Lydian dominant, and this is the scale used in the Simpsons theme song. Right, we're really getting into the depths of this ocean now. Metric Modulation. Metric modulation is when we switch from one time signature to another but the two are connected by a consistent mathematic relationship. For example, we could switch from 6-8 to 4-4. We could make the two sort of connect together by making the eighth note worth the same amount in 6-8 as it is in 4-4. So the two different meters sort of get married by this consistent note value. A polymeter is when we have effectively two different time signatures playing at the same time. What this means is that one part will effectively go out of time with the other until a full rotation has happened when they fall back into sync together. For example, the song 5-4 by Gorillaz has a guitar riff in 5-4 but a drum pattern in 4-4, so after the first bar the two go out of sync until they've rotated enough that they're back together again. An octatonic scale is technically any scale with 8 notes, but most commonly it's referring to one of two symmetrical scales. One that goes semitone, tone, semitone, tone, semitone, tone, semitone, tone and the other does the opposite going tone, semitone, tone, semitone, tone, semitone, tone, semitone. This second octatonic scale here that goes tone, semitone is also referred to as a diminished scale and is what we hear at the beginning of the song Just by Radiohead. The double harmonic scales are two scales that are often referred to with a variety of different names. The double harmonic major, sometimes just referred to as the double harmonic scale, is just like the major scale but with a flattened second degree. and a flattened 6th degree. And the double harmonic minor scale, sometimes referred to as the Hungarian minor scale, is exactly the same as our usual harmonic minor scale but with the 4th degree raised. The double harmonic minor is also actually the 4th mode of the double harmonic A Moo chord is just a particular name for what you might think of as an Add-To chord, a major chord with the second degree added in as well. The name Moo chord was popularised by the band Steely Dan, who were particularly fond of this chord type. Polytonality is when we have more than one key playing at the same time. A composer well known for his use of polytonality is Charles Ives. For example, in this piece, the two upper voices of the choir are in the key of C major and the two lower voices are in the key of Bb major. Be merciful unto us and bless us Bebop scales are variations on typical scales where an extra note has been added in. For example, the bebop dominant scale is just like the mixolydian scale, but also features the unaltered 7th degree, so we've got the b7th and natural 7th in the scale. Or you could have bebop dorian which is just like regular dorian but also includes the major third. These are the sort of scales that were used by bebop musicians like Charlie Parker, Miles Davis and John Coltrane. However, it's important to remember that the idea of the bebop scales wasn't theorised until years after the bebop era. It was more of a retrospective way of analysing how these players performed. Put simply, the Tristan chord is a half diminished chord and it gets its name from being the opening chord of Wagner's opera Tristan and Isolde. So this is a chord we could label Fm7b5, but that's kind of missing the point of the Tristan chord. The importance of the Tristan chord is the fact that it's opening an opera with tonal ambiguity. Typically an opera would open with a very clear statement of key, a clear statement of where we are tonally, but when Wagner opened his opera with this chord, it changed that. And many have argued that the use of this Tristan chord was the beginnings of A tonality in Western music. Which leads me on nicely to the last thing in this tier which is a tonality. A tonality is quite simply when a piece of music avoids having any sense of tonal centre, any sense of key. A atonal piece of music effectively has no key. This piece by Arnold Schoenberg very much avoids having any sense of key or resolution. Alright, we're approaching the bottom of this iceberg, the second to last tier, and we start off with swing ratios. Swing as a rhythm is effectively when two eighth notes have unequal rhythms to each other, where one eighth note is longer than the other eighth note, and a swing ratio is a way of describing how much that difference is. So for example, a one-to-one relationship would be not swing, it would be straight, because both eighth notes have equal duration. However, a two-to-one swing feel would be triplet fill because the first note has double the duration of the second. 3 to 1 ratio would be a dotted eighth note swing like this. The first note has three times as much duration as the latter. A 3 to 2 ratio would be a type of quintuplet swing like this. Or we could have a 4 to 1 relationship like this which is also a type of quintuplet swing. Of course it's very important to remember that swing players aren't thinking in terms of swing ratios when they play. They're just letting it naturally swing. and the ratio to which they're swinging might even change throughout the performance. But swing ratios can be very useful when you're trying to program swing into a DAW. Overtones. So pretty much any time you play a note, for example on a piano, you're not just hearing that note. If I play an A on the piano, we are hearing what's called the fundamental pitch of A, but we're also hearing a series of overtones above that. quieter sympathetic notes which effectively colour the tone of the note. And they always follow the exact same pattern of intervals in what's called the overtone series or the harmonic series. The intervals start off by being very fundamental recognisable intervals like octave, perfect fifth, perfect fourth, major third, minor third. Then as we get into the quieter and much harder to hear harmonics, they venture into intervals that we wouldn't find in our standard tuning system like a sub-minor third. a super major second, and so on. And the amazing thing is even though all of these are technically separate frequencies, separate pitches, our ear perceives them all as one cohesive note. 24-tet. So right at the beginning we talked about 12-tone equal temperament, where our instruments are tuned by tuning the octave and then dividing the space between those octaves into 12 equally spaced pitches. Well 24-tet is 24-tone equal temperament. TET is just short for Tone Equal Temperament. So 24TET is a way of creating what you might call microtonal music by giving us an extra microtonal note between every standard pitch on our piano. For example here's a piece of music by Ivan Vincengretsky which is written in 24 tone equal temperament. And off to the right of our 24th here we have some microtonal accidentals which we could use to notate our 24th music. We have a half sharp so we could have for example an A half sharp which is a note pitched between the notes A and Bb. We could have a half flat so an A half flat would be a note pitched between A and Ab and we could even have something like this which is a sharp and a half. A equals 415 hertz. So right at the beginning we were looking at A equals 440Hz, which is what we call concert pitch, the standard pitch that we tune A above middle C to. The standard of A440 was only brought in around 100 years ago, and before that historically a wide range of different tunings were used across different geographic areas. 415 is what we call Baroque tuning, and is almost exactly one semitone lower than modern concert pitch. Baroque tuning is used when a performer wants to try and recreate the original sound of the composition closer to the original tuning it would have been written in. However, it's important to remember that 415 wasn't a historic standard, it was just one of many different tunings a baroque instrument may have been tuned to. Just intervals. If an interval is just, it means it's been tuned to a perfect simple ratio. So for example, a justly tuned perfect fifth would be the ratio of 3 to 2. If you tune an instrument to just intervals, it's what we call just intonation or pure intonation. And although theoretically it's the purest way of tuning intervals, it presents a big problem. On any instrument with fixed tuning, like a keyboard instrument for example, you can't have pure intervals between every key without compromising other intervals. For example, if we tune our keyboard here in pure intonation in the key of A, so for example we have A and E as a 3-2 pure perfect fifth, unfortunately that means that by doing that some of the other perfect fifths in the key are not 3-2 relationships and are actually very dissonant. So although 3-2 is the perfect and purest way to tune a perfect 5th interval, for keyboard instruments and similarly fixed tuned instruments, we have to have some way of adjusting or tempering this tuning system. As we discussed earlier, almost all modern music fixes this problem by using 12 tone equal temperament, where rather than worrying about the particular ratios between each interval, We just tune the octaves to perfect intervals and then divide the space between them logarithmically into 12 equally spaced pitches. And although of course this means that none of these intervals are now pure apart from the octave, they're close enough that our ear doesn't really mind. But 12 tone equal temperament isn't the only way of fixing this problem. Historically other temperament systems were used, for example, mean tone temperament. Mean tone temperament for example is a system that was used historically to try and maintain justly tuned thirds, and it did this by slightly compromising the tuning of a fifth. Now exactly how this was managed is a topic for another video, but what is interesting is in old temperament systems like mean tone temperament, because each instance of each interval was actually tuned subtly differently, it meant that different key centers actually had different characters. Some key centers were more in tune than others. So unlike in our modern system of 12 tone equal temperament where every key sounds exactly the same, different keys could actually have different qualities. In D minor, which I always find is really the saddest of all keys, really. I don't know why, but it makes people weep instantly to play it. Nested Tuplets So a regular tuplet, an example of a regular tuplet would be a triplet. So a triplet is when we force three notes into the space where we would usually only have two notes. Another type of tuplet we could have would be a quintuplet where you fit five notes into the space where you might have previously only had two or previously only had four or you could have a sep tuplet where you force seven notes into a space. So that's regular tuplets but a nested tuplet is a tuplet inside of a tuplet and as you can imagine this starts getting quite confusing quite quickly. Here we have a triplet nested inside of a quinn tuplet and I've also placed these regular notes and this regular triplet here to give it a bit of context. Performing these can be very difficult and conceptualizing how the different tuplets are interacting with the pulse can be quite mind-boggling. Now we can take that mind-bogglingness to another level by having a double nested tuplet. A tuplet inside of a tuplet inside of a tuplet. So for example here we have a septuplet inside of a quintuplet inside of a triplet. But really at this point this rhythm is getting quite absurd and precise. There's almost always a easier and more intuitive way to transcribe a rhythm like this. For example rather than the septuplet quintuplet triplet situation, we could have had virtually the same rhythm notated like this, with just a regular nested tuplet. And the last thing we've got on this tier is neutral intervals. Earlier we were talking about microtonality and half flats and half sharps and that sort of thing. Well a neutral interval is a microtonal interval. For example a neutral third is a third where the note is between a major or minor third. So for example in the key of C major, a major third would be C and E natural, a minor third would be C and E flat, so a neutral third would be C and E half flat. So welcome to the deep, the bottom of our music theory ocean. And let's start off with a concept that really did blow my mind when I was first introduced to it and that is that pitch is equal to rhythm. Pitch and rhythm are ultimately the same thing. So a note, a pitch, for example middle C, it's just a frequency right? Middle C is 261.63 Hz, which means that the sound waves are completing their vibration, completing their cycle 261.63 times a second. Or you could times that by 60 and get 15,697.8 vibrations per minute, which effectively means that middle C is just a pulse, a regular pulse playing at 15,697.8 BPM. Pitch is the same thing as tempo. And we can actually hear that if we slow down this note, slow down our middle C, we eventually just get to a pulse. Sounds like a kick drum right? Well we can do the same thing in reverse. This is a quarter note kick drum pulse at 160 bpm. Now see what happens if we gradually increase the tempo of this pulse. At some point as we increase the tempo our ears stop perceiving that pulse as a rhythm and begin perceiving it as a pitch because rhythm and pitch are the same thing. Amazingly, this also applies to chords and intervals. Do you remember earlier when I mentioned that a justly tuned perfect fifth is the ratio of 3 to 2? One sound wave vibrates three times in the same amount of time as the other sound wave vibrates two times. So it's a 3 against 2 polyrhythm, right? If we take this rhythm, which is a 3 against 2 polyrhythm, and speed it up... 5th. And as I said, we can turn this into a chord as well. We've already got our 5th, so if we added in a major 3rd, which is the ratio of 5 to 4, a 5 against 4 polyrhythm, what begins as this rhythm turns into a major chord. A equals 432 hertz. So we've already mentioned A equals 440 hertz which is our standardized universal concert pitch and we've also mentioned A equals 415 hertz which is our baroque era standardized pitch. However A equals 432 hertz isn't some sort of standardized concert pitch, it's actually a pseudo-scientific idea in music that if you tune your music to 432 hertz it resonates better with I don't know aliens or space or something. I don't know if you're not getting the point This is the sort of homeopathy of music. Adam Neely's already got a great video debunking 432 So do check that out if you're interested Super ultra hyper mega meta lydian scale. So this is effectively a lydian scale But when you reach the fifth degree you then start a new lydian scale from that degree So for example, if we're in the key of C major we'd start doing C D E F sharp G, that's the beginning of C Lydian. But now that we've reached the fifth of G, we now continue with a G Lydian scale, G, A, B, C sharp, D. And now once again, now we're on the fifth of that scale, we continue with a new Lydian scale based on the scale degree of D. And the idea is that this is a scale that continues to get brighter and brighter as it ascends. Deutsch's scale illusion is when we've played one melody in one ear, and another melody in the other ear and we actually wind up hearing a third composite melody. So this will work best if you have headphones on but here's melody one that will be played in our left ear and here's melody two that will be played in our right ear and as you'll hear when they're played together we hear a third melody. Now this very much is a trick, an illusion. And it only really works because both melodies are played with the same timbre, the same instrument. If one of the melodies was played on a violin for example and the other on a piano, it wouldn't really work. What's happening is although these notes are split across our two ears and written here in two different staves, if we condense them down onto one stave we can see that really it's one harmonised melody going up and down. Each of our ears gets one fragment of the melody, but of course we perceive the entire experience as one piece of music. one melody. A shepherd tone is another auditory illusion where we seem to hear a pitch that's going up indefinitely, which of course would be physically impossible because eventually it would go beyond the limitations of our hearing. How this works is we're actually hearing various sine waves at the same time of the same note at different octaves. As the shepherd tone ascends, the sine waves at the top, the ones with the highest octave, start to become inaudible, but as that happens they're replaced with new sine waves at the bottom. So as the highest sine waves become too high pitched for us to hear, our ear just switches to listening to the sine wave an octave below it. Irrational time signatures. 7-12 is an example of an irrational time signature. With all time signatures, the top number is telling us how many beats there will be in each bar, and the bottom number is telling us what type of beat that will be. So 3-4 is telling us that there will be 3 quarter notes in each bar of the music. So how do we apply that with 7-12? There's no such thing as a 12th note, so how can we have 7 of them in a bar? Well let's go back to 3-4 for a minute. We think of it as 3 quarter notes, but what even is a quarter note? Quarter note is a quarter of a whole note. So what a time signature is effectively telling us is take a whole note, divide it into the fraction that we've given you in the time signature, so in this case quarters, and then give us three of those quarters per bar of the music. The same logic applies with our 7-12 irrational time signature. Take your whole note, divide it now into twelfths, eighth note triplets, and then each bar of our 7-12 music is going to have seven of those, seven eighth note triplets. Now you would never have a piece of music that was solely in an irrational time signature because it would be an over-engineered way of transcribing that music. There would always be an easier, more straightforward way to write that music down. Where irrational time signatures come in useful is when we mix them in with other rational time signatures. So for example, our music could be in 3-4 and then jump to a bar of 7-12. Microtonal Modulation So a modulation is effectively a key change where the music moves from one key to another. A very common practice in all types of music really. But a microtonal modulation is where we move to a key that is a microtonal interval away from where we started. So for example a regular modulation might be moving from G to A. Whereas a microtonal modulation could be moving from G to A half sharp. For example, in Jacob Collier's arrangement of In the Bleak Midwinter, he modulates from E major, regular E major, to the key of G half sharp major. So we've modulated up a neutral third. In this clip, Jacob shows how before the modulation, the piano is in tune with the music, but after the modulation, because we're now in a microtonal key, the piano is out of tune. And then… Pythagorean tuning. So we've talked a lot about different temperaments, different ways that we can tune our piano. Right at the top we had 12 tone equal temperament, which is the temperament that we use in all of our instruments today. We then later talked about mean tone temperament, which is a historic way of tuning an instrument that allows us to preserve a justly tuned third. But before that, people would tune their instruments to what's called Pythagorean tuning. This is a tuning system that instead of preserving the third, preserves the fifth of the key, meaning that all of the fifths are as well tuned as they can be. Now just like all other temperament systems, Pythagorean tuning does result in some intervals that are less pleasing to the ear. But to give you an idea of how these different temperament systems sound, I'm going to play you a major chord followed by a major scale, Initially in 12-tone equal temperament, our standard modern tuning system, then in mean tone temperament, which is the one that preserves the sound of the third, and finally in Pythagorean tuning, the one that preserves the sound of the fifth. Zen harmonic music is music that divides the octave into something different than just 12 degrees. For example, you could divide the octave into more degrees like 19 or 21. Or you could divide the octave by a smaller number than 12, for example 7 or 9. Zen harmonic music has a lot of overlap with microtonal music, but the main difference is that microtonal music sort of assumes that you're starting from 12 tone equal temperament as a starting point and then adding in extra notes between those notes, whereas Zen harmonic music throws out the entire idea of dividing the octave into 12 notes and then divides it by some other number which could be as small or as large as you like. Negative Harmony Negative harmony is the idea that each chord in the key can have a negative version of itself which has the same level of tension and release relative to the tonic chord of the key. For example, if we're in the key of C major and we had a perfect cadence G7 resolving to C major, the negative version of that would be F minor 6 resolving to C major. Both G7 to C and F minor 6 to C has the same level of tension, the same level of voice leading. and thus are effectively the same type of resolution but coming from two different angles, two different approaches. If we look at how the four notes of G7 resolve onto the notes of our C major chord, we can see that they have to move the exact same amount to get to their resolution as the notes of our F minor 6 chord do to get to C major. There's the same level of voice leading, the only difference is the direction of travel. The B in the G7 chord has to resolve upwards, whereas the Ab in the F minor 6 chord has to resolve downwards. downwards. So that is my music theory iceberg. Now I think what is so great about the iceberg as a way of explaining a concept is showing how you have to start at the top before you can progress downwards. Concepts like negative harmony and irrational time signatures are certainly interesting and can perk up the ear of a musician, but if you haven't already been through the layers above it, you're probably going to have a hard time understanding the concept. So in a similar way to my music theory tier list that I did a few months ago, You could use this iceberg as a way of informing how you should learn music theory and what order you should learn concepts.

So starting at the very top we've got A equals 440 hertz. This is what's called concert pitch, a standard universalized pitch that we tune A above middle C to, to allow all instruments to be in tune with each other without having to coordinate which note to tune to. Pretty much every piece of music you've ever listened to, particularly popular music, will be tuned to 440 hertz.

We've also got some time signatures here, most prominently 4-4. As I'm sure you're aware, the vast majority of popular music is in the time signature of 4-4. But we do get some other time signatures sometimes and the two most common ones beyond 4-4 would be 3-4 and 6-8.

Over here we've got 12 tone equal temperament. Pretty much every piece of music you've ever listened to will be in 12 tone equal temperament. Without going into too much depth, it's the way that we define how each note should be in tune with each other. All we have to do to tune something in 12 tone equal temperament is to tune all of the octaves first and then divide those octaves into 12 equally spaced pitches.

Over here we've got our three standard accidentals, natural, sharp and flat. We've got the pentatonic scale, perhaps the most fundamental and straightforward scale in all of music. We've got our two most common clefs, the treble clef and the bass clef. Major and minor, which of course are the two overarching types of tonality in western music.

And they've also snuck in power chords here which are chords that don't have a major or minor because they don't have a third, they're just a root and a fifth. Right, level two, so we still haven't gone below the surface yet but this is the tip of the iceberg with music theory. At the top here we've got harmonic minor.

So harmonic minor is a variation on the typical minor scale, on the natural minor scale, where we make one modification, we raise the seventh note. and this makes the scale more appropriate for writing harmony in the minor key. We've got a few more chord types here, chord types beyond major and minor.

We've got diminished, augmented, seventh chords, inversions and suspended chords. And although these chord types are certainly less common than major and minor, these will still turn up in a wide breadth of music in all styles. Over here we've got the blues scale which is exactly the same as the minor pentatonic scale but with one additional note that we could call the blue note.

the flat fifth. Now quite an important concept in this tier is circle of fifths. The circle of fifths is sort of a universal tool that ties together various concepts in western music.

On the most basic level it's a way of working out which sharps and flats are in each key, or in a more advanced usage you could use the circle of fifths to conceptualize how different key changes might feel brighter or darker. Sequence is a very fundamental element of melody writing. It's basically when you take a phrase and then you immediately repeat that phrase but now at a either higher or lower pitch.

And the last thing we've got on this tier is cadences. A cadence is basically just a short chord progression, a short chord movement that resolves a passage. The two main types of cadence that you'll hear used time and time again are the Perfect cadence, also known as the authentic cadence, which is 5 to 1. Or the plagal cadence, sometimes referred to as the Amen cadence, that resolves from 4 to 1. And now we enter the water.

And starting us off we've got this selection of odd time signatures. As the name would suggest, these time signatures are odd, they're unusual. But because of that, they have a really intriguing quality, a really unusual sound to the Western listener. Diatonic modes is what you'll think of as just modes. Mixolydian, Dorian, Lydian, all of those common modes you hear about.

A mode is when you take the notes of a scale, but then you treat a different note as the root point, as the starting point. So for example, G Mixolydian is C major but treating G as the root note. They're called diatonic modes here because they're referring to the modes of the major scale.

Modal interchange is obviously related to modes, it's when in a piece of music you might switch between using different parallel modes. So one part of the music might be in E Mixolydian and another might be in E Dorian. Here we've got some different accidental marks, we've got double accidentals.

This is a double flat and this is a double sharp. For example, A double flat would be the note G natural because we've flattened A twice and the note A double sharp would be the note B because we've sharpened A twice. There's various instances where you might need to use a double sharp or double flat when writing something down on sheet music. Down here we have the whole tone scale.

This is a very easy scale to remember because it's literally just whole tones, tones going up. Now we mentioned these odd time signatures or what we might call odd meters, but here we have mixed meter. Mixed meter is when a piece of music switches between different time signatures regularly, mixing different meters together.

For example, Good Morning Good Morning by The Beatles keeps switching time signatures, resulting in what you would call a mixed meter. Now earlier we had the harmonic minor, here we've got the melodic minor. The melodic minor is another variation on the minor scale.

This is the natural minor scale, the harmonic minor scale raises the seventh degree and the melodic minor then raises the sixth degree as well, effectively to bridge the gap that was created when we raised the seventh degree. Upper chord extensions is basically any time you have a 9th, 11th or 13th in a chord and it could be a flat 9 or a sharp 9 or it could even be an add 9 or an add 11, that sort of thing. Anytime you have a chord like that it's referred to as an upper chord extension.

And this funny symbol here is another type of clef. We already had the treble clef and the bass clef. This is what would usually be called the alto clef and is nowadays only really used for the viola. Now although normally when you see this symbol it will be an alto clef, this symbol in its most basic form is what we actually call a C clef.

The symbol is a stylized C and it works that whatever line you put the C on is the C line. So in a standard autoclef we put it so the middle line is passing through the middle of the C, so the middle line is C. This is actually the case with all clefs. A treble clef is what's called a G clef. So although we almost always place it on the second line up like this, making this line the G line, we could place it on a different line, changing where the note G is.

And same for the bass clef, this is the F clef. The idea is whatever line passes through these two dots is F. In basic terms, a Neapolitan chord is a major chord built on the flat second degree of the scale.

However, it comes with some context as well. A true Neapolitan chord will be voiced like this in the first inversion and will resolve onto the fifth chord of the key. And in Roman numeral analysis, we can even label the Neapolitan chord with its own unique symbol, a capital N. The augmented sixth is a similar type of chord where you have to use it in a particular context.

In basic terms it's a dominant seventh chord built on the sixth degree of the minor scale, so for example in the key of A minor it would be an F7 chord. But the way we use an augmented sixth chord is that our F7 here needs to now move to the fifth chord of the key, in this instance E major, and the voice leading has to be done in a particular way. The F at the bottom of the chord needs to resolve down onto E, and the E flat at the top of the F7 chord needs to resolve up onto E. And this is why it's called an augmented 6th chord.

Because here we've got Eb resolving onto E, we actually instead label this as a D sharp. Because this not only shows the player that this note is a leading note resolving up onto the E, but it also avoids a bit of an awkward accidental. And because we've labelled this Eb note as a D sharp, It's changed the interval of the chord from a dominant 7th, a minor 7th, into an augmented 6th, F to D sharp. And the last thing to remember with augmented 6th chords is there's actually three different types of voicing for them, each named after a different nationality. Another type of chord, this time from rock music rather than classical music, is the Hendrix chord.

The Hendrix chord is just another name for a sharp 9 chord, a 7 chord with a sharp 9 added on top. So for example we could have E7 sharp 9. This is our Hendrix chord. As the name suggests, Hendrix was quite a fan of this chord.

For example, we can see it here in Purple Haze. And what makes it so distinctive is that we simultaneously have the major third here, the G sharp, and we also have the minor third here, the G natural. Although the most accurate way to notate this would be with an F double sharp. Now of course this chord got its name by being used significantly by Jimi Hendrix, but we can also see it in other songs like here in Michelle. A picardy third is when a passage of music in the minor key resolves onto the major chord.

For example, this passage of music is in the key of B minor but resolves with a B major chord, giving it a grand and complete ending. An altered chord is an idea from jazz where the dominant chord of the key, the 5th chord of the key, has its 5th either flattened or sharpened and or could have its 9th flattened or sharpened. I say and or because if a chord chart says G-Alt for example, It's not specifying a particular type of altered chord, it's just telling the player that they need to play a G dominant 7 chord but with some alteration made to the 5th and or the 9th.

The alterations made to the dominant chord will add extra tension to the chord meaning it will have a sweeter resolution when it reaches back to the tonic chord. Polyrhythm is when we have more than one consistent pulse playing at the same time. So for example a very common polyrhythm is 3 against 2. two consistent pulses in the same time as three consistent pulses.

A tritone substitution is an idea from jazz music where we substitute a dominant chord with the dominant chord a tritone away from it. This is most commonly done with the fifth chord of the key so for example in the key of C major we would be substituting our G7 chord for a Db7 chord. And what allows this to work is that both those chords G7 and Db7 both contain the same tritone, so they both have the same effective resolution back to the tonic chord. Quartal harmony is harmony built from stacks of fourths. So most of the harmony we deal with is what we would call tertiary harmony, harmony built from thirds.

All our common chord types, major, minor, diminished, seventh, ninth, anything like that is built by stacking thirds up. But alternatively we could make chords by stacking different intervals like fourths. For example in Tarkus by Emerson, Lake and Palmer, these arpeggiated chords played on the organ are all built by stacking fourths up. And as you can see from the chord labels, because our chord labelling system is built around tertiary harmony, when we're dealing with quartal harmony the names can get a little bit odd.

You'll see a lot of sus4 for example. And the last thing we've got in this tier is minor scale modes. So earlier we mentioned diatonic modes, these are modes of the major scale, where we've taken the major scale but we've started on a different degree resulting in a new scale like Mixolydian, Dorian etc. Minor scale modes are when we make modes from a minor scale.

So for example we might take the melodic minor scale and by starting on a different scale degree we generate a new alternative scale. For example, the fourth mode of the melodic minor scale is what we would call Lydian dominant, and this is the scale used in the Simpsons theme song. Right, we're really getting into the depths of this ocean now. Metric Modulation.

Metric modulation is when we switch from one time signature to another but the two are connected by a consistent mathematic relationship. For example, we could switch from 6-8 to 4-4. We could make the two sort of connect together by making the eighth note worth the same amount in 6-8 as it is in 4-4.

So the two different meters sort of get married by this consistent note value. A polymeter is when we have effectively two different time signatures playing at the same time. What this means is that one part will effectively go out of time with the other until a full rotation has happened when they fall back into sync together.

For example, the song 5-4 by Gorillaz has a guitar riff in 5-4 but a drum pattern in 4-4, so after the first bar the two go out of sync until they've rotated enough that they're back together again. An octatonic scale is technically any scale with 8 notes, but most commonly it's referring to one of two symmetrical scales. One that goes semitone, tone, semitone, tone, semitone, tone, semitone, tone and the other does the opposite going tone, semitone, tone, semitone, tone, semitone, tone, semitone.

This second octatonic scale here that goes tone, semitone is also referred to as a diminished scale and is what we hear at the beginning of the song Just by Radiohead. The double harmonic scales are two scales that are often referred to with a variety of different names. The double harmonic major, sometimes just referred to as the double harmonic scale, is just like the major scale but with a flattened second degree.

and a flattened 6th degree. And the double harmonic minor scale, sometimes referred to as the Hungarian minor scale, is exactly the same as our usual harmonic minor scale but with the 4th degree raised. The double harmonic minor is also actually the 4th mode of the double harmonic A Moo chord is just a particular name for what you might think of as an Add-To chord, a major chord with the second degree added in as well. The name Moo chord was popularised by the band Steely Dan, who were particularly fond of this chord type.

Polytonality is when we have more than one key playing at the same time. A composer well known for his use of polytonality is Charles Ives. For example, in this piece, the two upper voices of the choir are in the key of C major and the two lower voices are in the key of Bb major. Be merciful unto us and bless us Bebop scales are variations on typical scales where an extra note has been added in.

For example, the bebop dominant scale is just like the mixolydian scale, but also features the unaltered 7th degree, so we've got the b7th and natural 7th in the scale. Or you could have bebop dorian which is just like regular dorian but also includes the major third. These are the sort of scales that were used by bebop musicians like Charlie Parker, Miles Davis and John Coltrane. However, it's important to remember that the idea of the bebop scales wasn't theorised until years after the bebop era.

It was more of a retrospective way of analysing how these players performed. Put simply, the Tristan chord is a half diminished chord and it gets its name from being the opening chord of Wagner's opera Tristan and Isolde. So this is a chord we could label Fm7b5, but that's kind of missing the point of the Tristan chord. The importance of the Tristan chord is the fact that it's opening an opera with tonal ambiguity. Typically an opera would open with a very clear statement of key, a clear statement of where we are tonally, but when Wagner opened his opera with this chord, it changed that.

And many have argued that the use of this Tristan chord was the beginnings of A tonality in Western music. Which leads me on nicely to the last thing in this tier which is a tonality. A tonality is quite simply when a piece of music avoids having any sense of tonal centre, any sense of key.

A atonal piece of music effectively has no key. This piece by Arnold Schoenberg very much avoids having any sense of key or resolution. Alright, we're approaching the bottom of this iceberg, the second to last tier, and we start off with swing ratios. Swing as a rhythm is effectively when two eighth notes have unequal rhythms to each other, where one eighth note is longer than the other eighth note, and a swing ratio is a way of describing how much that difference is.

So for example, a one-to-one relationship would be not swing, it would be straight, because both eighth notes have equal duration. However, a two-to-one swing feel would be triplet fill because the first note has double the duration of the second. 3 to 1 ratio would be a dotted eighth note swing like this.

The first note has three times as much duration as the latter. A 3 to 2 ratio would be a type of quintuplet swing like this. Or we could have a 4 to 1 relationship like this which is also a type of quintuplet swing.

Of course it's very important to remember that swing players aren't thinking in terms of swing ratios when they play. They're just letting it naturally swing. and the ratio to which they're swinging might even change throughout the performance.

But swing ratios can be very useful when you're trying to program swing into a DAW. Overtones. So pretty much any time you play a note, for example on a piano, you're not just hearing that note.

If I play an A on the piano, we are hearing what's called the fundamental pitch of A, but we're also hearing a series of overtones above that. quieter sympathetic notes which effectively colour the tone of the note. And they always follow the exact same pattern of intervals in what's called the overtone series or the harmonic series.

The intervals start off by being very fundamental recognisable intervals like octave, perfect fifth, perfect fourth, major third, minor third. Then as we get into the quieter and much harder to hear harmonics, they venture into intervals that we wouldn't find in our standard tuning system like a sub-minor third. a super major second, and so on. And the amazing thing is even though all of these are technically separate frequencies, separate pitches, our ear perceives them all as one cohesive note.

24-tet. So right at the beginning we talked about 12-tone equal temperament, where our instruments are tuned by tuning the octave and then dividing the space between those octaves into 12 equally spaced pitches. Well 24-tet is 24-tone equal temperament.

TET is just short for Tone Equal Temperament. So 24TET is a way of creating what you might call microtonal music by giving us an extra microtonal note between every standard pitch on our piano. For example here's a piece of music by Ivan Vincengretsky which is written in 24 tone equal temperament.

And off to the right of our 24th here we have some microtonal accidentals which we could use to notate our 24th music. We have a half sharp so we could have for example an A half sharp which is a note pitched between the notes A and Bb. We could have a half flat so an A half flat would be a note pitched between A and Ab and we could even have something like this which is a sharp and a half. A equals 415 hertz. So right at the beginning we were looking at A equals 440Hz, which is what we call concert pitch, the standard pitch that we tune A above middle C to.

The standard of A440 was only brought in around 100 years ago, and before that historically a wide range of different tunings were used across different geographic areas. 415 is what we call Baroque tuning, and is almost exactly one semitone lower than modern concert pitch. Baroque tuning is used when a performer wants to try and recreate the original sound of the composition closer to the original tuning it would have been written in. However, it's important to remember that 415 wasn't a historic standard, it was just one of many different tunings a baroque instrument may have been tuned to. Just intervals.

If an interval is just, it means it's been tuned to a perfect simple ratio. So for example, a justly tuned perfect fifth would be the ratio of 3 to 2. If you tune an instrument to just intervals, it's what we call just intonation or pure intonation. And although theoretically it's the purest way of tuning intervals, it presents a big problem. On any instrument with fixed tuning, like a keyboard instrument for example, you can't have pure intervals between every key without compromising other intervals. For example, if we tune our keyboard here in pure intonation in the key of A, so for example we have A and E as a 3-2 pure perfect fifth, unfortunately that means that by doing that some of the other perfect fifths in the key are not 3-2 relationships and are actually very dissonant.

So although 3-2 is the perfect and purest way to tune a perfect 5th interval, for keyboard instruments and similarly fixed tuned instruments, we have to have some way of adjusting or tempering this tuning system. As we discussed earlier, almost all modern music fixes this problem by using 12 tone equal temperament, where rather than worrying about the particular ratios between each interval, We just tune the octaves to perfect intervals and then divide the space between them logarithmically into 12 equally spaced pitches. And although of course this means that none of these intervals are now pure apart from the octave, they're close enough that our ear doesn't really mind.

But 12 tone equal temperament isn't the only way of fixing this problem. Historically other temperament systems were used, for example, mean tone temperament. Mean tone temperament for example is a system that was used historically to try and maintain justly tuned thirds, and it did this by slightly compromising the tuning of a fifth. Now exactly how this was managed is a topic for another video, but what is interesting is in old temperament systems like mean tone temperament, because each instance of each interval was actually tuned subtly differently, it meant that different key centers actually had different characters.

Some key centers were more in tune than others. So unlike in our modern system of 12 tone equal temperament where every key sounds exactly the same, different keys could actually have different qualities. In D minor, which I always find is really the saddest of all keys, really.

I don't know why, but it makes people weep instantly to play it. Nested Tuplets So a regular tuplet, an example of a regular tuplet would be a triplet. So a triplet is when we force three notes into the space where we would usually only have two notes. Another type of tuplet we could have would be a quintuplet where you fit five notes into the space where you might have previously only had two or previously only had four or you could have a sep tuplet where you force seven notes into a space. So that's regular tuplets but a nested tuplet is a tuplet inside of a tuplet and as you can imagine this starts getting quite confusing quite quickly.

Here we have a triplet nested inside of a quinn tuplet and I've also placed these regular notes and this regular triplet here to give it a bit of context. Performing these can be very difficult and conceptualizing how the different tuplets are interacting with the pulse can be quite mind-boggling. Now we can take that mind-bogglingness to another level by having a double nested tuplet. A tuplet inside of a tuplet inside of a tuplet. So for example here we have a septuplet inside of a quintuplet inside of a triplet.

But really at this point this rhythm is getting quite absurd and precise. There's almost always a easier and more intuitive way to transcribe a rhythm like this. For example rather than the septuplet quintuplet triplet situation, we could have had virtually the same rhythm notated like this, with just a regular nested tuplet.

And the last thing we've got on this tier is neutral intervals. Earlier we were talking about microtonality and half flats and half sharps and that sort of thing. Well a neutral interval is a microtonal interval. For example a neutral third is a third where the note is between a major or minor third. So for example in the key of C major, a major third would be C and E natural, a minor third would be C and E flat, so a neutral third would be C and E half flat.

So welcome to the deep, the bottom of our music theory ocean. And let's start off with a concept that really did blow my mind when I was first introduced to it and that is that pitch is equal to rhythm. Pitch and rhythm are ultimately the same thing.

So a note, a pitch, for example middle C, it's just a frequency right? Middle C is 261.63 Hz, which means that the sound waves are completing their vibration, completing their cycle 261.63 times a second. Or you could times that by 60 and get 15,697.8 vibrations per minute, which effectively means that middle C is just a pulse, a regular pulse playing at 15,697.8 BPM.

Pitch is the same thing as tempo. And we can actually hear that if we slow down this note, slow down our middle C, we eventually just get to a pulse. Sounds like a kick drum right? Well we can do the same thing in reverse. This is a quarter note kick drum pulse at 160 bpm.

Now see what happens if we gradually increase the tempo of this pulse. At some point as we increase the tempo our ears stop perceiving that pulse as a rhythm and begin perceiving it as a pitch because rhythm and pitch are the same thing. Amazingly, this also applies to chords and intervals.

Do you remember earlier when I mentioned that a justly tuned perfect fifth is the ratio of 3 to 2? One sound wave vibrates three times in the same amount of time as the other sound wave vibrates two times. So it's a 3 against 2 polyrhythm, right?

If we take this rhythm, which is a 3 against 2 polyrhythm, and speed it up... 5th. And as I said, we can turn this into a chord as well. We've already got our 5th, so if we added in a major 3rd, which is the ratio of 5 to 4, a 5 against 4 polyrhythm, what begins as this rhythm turns into a major chord.

A equals 432 hertz. So we've already mentioned A equals 440 hertz which is our standardized universal concert pitch and we've also mentioned A equals 415 hertz which is our baroque era standardized pitch. However A equals 432 hertz isn't some sort of standardized concert pitch, it's actually a pseudo-scientific idea in music that if you tune your music to 432 hertz it resonates better with I don't know aliens or space or something. I don't know if you're not getting the point This is the sort of homeopathy of music. Adam Neely's already got a great video debunking 432 So do check that out if you're interested Super ultra hyper mega meta lydian scale.

So this is effectively a lydian scale But when you reach the fifth degree you then start a new lydian scale from that degree So for example, if we're in the key of C major we'd start doing C D E F sharp G, that's the beginning of C Lydian. But now that we've reached the fifth of G, we now continue with a G Lydian scale, G, A, B, C sharp, D. And now once again, now we're on the fifth of that scale, we continue with a new Lydian scale based on the scale degree of D.

And the idea is that this is a scale that continues to get brighter and brighter as it ascends. Deutsch's scale illusion is when we've played one melody in one ear, and another melody in the other ear and we actually wind up hearing a third composite melody. So this will work best if you have headphones on but here's melody one that will be played in our left ear and here's melody two that will be played in our right ear and as you'll hear when they're played together we hear a third melody.

Now this very much is a trick, an illusion. And it only really works because both melodies are played with the same timbre, the same instrument. If one of the melodies was played on a violin for example and the other on a piano, it wouldn't really work. What's happening is although these notes are split across our two ears and written here in two different staves, if we condense them down onto one stave we can see that really it's one harmonised melody going up and down. Each of our ears gets one fragment of the melody, but of course we perceive the entire experience as one piece of music.

one melody. A shepherd tone is another auditory illusion where we seem to hear a pitch that's going up indefinitely, which of course would be physically impossible because eventually it would go beyond the limitations of our hearing. How this works is we're actually hearing various sine waves at the same time of the same note at different octaves. As the shepherd tone ascends, the sine waves at the top, the ones with the highest octave, start to become inaudible, but as that happens they're replaced with new sine waves at the bottom. So as the highest sine waves become too high pitched for us to hear, our ear just switches to listening to the sine wave an octave below it.

Irrational time signatures. 7-12 is an example of an irrational time signature. With all time signatures, the top number is telling us how many beats there will be in each bar, and the bottom number is telling us what type of beat that will be.

So 3-4 is telling us that there will be 3 quarter notes in each bar of the music. So how do we apply that with 7-12? There's no such thing as a 12th note, so how can we have 7 of them in a bar?

Well let's go back to 3-4 for a minute. We think of it as 3 quarter notes, but what even is a quarter note? Quarter note is a quarter of a whole note. So what a time signature is effectively telling us is take a whole note, divide it into the fraction that we've given you in the time signature, so in this case quarters, and then give us three of those quarters per bar of the music. The same logic applies with our 7-12 irrational time signature.

Take your whole note, divide it now into twelfths, eighth note triplets, and then each bar of our 7-12 music is going to have seven of those, seven eighth note triplets. Now you would never have a piece of music that was solely in an irrational time signature because it would be an over-engineered way of transcribing that music. There would always be an easier, more straightforward way to write that music down.

Where irrational time signatures come in useful is when we mix them in with other rational time signatures. So for example, our music could be in 3-4 and then jump to a bar of 7-12. Microtonal Modulation So a modulation is effectively a key change where the music moves from one key to another.

A very common practice in all types of music really. But a microtonal modulation is where we move to a key that is a microtonal interval away from where we started. So for example a regular modulation might be moving from G to A. Whereas a microtonal modulation could be moving from G to A half sharp.

For example, in Jacob Collier's arrangement of In the Bleak Midwinter, he modulates from E major, regular E major, to the key of G half sharp major. So we've modulated up a neutral third. In this clip, Jacob shows how before the modulation, the piano is in tune with the music, but after the modulation, because we're now in a microtonal key, the piano is out of tune.

And then… Pythagorean tuning. So we've talked a lot about different temperaments, different ways that we can tune our piano. Right at the top we had 12 tone equal temperament, which is the temperament that we use in all of our instruments today.

We then later talked about mean tone temperament, which is a historic way of tuning an instrument that allows us to preserve a justly tuned third. But before that, people would tune their instruments to what's called Pythagorean tuning. This is a tuning system that instead of preserving the third, preserves the fifth of the key, meaning that all of the fifths are as well tuned as they can be. Now just like all other temperament systems, Pythagorean tuning does result in some intervals that are less pleasing to the ear. But to give you an idea of how these different temperament systems sound, I'm going to play you a major chord followed by a major scale, Initially in 12-tone equal temperament, our standard modern tuning system, then in mean tone temperament, which is the one that preserves the sound of the third, and finally in Pythagorean tuning, the one that preserves the sound of the fifth.

Zen harmonic music is music that divides the octave into something different than just 12 degrees. For example, you could divide the octave into more degrees like 19 or 21. Or you could divide the octave by a smaller number than 12, for example 7 or 9. Zen harmonic music has a lot of overlap with microtonal music, but the main difference is that microtonal music sort of assumes that you're starting from 12 tone equal temperament as a starting point and then adding in extra notes between those notes, whereas Zen harmonic music throws out the entire idea of dividing the octave into 12 notes and then divides it by some other number which could be as small or as large as you like. Negative Harmony Negative harmony is the idea that each chord in the key can have a negative version of itself which has the same level of tension and release relative to the tonic chord of the key. For example, if we're in the key of C major and we had a perfect cadence G7 resolving to C major, the negative version of that would be F minor 6 resolving to C major.

Both G7 to C and F minor 6 to C has the same level of tension, the same level of voice leading. and thus are effectively the same type of resolution but coming from two different angles, two different approaches. If we look at how the four notes of G7 resolve onto the notes of our C major chord, we can see that they have to move the exact same amount to get to their resolution as the notes of our F minor 6 chord do to get to C major. There's the same level of voice leading, the only difference is the direction of travel.

The B in the G7 chord has to resolve upwards, whereas the Ab in the F minor 6 chord has to resolve downwards. downwards. So that is my music theory iceberg. Now I think what is so great about the iceberg as a way of explaining a concept is showing how you have to start at the top before you can progress downwards. Concepts like negative harmony and irrational time signatures are certainly interesting and can perk up the ear of a musician, but if you haven't already been through the layers above it, you're probably going to have a hard time understanding the concept.

So in a similar way to my music theory tier list that I did a few months ago, You could use this iceberg as a way of informing how you should learn music theory and what order you should learn concepts.

Transcript for:Exploring the Music Theory Iceberg

Transcript for:
Exploring the Music Theory Iceberg