This video is wrong within the first min and a half. While G is the dom of C, D is not the dom of F. E is not the dom of Eb. The entire principle of this video is based on really flawed and bad math. This video objectively doesn't make sense.
@@thespritewithinthat is just not how it works, it is a reflection around the middle of the circle of fifths. The circle of fifths is created out of each notes dominant, not the negative counterpart. Very disappointed in you young man
This is fantastic. For a while I have been thinking about that "axis" between C and G that Jacob mentioned, and I couldn't understand WHAT is was dividing. I concluded that you would take the interval between C and the other note(for example, an E) and then use that same interval on descending fashion starting from G. In this case, E would become Eb. It doesn't work every single time, but it works enough to get me really confused. This video really helped to clarify things. Thank you.
I'm glad you find this topic interesting! The "axis" between C and G that you mentioned is actually a concept in music theory known as the Circle of Fifths. It's a circular arrangement of the 12 pitch classes, or notes, in Western music. The Circle of Fifths is divided into two sections: the sharp keys on the right side and the flat keys on the left side. The notes on the right side have sharps in their key signatures, while the notes on the left side have flats in their key signatures. The relationship between C and G on the Circle of Fifths is that they are a perfect fifth apart. Moving clockwise around the circle, each new key is a perfect fifth higher than the previous one. For example, from C to G is a perfect fifth, from G to D is another perfect fifth, and so on. Now, when it comes to the intervals between specific notes within a key, things can get a bit more complicated. While the Circle of Fifths can help you determine the key signatures, it doesn't directly determine the intervals between individual notes. To determine the intervals between notes within a key, you need to consider the specific scale or mode you're working with. In the case of the major scale, which is the most common scale in Western music, the intervals between consecutive notes are typically a combination of whole steps (W) and half steps (H). The pattern for a major scale is: W-W-H-W-W-W-H, where W represents a whole step and H represents a half step. So, if we take the example you mentioned, starting with C and moving up a perfect fifth to G, the notes within the G major scale would be G-A-B-C-D-E-F#. The interval between E and F# is actually a half step, not a whole step. It's important to note that while the Circle of Fifths provides a helpful framework for understanding key relationships, the specific intervals between notes within a key depend on the scale or mode being used. Different scales and modes have different interval patterns, which can lead to variations in the intervals between specific notes. I hope this clarifies the concept for you! Let me know if you have any more questions.
_I'm copy and pasting this from my comment on this video because I think it'll provide a pretty good explanation of what you're talking about:_ TL;DR: Negative Harmony is only one way out of many of applying the same principle of symmetry, but not the simplest one, as the diatonic scale is already symmetrical to begin with. Something I find really funny is that Negative Harmony is not the most straightforward way of finding the image of a musical structure (set of notes). See, any diatonic key is symmetrical around one specific axis, which means that you can find the image of a structure in the same key as that structure. Negative Harmony uses the axis of another key rather than the original key. If you look at the major scale (ionian mode), the formula is: W-W-H-W-W-W-H (W being whole steps and H being half steps) Well, because of octave equivalency, the scale loops back upon itself endlessly; it's circular, not linear. Well the series of intervals which makes up the distonic scale is symmetrical around one axis, like so: H-W-W-W-H-W | W-H-W-W-W-H If you were to continue the pattern on both sides, it would always be symmetrical, or you could just draw it on a circle containing all twelve chromatic notes. Every single chromatic note has an image around this axis: • 2 | 2 • #1/b2 | b3/#2 • 1 | 3 • 7 | 4 • #6/b7 | b5/#4 • 6 | 5 • #5/b6 | b6/#5 (with reference to the ionian mode) Well then every chord in the diatonic scale already has an image that is diatonic to the scale: • vi | I • V | ii • IV | iii • vii° | vii° (with reference to the ionian mode) You can actually find the image of any chord, even chromatic ones. But because of how symmetry works, you will always find the exact same image even if you use another axis than the one that is diatonic to the key, albeit in a different key; this is what Negative Harmony does as we'll get to later. If the idea with Negative Harmony is that the image of a chord has the same function because it has the same interval relationships, then this has super interesting implications concerning diatonic chord functions as opposed to how they've always traditionally been viewed. The really important bit is how it affects chord functions. This all implies that the ii chord has the same function as the V chord, a "tense" chord. But in traditional theory, the ii chord isn't a tense dominant function chord, it's an unresolved but not very tense subdominant function chord, like the IV chord. The symmetry of the scale completely contradicts this. I think looking at the notes which compose each chord helps here. We can assign a function to each of these notes, and notes that are the images of each other have the same function. This gives us four distinct note functions within the diatonic scale: • 7 and 4 are the obvious place to start as they drive the entire harmony of the scale. They're tense and unresolved, specifically because of their relationship to each other, which is that of a dissonant tritone. They're the leading tones. • 1 and 3 are the points of resolution of that dissonant tritone. They form a consonant major third that is the symmetrical (and stepwise) resolution from this tritone, and actually the only possible symmetrical resolution for a tritone. • 6 and 5 are the completion notes. They complete the resolved major third into a stable triad, aka a major or minor chord. 6 turns the third into a minor chord (vi = 6-1-3), and 5 turns the third into a major chord (I = 1-3-5). • 2 is the neutral note. It's not particularly dissonant, but it's also not resolved as it's not part of the two resolved triads. It's just there. You'll notice that if we remove the leading tones from the diatonic scale, we get the pentatonic scale, which is always stable; 2 is the only note there that isn't part of a major or minor chord. It's just... there... minding its own business. Well, chords that are the image of each other share the same formula, which is why they have the same function: • I and vi are the resolved chords, as they are both composed of both points of resolution (1 and 3) and one completion note (5 or 6). They only contain resolved notes. • V and ii are the tense chords, as they are composed of a leading tone (7 or 4), a completion note (5 or 6), and the neutral note (2). The only part of them that is resolved is a completion note, which isn't even a point of resolution, and then they have a leading tone which is very tense and unresolved, and the neutral note which is not very tense but still not resolved. These chords are honestly not that tense until you make the tritone explicit by playing V7 or ii6, because otherwise they're just stable triads that are only _contextually_ unstable. • iii and IV are kind of in-between chords, partly resolved and partly unresolved. They are composed of a point of resolution (3 or 1), a completion note (5 or 6), and a leading tone (7 or 4). Part of them is resolved, which dilutes their tension, but they still have a leading tone which makes them definitely unresolved. • vii° is super tense because no part of it is resolved, unlike the other tense chords which had a completion note. It has both leading tones (7 and 4) and the neutral note (2), and unlike the other tense chords, it isn't a stable triad (major or minor) but is an unstable diminished triad which lacks that stable perfect fifth and instead has an unstable diminished fifth (which is made up of both leading tones, explaining why they're so tense). So the image of each chord has the same function, even chromatic chords, which means that the image of any chord progression will always have the same functional structure. This means for example that the image of a 2-5-1 is 5-2-6 (which can always be viewed as b7-4-1 if that helps), and if we look at all the variations of that: • diatonic major 2-5: ii-V-I | V-ii-vi • parallel minor 2-5: ii-V-i | V-ii-VI • "diatonic" minor 2-5: vii°-III-vi | vii°-iv-I • parallel major 2-5: vii°-III-VI | vii°-iv-i • diatonic backdoor 2-5: ii-V-vi | V-ii-I • major backdoor 2-5: ii-V-VI | V-ii-i Again, 5-2-6 can always be viewed as b7-4-1. By convention, the V always has to be major in a 2-5-1, so to match that, the ii always has to be minor in a 5-2-6; more specifically, to match the V7, you need a ii6. So a chain of dominants becomes a chain of minor 6s. Lastly, a tritone substitution, which is bII7 instead of V7, becomes #v6 instead of ii6 (which is what was said in the video as well, because again you find the same image but in a different key using Negative Harmony). This is super fun to experiment with, and you should find that it functions exactly like 2-5-1s do, as in it tonicizes keys just as unambiguously. Again, the images we find here are the same as with Negative Harmony, only this time they're in the same key rather than another key. With Negative Harmony, you get the exact same result, but in the key of the bIII chord (the parallel minor) rather than the... well, the I chord. In fact, you can find the image of a chord progression relative to literally any axis of symmetry, and you will always find the same result (which is not surprising as that's just how symmetry works). Interestingly, though, the image you find will always be in the key that is symmetrical _on the circle of fifths_ to the key of the I, relative to the key whose axis you were using. Now that sounds very confusing because there are two different symmetries going on at once, but if you look at the circle of fifths: C F G Bb D Eb A Ab E Db B Gb/F# (I spent way too long trying to make that look like a circle, hopefully it comes out right for you lol) Let's say we're playing a chord progression diatonic to C, for example C-G-Am-F which is I-V-vi-IV, and we decide to find its image relative to the axis of symmetry of the key of C. The result will, unsurprisingly, be diatonic to C, and it'll be Am-Dm-C-Em which is vi-ii-I-iii in C. Nothing new here. But let's say we want to find its image relative to the axis of the key of G, then what? Well we find Bm-Em-D-F#m, which is iii-vi-V-vii in G, but way more importantly, vi-ii-I-iii in the key of D. It's the exact same result, the same chord progression as before, only this time it's in the key D rather than C. But if you look back to the circle of fifths, D is the image of C relative to G. So this is a new symmetry we're talking about, not the same as before; this one is the symmetry of two keys or notes relative to a key or note on the circle of fifths, as opposed to the symmetry of notes relative to an axis in the diatonic scale like before. And you'll find that this is always true; no matter which key's axis you invert relative to, you will always get the same image (in this instance the image of I-V-vi-IV is always vi-ii-I-iii), but every time, it'll be in a different key, that key being the image of the original key on the circle of fifths relative to the key whose axis you used. Coincidentally, keys that are a tritone away share the same axis of symmetry, so in this instance, if you used the axis of Db, which is a tritone away from G, you'd get the same result in the key of D. The real kicker is that Negative Harmony finds the image like this but (if we're in C) using the axis of the key that is between F and Bb, and coincidentally the axis of the key that is between E and B (so the axis of D half flat, which is the same as the axis of G half sharp), so that the result is in the key of Eb.
The frustrating thing about Jacob when he explains things is he unnecessarily embellishes things. You can argue all day about the complexity in his music, but playing E A D G C really plainly before embellishing the hell out of the plagal version really doesn't help people to listen critically and actually understand the point he's making. There is a difference between teaching and performing and a lot of teachers get that wrong.
Totally agree. I love Jacob, but I have noticed that this is a theme in his teaching. He doesn’t necessarily compare apples to oranges, but it wouldn’t be a stretch to say he compares apples to apple pies. I know there are so many wonderful things going on inside his head, but just the plain, unadorned example would be nice sometimes.
As a pianist I can follow his fingers AND hear what he's doing. Perhaps don't start with negative harmony, Microtonality, or Jacob Collier until you've trained your ear more?
@arosonomy I understand this viewpoint, but I think what cannot be ignored here is that Jacob markets himself to anyone who is interested in music - not just those at a highly advanced level. This isn’t to lambast in any way, simply to criticise constructively.
@@arosonomy oh I understand what he's Showing, I'm a teacher myself, that's why I watch these kinds of videos. There's no need to be so snobby about it. My point is, if he attempted to make E A D G C sound good using extensions and embellishments, the difference wouldn't be so stark, and if he just played the changes as individual chords his point would be much clearer. If you're teaching/demonstrating then your #1 goal should be demonstrating a point clearly, not playing as many notes as you can.
@@_the_concestor_8185 That's a fair observation, but this isn't one of his videos. His videos appear to be marketed towards *musicians*. Unless you have a fundamental understanding of music theory. 90% of what he's talking about will not make sense. That being said, a vast majority of people watching theory videos don't understand it at all and just think it's interesting to try and learn (like my fondness for etymology). I wouldn't recommend Jacob Collier for a beginner. I've been playing for 20 years and I see how most of this WORKS but putting it into practice and composing original material is still challenging.
Its good to invent wheels isn't it? (By wheels i mean ways of thinking about chords and function) If I'm understanding it they are just saying the plagal cadence contains the same intervalic tensions as the dominant-tonic cadence but inverted?
Glad theres a video out there now demystifying negative harmony. About maybe 5 years back I had the idea of how to make a video called "negative harmonic equivalents in under 10 seconds," explaining the circle of fifths and axis extremely efficiently, but i had never posted on youtube before so never got around to it. It really bugged me that it was such a simple concept and there were all these really daunting 20 minite videos that explained it but not simply. But this video here will certainly do for those young and interested!
I don’t necessarily here major as happy or minor as sad anymore, it’s all about context. I used to before I became the musician I am today but I like to think of harmony in terms of brightness/color now. But yeah totally agree with what you say here!
It’s also negative because the fifths follow from the overtones of the root, whereas the fourth is reciprocal; it contains the root as an overtone but the root does not contain it. Fourths are cool that way. So in the cadence Collier plays, it’s a full reciprocal cadence, which is a whole other beast. Harmonic Experience by W.A. Mathieu really does this concept (and way more) justice. Love your videos btw, keep on keeping on! ❤
I enjoyed this. I think you should make more explanatory videos like this instead of just exclusively educational transcriptions. Also, it's pretty cool to hear your voice.
Nah, that would be microtonality Things analogous to "negative harmony" have surely existed at least since the late 19th century; there is little we don't know about how to use harmony in 12-TET, whether it be in the most consonant or atonal registers.
@@commentingchannel9776 the aspect I was drawing an analogy to was that of an inverse quantum operator in the quantum harmonic oscillator problem. But sure, belittle my comment that I appreciated art in a subjective manner…
1:30 - Each chord is spelt from the bottom up or the top down of the triad. The triad is important because it is composed of the root (identity / first overtone), the third (tonal color / fourth overtone), and fifth (dominant / second overtone). The root provides key, while the fifth provides an authentic cadence - a resolution from the first unfinished partial. The third can be reversed between major and minor through inverting the spelling, which is what negative harmony asks for. I (major tonic) upside down changes from one major third and perfect fifth upward to one major third and perfect fifth downward. V7 (the dominant chord) upside down changes from one major third and minor seventh built upward from the fifth to one major third and minor seventh built downward from the tonic’s root, forming an ii°7 or iv6. Plagal chords are formed below the tonic, because acoustically a fourth is utonal or “undertonal” and is a reversal of a fifth (otonal/overtonal). Undertones are simply inversions of overtones. Instead of the harmonic arising from integer multiples of the fundamental frequency, it arises from integer multiples of the FF’s inverse, the wavelength. The first five overtones are at the octave, perfect fifth, major third, harmonic seventh, and major ninth (ignoring duplicates), while the first five undertones are at the octave below, perfect fifth below, major third below, harmonic seventh below, and major ninth below… which when inverted into upward intervals (the way sounds are heard), creates the octave, perfect fourth, minor sixth, septimal major second, and minor seventh. Indeed these two series together form a 7/9 chord on the tonic and a m6 chord on the subdominant. Further extension of both series reveals a partial at another quintal degree, the augmented fourth which inverts to the diminished fifth, and the augmented fifth, which inverts to the diminished fourth. The scale most adjacent up to the augmented fourth partial is the Lydian dominant scale, and down to the diminished fifth the Dorian b2 scale. Those scales are notable by the way as the LD scale is a sort of integration of the major dominant (Mixolydian) with the major subdominant (Lydian), and Dorian b2 is LD’s relative minor scale, built in thirds directly below. Dorian b2 integrates minor subdominant (Dorian) harmony with minor dominant (Phrygian) harmony. Indeed this makes them negatives of each other. Lydian & Phrygian, and Mixolydian & Dorian, also each form negative pairs respectively. Adding in the augmented fifth and diminished fourth though creates scales akin to the Lydian augmented and Locrian modes, which supports them as negatives of each other too. Locrian doesn’t have a negative in its parent scale, as it lacks a perfect fifth. Likewise with Lydian augmented. One can be thought of as a more unstable version of Aeolian b5, and the other as a more unstable version of Ionian #4, also known as Lydian. Both can be thought of as hyperextensions of the major and minor tonalities, resulting in dissonance where brightness or darkness is no longer tenably created. This to me also corresponds with my understanding of the diminished triad as negative to the augmented triad. The diminished seventh chord probably negates to a +7 chord, which can be formed through the whole tone scale. That the diminished seventh and minor seventh are enharmonic to the major sixth and augmented sixth probably helps my claim too. Going back to the diagram… IV as major is more of a Western sound, as other cultures tend to use the b6 more than in Western music, as well as the b2 as opposed to the leading seventh and augmented fourth. In juxtaposition with the leading seventh, the b6 creates a sublime sense of tonal urgency which is compatible with a minor tonic (harmonic minor) as much as with a major tonic (harmonic major). It does however correspond well with the major pentatonic scale, which is extremely instinctive in its construction (most will default to singing in it). The IVmaj7 and v7 chords as well as the Imaj9 and i7(b13) chords form negative pairs… indeed the first two arise as sort of neutralizations of the more harmonically potent iv6 and V7, while the last two form sounds essential to the Ionian and Aeolian modes. ii6/7 and bVII6/7 match well as one works as Dorian b2 (minor supertonic) and the other as Lydian dominant (major subtonic). Indeed these two are essential to the melodic minor (Ionian b3) and melodic major (Aeolian dominant) modes respectively. The bIII is opposite to the vi for fairly easy to grasp reasons, as the bIII is relative major of the tonic, while the vi is relative minor of the tonic. This is contextual though, namely it only works in an Ionian-Aeolian context. In fact all of the chords listed at the timestamp do. Dorian has a øvi, but the negative of Dorian is Mixolydian. Dorian, like melodic major, is a symmetric scale though - which also makes it a true androgyne between major and minor - and thus negative harmony can be a bit unwieldy or paradoxical for it, as the reversal of its notes from the tonic root on is itself. It’s perhaps best to look at negative harmony as perspective rather than law… but it does have its axioms. The negative of a bIII+ (as found in Ionian b3) is likely a vi° (as found in Dorian)… but what is the negative of a viø9, as found in Ionian b3? Well I guess since a viø9 is just a m6maj7 chord in inversion, it would have to be the I7b13. Likewise then, the viø7 in Dorian, being an inversion of i6, translates to a negative of I7 inverted, which is simply bVII#11. This does in fact correspond with Dorian and Mixolydian as negatives. And indeed modally they resolve downward to I and upward to vi respectively. The tonicizations of them resolve to each other though, one downward to V and the other upward to i: melodic minor (Ionian b3) resolves down to melodic major (Aeolian dominant/Mixolydian b6), which in turn resolves back up to melodic minor. And adding further harmonic weight by adding a b6 or a #7 creates harmonic minor and harmonic major, which are separate scales that are negatives of each other: melodic minor with a b6 is harmonic minor; melodic major with a #7 is harmonic major.
@@gillianomotoso328 Are you able to sit at the piano and come up with interesting harmonies and chord progressions based on your theory knowledge? I'd like some examples of a good chord progression or harmony.
A few weeks ago I attended a masterclass with Steve Coleman in Italy, Modena, and on the second day he starts talking about negative harmony. It was interesting because his weird way to explain it (I only happen to understand something about it after watching this 4 minutes video that made me understand much more than that 2 days-jazz masterclass) was by flipping the chord construction on the piano. E.g: he was builiding a normal chord (let's say G7) with stack 3rd intervals from left to right (so G B D F) and then constructing the equivalent negative chord by calculating the exact same intervals starting from the tonic but this time calculating them from right to left (in this case it would be, from right to left, G Eb C A), resulting infact in a C-6 inversion. This is really weird to me, not only because it contrast what I just saw on this video, but also because this way of visualizing it on the piano inverting the chords wasn't even mentioned in the video. @Georgecollier I would like to know your opinion about this
I like that way of explaining it intervallically. It's interesting though, you're right, the mechanisms of that would almost always cause an inversion in the resulting chord
I worked out the missing III chord you omitted from 01:27 and it seems like the III chord doesn't follow the same rules of 'extensions' (minor seventh to major sixth, and major seventh to minor sixth) When 'reversed', the usual diatonic minor III chord will turn flat VI major chord. So a simple E minor will turn into A flat major chord. Don't get me wrong, that's 🌶️. But if you add another seventh interval to the III minor chord, it will turn into a IV minor 7 (minor seventh chord), so an Em7 chord will become Fm7, disregarding the 'extensions' rule. That naughty III chord is so badass 😎
Two things. The whole labeling of chord tones and chords in the diatonic system is based a mirror relationship to the tonic. In other words, the subdominant is the dominant underneath the tonic, the subtonic is a step below the tonic, and so on. And secondly, this seems as another source of substitute chords, as an occasional interesting diversion. PS This may be just another labeling for things we already know. The F-6 chord is so close to the tritone substitution for G7, Db7.
Another thing that’s very important, resolution in negative harmony doesn’t only flip the dominant chord, but also the tonic if equal tension is to be preserved. ivm6 resolving to a Imaj is strong, but in the same way of a V7 resolving to a im. There is strength, but none of the tritone collapsing to a major third that is so prominent in a V7 to Imaj. To preserve this, you can flip both chords into their negative equivalents, making it a ivm6 into a im, with the tritone between the minor third and major sixth resolving to the major third between the minor third and perfect fifth. This is a small change, but still an important one to mention, as in the key of C major, Fmi6 may be the negative equivalent of G7 but it’s resolution is not exactly of equal strength.
It’s interesting how the minor 6 shows up here, it’s an integral chord in the Barry Harris system too which thinks of harmony in a very different but sensible way in comparison to what’s actually taught everywhere.
I dont think ivm6 is inherently timid or gentle, nor V7 inherently triumphant or loud. A ivm6 in barbershop is often very triumphant and loud, just for one example.
I think it’s the tendency. One tends to carry this sensation on its own, while the other tends to carry an opposite one. A V7 tends to have a bright intensity and urgency to it, while an iv6 tends to carry a solemn flow. Both have that tritone in them though, which begs the resolution.
@@gillianomotoso328 i think that speaks more to how these chords get used rather than their inherent properties. Like how certain words come in and out of popular vernacular.
@@keysradiotheradio But don’t you think there’s a cause for why people pick these vibrations to elicit what they wish to elicit? These are vibrations, not just words… I think there’s a difference between simple ligatures that are somewhat arbitrary in how they appear and physical ratios between rates of vibration
@@keysradiotheradio I have to believe there’s some underlying inherency to music… as much as we can recontextualize it, there’s something clearly universal about it to me.
@@gillianomotoso328 I agree that music is a universal language, but I don't agree with the broad generalizations made about the qualities of V7/iv6 chords. A V7 written by Beethoven does not have the same inherent non-theoretical properties as one written by Ellington, for example. Another example - the word "sick" can be used to describe something positive in current vernacular
2:17 plays five major chords with additional steps and then proceeds to play an absolute mess of notes without any readable melodical message. «Don't you think it's cool?» Well, I probably don't.
I enjoyed the video, but found the audio for the chords a little low. They sound like they are an octave or more below the notes shown (or maybe just doubled down an octave). The tightly clustered notes in the lower register sound muddled and unclear. Playing just the notes shown (with perhaps just the root doubled down an octave) would make it a lot easier to hear the harmonic effects you are talking about.
All major/minor triad possibilities should be covered but make sure to remember symmetric property (i.e. if looking for VI remember to read right to left as well) Major and Minor Scales Diatonic Triads I = i ii = bVII iii = bVI IV = v V = iv vi = bIII vii* = ii* Nondiatonic Triads bII = vii bii = VII II = bvii biii = VI III = bvi #IV = #iv #iv = #IV
I play on a Striso (midi controller/synth using the DCompose isomorphic layout) created by @pierstitusvandertorren7068 . If I set the pivot point between the I and V, (just above and to the right of the C for the key of C), and turn my board upside down, and pivot my starting note or chord around the pivot point, I then play the exact same physical patterns and get the negative. This is awesome! As an experiment, I played Leaves on the Vine (the song Uncle Iroh sings for his son). and it feels so different, yet has similar tension and release (though ending with notes going up, which feels unresolved, like it's asking a question).
FINALLY SOMEONE GOT IT RIGHT! A common misconception is to translate chords and read them in the same way Cmaj7-GEbCAb and people read it as an Abmaj7 and the progression just stays the same but in Ab and so on....PRO TIP: reduce all chords to BASIC TRIADS and only add 7ths and extensions AFTER negativefying them, and pay attention aka have an asthetic oriented ear for it, as in: treat it like art and not math. Imaj7 becomes a Im6 or Im(b13) and it sucks, but is the Imaj7 a point of release? Then consider it a I6 chord, more stable version of the same major I degree chord, and translates directly to Im7, a more stable minor chord. BUT for example V7: G7 -> G triad GBD : CAbF -> IVm Fm. If we took G7 GBDF-> CAbFD Dm7b5 and we lost functions. But V7 is a tension,, add the F last after the triad, becomes a D, the natureal 6 of the IVm6. The same way we can use a V7 or a V6, we can change them to IVm6 or IVm7 :D Reason is we swap the 1 and 5 degrees by the axis, adding a note after altering the 5-1 degree changes the whole reason of the axis
What? Just flip the notes (C major for example) around a "center" "between" E and Eb. So each E in original melody becomes Eb in negative harmony and vice versa. D changes places with F, C# with F# and so on. That's it!
Weird, but I heard so many progressions like these when I listened to my parents hippy music. Wonderful and kid of exiting stuff for sure, but not really new to me though and I think not new for the average contemporary music composer too.
0:29 not emotions, but sensations 1:12 it is not "become" it is a relation. The relation is not explained. At the end it is said it is a theory ; if it is a theory it is not a technique. But a condition. The video speaks about a technique. Resume: a clickbaity trend
I'm not sure I agree with the idea that each chord has a counterpart which carries the opposite emotion, because to me, chords do not by themselves necessarily evoke one particular emotion. Instead, much like how everything else in the universe seems to work, it is all contextual. A minor chord can evoke a positive emotion when played after certain chords, for example. An ugly puke green colour can look absolutely gorgeous when the colours around it are complementary. An angry person might be angry because of the situation, yet only those who witnessed the initial state of the person will realize this. Anyway, just wanted to comment because I'm bored. Haha.
Thanks for the video. 3:06 Chord Bbm. It is very interesting. If You flip notes in 1:16 "B" "Gb" becomes "Db" And it is not in the scale. But here it is in Bbm in 3:06. it is not correspond with rotation around C|G Db/Gb axis. Where is the catch?
In that "Tension" sheet music at 1:50, you write G F# G followed by a G# and a G natural. Since we are in C, I'm wondering what the theoretical reasoning is behind viewing that as a #5 rather than a b6? To my ears, it really has a b6 feel to it in this context, especially with the G natural being on both sides of it. What makes it a #5 rather than a b6 here?
I'm guessing the convention is to combine sharps and flats as little as possible. Since he just used a sharp, then he should continue to use sharps unless it becomes absolutely necessary to use a flat.
Also, I get why you would think he should use a flat, to preserve the distinction in lettering as much as possible like we do with all scales, but following that logic, it would imply that the scale he's using contains F#, G, and Ab, which is unlikely to be his intention. It makes sense to allow for the most equal dispersion of same-lettered notes as possible across the twelve tones. So if there's F#, that implies that there's two notes named F; therefore, there should be two notes named G if one of them is a black note, which is the case.
Great video! So does it mean, that Thom Yorke used negative harmony in No surprises? I mean, it goes D - Gm6 - D And as I understand Gm6 is a negative A7
It actually goes F - Bbm6/7 :) The bridge goes C - Bbm6/7 and then Gm7 - Bbm6/7. I think he used a harmonic major backdrop for the song (Aeolian with a major seventh chord as tonic), and in that maybe there was an understanding of reversing the polarity of the harmony. The strictest reversal of it would be Fm - C9, then Bbm - C7, followed by Eb6 - C9. I almost would say this doesn’t help much, because harmonic minor and harmonic major are negatives of each other that happen to be very similar, but C9 is actually found in melodic minor, not harmonic minor. Recognizing that Ionian and Aeolian are negatives helps too. You’ll notice that the b7 of the key is played up until the bridge. This is a borrowing from natural minor into major. The major dominant (C7) in the bridge is the slightest burst of joy that is negative to the Bb6/7. Likewise that Gm7 introduces a moment of that major sixth in Ionian, but it is eclipsed again by the sink of the Bb6/7.
@@massacomqueijo2023 Hehe, I think it definitely is by default. It helps to remember that in negative harmony, the intervals and scales are spelt in reverse *from the top of the triad* … This means that the negative of each mode follows this sequence: Ionian Aeolian Dorian Mixolydian Phrygian Lydian Locrian Lydian Augmented (Locrian is a flat darker than Phrygian and Lydian Aug is a sharp brighter than Lydian) Melodic minor Melodic major (Mixolydian b6) Lydian dominant Dorian b2 Aeolian diminished Ionian augmented Harmonic major Harmonic minor Lydian minor Phrygian dominant And triads, tetrads, and pentads follow this: M m Maj7 mb13 (see Ionian & Aeolian) 7 mM6 mM7 majb13 (see harmonic minor & major) + (aug) ° (dim) or + + (see Lydian & Ionian augmented) ° + or ° 7 w/o 3rd (because a diminished chord is an inversion of a mM6 chord without its 5th) m7b5 7 in 1st inv. dim7 dim7 or dim7 +M7 9 mM6/7 (see mel. major & minor) 7b9 mM7#11 (see Lyd. minor & Phryg. Dom) M9 m9 (see Ionian & Aeolian) mM9 7b13 7#11 mM6b9
The more I learn about this, the more I think "There's no there, there!" There are perfectly normal tonal explanations for why these substitutions sometimes work. For example, iv-6 might substitute for V7 because iv-6 is a subdominant suspension over the tonic and three of the four notes in iv-6 are contained in V7b9. bVII6 might substitute for ii-7 because they are both approaching the tonic by a whole step, one from above and one from below. Similarly, bIII and vi- are both a third from the tonic. Now THAT is sort of what you're talking about, the symmetrical relationship. Honestly though, the visual representation of the circle of fifths with the line down the middle of it is just confusing me. Mind you it isn't confusing me as much as Jacob's explanation which really makes no sense at all.
00:40 - 01:15 - About as clear as mud. One other thing: First you said 2 notes together is "harmony." Then later you said that "movement" is harmony. ---- What is it I've missed?
If such a thing as negative harmony even exists other than s a dubious concept, what does it matter? It sounds like the difference between major in minor. Why do we have to rename it something else?
I don't understand. You said that a major chord's negative counterpart is a minor chord, so D major's counterpart should be D minor. But when I use that conversion chart, the opposite of D is F, the opposite of F# is C#, and the opposite of A is B flat. What am I missing?
Axis Theory and Negative Harmony are excellent tools but are based on the the Circle of 5ths and Functional Harmony which both assume that 12TET or JI is correct and that the perfect cadence (the 5th to tonic, as opposed to the 4th's plagal cadence) is the ultimate cadence in music.
For example if F was the key centre the harmonic axis would lie between F and C so the visual would rotate around by 1 and the new pairs could be seen.
so does the axis go between the tonic and the dominant or just through the tonic??? this video is so confusing because the clip with jacob collier contradicts your diagram
A plagal cadence is timid and gentle? Not only do I disagree that a plagal cadence is inherently timid/gentle (cf Bach BWV 565) but I also disagree that authentic cadences aren’t gentle (cf Goldberg aria). I frequently find plagal cadences to be extremely powerful, even stern. You run into trouble when you try to mandate emotional responses to given artistic phenomena. Sometimes you can paint with a broad brush (ie, fast = exciting), but not here. This is too broad, there are too many counter examples, it’s too subjective to have any explanatory power.
Well, I think a Bbm-Fm6-C progression is generally timid and gentle, but a Bb-F-C progression isnt. Of course it always depends on context, but that's what I hear in a vacuum
It’s descriptive not prescriptive. You can do other things play around with dynamics etc to make it not timid and gentle but on its own at regular volumes this is indeed the sense that most people get.
btw: I tried clicking the link for the Qwest Masterclass, but it links to youtube studio and looks like an edit page for the video (for your channel, I just get a broken link "Oops, something went wrong.")
Wouldn’t C major reflect to C minor? So if we reflected E7 A7 D7 G7 C around the axis it would be Fø7 Cø7 Gø7 Dø7 Cm (Or A♭m6 E♭m6 B♭m6 Fm6 Cm) instead of Fø7 Cø7 Gø7 Dø7 C. Jacob didn’t mention anything about flipping the final chord in his interview with June Lee so I was kind of confused like maybe he forgot to or something. Of course Dø7 resolving to Cmaj is the inverse of G7 resolving to Cm, but G7 C still inverts to Dø7 Cm. It kinda bugged my OCD but maybe you could help explain why he didn’t invert Cmaj to Cm.
Hi, i have a question If you want to reflect something that's in a minor key(e.g. Cm), do you reflect it according to it's relative major (Eb) or the tonal centre (i.e. C)?
It's from an old song called "Shave and a haircut, two bits." But it's really just a classic jazz progression that was probably around a lot earlier than that.
![How To Write Chord Progressions With NEGATIVE HARMONY [Simple Explanation]](http://i.ytimg.com/vi/qHH8siNm3ts/mqdefault.jpg)
![How To Write Chord Progressions With NEGATIVE HARMONY [Simple Explanation]](/img/tr.png)
This is it! This is the video that has finally chipped this concept through the dense eggshell that is my brain!
Same
saME
This video is wrong within the first min and a half.
While G is the dom of C, D is not the dom of F. E is not the dom of Eb.
The entire principle of this video is based on really flawed and bad math.
This video objectively doesn't make sense.
@@thespritewithinthat is just not how it works, it is a reflection around the middle of the circle of fifths. The circle of fifths is created out of each notes dominant, not the negative counterpart. Very disappointed in you young man
@@thespritewithindang, I used to think music is art, but I see there's a lot of science to it too... This makes me more intrigued..
“1 minute music theory” 4 minutes long
What a fraud
🤓
0:40 to 1:40
Person in the comments saying ""1 minute music theory" 4 minutes long" 4 minutes and 31 seconds long
Nah, it's a compilation of 4 episodes
This is fantastic. For a while I have been thinking about that "axis" between C and G that Jacob mentioned, and I couldn't understand WHAT is was dividing. I concluded that you would take the interval between C and the other note(for example, an E) and then use that same interval on descending fashion starting from G. In this case, E would become Eb. It doesn't work every single time, but it works enough to get me really confused. This video really helped to clarify things. Thank you.
Thanks so much for this comment. I finally understand the axis now.
I'm glad you find this topic interesting! The "axis" between C and G that you mentioned is actually a concept in music theory known as the Circle of Fifths. It's a circular arrangement of the 12 pitch classes, or notes, in Western music.
The Circle of Fifths is divided into two sections: the sharp keys on the right side and the flat keys on the left side. The notes on the right side have sharps in their key signatures, while the notes on the left side have flats in their key signatures.
The relationship between C and G on the Circle of Fifths is that they are a perfect fifth apart. Moving clockwise around the circle, each new key is a perfect fifth higher than the previous one. For example, from C to G is a perfect fifth, from G to D is another perfect fifth, and so on.
Now, when it comes to the intervals between specific notes within a key, things can get a bit more complicated. While the Circle of Fifths can help you determine the key signatures, it doesn't directly determine the intervals between individual notes.
To determine the intervals between notes within a key, you need to consider the specific scale or mode you're working with. In the case of the major scale, which is the most common scale in Western music, the intervals between consecutive notes are typically a combination of whole steps (W) and half steps (H). The pattern for a major scale is: W-W-H-W-W-W-H, where W represents a whole step and H represents a half step.
So, if we take the example you mentioned, starting with C and moving up a perfect fifth to G, the notes within the G major scale would be G-A-B-C-D-E-F#. The interval between E and F# is actually a half step, not a whole step.
It's important to note that while the Circle of Fifths provides a helpful framework for understanding key relationships, the specific intervals between notes within a key depend on the scale or mode being used. Different scales and modes have different interval patterns, which can lead to variations in the intervals between specific notes.
I hope this clarifies the concept for you! Let me know if you have any more questions.
@@Pillowpetlover dude why did you even bother throwing this into an AI
_I'm copy and pasting this from my comment on this video because I think it'll provide a pretty good explanation of what you're talking about:_
TL;DR: Negative Harmony is only one way out of many of applying the same principle of symmetry, but not the simplest one, as the diatonic scale is already symmetrical to begin with.
Something I find really funny is that Negative Harmony is not the most straightforward way of finding the image of a musical structure (set of notes). See, any diatonic key is symmetrical around one specific axis, which means that you can find the image of a structure in the same key as that structure. Negative Harmony uses the axis of another key rather than the original key.
If you look at the major scale (ionian mode), the formula is:
W-W-H-W-W-W-H
(W being whole steps and H being half steps)
Well, because of octave equivalency, the scale loops back upon itself endlessly; it's circular, not linear. Well the series of intervals which makes up the distonic scale is symmetrical around one axis, like so:
H-W-W-W-H-W | W-H-W-W-W-H
If you were to continue the pattern on both sides, it would always be symmetrical, or you could just draw it on a circle containing all twelve chromatic notes.
Every single chromatic note has an image around this axis:
• 2 | 2
• #1/b2 | b3/#2
• 1 | 3
• 7 | 4
• #6/b7 | b5/#4
• 6 | 5
• #5/b6 | b6/#5
(with reference to the ionian mode)
Well then every chord in the diatonic scale already has an image that is diatonic to the scale:
• vi | I
• V | ii
• IV | iii
• vii° | vii°
(with reference to the ionian mode)
You can actually find the image of any chord, even chromatic ones. But because of how symmetry works, you will always find the exact same image even if you use another axis than the one that is diatonic to the key, albeit in a different key; this is what Negative Harmony does as we'll get to later.
If the idea with Negative Harmony is that the image of a chord has the same function because it has the same interval relationships, then this has super interesting implications concerning diatonic chord functions as opposed to how they've always traditionally been viewed.
The really important bit is how it affects chord functions. This all implies that the ii chord has the same function as the V chord, a "tense" chord. But in traditional theory, the ii chord isn't a tense dominant function chord, it's an unresolved but not very tense subdominant function chord, like the IV chord. The symmetry of the scale completely contradicts this.
I think looking at the notes which compose each chord helps here. We can assign a function to each of these notes, and notes that are the images of each other have the same function. This gives us four distinct note functions within the diatonic scale:
• 7 and 4 are the obvious place to start as they drive the entire harmony of the scale. They're tense and unresolved, specifically because of their relationship to each other, which is that of a dissonant tritone. They're the leading tones.
• 1 and 3 are the points of resolution of that dissonant tritone. They form a consonant major third that is the symmetrical (and stepwise) resolution from this tritone, and actually the only possible symmetrical resolution for a tritone.
• 6 and 5 are the completion notes. They complete the resolved major third into a stable triad, aka a major or minor chord. 6 turns the third into a minor chord (vi = 6-1-3), and 5 turns the third into a major chord (I = 1-3-5).
• 2 is the neutral note. It's not particularly dissonant, but it's also not resolved as it's not part of the two resolved triads. It's just there. You'll notice that if we remove the leading tones from the diatonic scale, we get the pentatonic scale, which is always stable; 2 is the only note there that isn't part of a major or minor chord. It's just... there... minding its own business.
Well, chords that are the image of each other share the same formula, which is why they have the same function:
• I and vi are the resolved chords, as they are both composed of both points of resolution (1 and 3) and one completion note (5 or 6). They only contain resolved notes.
• V and ii are the tense chords, as they are composed of a leading tone (7 or 4), a completion note (5 or 6), and the neutral note (2). The only part of them that is resolved is a completion note, which isn't even a point of resolution, and then they have a leading tone which is very tense and unresolved, and the neutral note which is not very tense but still not resolved. These chords are honestly not that tense until you make the tritone explicit by playing V7 or ii6, because otherwise they're just stable triads that are only _contextually_ unstable.
• iii and IV are kind of in-between chords, partly resolved and partly unresolved. They are composed of a point of resolution (3 or 1), a completion note (5 or 6), and a leading tone (7 or 4). Part of them is resolved, which dilutes their tension, but they still have a leading tone which makes them definitely unresolved.
• vii° is super tense because no part of it is resolved, unlike the other tense chords which had a completion note. It has both leading tones (7 and 4) and the neutral note (2), and unlike the other tense chords, it isn't a stable triad (major or minor) but is an unstable diminished triad which lacks that stable perfect fifth and instead has an unstable diminished fifth (which is made up of both leading tones, explaining why they're so tense).
So the image of each chord has the same function, even chromatic chords, which means that the image of any chord progression will always have the same functional structure. This means for example that the image of a 2-5-1 is 5-2-6 (which can always be viewed as b7-4-1 if that helps), and if we look at all the variations of that:
• diatonic major 2-5: ii-V-I | V-ii-vi
• parallel minor 2-5: ii-V-i | V-ii-VI
• "diatonic" minor 2-5: vii°-III-vi | vii°-iv-I
• parallel major 2-5: vii°-III-VI | vii°-iv-i
• diatonic backdoor 2-5: ii-V-vi | V-ii-I
• major backdoor 2-5: ii-V-VI | V-ii-i
Again, 5-2-6 can always be viewed as b7-4-1. By convention, the V always has to be major in a 2-5-1, so to match that, the ii always has to be minor in a 5-2-6; more specifically, to match the V7, you need a ii6. So a chain of dominants becomes a chain of minor 6s. Lastly, a tritone substitution, which is bII7 instead of V7, becomes #v6 instead of ii6 (which is what was said in the video as well, because again you find the same image but in a different key using Negative Harmony).
This is super fun to experiment with, and you should find that it functions exactly like 2-5-1s do, as in it tonicizes keys just as unambiguously.
Again, the images we find here are the same as with Negative Harmony, only this time they're in the same key rather than another key. With Negative Harmony, you get the exact same result, but in the key of the bIII chord (the parallel minor) rather than the... well, the I chord.
In fact, you can find the image of a chord progression relative to literally any axis of symmetry, and you will always find the same result (which is not surprising as that's just how symmetry works). Interestingly, though, the image you find will always be in the key that is symmetrical _on the circle of fifths_ to the key of the I, relative to the key whose axis you were using. Now that sounds very confusing because there are two different symmetries going on at once, but if you look at the circle of fifths:
C
F G
Bb D
Eb A
Ab E
Db B
Gb/F#
(I spent way too long trying to make that look like a circle, hopefully it comes out right for you lol)
Let's say we're playing a chord progression diatonic to C, for example C-G-Am-F which is I-V-vi-IV, and we decide to find its image relative to the axis of symmetry of the key of C. The result will, unsurprisingly, be diatonic to C, and it'll be Am-Dm-C-Em which is vi-ii-I-iii in C. Nothing new here.
But let's say we want to find its image relative to the axis of the key of G, then what? Well we find Bm-Em-D-F#m, which is iii-vi-V-vii in G, but way more importantly, vi-ii-I-iii in the key of D. It's the exact same result, the same chord progression as before, only this time it's in the key D rather than C. But if you look back to the circle of fifths, D is the image of C relative to G. So this is a new symmetry we're talking about, not the same as before; this one is the symmetry of two keys or notes relative to a key or note on the circle of fifths, as opposed to the symmetry of notes relative to an axis in the diatonic scale like before.
And you'll find that this is always true; no matter which key's axis you invert relative to, you will always get the same image (in this instance the image of I-V-vi-IV is always vi-ii-I-iii), but every time, it'll be in a different key, that key being the image of the original key on the circle of fifths relative to the key whose axis you used. Coincidentally, keys that are a tritone away share the same axis of symmetry, so in this instance, if you used the axis of Db, which is a tritone away from G, you'd get the same result in the key of D.
The real kicker is that Negative Harmony finds the image like this but (if we're in C) using the axis of the key that is between F and Bb, and coincidentally the axis of the key that is between E and B (so the axis of D half flat, which is the same as the axis of G half sharp), so that the result is in the key of Eb.
I’ve studied arrangement, orchestration and composition and think this is the most confusing, useless and overrated concept I’ve ever come across.
The frustrating thing about Jacob when he explains things is he unnecessarily embellishes things. You can argue all day about the complexity in his music, but playing E A D G C really plainly before embellishing the hell out of the plagal version really doesn't help people to listen critically and actually understand the point he's making.
There is a difference between teaching and performing and a lot of teachers get that wrong.
Totally agree. I love Jacob, but I have noticed that this is a theme in his teaching. He doesn’t necessarily compare apples to oranges, but it wouldn’t be a stretch to say he compares apples to apple pies.
I know there are so many wonderful things going on inside his head, but just the plain, unadorned example would be nice sometimes.
As a pianist I can follow his fingers AND hear what he's doing. Perhaps don't start with negative harmony, Microtonality, or Jacob Collier until you've trained your ear more?
@arosonomy
I understand this viewpoint, but I think what cannot be ignored here is that Jacob markets himself to anyone who is interested in music - not just those at a highly advanced level. This isn’t to lambast in any way, simply to criticise constructively.
@@arosonomy oh I understand what he's Showing, I'm a teacher myself, that's why I watch these kinds of videos. There's no need to be so snobby about it.
My point is, if he attempted to make E A D G C sound good using extensions and embellishments, the difference wouldn't be so stark, and if he just played the changes as individual chords his point would be much clearer.
If you're teaching/demonstrating then your #1 goal should be demonstrating a point clearly, not playing as many notes as you can.
@@_the_concestor_8185 That's a fair observation, but this isn't one of his videos. His videos appear to be marketed towards *musicians*. Unless you have a fundamental understanding of music theory. 90% of what he's talking about will not make sense. That being said, a vast majority of people watching theory videos don't understand it at all and just think it's interesting to try and learn (like my fondness for etymology).
I wouldn't recommend Jacob Collier for a beginner. I've been playing for 20 years and I see how most of this WORKS but putting it into practice and composing original material is still challenging.
I absolutely love the 4m6 chord resolving to the tonic but ive never thought of it as a (negative) dominant chord ! How interesting
It's literally just a plagal cadence. "Negative Harmony" is reinventing the wheel.
Its good to invent wheels isn't it? (By wheels i mean ways of thinking about chords and function) If I'm understanding it they are just saying the plagal cadence contains the same intervalic tensions as the dominant-tonic cadence but inverted?
(Is a plain plagal cadence a m6 chord - tonic even? I always thought of it as just 4-1?)
@@charlottemarceau8062 A plagal cadence is just defined be the IV-I motion, it doesn't need any m6 stuff or anything
Right exactly
Glad theres a video out there now demystifying negative harmony. About maybe 5 years back I had the idea of how to make a video called "negative harmonic equivalents in under 10 seconds," explaining the circle of fifths and axis extremely efficiently, but i had never posted on youtube before so never got around to it. It really bugged me that it was such a simple concept and there were all these really daunting 20 minite videos that explained it but not simply. But this video here will certainly do for those young and interested!
I don’t necessarily here major as happy or minor as sad anymore, it’s all about context. I used to before I became the musician I am today but I like to think of harmony in terms of brightness/color now. But yeah totally agree with what you say here!
It’s also negative because the fifths follow from the overtones of the root, whereas the fourth is reciprocal; it contains the root as an overtone but the root does not contain it. Fourths are cool that way. So in the cadence Collier plays, it’s a full reciprocal cadence, which is a whole other beast. Harmonic Experience by W.A. Mathieu really does this concept (and way more) justice. Love your videos btw, keep on keeping on! ❤
From popping up in my recommendations for weeks with some weird short clips, you finally got my subscription sir, keep it up
it took weeks to subscribe?!?
I enjoyed this. I think you should make more explanatory videos like this instead of just exclusively educational transcriptions. Also, it's pretty cool to hear your voice.
not my voice unfortunately
Until proven otherwise, I'm sticking to my hunch that you and Jacob Collier are one and the same 😂😂
This is like acoustic quantum physics. I love it
are you certain?
@@peaelle42 I’m certain it’s uncertain.
in that case, it must be certain as well.
Nah, that would be microtonality
Things analogous to "negative harmony" have surely existed at least since the late 19th century; there is little we don't know about how to use harmony in 12-TET, whether it be in the most consonant or atonal registers.
@@commentingchannel9776 the aspect I was drawing an analogy to was that of an inverse quantum operator in the quantum harmonic oscillator problem. But sure, belittle my comment that I appreciated art in a subjective manner…
1:30 - Each chord is spelt from the bottom up or the top down of the triad. The triad is important because it is composed of the root (identity / first overtone), the third (tonal color / fourth overtone), and fifth (dominant / second overtone). The root provides key, while the fifth provides an authentic cadence - a resolution from the first unfinished partial. The third can be reversed between major and minor through inverting the spelling, which is what negative harmony asks for.
I (major tonic) upside down changes from one major third and perfect fifth upward to one major third and perfect fifth downward.
V7 (the dominant chord) upside down changes from one major third and minor seventh built upward from the fifth to one major third and minor seventh built downward from the tonic’s root, forming an ii°7 or iv6.
Plagal chords are formed below the tonic, because acoustically a fourth is utonal or “undertonal” and is a reversal of a fifth (otonal/overtonal). Undertones are simply inversions of overtones. Instead of the harmonic arising from integer multiples of the fundamental frequency, it arises from integer multiples of the FF’s inverse, the wavelength.
The first five overtones are at the octave, perfect fifth, major third, harmonic seventh, and major ninth (ignoring duplicates), while the first five undertones are at the octave below, perfect fifth below, major third below, harmonic seventh below, and major ninth below… which when inverted into upward intervals (the way sounds are heard), creates the octave, perfect fourth, minor sixth, septimal major second, and minor seventh.
Indeed these two series together form a 7/9 chord on the tonic and a m6 chord on the subdominant. Further extension of both series reveals a partial at another quintal degree, the augmented fourth which inverts to the diminished fifth, and the augmented fifth, which inverts to the diminished fourth. The scale most adjacent up to the augmented fourth partial is the Lydian dominant scale, and down to the diminished fifth the Dorian b2 scale.
Those scales are notable by the way as the LD scale is a sort of integration of the major dominant (Mixolydian) with the major subdominant (Lydian), and Dorian b2 is LD’s relative minor scale, built in thirds directly below. Dorian b2 integrates minor subdominant (Dorian) harmony with minor dominant (Phrygian) harmony. Indeed this makes them negatives of each other. Lydian & Phrygian, and Mixolydian & Dorian, also each form negative pairs respectively. Adding in the augmented fifth and diminished fourth though creates scales akin to the Lydian augmented and Locrian modes, which supports them as negatives of each other too. Locrian doesn’t have a negative in its parent scale, as it lacks a perfect fifth. Likewise with Lydian augmented. One can be thought of as a more unstable version of Aeolian b5, and the other as a more unstable version of Ionian #4, also known as Lydian. Both can be thought of as hyperextensions of the major and minor tonalities, resulting in dissonance where brightness or darkness is no longer tenably created. This to me also corresponds with my understanding of the diminished triad as negative to the augmented triad. The diminished seventh chord probably negates to a +7 chord, which can be formed through the whole tone scale. That the diminished seventh and minor seventh are enharmonic to the major sixth and augmented sixth probably helps my claim too.
Going back to the diagram… IV as major is more of a Western sound, as other cultures tend to use the b6 more than in Western music, as well as the b2 as opposed to the leading seventh and augmented fourth. In juxtaposition with the leading seventh, the b6 creates a sublime sense of tonal urgency which is compatible with a minor tonic (harmonic minor) as much as with a major tonic (harmonic major). It does however correspond well with the major pentatonic scale, which is extremely instinctive in its construction (most will default to singing in it).
The IVmaj7 and v7 chords as well as the Imaj9 and i7(b13) chords form negative pairs… indeed the first two arise as sort of neutralizations of the more harmonically potent iv6 and V7, while the last two form sounds essential to the Ionian and Aeolian modes. ii6/7 and bVII6/7 match well as one works as Dorian b2 (minor supertonic) and the other as Lydian dominant (major subtonic). Indeed these two are essential to the melodic minor (Ionian b3) and melodic major (Aeolian dominant) modes respectively.
The bIII is opposite to the vi for fairly easy to grasp reasons, as the bIII is relative major of the tonic, while the vi is relative minor of the tonic. This is contextual though, namely it only works in an Ionian-Aeolian context. In fact all of the chords listed at the timestamp do. Dorian has a øvi, but the negative of Dorian is Mixolydian. Dorian, like melodic major, is a symmetric scale though - which also makes it a true androgyne between major and minor - and thus negative harmony can be a bit unwieldy or paradoxical for it, as the reversal of its notes from the tonic root on is itself. It’s perhaps best to look at negative harmony as perspective rather than law… but it does have its axioms. The negative of a bIII+ (as found in Ionian b3) is likely a vi° (as found in Dorian)… but what is the negative of a viø9, as found in Ionian b3? Well I guess since a viø9 is just a m6maj7 chord in inversion, it would have to be the I7b13. Likewise then, the viø7 in Dorian, being an inversion of i6, translates to a negative of I7 inverted, which is simply bVII#11. This does in fact correspond with Dorian and Mixolydian as negatives. And indeed modally they resolve downward to I and upward to vi respectively. The tonicizations of them resolve to each other though, one downward to V and the other upward to i: melodic minor (Ionian b3) resolves down to melodic major (Aeolian dominant/Mixolydian b6), which in turn resolves back up to melodic minor. And adding further harmonic weight by adding a b6 or a #7 creates harmonic minor and harmonic major, which are separate scales that are negatives of each other: melodic minor with a b6 is harmonic minor; melodic major with a #7 is harmonic major.
This is interesting, but also incredibly lengthy
@@tsg_frank5829 Fair point lol
@@gillianomotoso328 Are you able to sit at the piano and come up with interesting harmonies and chord progressions based on your theory knowledge? I'd like some examples of a good chord progression or harmony.
Wow!
This makes a lot more sense now, thanks
A few weeks ago I attended a masterclass with Steve Coleman in Italy, Modena, and on the second day he starts talking about negative harmony. It was interesting because his weird way to explain it (I only happen to understand something about it after watching this 4 minutes video that made me understand much more than that 2 days-jazz masterclass) was by flipping the chord construction on the piano. E.g: he was builiding a normal chord (let's say G7) with stack 3rd intervals from left to right (so G B D F) and then constructing the equivalent negative chord by calculating the exact same intervals starting from the tonic but this time calculating them from right to left (in this case it would be, from right to left, G Eb C A), resulting infact in a C-6 inversion. This is really weird to me, not only because it contrast what I just saw on this video, but also because this way of visualizing it on the piano inverting the chords wasn't even mentioned in the video. @Georgecollier I would like to know your opinion about this
I like that way of explaining it intervallically. It's interesting though, you're right, the mechanisms of that would almost always cause an inversion in the resulting chord
You’ve earned a subscriber from this. You’ve explained these things so well
I worked out the missing III chord you omitted from 01:27 and it seems like the III chord doesn't follow the same rules of 'extensions' (minor seventh to major sixth, and major seventh to minor sixth)
When 'reversed', the usual diatonic minor III chord will turn flat VI major chord. So a simple E minor will turn into A flat major chord. Don't get me wrong, that's 🌶️. But if you add another seventh interval to the III minor chord, it will turn into a IV minor 7 (minor seventh chord), so an Em7 chord will become Fm7, disregarding the 'extensions' rule.
That naughty III chord is so badass 😎
Does it not just become a bVI6? (Ab6 in C)
That still fits into that rule, it's just that Fm7 and Ab6 are the same set of notes.
Two things. The whole labeling of chord tones and chords in the diatonic system is based a mirror relationship to the tonic. In other words, the subdominant is the dominant underneath the tonic, the subtonic is a step below the tonic, and so on. And secondly, this seems as another source of substitute chords, as an occasional interesting diversion. PS This may be just another labeling for things we already know. The F-6 chord is so close to the tritone substitution for G7, Db7.
Man this amazing. I hope to see more like this from you
Thanks for this video, it helps me understand music :D finally xd
Another thing that’s very important, resolution in negative harmony doesn’t only flip the dominant chord, but also the tonic if equal tension is to be preserved. ivm6 resolving to a Imaj is strong, but in the same way of a V7 resolving to a im. There is strength, but none of the tritone collapsing to a major third that is so prominent in a V7 to Imaj. To preserve this, you can flip both chords into their negative equivalents, making it a ivm6 into a im, with the tritone between the minor third and major sixth resolving to the major third between the minor third and perfect fifth. This is a small change, but still an important one to mention, as in the key of C major, Fmi6 may be the negative equivalent of G7 but it’s resolution is not exactly of equal strength.
Great video!! Please keep making more videos like this
Thats is an interesting theory!
It’s interesting how the minor 6 shows up here, it’s an integral chord in the Barry Harris system too which thinks of harmony in a very different but sensible way in comparison to what’s actually taught everywhere.
Great video! Love these videos
Thank you so much!!!
As an amusic, the G7 and Fm6 at 3:47 were EXACTLY the same.
I haven't asked for it but I'm really proud that I've seen it!
I dont think ivm6 is inherently timid or gentle, nor V7 inherently triumphant or loud.
A ivm6 in barbershop is often very triumphant and loud, just for one example.
I think it’s the tendency. One tends to carry this sensation on its own, while the other tends to carry an opposite one. A V7 tends to have a bright intensity and urgency to it, while an iv6 tends to carry a solemn flow. Both have that tritone in them though, which begs the resolution.
@@gillianomotoso328 i think that speaks more to how these chords get used rather than their inherent properties. Like how certain words come in and out of popular vernacular.
@@keysradiotheradio But don’t you think there’s a cause for why people pick these vibrations to elicit what they wish to elicit? These are vibrations, not just words… I think there’s a difference between simple ligatures that are somewhat arbitrary in how they appear and physical ratios between rates of vibration
@@keysradiotheradio I have to believe there’s some underlying inherency to music… as much as we can recontextualize it, there’s something clearly universal about it to me.
@@gillianomotoso328 I agree that music is a universal language, but I don't agree with the broad generalizations made about the qualities of V7/iv6 chords. A V7 written by Beethoven does not have the same inherent non-theoretical properties as one written by Ellington, for example.
Another example - the word "sick" can be used to describe something positive in current vernacular
I like it when the music plays
Thanks for explanation! Very nice!!!
This is quadruple the time promised in the title
Love all your videos. Great work.
Finally understand how to find the negative harmony, thank u
Thank you
2:17 plays five major chords with additional steps and then proceeds to play an absolute mess of notes without any readable melodical message.
«Don't you think it's cool?»
Well, I probably don't.
Thanks for the content
Interesting AF
"1 minute music theory" "4 minutes" LIAR
I want to learn more about music, and this is helping me
I enjoyed the video, but found the audio for the chords a little low. They sound like they are an octave or more below the notes shown (or maybe just doubled down an octave). The tightly clustered notes in the lower register sound muddled and unclear. Playing just the notes shown (with perhaps just the root doubled down an octave) would make it a lot easier to hear the harmonic effects you are talking about.
Definitely. I would love to hear more open, spread out chords
Rick Beato : I have best Old musicians.
12 Tone music : We have Jacob collier.
All major/minor triad possibilities should be covered but make sure to remember symmetric property (i.e. if looking for VI remember to read right to left as well)
Major and Minor Scales Diatonic Triads
I = i
ii = bVII
iii = bVI
IV = v
V = iv
vi = bIII
vii* = ii*
Nondiatonic Triads
bII = vii
bii = VII
II = bvii
biii = VI
III = bvi
#IV = #iv
#iv = #IV
I play on a Striso (midi controller/synth using the DCompose isomorphic layout) created by @pierstitusvandertorren7068 . If I set the pivot point between the I and V, (just above and to the right of the C for the key of C), and turn my board upside down, and pivot my starting note or chord around the pivot point, I then play the exact same physical patterns and get the negative. This is awesome!
As an experiment, I played Leaves on the Vine (the song Uncle Iroh sings for his son). and it feels so different, yet has similar tension and release (though ending with notes going up, which feels unresolved, like it's asking a question).
some quality content
Note that a prerequisite for this video is an understanding of right-side-up functional harmony.
appreciate the explanation!
This is the first time I’ve heard you talk.
0:21 drops of Jupiter
I have no experience with music this video felt like I’m taking math, science, and english classes all at once.
This is brilliant!
cool!, every body must read Palindromes 1 and 2 From "The book of movements " colection
The iv6 is actually a iim7b5 in 1st inversion, thus the tension.
FINALLY SOMEONE GOT IT RIGHT! A common misconception is to translate chords and read them in the same way Cmaj7-GEbCAb and people read it as an Abmaj7 and the progression just stays the same but in Ab and so on....PRO TIP: reduce all chords to BASIC TRIADS and only add 7ths and extensions AFTER negativefying them, and pay attention aka have an asthetic oriented ear for it, as in: treat it like art and not math. Imaj7 becomes a Im6 or Im(b13) and it sucks, but is the Imaj7 a point of release? Then consider it a I6 chord, more stable version of the same major I degree chord, and translates directly to Im7, a more stable minor chord. BUT for example V7: G7 -> G triad GBD : CAbF -> IVm Fm. If we took G7 GBDF-> CAbFD Dm7b5 and we lost functions. But V7 is a tension,, add the F last after the triad, becomes a D, the natureal 6 of the IVm6. The same way we can use a V7 or a V6, we can change them to IVm6 or IVm7 :D Reason is we swap the 1 and 5 degrees by the axis, adding a note after altering the 5-1 degree changes the whole reason of the axis
What?
Just flip the notes (C major for example) around a "center" "between" E and Eb. So each E in original melody becomes Eb in negative harmony and vice versa. D changes places with F, C# with F# and so on. That's it!
Damn. That's a good video
well done
Terrific !!
Weird, but I heard so many progressions like these when I listened to my parents hippy music. Wonderful and kid of exiting stuff for sure, but not really new to me though and I think not new for the average contemporary music composer too.
0:29 not emotions, but sensations 1:12 it is not "become" it is a relation. The relation is not explained. At the end it is said it is a theory ; if it is a theory it is not a technique. But a condition. The video speaks about a technique. Resume: a clickbaity trend
I'm not sure I agree with the idea that each chord has a counterpart which carries the opposite emotion, because to me, chords do not by themselves necessarily evoke one particular emotion. Instead, much like how everything else in the universe seems to work, it is all contextual. A minor chord can evoke a positive emotion when played after certain chords, for example. An ugly puke green colour can look absolutely gorgeous when the colours around it are complementary. An angry person might be angry because of the situation, yet only those who witnessed the initial state of the person will realize this. Anyway, just wanted to comment because I'm bored. Haha.
you are right. DOn´t follow fake uncertified music theorists without questioning 10 times
Do the key change part next
Thanks for the video. 3:06 Chord Bbm. It is very interesting. If You flip notes in 1:16 "B" "Gb" becomes "Db" And it is not in the scale. But here it is in Bbm in 3:06. it is not correspond with rotation around C|G Db/Gb axis. Where is the catch?
This was in fact not 1 minute but still good
good video !
Title: 1 Minute Music Theory
Video: 4.5 minutes long
hmmmmmmm
nice
In that "Tension" sheet music at 1:50, you write G F# G followed by a G# and a G natural. Since we are in C, I'm wondering what the theoretical reasoning is behind viewing that as a #5 rather than a b6? To my ears, it really has a b6 feel to it in this context, especially with the G natural being on both sides of it. What makes it a #5 rather than a b6 here?
I'm guessing the convention is to combine sharps and flats as little as possible. Since he just used a sharp, then he should continue to use sharps unless it becomes absolutely necessary to use a flat.
Also, I get why you would think he should use a flat, to preserve the distinction in lettering as much as possible like we do with all scales, but following that logic, it would imply that the scale he's using contains F#, G, and Ab, which is unlikely to be his intention. It makes sense to allow for the most equal dispersion of same-lettered notes as possible across the twelve tones. So if there's F#, that implies that there's two notes named F; therefore, there should be two notes named G if one of them is a black note, which is the case.
Funny words, magic man.
Great video!
So does it mean, that Thom Yorke used negative harmony in No surprises?
I mean, it goes D - Gm6 - D
And as I understand Gm6 is a negative A7
It actually goes F - Bbm6/7 :) The bridge goes C - Bbm6/7 and then Gm7 - Bbm6/7. I think he used a harmonic major backdrop for the song (Aeolian with a major seventh chord as tonic), and in that maybe there was an understanding of reversing the polarity of the harmony. The strictest reversal of it would be Fm - C9, then Bbm - C7, followed by Eb6 - C9. I almost would say this doesn’t help much, because harmonic minor and harmonic major are negatives of each other that happen to be very similar, but C9 is actually found in melodic minor, not harmonic minor. Recognizing that Ionian and Aeolian are negatives helps too. You’ll notice that the b7 of the key is played up until the bridge. This is a borrowing from natural minor into major. The major dominant (C7) in the bridge is the slightest burst of joy that is negative to the Bb6/7. Likewise that Gm7 introduces a moment of that major sixth in Ionian, but it is eclipsed again by the sink of the Bb6/7.
@@gillianomotoso328 Thanks a lot for explaining!
It turned out to be way more complicated :)
@@massacomqueijo2023 Hehe, I think it definitely is by default. It helps to remember that in negative harmony, the intervals and scales are spelt in reverse *from the top of the triad* … This means that the negative of each mode follows this sequence:
Ionian Aeolian
Dorian Mixolydian
Phrygian Lydian
Locrian Lydian Augmented
(Locrian is a flat darker than Phrygian and Lydian Aug is a sharp brighter than Lydian)
Melodic minor Melodic major (Mixolydian b6)
Lydian dominant Dorian b2
Aeolian diminished Ionian augmented
Harmonic major Harmonic minor
Lydian minor Phrygian dominant
And triads, tetrads, and pentads follow this:
M m
Maj7 mb13
(see Ionian & Aeolian)
7 mM6
mM7 majb13
(see harmonic minor & major)
+ (aug) ° (dim) or + +
(see Lydian & Ionian augmented)
° + or ° 7 w/o 3rd
(because a diminished chord is an inversion of a mM6 chord without its 5th)
m7b5 7 in 1st inv.
dim7 dim7 or dim7 +M7
9 mM6/7 (see mel. major & minor)
7b9 mM7#11 (see Lyd. minor & Phryg. Dom)
M9 m9 (see Ionian & Aeolian)
mM9 7b13
7#11 mM6b9
Negative times negative = positive
If we were in C Major in the video, does this mean that the seperation line would go to the right of - say - G in G Major?
The more I learn about this, the more I think "There's no there, there!"
There are perfectly normal tonal explanations for why these substitutions sometimes work.
For example, iv-6 might substitute for V7 because iv-6 is a subdominant suspension over the tonic and three of the four notes in iv-6 are contained in V7b9.
bVII6 might substitute for ii-7 because they are both approaching the tonic by a whole step, one from above and one from below. Similarly, bIII and vi- are both a third from the tonic.
Now THAT is sort of what you're talking about, the symmetrical relationship. Honestly though, the visual representation of the circle of fifths with the line down the middle of it is just confusing me. Mind you it isn't confusing me as much as Jacob's explanation which really makes no sense at all.
I don’t understand any of this. Im a rapper looking to improve my music so all I can feel is how beautiful the sounds are. I want to understand so bad
watch Rick Beato for some music theory
@@konroh2 thanks man. Cause I’m still confused
@@suncworm Sit at the piano and understand triads. C,E,G, then C,F,A (the IV chord inverted). All comes together.
I like this video :)
I'm trying to do sometime similar on guitar currently.
So you said the tonic stays the same, but earlier in the vid with the axis, it shows that the tonic is converted to the fifth
00:40 - 01:15 - About as clear as mud. One other thing: First you said 2 notes together is "harmony." Then later you said that "movement" is harmony. ---- What is it I've missed?
If such a thing as negative harmony even exists other than s a dubious concept, what does it matter? It sounds like the difference between major in minor. Why do we have to rename it something else?
I don't understand. You said that a major chord's negative counterpart is a minor chord, so D major's counterpart should be D minor. But when I use that conversion chart, the opposite of D is F, the opposite of F# is C#, and the opposite of A is B flat. What am I missing?
Axis Theory and Negative Harmony are excellent tools but are based on the the Circle of 5ths and Functional Harmony which both assume that 12TET or JI is correct and that the perfect cadence (the 5th to tonic, as opposed to the 4th's plagal cadence) is the ultimate cadence in music.
Would you need to rotate the circle of 5ths around the key center in order for the translated relationships to be truly negative to that key?
For example if F was the key centre the harmonic axis would lie between F and C so the visual would rotate around by 1 and the new pairs could be seen.
@@GeorgeCollier thanks GC
so does the axis go between the tonic and the dominant or just through the tonic??? this video is so confusing because the clip with jacob collier contradicts your diagram
good vid :)
Why negation axe is placed between C and G ?
I thought that drops of jupiter started playing after the first chord was played..
A plagal cadence is timid and gentle? Not only do I disagree that a plagal cadence is inherently timid/gentle (cf Bach BWV 565) but I also disagree that authentic cadences aren’t gentle (cf Goldberg aria). I frequently find plagal cadences to be extremely powerful, even stern. You run into trouble when you try to mandate emotional responses to given artistic phenomena. Sometimes you can paint with a broad brush (ie, fast = exciting), but not here. This is too broad, there are too many counter examples, it’s too subjective to have any explanatory power.
User name checks out
Yes, I agree!
Well, I think a Bbm-Fm6-C progression is generally timid and gentle, but a Bb-F-C progression isnt. Of course it always depends on context, but that's what I hear in a vacuum
It’s descriptive not prescriptive.
You can do other things play around with dynamics etc to make it not timid and gentle but on its own at regular volumes this is indeed the sense that most people get.
Well sounds dont mean the same for everyone, thats why we all understand music but in a unique way. We can relate but never from the same perspective.
btw: I tried clicking the link for the Qwest Masterclass, but it links to youtube studio and looks like an edit page for the video (for your channel, I just get a broken link "Oops, something went wrong.")
Does anybody know what is playing on the background?
Wouldn’t C major reflect to C minor? So if we reflected E7 A7 D7 G7 C around the axis it would be Fø7 Cø7 Gø7 Dø7 Cm (Or A♭m6 E♭m6 B♭m6 Fm6 Cm) instead of Fø7 Cø7 Gø7 Dø7 C. Jacob didn’t mention anything about flipping the final chord in his interview with June Lee so I was kind of confused like maybe he forgot to or something. Of course Dø7 resolving to Cmaj is the inverse of G7 resolving to Cm, but G7 C still inverts to Dø7 Cm. It kinda bugged my OCD but maybe you could help explain why he didn’t invert Cmaj to Cm.
I think he did.
Hi, i have a question
If you want to reflect something that's in a minor key(e.g. Cm), do you reflect it according to it's relative major (Eb) or the tonal centre (i.e. C)?
I'd suggest fucking around and finding out😂
Can u do a Dm line cliche flipped?
Wouldn't negative harmony be forgetting it,?
what is that melody at 1:46 !! i hear it everywhere but ive never found what it's from please resolve my curse
It's from an old song called "Shave and a haircut, two bits." But it's really just a classic jazz progression that was probably around a lot earlier than that.
FINALLY CLICKED
what about non diatonic chords?
say Bb7#11 in key of C
how would the dominant/tonic relationship work if notes are out with it
Gillian Omotoso? Ask him.
Interesting, are we talking Hz here? Like 432Hz, was the norm until the 1940s. Now we know, hopefully that 440Hz, is not good.
F* that. You will hear what your heart wants to hear at the time.
Who taught u 2-5-1 with major chord on 2nd degree?
What music is being played in the background?
what is/are the piece(s) in the background?
I dont ageee with the emotions part