The Positive Impact Of Negative Harmony
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- Опубліковано 2 чер 2024
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Remember negative harmony? Jacob Collier mentioned it at one point a couple years ago and the whole music world went nuts. Whatever happened to that? Anyway, now that the dust has settled a bit, I figure it's time to take a closer look at the theory and see what it actually has to tell us. And it turns out? There's something pretty cool at the heart of it.
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Also, thanks to Jareth Arnold for proofreading the script to make sure this all makes sense hopefully!
Some additional thoughts/corrections:
1) As always, I make no claim to have discovered any of this. Levy, Coleman, and Collier all alluded to the note-function thing in one way or another. in fact, Coleman's initial conception was melodic, not harmonic, so individual notes are an especially important part of his version. I haven't seen any of them explicitly lay out the concept of function pairs, at least not in a formalized way, but it's a relevant, extant part of all their work. The names are mine, but I'm just shining a light on the idea, not claiming ownership.
2) When I say the system isn't well-defined, I just mean that it doesn't really exist much in the literature. In addition to the lack of a wikipedia page, Google Scholar turns up basically no relevant results. That doesn't mean it's not useful or valid: It just means it's still in the process of formalization.
3) One of my favorite results of this system is the fact that Imi7 inverts to Ima6, not Ima7. This matches most harmonizers' intuitions: The Ima7 chord is good at the start of a progression, to create motion, but it's not good at creating _rest_, because the major 7th interval is too dissonant, so while in minor it's not uncommon to end on the Imi7 chord, in major if you want to resolve to I but you don't want to drop down to just a triad, it's much more common to add the major 6th instead. (In fact, Ima6 _is_ a voicing of Imi7 borrowed from the relative minor.)
4) The specific chord observations I made at the end are not, in and of themselves, groundbreaking. There's some more interesting results, but I wanted to focus on the obvious ones to demonstrate the premise of the model. Feel free to experiment with it yourself and see if you can't find anything more interesting.
5) Some people are objecting to the claim that the undertone series doesn't exist in nature, so let me clarify that a bit: When you play a note on a normal instrument, you produce overtones, but not undertones. There are ways to contrive the undertone series in specific experimental set-ups, but it is not a noteworthy part of the sounds we're most used to hearing. You can synthesize the undertone series through mechanical means, which means that to an extent it does exist, but being able to produce a thing under controlled experimental conditions is not the same as that thing existing in nature, and when we're talking about what human beings are used to, that distinction is incredibly important.
I think you got a little messed up there with your numbering...
this is the clearest explanation of negative harmony I've seen, thanks so much
I would disagree about your second point. Jazz composers tend to favor a i minor 6/9 chord as a an ending chord over i mi7 chord. I also think the dissonance of I maj7 is over rated it's pretty common, even if I maj6 gets a lot of use too.
The undertone series does actually exist in nature, Adam Neely made a video about it.
Didn't Adam show the undertone series in one of his older videos, where he takes a tuning fork and makes it ring against a piece of paper?
Harmonyn’t
lol smart :D
Those pairs of notes are really interesting. "Leading tone" and "root" are terms you hear often in terms of functions of notes, but the other ten are less talked-about, certainly not in this sort of orderly categorization.
The "uncanny notes" also explain why, to my ear, of the modes of the major scale, Lydian and Phrygian (and Locrian, of course) sound the most unusual/interesting, since their characteristic notes when compared to normal major/minor are the flat 2 and sharp 4 (and flat 5, for Locrian), which are these uncanny "alien" notes, while the raised (natural) 6 and flat 7 in Dorian and Mixolydian are the hollow notes, which sound less jarring and thus less unusual.
Maybë it's also a possible explanation of why a lot of people seem to think of Dorian and Mixolydian as more mysterious or inscrutable, since the normal leading tones of Ionian and Æolian are switched out for hollow notes
It's just that all other modes are "between" major / minor. But Lydian is "bright then major" and Phrygian or Locrian are "darker then minor". They are all somehow less common and even when used they create a very unique feeling, usually less stable.
Wow - I never thought of b6 as a leading tone, but if it leads to 5... it makes so much sense.
Yeah, that's how I view the minor plagal cadence. In fact iv-I is the negative version of... V-I!
Because it is a tension tone.b6 makes up a tritone with the 2 so it has tension.Just like 7th in a major scale that makes up a tritone with the Fourth.
Makes me think of IV-iv-I. Also possibly bII-V-I.
(Not sure how to think of bVI-bVII-I in terms of this, or i-bVI-bIII-bVII)
@@SillyMakesVids Negative version of V-i, not V-I
therefore lydian’s #4 is also a leading tone
The undertone series does exist in nature! You can create undertones by gently dangling a piece of paper and a tuning fork next to one another so that they touch, allowing the paper to vibrate in frequency with the tuning fork, but so that the paper misses every second, third, fourth (or so on) vibration. I haven't explained it well, but there are videos on youtube demonstrating this.
The undertone series can be constructed mechanically if you're clever enough about it (I talked about that a bit back in my Harmonic Dualism) video, but I think that's extremely different from the overtone series, which is almost impossible to avoid. Almost every non-digital note source creates overtones as a matter of course, whereas undertones require specific experimentation set-ups that don't occur naturally.
Also thought about this immediately. Great that you are also aware of this!
Still, 12tone has a good point.
@@12tone Maybe our brains construct the undertone series in some kind of gestalt-ish way, but I am not sure I am buying it, especially as a basis for minor chords. For me it seems more plausible that I hear the minor third in a minor chord almost like a sonic metaphor for a messed-up 5th harmonic. If the 5th harmonic is essentially Major third in almost every circumstance in which I've heard a harmonic series in nature since having been born (often, to say the least), then perhaps using a major 3rd in a chord suggests reality as it is, if not enhanced, and perhaps the flattened-third screams "not reality, this is messed up!" to our brains. These ideas are mostly from this paper I found a while ago, and I would love to know your thoughts on it: arxiv.org/html/1202.4212v1
You heard this from adam neely, didn't u?
YES! I’ve been waiting for this video forever! Awesome analysis. Now Excuse me while I go listen to Smashmouth in negative harmony.
i'm surprised to see you here
ua-cam.com/video/jAT5rNkmGWg/v-deo.html&ab_channel=SteveCruickshank
Well done. A lot more illustrative than the simple mechanics of negative harmony.
Thanks for this! 😍
DON’T be afraid to create a video because someone else already covered the topic. I’m subscribed to *_your_* content and have never heard of the other guy, so without you I would have never heard of negative harmony :)
Thank you for the video
Of course, one day the physical requirements of UA-cam's storage capacity may become unsustainable, so they'll need to fight it out to see which video gets to stay!
I REALLY like your note functions. They're the best way of explaining chords and their relationships that I have seen so far. When I started learning music I noticed pretty early that chords and melodies work based on the relationship between their notes, but I didn't have a framework to work with until now, and it seems like this one is a easy to work with tool, but also very powerful.
I feel like this would be able to consistently and accurately explain both functional and non functional harmony. Though, I'm not very experienced with music theory. I think it's worth exploring further.
I think something worth mentioning is that when you invert a chord with upper extensions, it can be thought of as inverting the triad and the extensions separately. When inverting a V7 chord, the V triad becomes a iv chord, and the seventh of the V chord becomes the sixth of the new iv chord. This way the perfect/plagal duality is still consistent, and a tonic m7 still inverts to a tonic M6.
we can also think of a iv6 chord as a iim7b5 chord in first inversion resolving down to i.
@@Bronze_Age_Sea_Person yeah, first inversion is good since the jump from the 4th degree to 1st degree is so strong (as 5-1 jump). If we play ii(m7b5) instead, the bass walks down from 2 to 1.
I wish this had come out before your IIIm video, because then you could've explained that IIIm maybe doesn't sound quite tonic or dominant because it has a leading tone but isn't unstable enough to be a decent departure from the I
Also hey, an explanation for the minor plagal cadence
I don't know anything about music, and it doesn't help that the only things I know about it are from the other way of naming the keys (Do, Re, Mi, Fa, Sol, La, Si) and some of the vocabulary is a bit strange for me, but that doesn't stop me from trying to grasp the concept you're trying to explain and I did keep up with your comments all the way through.
I'm a writer, so I'm well versed on that topic, but music has always been a huge component of my art, so I'm really glad you make this rather 'silly' drawings for concepts so intriguing.
Plus, now I got the inspiration for two new characters for my book extrapolating the properties of two of the pairs that you mentioned so, thanks.
Weird, but intriguing. I love your take on this, especially in chord qualities. I've always wondered how certain chords resolve to certain others.
Dude. One of the best videos you’ve made. Love that I subbed to you. Keep up the awesome work man!
This blew my mind multiple times over. Well done.
Wow! That's your best video so far. Very interesting!!
I feel like the function pairs could also useful for analyzing scales. Just a couple observations:
Locrian is missing a stable note, one of its unstable notes is uncanny, it has no modal/hollow tritone, and it has no leading notes.
Harmonic Major has two leading notes. Double Harmonic has two leading tones and no hollow notes.
Of the seven modes of Major, only Dorian and Mixolydian have a modal/hollow tritone. They also lack leading notes.
Lydian, Phrygian and Locrian don't have unstable notes.
Lydian and Major have leading notes that pull up, while Minor and Phrygian have leading notes that pull down.
You have such an awesome channel. I enjoy and learn so much. What I really want you to know though. The GUMMY BEARS at the end of each of your videos, is absolute pure genius and I watch just for the gummy toss. It shows compassion, humor, intimacy, and a lot of the Character of your channel. Keep up the great work!
So glad you did this! I missed out a lot of the negative harmony hype just from being busy with work and school and now I hear everybody talking about it without the time to research it 😭
But you’re videos clarify so much
Damn dude, what an excellent video. I love the list you've created. It will be so handy when composing. Thank you so much, keep up the great work!
0:27 see, now you get it
But seriously, UA-cam videos are usually where I go when I want to learn any music theory, including your channel. Maybe people in the music community were talking about it, I just heard all star in negative harmony and thought that was cool.
It's incredible how you broke into negative harmony and found a gold nugget such as this.
This was a really excellent explanation, thank you so much!
8:00 Oh my god. This is literally how I organise each note in my head with regards to function, and i've always treated them as interchangeable. Now i'm being shown that they are literally interchangeable, and it feels like i've unlocked something. I dont know what it is, but it's something XD
Thank you 12tone, Very Cool !
Whoa... I love that system of grouping notes you show at the end!
A menu of notes- I like such menus. I came up with a mental ‘menu’ when I started playing at blues jams; it was specific to the genre and better developed for major blues. This adds several things to that idea. Good work!
Here's a quick way to calculate the negative harmonization of any major or minor triad if you know your modes:
Let's say you have a chord that's built off of the nth member of the lydian scale. If it's sharp, make it flat, and vise versa. If it's minor, then make it major and vise versa. The negative chord will be built off of the 9 minus nth member of the locrian scale.
For example, let's say you want to negative harmonize the major chord built off of the flat 3rd of the lydian scale. Make it minor (because our input is major), make it flat (because our input is sharp), and build it off the 9 minus 3 = 6th member of Locrian. You wind up with sharp 6 minor (of locrian), or in standard roman numeral notation, bIII -> vii. You can do the same thing from locrian to lydian too. This works for all 24 basic major and minor chords. Have fun!
That was AWESOME! Thank you for expanding our musical landscape! I know that you didn't invent anything but you contribute with a new approach that's really exciting!
I love this channel!
0:43 I've just created the Wikipedia page for Negative Harmony by making a redirection to the page on Riemannian theory since I don't see the difference between negative harmony and the harmonic dualism described by Hugo Riemann. (See en.wikipedia.org/w/index.php?title=Negative_harmony&redirect=no )
Below is the list of diatonic chords' negative harmony inversion written in Sposobin's harmonic function notation:
T -- t
SⅡ -- dⅦ
DTⅢ -- tsⅥ
S -- d
D -- s
TSⅥ -- dtⅢ
DⅦ -- sⅡ
All the major dominant functioning chords (chords with capital D) are inverted to minor subdominant functioning chords (chords with lower case s). All the major subdominant functioning chords (chords with capital S) are inverted to minor dominant functioning chords (chords with lower case d). All the major tonic functioning chords (chords with capital T) are inverted to minor tonic functioning chords (chords with lower case t).
This explains why the D to S progression is considered as harmonic functional regression/retrogression and is advised to be avoided or used with caution, whereas the d to s progression is not (since it is just the negative harmony of the S to D progression).
(By the way, Sposobin's harmonic function theory was developed from Hugo Riemannian theory of harmonic function. It is still being used and taught in Russia, Belgium, China, and perhaps some other countries to this day).
Below is a list of negative harmony pairs of scales and modes:
Natural Major -- Natural minor
Harmonic Major -- Harmonic minor
Melodic Major -- Melodic minor
Lydian -- Phrygian
Mixolydian -- Dorian
(Locrian mode does not have a negative harmony pair since the fifth degree is lowered which means the first degree needs to be raised in the negative harmony pair)
Do Pentatonic -- La pentatonic
Re Pentatonic -- Sol pentatonic
(Mi pentatonic does not have a negative harmony pair due to the lack of the fifth degree)
Also, I argue that all the non triadic notes in a chord (i.e. notes that are not the root, 3rd, or the 5th of the chord) are considered as extensions. The negative harmony inversion of a extension note is still a extension note, which should note be placed in the bass line. Hence, the D₇ (i.e. V⁷) chord is really just a D (i.e. V) chord with a 7th note (subdominant note / unstable note) extension. The negative harmony inversion of D (i.e. V) is s (i.e.iv). The negative harmony inversion of the subdominant note / unstable note is the supertonic note / unstable note. Hence, the negative harmony inversion of D₇ (i.e. V⁷) is the s (i.e.iv) chord with a sixth extension, which is commonly known as sII₅⁶ (i.e.iiø⁶₅).
Loved how you drew the Tri-force symbol when referencing "three's". LOZ OOT is the single-most greatest gift to humanity since fire
Honestly, you don't need to add anything. Just compiling it all into one place and presenting it coherently is difficult and rewarding enough. Thank you.
After watching the video, this is a fascinating concept and I'll probably be using it as I learn to compose. I like this idea a lot.
I had similar ideas about that subject some days Ago. It's wonderful to think about the function of each note on the scale and its negative version
I'm speechless. Wonderful job.
Amazingly (to me), those note categories you produced at the end are exactly how I think of chords on a guitar when I'm writing songs.
You missed a theorist, although it's understandable if you don't know the terminology. Harry Partch had "otonal" (shorthand for over-tonal) and "utonal" (shorthand for under-tonal) harmonic definitions in his music, which basically amount to the same thing as 'positive' and 'negative' harmony. Partch's book "Genesis Of A Music" is a great read for music theory nerds.
Also of note: all undertonal intervals can be expressed as some overtonal interval, and vice versa. For example, the minor triad happens in the 10-12-15 series of overtones, and the major triad similarly happens in the 10-12-15 series of undertones. Consider any rational triad: you can measure it from the bottom note going up (overtonal) or from the top note going down (undertonal).
Oh, and there is a Wikipedia page: en.wikipedia.org/wiki/Otonality_and_Utonality
I think it's a bit inaccurate to label Partch's work as "negative harmony". His work related to harmonic dualism, for sure, but so did plenty of other people like Hauptmann, Oettingen, and, of course, Riemann. What sets negative harmony apart isn't so much the idea of reflected chords: That's been around for ages. I think the key ideas that make negative harmony its own thing are Levy's gravitational conception and Coleman's movable, non-root axis. Admittedly I've only read portions of Genesis, but to my knowledge neither of those feature prominently in Partch's work, nor are either of them present on the wikipedia page you linked. (Beyond a small section on consonance which vaguely affirms Levy's gravitational model.)
@@12tone Chapter 11: page 188. He talks about how effective the utonal resolution is from 4/3 to 1/1 - effectively, iv6-I with more extensions. Yes, he had a different purpose than others, but IMHO did represent a voice in this idea.
Very interesting, thanks! I'm still not entirely convinced it's the same thing (And it's worth noting that none of the other Negative Harmony people cite Partch as an influence on their models, so if he _was_ working in the same space it appears to be coincidental.) but given how loosely defined the whole thing is I can certainly see how one could argue for his inclusion.
I have recently discovered your channel in my quest to get back into music theory. Its been a decade since I have studied it very intensely so I know I am behind the curve on a lot of things. There are also a lot of newer models for things I am excited to embrace because they make more sense than the ones I learned originally but there are a few things I don't understand that you do a lot. Firstly, I always see you write uppercase roman numerals and then writing minor next to it, but I was taught lower case for minor a diminished and then upper case for major and augmented with the superscript 0 and + added for diminished and augmented respectively. Secondly you and others refer to the six and seven chords of the minor scale as the flat six or flat seven but that terminology I always assumed meant you were making an alteration to the scale degree and in minor those are the natural position of those notes so it seems strange to call them flattened. I guess if you are comparing it to the major key they are flat but why define a chord in one mode based off their relative positions to chords in a another mode? There are a few other things like naming conventions for Sus or numbers less than seven like 6 or 2. It always seemed off to me why you would call something a sus 2 when that just seems like a 9 chord voiced differently, and if you add a 6th, that seems like a 7 chord in first inversion, but then it would be named by the added 6th and not the root of the original chord, and I don't understand how having a sustained pitch that isn't part of the chord would make something a new chord anyway, so sus seems like a odd name for a chord. Maybe I am missing some more fundamentals than I thought and all of this will make sense but I don't know where to start in looking it up.
I do love your videos and feel like I have learned a lot but these little things really confuse me and make me annoyed at myself for not understanding them.
Like, I have to comment again just to emphasize... that system of note groupings at the end is completely genius and maybe one of the most insightful music theory things I’ve seen in a long time!
I find the function pairs idea fascinating. Would this explain why the functional substitutions in Bela Bartok's Infinite Tonality work?
You mean the Axis System? en.wikipedia.org/wiki/Axis_system
@@AbhiBass96 Yes. I wonder if one would find a correlation between these note groupings and axis theory. I. E. Will we find destabilising and leading notes in all of the dominant chords in the axis model?
@@jameskentdeakin Its hard to say, I didn't study Bela's theory to a point where I can use it for composition.
I made an informal paper with a friend on this though.
If I find time I will check and post the result here.
@@jameskentdeakin Yes, please
So this is where I start getting confused by my own experiments. I am a subharmonic singer. I can control the muscles in my throat in such a way to sing the undertone series as you call it. I can start on a high E(E4) then do the magic and produce an E3 then a B2 and so on an so forth. The fundamental E4 is still being sung constantly but you can here each of the undertones and I can control which is loudest in a similar way to overtones.
Paul Rescigno That’s an amazing talent!! It sounds like you could do some pretty creative and intriguing things by doing that. Perhaps learning more about negative harmony could help you improve as a songwriter using your unique skills!
That iv6 chord is in classical music theory just a II° chord borrowed from the parallel minor (hence why it sounds so dark) with an added minor 7th on top. I'm not a particular fan of negative harmony, because all it does is arrive at the same conclusions about harmony that classical theory does, it just does it from a different starting point. It feels redundant. Furthermore, I feel like people aren't giving the II° chord enough credit. In fact, I'd consider it to be THE dominant chord of the natural minor scale. Why borrow the V7 from major, when you can have an in-scale cadence chord?
@@ska4dragons No, I meant that this particular example of negative harmony produces the exact same result as classical theory. That spiel about the borrowed ii° was just me expressing my frustration with people so often forgetting about it, always blindly sticking to their V7.
Great video! well researched and documented. And, as usual, very well explained and argued.
My favorite point is the grouping of notes in pairs regarding their "gravity" and function. Putting together the 7 and the b6 of a tonality as the "leading notes". A concept (b6 being the "upper" leading note) I support completely. b6 is the "Queen note" of "negative harmony" to my understanding
Thank You!
Any chance it's linked to it being the M7 of the relative minor scale?
I don't see it... I refer to notes alone not to chords... the fact that a chord includes a certain note gives its "gravity" and its function in the tonality. So the note b6 can be present in so many chords in both major (as modal interchange) and minor (pure minor and harmonic minor). I refer to the movement b6-to-5 that it's present in cadences such as: IVm-Im and IVm-IMajor (MI), V7b9-Im and also IMajor, etc.
Glad to see this, and glad for that freah take on the theory! Two things I’ve discovered about negative harmony: there’s a simpler workaround for major and minor chords (including any extensions they may have:) if you look at just the root, you can invert about the root of the scale. In C, G is a 5th above, so it’s negative is F a 5th below. Then you invert the quality of the triad and its extensions: major and minor flip to the other. With extensions there’s an added step in addition to changing from minor to major or major to minor: 7ths become 6ths, 9ths become 11ths. This trick falls apart with symetric triads diminished and augmented, but I noticed a pattern a bit harder to describe with the circle of ficths with how those move.
The second thing I noticed is that negative harmony also provides a way of understanding modal mixture as well as opens up other modal options not commonly employed when using modal mixture.
Related to modes, I also noticed the plolarity of modes can be understood as three sets of positive/ negagive pairs and one non-invertable mode: if the intervals of, say, lydian are inverted, you get locrian. In this way, ionian inverts to phrygian, mixolydian to aeolian, and dorian remains itself. I’ve been facinated with how this implies a brightness/ darkness and strength of said brightness and darkness to the modes with dorian being a neutral mode.
Also on the tolic of Jacob Collier: the super ultra hyper mega meta lydian. I haven’t seen him talk about it as a scale, but as just emplying the circle of fifths as a means of broader harmonic color. I found that a scale can represent it: a series of whole tone tetrachords connected by minor seconds, or a lydian scale that jumps to the next lydian a 5th up as you reach that note.
I’ve also thought about other tetrachords and trichords that could produce ascending brightening or darkening modes, but haven’t gotten too far with that yet.
I'd actually prefer to think of the "unstable" tones as the "suspension" tones, since they're used in the sus chords of the tonic before resolving to one of the modal notes. This is all super fascinating! It's a much more robust framework to do things that are usually justified with some combination of hand-waving, voice leading, and modal borrowing.
Funnily enough, "suspended notes" was another name I considered for that pair! I went with "unstable" just 'cause I liked the parallel with the stable ones, but either way works.
8:25 who else had bohemian rhapsody coming to mind immediately with that sequence?
Yes.... Jumped right into the comments
Thank you!!!
b6 as a leading tone makes loads of sense, augmented chords do have a sort of dominant function because of it. Also, the over and undertone series basically say that one chord can be connected to the other via a chromatic secondary dominant one way and a chromatic secondary subdominant the other which is just like the 4ths/5ths and plagal/perfect on the circle
I love how straight up and truthful that intro is XD
the second half is gold!
never disappoints
Super cool and makes a lot of sense.
The way you explain things is a thing to add.
So now I know. Bless you!
@12tone Excellent summary. It shows that Ionian and Aeolian are 'mirror images' in that particular transformation. What about the other modes? If Ionian converts to Aeolian and vice versa, is there any useful structure that would tie together things like Lydian, Dorian, etc.?
Dorian Mixolydian
Phrygian Lydian
C Locrian converts to a scale not containing C (because it does not contain G)
BTW I find the simplest and most concise way to explain it is: invert about the tonic and then transpose up a fifth.
It's a transposed inversion.
It's interesting when you mention fifths "becoming" roots - I wonder if there's anything similar in the aural effect (that I hear) of dominant pedals "becoming" a new tonic too?
Convoluted description of a relatively unusual tropic.
this means that axis reflection is one alternative chord, but for a given 4 tone chord there should be at least 4 variations we could replace it with (by mirroring either or both chord components). and thats just for the root chord.
I need to learn about since I heard All star- Negative Harmony
So, quick question (and I honestly hoped you were going this way in the video): if you negativize harmony, don't you also somehow negativize voice leading? What exactly would that end up sounding like? It sounds like it might be a lot of nerdy skull-muscle-flexing fun, so I'm going to mess around with it myself. Why not?
Fun explanation!
I'm concerned with calling fourths "unstable", they seem pretty stable and rested to me.
E.g. if you start a piece modulating to the fourth then when you return to the tonal it feels off. It means that the subdominant has just as much attraction as the tonic.
Variation Form will never be the same
Here it is three years later, and Wikipedia has only 1 entry under the topic - Negative harmony. It is Riemannian theory by Hugo Riemann (1849-1919) and is only one-half page long.
This video and concept helped me understand chord structure better than any book ever has.
What does negative harmony start to look like if you apply the reflection to different scales such as Lydian and the like?
Lydian and Phrygian are reflections, as are Mixolydian and Dorian
Awesome. Could you also apply this to melodies, making negative melody?
One thing i found interesting about this is that if the iv6 is the "reflection" of the V7, then does the iv6 have an equivalent to a tritone substitution? Turns out, it does. raising iv6 by a tritone gives you the vii6 chord, which also resolves to the i chord, in the same way a bII7 (tritone sub of V7) resolves to the I chord
So Fm6 resolves to Cm, but so does Bm6 because F and B are a tritone apart
Interesting thing about the iv6-vii6 pair of tritone subs is that vii6 is useless (differs than the positive ones, V7-bII7), because... You get it, vii is the leading note. It itself is strong, but the stabilizing effect of p5 in vii6 chord seems destroy the purpose of the 2-b6 tritone (in relation to the root) that exist in vii6. Why? The 4 is useful too due to the strong guidance to 3 (and probably b3) and by raising it to #4, it lacks the guidance quality, especially from #4 to b3 (#4 to 3 is pretty neat). That's why, although #4 is a tritone apart from 1 and a halfstep down from 5 (thus is labelled as "uncanny note"), it's not that uncanny ; in fact, #4 is more stable than 4, and that's why we are struggling to purely make a song of lydian scale.
The undertone series does actually exist in nature (but obviously not as prominently as the overtone series). The easiest way I know of to produce it is to strike a tuning fork and then hold it against a piece of paper. The system can enter modes where the fork only strikes the paper on every second/third/etc oscillation, producing an undertone of the fork's fundamental. I'm pretty sure Adam Neely has done a video about this concept, and I think Matt Parker (a math youtuber) has done a video about tuning forks where this also come up.
So I checked wikipedia, it's mentioned in the article called "Riemannian theory", and it's apparently called "Dualism".
Also, wikipedia says this:
Some people today (such as Jacob Collier) refer to the theory of dualism as the theory of "negative harmony".
First off, I just want to thank you for this video. It has really helped clear up negative harmony for me.
Second off, bear with me. since all of C's parallel modes (except locrian) have the same tonic and dominant notes, they will have the same axis of reflection. Does this mean that negative modality is technically a thing?
I've heard about how undertones don't actually exist in nature, but I can't help but wonder if there's something _sort of_ like them.
When I'm mixing music, I can use EQ or a high pass filter to remove lower frequencies, but I can still hear the fundamental note. But it sounds less "bassy". Is this merely a matter of the lower frequencies being _quieter_ or are there tones lower than the fundamental present?
I mean, I can make an acoustic guitar sound thin and tinny if I remove the bass tones that were recorded, but the lower notes don't just disappear, and even lowering the subbass frequencies in an EQ plugin makes a difference...
I wrote out the Major scale by their functions and got the natural minor scale but, what's cool is the chord functions change.
Negative Major / natural minor
Tonic: i, bIII
Subdom: v, bVII
Dom: iv, ii
Tonic/Dom: bVI
The one chord I disagree with here is the bVII,, because while by itself it's subdominant (two unstable notes and a hollow one), the moment you add the seventh to it ,you're adding the bVI leading tone and making it dominant. (Which makes sense, as that's the V7 of the relative major.)
Which explains why it's such a versatile chord even in traditional harmony.
@@Guerin78 True. I myself often lead back to C minor using 1 of these chords:
Bb major(bVII of C minor)
Bdim7(vii°7 of both C major and C minor)
Ddim7(ii°7 of C minor)
So for example, a chord progression that I might use would be:
Cm -> Fm -> Ab -> Bb -> Cm
In other words, despite no Eb major to put the Bb in a dominant context and despite no chordal seventh, I still feel as though the Bb wants to go up to C and is close enough to a chromatic movement that it acts similar to Bdim7 and thus has dominant function in the key of C minor. To me, I feel as though the Bb only really provides a subdominant feel after a modulation to a major key(more specifically F major) and here, I'm just showing a chord progression and it is pretty clear that the C minor is the tonic, especially since I am 1) using only chords from C natural minor and 2) Cm is both the beginning and ending chord of the progression.
dude that note pair framework blew my fucking mind
You should of spend more time research Coleman on the topic or better yet talk to him. Coleman is more about practical use of Negative than just talking theory and in use there is more involved. Hearing the sound of negative in use you start recognizing sounds from the past and have a way to understand where they came from.
Video on Snarky Puppy!!!!! Why is it so good?
Got the Prisoner reference! Be seeing you!
Really wish this wasn't referred to as negative harmony but I guess its stuck now. There is nothing "negative" about this harmony space, we're dividing the root instead of multiplying it. Division is the same as multiplication (just raising a value to a negative power instead of a positive one) and doesn't inherently lead to negative outcomes. (Certainly, we aren't producing negative frequencies by following this method) I think a better name would be Undertone Harmony with the traditional harmony being referred to as Overtone Harmony.
I also think one of the things that gets lost in conversations about this topic is how kind of arbitrary this all really is. We're grouping stuff into categories but leaving parts out because they don't work with our formalization of this topic despite them being there in nature. What I'm referring to is how we just stop at 6 overtones and say "Thats the major chord" and leave out the fact that if you keep following this method you end up with a theoretically infinite number of overtones (though we limit to ≤ 20kHz) that we ignore because they don't fit into formalized tonal harmony. This reeks of confirmation bias to me, we're just using cherrypicking acoustics to justify our preconceived system that we've formalized for 800 years or so and ignoring any evidence that doesn't support that system. To be clear as well, there is nothing wrong with this so long as we admit what we're doing is just arbitrary, we like it because it sounds good to us, but its inherently based on our perceptions and not based on something that is truly universal. Even amongst our own species, we can see there are tons of ways to formalize harmony and the western tradition isn't correct, it's just one way of doing so.
If you simply go one overtone further you end up with a ratio that is close to what we'd call a 7th and yet is actually inharmonic in our system as it is 31 cents below where it "should" be in 12 tone equal temperament. In fact, if you compare what comes out of the harmonic series compared to 12 tone equal temperament only a few of the notes line up and would be considered "correct" in traditional western harmony. en.wikipedia.org/wiki/Harmonic_series_(music)#/media/File:Harmonic_Series.png
This is was a really fascinating video though that really added something useful to the dialogue on this new framework for building harmony (especially the end part on overtone and undertone notes and grouping them into note types / "jobs").
Wow you do a much better job at teaching than my university professor!
Could the Double Harmonic scale work on negative harmony?
I think this is the first time I’ve been completely lost in one of your videos. This topic hurts my brain haha
Jacob Collier is a bloody genius. Listen to Mahogany’s version of “ocean wide, canyon deep” by Jacob, featuring Maro I have been playing it constantly all week.
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.
Is someone hearing a Gojira song at 7:45? :D
I havent get it at first but I believe it's the heaviest matter of the universe during the part where Joe sings, after the intro riff.
I'm beginning to think that negative harmony is not only a fascinating theory and a fun way to cover a song and see how it sounds 'flipped,' but also a useful analytic tool for understanding how a song initially works.
That is to say, if you listen to some of the negative harmony covers of songs online, you'll notice that they don't always 'work,' as it were, for while negative harmony preserves the functional harmonic relationships, it does not necessarily preserve other aspects. I think that if you're trying to analyze a song and are stuck, it may be a useful way to get an idea of where the song is and is not relying on functional harmony-- if you 'flip' it, and a certain section does not sound good, then you know to approach that section from another angle. Conversely, if a section sounds quite good in its 'flipped' version, a purely harmonic analysis will likely be sufficient for that section.
What do you think?
Can anyone explain why he uses the notes he does to reflect on their axis at @5:19? I imagine its to do with degrees of the scale but how are they inverting?
Does negative harmony work to explain how I can use Bb as a perfectly good chord to lead back to Cm while conserving the minor quality?
You can do that since Bb (flat 7th chord) has both the unstable notes (where D is more leading to Eb than the F). But, some prefer the dom7 version, where the Ab (b6 of C) is really leading us to the Cm triad.
Cool video, though I can't accept the drawing of an XOR gate at 5:34 for talking of negation
How does negative harmony relate to axis theory, I just watched your axis theory video right before this and it sounds like a very similar concept.
Meh. People point to the whole "iv6 works like V7" thing as a jumping-off point for why this theory is applicable, but that has been around for a long time as a substitution in jazz, because they are both chords you can derive by altering a note in the dim7 chord that gives you all those tasty 7b9 chords.
I don't think anyone would argue that doing this to the I chord yields the same "gravity" as just playing the actual I chord, right - inverting a major I gives you a minor v, doesn't it? I would not argue that Gmin function as a root chord in the key of C major. (Edit - no, I was wrong about this, the I major becomes i minor. thanks 12tone)
I feel like the V7 -> iv6 thing was a happy accident and a lot of people hang their hat on it but it's more prudent to get after the fact that they both belong to a cycle of chords that are derived from a key's iidim7 and found by simply altering one note while keeping the rest of the tensions and then resolving it. v0v
The I chord actually stays constant: Inverting it just gives you Imi, and inverting Ima6 gives you Imi7. That's why the axis is where it is: To allow you to invert the I chord and maintain its I-chord-iness. I agree that the "this chord is actually this chord!" thing runs out of steam pretty fast, which is why I wanted to focus on the underlying question of *why*.
Ohh I see my error, I inverted the whole scale but got mixed up and used the resulting G Phrygian scale *ascending* to build the chords. OPE.
I still have reservations about applying this too liberally, I mean - the "negative iii" is, what, bVI? Oof.
As a math guy, I would bet you the undertone series likely does show up somewhere in nature, and it's more likely we just haven't found it yet.
Interesting. The first thing I'm thinking is:
What happens with other axës? As in, what happens when you put the axis somewhere else in the chord?
You might find the answer in this article: jazzmodes.wordpress.com/2017/09/20/negative-harmony-part-3-the-levy-legacy/
So inverting the major scale over 3-half-flat gets you to the minor scale, I wonder what inverting over other quarter tones or notes would get you?
Edit: I just did it for the first four notes in a 24 chromatic quartertone scale and got this
Inverting a major scale around
1= 4 minor
1-half-sharp= 2 Lydian
1-sharp= 2 Phrygian
1-3/4-sharp= flat-3 Dorian
That's REALLY weird, is there a use for this?
2: 1 major (or maybe 6 minor, but that's the same set of notes)
i want these videos' doodle sheets as pdfs.
Please check out ’If There Is Something’ by Roxy Music, it’s an amazingly structured song!
D mi is also the 4mi in the key of A, thus creating a minor plagal cadence!
understanding still loving you by scorpions please
H. Levy’s book is an interesting booklet, a collection of notes & thoughts that are sadly not too systematic. It relies heavily on subharmonics and the theory related to that. Yet the best comeback to this argument has already been written decades ago by none other than Paul Hindemith in his 1st theory book. Want to explore something interesting and that generated incredible music? Study him.
Taking A as root, here are the notes and their functions according to 6:39
The Stable Notes
Root: A
Fifth: E
The Modal Notes
Maj 3th: #C
Minor 3th: C
The Hollow Notes
Major 6th: #F
Minor 7th: G
The Unstable Notes
Major 2nd: B
Perfect 4th: D
The Leading Notes
Major 7th: #G
Minor 6th: F
The Uncanny Notes
Minor 2nd: bB (B flat)
Augmented 4th: #D
I can't really read music so mistakes could've been made, I'm just posting this here because someone - somewhere else - asked about it and I tried to figure it out.