I would like to address the apparent controversy and chaos that I’ve triggered starting at 7:45 in the video. Please watch this section and listen carefully to how I describe where the middle number comes from. In the key of C, the root C resonates at 261.65Hz. The dominant above it, G, resonates at 392 Hz. At this point I added 392 and 261.63, then divided by 2 to get the median. I showed this as 327.32 Hz in the video. This is when all hell recently broke loose for some reason. I have discovered my mistake: when I did the math, I fat-fingered 393 instead of 392 when determining the median. This is where the 327.32 comes from. (393+261.63)/2 = 327.32. The actual number in red should be (392.00+261.63)/2 = 326.815. Note, this is a THEORETICAL concept based on the relationship of the Tonic and Dominant. The “axis” is the midpoint between the two. It is not the median between E and Eb, which would be 320.38 if this was actually the case. It is not. The axis of this THEORETICAL concept is the median between Tonic and Dominant, which is the result of (392.00+261.63)/2 = 326.815. Sorry for the mistake, I appreciate the attention of those who felt compelled to complain and insult me based on this small error, keeping in mind that almost all of you doing so missed the very foundation of the median, which again, is based on the median between Tonic and Dominant. Thanks for watching!
I figured that mismatch was just an error, but what about the fact that linear changes of pitch correspond to logarithmic changes of frequency? So the midpoint between two pitches isn't going to be half the sum of their frequencies.
I don't know what other people's complaints were but I can tell you that the average you are using (which is mean, not median, by the way) won't find you the midpoint between two pitches because pitch is not linearly related to frequency. For example if you took the mean of the frequencies of A4 and A6 you might expect to get A5, but you don't: A4 is 440hz, A5 is 880hz and A6 is 1760hz, they double each time. So the mean of A4 and A6 would be (440+1760)/2 = 1100 which is somewhere between C6 and C#6. Either way the whole discussion seems pointless because this negative harmony concept is clearly a theory concerning the order of discrete pitch classes in the abstract and doesn't really have anything to do with exact frequencies.
Corrections/elaborations (as a music theory teacher): 13:25 Fyi, if you're going to label a scale out of it starting on C, people have been calling it C natural minor for centuries. It's not a fancy new scale pattern and would be disingenuous to imply so. All this method eventually does is find an inverted parallel natural minor when grouped with Major. When used with adjusted chords it just sometimes inverts chord quality. This idea can be a fun process for material generation, but it isn't anything new. Brief aside: Imo, just using chords with common tones with the melody is a much simpler way of adjusting chords. Consonance is the opposite of dissonance. You can have dissonant sounding harmonics (especially if it's distant). In standard notation, half flats/sharps and quarter flats/sharps do exist as well. You can derive that building fourths are minor, while building fifths are Major since: 1. building on fourths outlines a natural minor scale (locrian if you go further) 2. building on fifths (with the same fundamental/starting note) outlines a Major pentatonic scale (lydian if you go further) Also, there was a leap in logic going from an "axis" to "light and dark." Why is it potentially light or dark? The building on fourths/fifths (mentioned directly above) with the same fundamental (starting note) is essential to understand that way of thinking. 16:40 You mislabeled GMaj7 instead of the BbMaj7 as a substitute chord. Lastly, check out serialism if you're that interested in categorizing pitch sets (for material generation). It's been done to excess there.
Light and dark just about the number of flats and sharps, major II V I decreases sharps (darkens, from the light side) while the VII IV I negative minor decreases flats (lightens, from the darker side). IF you consider the circle of fifths/fourths direction as whole keys
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.
THIS is why I love the interwebs. I haven't had to wait long. TONS of people are cracking this and uploading thoughtful, creative videos, with comments sections that are illuminating. This stuff has lain around almost unnoticed for the proverbial four score, and within WEEKS of the name-drop, WE'RE OFF. Even if it does turn out to be isomorphic to something we already know, I haven't quite cracked that part of theory yet, so I get two explanations for the same thing. I SHOULD be able to get my tired, addled brain around the idea with that.* Sincere thanks, Paul. *er...
I've watched a bunch of videos on this topic and this is by FAR the clearest and the one that makes the most sense. Congrats for managing to do that, and thank you.
That's one way to look at it, but Levy's theory explains why that actually works. It's based on the concept of positive and negative, opposites, etc. Calling it another name doesn't change the concepts in the theory.
What Martin means is that you can play the Lydian mode of the sixth scale degree (actually, the flatted six in this theory). So, if you are in C you would play Ab Lydian. If you were in F you would play Db Lydian. Make sense?
Erm, this is also called "borrowing from the minor key". If you notice in the chart at 12:54, the "negative" chords all come from Eb-major, which has the parallel minor key of C-minor. So, this is a nice "theory" for explaining "why" borrowing from the minor key might work, but the concept has been around for ages.. Turnarounds (to C) like Fm Ab7 Cmaj7 or Ab7 G7 Cmaj7 or Bb7 Ab7 G7 Cmaj7 or even extensions like Dm7b5 G7b9 Cmaj7 are all "borrowing notes from the C minor scale".. You can mix and match them depending on your preference of how heavy coloured you want your chords to be..
Yup. I think the author misunderstands; one wouldn't write a piece in 'negative harmony' as that doesn't really make sense. But, its most appropriate application is in changing the colour of a repeated section. Essentially it suggests that a perfect cadence and a minor plagal cadence (add6) have the same weight towards the key centre and could be interchanged for variety.
To all... THANK YOU! This has been a excellent discussion on music theory. Thank you for everyone that has been asking questions and contributing content. I've been trying to wrap my head around this concept, so last night I read Steve Coleman's essay. He describes negative harmony in a different way. I'm going to revisit my negative C major transposition to see what I've missed. Perhaps to help everyone out, can someone take a stab at negative harmonizing Autumn Leaves on their own to see if it compares to my version? It is in G, the changes used in the video are: || A-7 | D7 | Gma7 | Cmaj7 | F#ø | B7 | E- | || Thanks again for your participation and interaction!
I watched two videos before this one and was thinking I'd never understand it. It's still wobbly for me, but this video actually helped me grasp the basic concept, so thank you so much for taking the time to do this. My third time was indeed a charm. Cheers.
I like this video a lot, but there is one thing wrong with it. Let's take the I in the negative C major scale, (that scale being G F Eb D C Bb Ab G) the notes are correct, but it's not a AbM7, It's a Cm(b)6, so the notes are C Eb G Ab not Ab C Eb G, this is because adding a 7th or not would in your case completely change the root of the chord and destroys the intended root note. Yes they contain the same notes, but it is important that in the scale the tonic chord reflects the tonic, an AbM7 though containing the same notes as a Cm(b)6 chord, function differently. And that process continues, the ii7 in the original C Major key is D F A C (Root of the chord a major second above the tonic, then ascends by thirds leaving D as the root), would be Bb D F G in the negative (Root of the chord a major second below the tonic, and reflecting the Dm chord over the negative axis leaving the Bb as the root).So it's important to specify that 7th chords become 6th chords when inverted to the negative and do not shift the root of the chord.
You could also think of it like the c major scale reflects with the c aeolian scale (natural minor). When each of the notes of the c major scale get reflected, you get all of the notes of the c aeolian scale, and going counter clockwise starting with the reflected DOMINANT (which is G-C), it actually makes up a c aeolian scale, and that scale works PERFECTLY with c minor (b6). If it were a C mixolydian scale, all the notes of its reflection would make up a Dorian, and then C Phrygian with C Lydian, and then C locrian with C locrian (it reflects with itself). Going with your example with D-7, if we started with the root and went up to the right, that would obviously make up a D Dorian scale, but if we reflected all of the notes of the D Dorian scale, we would get all of the notes of the Bb mixolydian scale, and the root would have to be Bb because the dominant of D is A, and the opposite of A is Bb. Thank y’all for listening to my Ted talk lololol😂😂
@@Kristian_Raices_ I don't believe I'm following (although it has been a few years haha), mode flipping into the negative looks like *Positive* "Major" Lydian Ionian Mixolydian ----Dorian---- Aeolian Phyrigian Locrian *Negative* "Minor" (negative Dorian is Dorian it's kinda like an axis) EDIT: Since making the original comment, I now have a degree in music theory and history and this topic (Negative Harmony) was my senior thesis. If anyone ever wants to DM me questions or whatever I love talking about this sort of stuff!
Heya, you might have already noticed this, but the negative harmony version of C major is actually C major's parallel minor, starting on Lydian, and going backwards! Your table made that really clear, I feel like it's kind of a shortcut to finding the negative version of a key :)
I've tried to find lots of videos explaining negaive harmony and this is, by far, the best one I've found. Amazingly well explained, but not patronisingly slowly. Great job!
You actually made me understand "negative harmony"! You should make more videos like this. It seems you have a gift for explaining technical stuff the easy way.
15:37 you can also apply note substituons in melody. When you do it you will get completely different feeling. If you write the most happiest melody, you will get the most saddest one in negative version. So basically by using negative harmony, it is possible to compose two different melody by only creating one
Finally a digestible explanation of this much talked about "Negative Harmony". I find that a good deal of You tuber's just like to hear themselves talk and over complicate topics thinking this make for recondite scholastic. Thank you for keeping it simple.
Thank you for this. I was trying to find some rhyme or reason behind negative harmony covers other than making major chords minor and vice versa. It's really cool when the melody is swapped for its negative counterpart as well.
this was a fantastic 10/10 explanation, but then you did the real book changes for autumn leaves and I was confused for like 10 minutes until I realized it was a different key lol
Yeah... I wanted something simple in a C or G to keep it close to the earlier charts. :) I'll be doing a follow up later this month probably. Thanks for the feedback!
Wow, I'd never learned about this concept before. This explains some of the interesting chord changes I've found in songs that I've often wondered about (how did they come up with that?), from people like Brian Wilson, .Donald Fagen, and Burt Bacharach. I'm thinking that negative harmony options where used for some of these surprisingly odd chord movements that sound "right" , this is way cool!!
Hey there. I've studied Levy's book and found no mention of this, maybe I missed something. The axis is not a mid-point between the C and G but C itself. I heard you saying you haven't read it so I strongly suggest you read it before paraphrasing the author. Howard's theory is that the overtones are found in nature while the undertones is found in the human "spirit", it resonates with us, thus while we may hear a C triad, our psyche may actually perceive simultaneously an Fmin. This is because E is a maj 3rd upwards for C and Ab is a maj 3rd downwards from C. This perception builds itself into a cadence with C maj gravitating towards Fmin and vice versa. If you alter a note from the cadence, say Cmaj -> Fmaj it creates movement as it is not a stationary cadence anymore, because now, Fmaj wants to resolve towards Cmin. The axis of rotation is the root itself. While these ideas presented by Jacob are very enlightening, it seems its another perspective on Levy's theory. L's idea is that while studying this concept you don't come up with chord progressions but simply relate harmony to the human spirit and psyche.
I completely agree. I've read the book twice since posting this video, the second time because I didn't find anything about the axis that Jacob Collier mentioned in his video. My video is more of an explanation of Collier's understanding of negative harmony. The personal conclusion I've reached is that negative harmony is just a theory that provided potentially interesting chord substations relating to modal interchange, but that it's an idea, not an actual thing. Harmony is based on harmonics, something that actually occurs in nature and can be reproduced.
Yes, Collier uses negative harmony in a way that preserves the tonic. If you used C as the mirror point, the chords would be from F minor. But he wants to use negative harmony to have new ways to get to the same tonic. Therefore he uses a different axis to make this possible. The drawback would be that a mirrored melody would be in G Phrygian instead of C Phrygian. In addition to this, he mirrors the chords extensions separately, so they're still extensions. And the basic triads still work nicely.
Paul, I really appreciate the effort that you have taken to assimilate this subject and make it easily understandable. I heard Collier on this and did not fully grasp how he was making the note substitutions and now I do!! Great Work!!
You can divide the octave across any one of twelve different axes and still produce negative harmony. Each just produces it in a different key. To simply produce a negative version of a given chord sequence or melody, any division will produce exactly the same harmony, but each will produce a different transposition thereof. For some purposes, it may be preferable to chose the division that renders the parallel minor key to your major key original (or Vice versa). For other purposes, the relative key may serve better (either may represent a neat way to compose a B section, one that literally mirrors your A section, and which it turns out you’d already composed without realising it). The axis that falls halfway between the tonic and the dominant is specifically useful for swapping back and forth between your positive and negative chords.
Wow....great presentation! I think I'm finally getting it! Thanx! I watched this video 3x....there is so much practical information in less than 20 min.! This is the best presentation on this challenging topic. Yes...I watched the video several times, took 8 pages of notes, worked out the examples...but I'm really grasping the material from your video that s less than half the time of a standard college lecture. Thanx again!
I think the issue here is Collier is not getting all of his information correct. If you look at what Steve Coleman is doing versus what Collier is doing, it's almost like they were reading two completely different books. I've been trying to impress this fact upon people because the difference in sound is tremendous. If you think of negative as static and positive as static, these super impositions are just going to change your key center, which is exactly why everyone is complaining about the "dissonance" (it's not really that dissonant if you're doing it correctly) and using a combination of the two, which ends up ultimately only moving between major and minor, adding some tritone subs, and minor third substitutions, which are all extremely common in jazz. Here's the essay: m-base.com/essays/symmetrical-movement-concept/ Remember that negative harmony is "harmony," not "negative tonal centers." I think this speculation has sent everyone down a path (no pun intended) to compromise between the two instead of treating your ii V's as directional moves. And when this happens there is this tendency to "do what sounds better," which is a typical "I didn't transcribe this from anything" move.
Just an error I found @8:10 : in using equal temperament, finding the middle note requires you to use the logarithmic function and apply the two numbers in it. The middle note, C, and G's frequencies are C=261.63, G=261.63 * 2^(7/12)=392, middle note is 261.63*2^(3.5/12) = 320.249 Hz
Added a pinned comment to explain the math error. Here is the summary: In the key of C, the root C resonates at 261.65Hz. The dominant above it, G, resonates at 392 Hz. At this point I added 392 and 261.63, then divided by 2 to get the median. I showed this as 327.32 Hz in the video. This is when all hell recently broke loose for some reason. I have discovered my mistake: when I did the math, I fat-fingered 393 instead of 392 when determining the median. This is where the 327.32 comes from. (393+261.63)/2 = 327.32. The actual number in red should be (392.00+261.63)/2 = 326.815. Note, this is a THEORETICAL concept based on the relationship of the Tonic and Dominant. The “axis” is the midpoint between the two. It is not the median between E and Eb, which would be 320.38 if this was actually the case. It is not. The axis of this THEORETICAL concept is the median between Tonic and Dominant, which is the result of (392.00+261.63)/2 = 326.815.
Great video. I really enjoy your approaches to finding the axis. However, the chords subs are incorrect. If I may offer clarification about the parameters of negative reflection: (very) Simply Put 1)All major chords become minor 2)All dominant chords become minor 6 3) Because the negative reflection of the major 1 chord is just minor all negative harmonies can be calculated by using the V chord as the root of a descending phrygian scale against the original ascending Ionian ie Positive (C major) Left Negative ( G Phrygian) Right C=G D=F E=Eb F=D G=C A=Bb B=Ab So: C= C minor G7 = Fm6 Hope this might help!
Thanks for the video. I think one common example of a negative harmony substitution that everyone has heard is V - I becoming iv6 - I. Although you've written Dm7b5 here, the negative version of the V7 chord could also be written as iv6 (in C, Fm6). iv6 - I is a plagal cadence that is commonly used and sounds very strong, almost as strong as V - I. Jacob seems to associate positive harmony with perfect cadences and negative harmony with plagal cadences. That suggests that we might want to think of the -I chord as being Cm rather than Ab. Then V7 - I turns into a nice plagal Fm6 - Cm. Cm as the i chord makes even more sense considering that the notes in -C are really from the parallel minor, C aeolian.
The 4th degree is called a subdominant because it is a dominant below the tonic not because it is slightly less dominant than the dominant. A fifth below C is an F so F is the subdominant.
Pretty cool. If you play a progression in C and then play the same thing right after using the substitute chords it's almost like an eerie call and response.
Maybe I'm missing something, but how is this any different from "modal interchange," simply borrowing chords from the parallel minor ("interchanging" between C major and C minor, two "modes" sharing the same "tonic")? Other than, of course, it (the "negative") giving you suggested "opposites" to "try" when trying to fabricate a progression, for songwriting.
Well if u took the six of c major (A) and compared it to the 6 of c minor (Ab) it doesnt match up as shown in the video where the "negative" A in c major is Bb
Thanks! Yeah, I understand all that... but still, really, it ONLY is generating chords between C major and C minor keys, right? That's what it seems... Which is... hilarious! Because I see this polluting the brains of many a theory student, lol. That said, if it gives someone a "replacement" chord in a way they (for whatever reason) wouldn't have arrived at by any other means, all good :-) Thanks Darius!
Hey Dale! What the whole concept seems to me is just an explanation of "why a iv minor would want to resolve back to the tonic." What I feel Levy and Rusell talk about in their books is the idea that the gravity of every chord against the tonic remaining the same even if the "axis" or the "scale" is flipped over. The whole jargon is borderline hilarious with so many people buying Levy's book now when people like the Beatles, Bowie and the Shadows were doing it in the 60's and I'm pretty sure they weren't thinking of the term negative harmony.
Very goodd video, lately I’ve been searching so much about all the techniques that Jacob uses, and it’s so hard to find good and well explained content speaking portuguese, but I’m giving my maximum to understand it all Thank you very much!!!
take the triton from C ...Gb!... use it as the mirror...so you get the scale C Bb Ab G F Eb Db C...start with Cmaj and continue with the maj chords downwords to C....works for me in ANY scale...altered...-6...+5...
The strength of this system is that it relates to standard chromatic theory concepts while forcing the composer into harmonic areas which are not completely intuitive or easy to come by through experimenting with voice leading, enharmonic equivalents, chord substitutions, etc. It's easy to think it "sounds bad" if you're trying to force the music to stay in the original key, but it would be a cool way to transition to a new key, develop a theme, or just perform a chord substitution for dramatic effect. It would be fun to play around with implementing negative harmony to a non-diatonic borrowed chord in a progression. Say you have a ii-V-I, substitute a minor v, then transition to the negative equivalent before resolving to wherever that takes you, which doesn't need to be in the original key. If you're just thinking of using negative harmony for the occasional chord substitutions, yeah you could better explain it as a chromatic 3rd, borrowed chord, etc, but it seems like there is potential if you take a more compositional approach. edit: much like set theory or serialism, the whole point is that the system gives you a way to find something you weren't looking for or would never find on your own in the first place. edit 2: it would also be helpful to have some way of notating the "negativity" of a chord for the purpose of analysis and performance.
Very fascinating. I have heard this term "negative harmony" used but didn't know exactly what it meant...kind of brings to mind George Russell's lydian chromatic concept. Just a different way of organizing tonal structures
think of it this way: now apart from 7 diatonic chords in C major you also have another 7 chords in Eb major. So, playing in C major you have extra options for unexpected harmonies and colors, pretty fun
I get what you saying, but how is this different from borrowing from the Eb key, or is it just the same but called negative harmony. Just trying to make sense of this in a physical playing way
@@pedroberoes49 to me it’s the same, but it tells you exactly What chord from Eb substitutes for each chord from C. However for me personally it’s not very practical and musical, it’s much better to find those alt chords manually, Even if you’re only restricted to Eb
@@pedroberoes49 I mean if you're using the system laid out in this video, all that you're really doing is borrowing chords from the parallel minor. All the chords in Eb major are really just C natural minor.
Clearest explanation on Negative Harmony out there. Did not get some bits by the end but i tried to follow and the most I could understand was this transposition thing but there was examples that did not seem to fit.
I think, to be more simple, we can say that the negative key is the bIII major key. For example like in the video, the negative key of C major is Eb major. But the Eb is starting at IV of C major key. And counting it backwards.
"Negative harmony" is otherwise known in traditional theory as "interval inversion." Why on earth would it be viewed as controversial? It's a common element of compositional technique dating back to the Renaissance.
They are not actually the same when you look at the origin of the theory. The entire concept is based on sonething called "undertones," which are supposed to be the opposite of "overtones." Overtones are a naturally occuring thing, while undertones are not. I consider the entire thing an exercise in creating something out of nothing to try and find new ways to approach music. Inversions, transpotition, retrograde, modal substitution, etc.... are all musical concepts based on changing notes or chords. Undertones don't exist, so the theory is basically useless. Thanks for commenting!
Great video, super instructive! I wonder about the harmonic content as a way to understand the consonance (literally the interacting frequencies). To my ear the "pure negative" is dissonant, your version does rescue it a bit.
The explanation "G is the dominant so we take it as the counterpart of the tonic C" still is arbitrary, but the axis circle makes sense. It would be possible to actually use G as the zero-point, or D, or any other note. Using G as the zero-point, G minor triad would sub for C major triad. I think this concept is worth generalizing and not restricting to only the axis between third and minor third.
No, its not, because each chord has his own substitution. It works with non diatonic chords too, for example the secundary dominants follows the cicle of fourths (in C: G7 becomes Fm6; D7 becomes Bbm6 A7 becomes Ebm6). You couldnt do it only with modal intechange
Great tutorial. But I think there is a mistake. The frequency of the "axis" should be the geometric mean √(ab) instead of arithmetic mean (a+b)/2. That is to say, the axis = square root of (392Hz × 261.63Hz) = .... = square root of (the product of frequencies of any two symmetric notes) = 320.25Hz. Because the frequencies of each note on keyboard is ordered as a geometric sequence instead of arithmetic sequence.
A couple of people have brought up the math situation regarding the axis. In every case, the frequency still falls between the 3rd and flatted third of the key, so there is no real change to the method of finding the axis. In C it is still between E and Eb. :) Thanks for taking the time to comment, I appreciate it!
Thank you for this! I was worried it would be too long but I was actually surprised that 18 mins already passed by. Great concise and coherent explanation!
7:58 Talking about linear midpoints between frequencies is a little suspect given that pitch is a logarithmic scale. The perceived midpoint between two pitches is not the midpoint between the corresponding frequencies.
@@YoPaulieMusic While it isn't a big deal, I think using correct math matters, you used the arithmetic mean instead of the geometric mean. It just happened in this case to give you a value in the correct range this time. Say we have a note at 400 hz, we go up two octaves to 1600 hz, if we use the arithmetic mean to find their midpoint we'll get (400+1600)/2=1000, but one octave up from 400 hz is 800 hz If we instead use the geometric mean we'll get sqrt(400*1600)=800 hz The value at the timestamp should then be sqrt(392*261.63)=320.248 hz
Well, correct math always matters if you care about math,@@paulfoss5385 . :) But in this case we are talking about Western-based musical theory concepts and the goal is to find where on the piano keyboard the split point is. There is plenty of room for mathematical variance... thanks for commenting!
@@YoPaulieMusic First of all, you made a good video. What I care about is that you'll be able to find note midpoints consistently in the future. The arithmetic mean happened to land in the relevant range this time, but it won't always, as in the example I gave. You can't dismiss math as irrelevant while you're in the process of using it. That you are trying to dismiss it suggests that embarrassed and are being slightly passive aggressive, which I think is an understandable response for a creator being subjected to scrutiny from thousands of strangers, but there's no reason for embarrassment here, they don't teach the geometric mean in school and the situations where it is the correct average to use.
Thanks@@paulfoss5385. I don't mind the constant flow of people discussing the mathematical mean, vs average, etc. There are actually several different takes on the concept within the comments, I would estimate there are at least three or four different theories on what that mysterty mid point should be. Composers that want to try to usw this theorhetical concept will never need to know the specific frequency between E and Eb, they will just need to know that the approximate split point is between E and Eb (in the example from the video). There is some frustration that people are choosing to focus on this mathematical situation instead of the larger overall concept/theory. :) I appreciate the dialogue.
This is very well done, and shows how to arrive at the substitute chords. Based on watching another video it only works well (meaning sounds good) when certain negative chords are substituted for their positive counter part in a given chord progression. This is obviously dictated by musical taste. At least your video gives a clear explanation of what chords to try as this is different from tritone substitution.
"Now youre probably wonder why im gonna need all this notes for, after all, i build up negative C major chords for 12 hours. But to awnser that, we need to talk about pararell universes"
I think the calculation of the midpoint should be in notes, not in hertz, because the mapping of notes to hertz is not linear. That gives 3.5 notes above C, or the midpoint between Eb and E - same answer, but sounder reasoning I believe.
wait... in 15:28 there is no point of negative harmony substitution if it is not applied to the melody as well. If you paint a tree, then mirror the branches to its roots and then superpose the leaves what do you have? a mess
I think you can do it either way. Negative Harmony just provides chord substitutions for your given melody. You have the choice of changing the melody, but it is not required.
Hello Paul, from my opinion, I don’t think there is any mistake, it is just that after translating all the chords into their negative, then the melody is misplaced, it would need to be mirrored as well. As an observation, in the case of dominants, for instance, G7->C translated to its negative version would be Fm6->C instead of Dø->C. G minor Phrygian is the negative scale of C major Ionian; the scale is Fm with the base on the 6th for its substitution, as well the plagal harmonic resolution, that's why in many cases if we keep the melody as it was, the scale doesn't correspond to its negative version, however, we can't say it is a mistake of course it depends of the context. "Giant Steps" sounds very well with some negative substitutions over the melody.
Paul Croteau I don't find any problem yet in theory explanation, but if you applied that into a song, make sure you made an axis melody too. Like C major ionian ascending scale into G minor phrygian descending scale with the same rhythmic. But this is actually very helping me out, so congrats, you got a new subscriber! 👍
Nice presentation, but I do not think "reversing" the chords of "Autumn Leaves" while keeping the melody the same worked at all. As other points out, you are just rewriting Ionian to Aeolian in the end, so going by the whole "negative" concept seems overly complicated and counterintuitive.
I'm confused - he starts off by saying that, in the key of C, the axis point is between Eb and E. OK, so far so good, but then he draws a circle of fifths which shows the axis dividing C and G. So which is it?
I would like to address the apparent controversy and chaos that I’ve triggered starting at 7:45 in the video. Please watch this section and listen carefully to how I describe where the middle number comes from.
In the key of C, the root C resonates at 261.65Hz. The dominant above it, G, resonates at 392 Hz. At this point I added 392 and 261.63, then divided by 2 to get the median. I showed this as 327.32 Hz in the video. This is when all hell recently broke loose for some reason. I have discovered my mistake: when I did the math, I fat-fingered 393 instead of 392 when determining the median. This is where the 327.32 comes from. (393+261.63)/2 = 327.32. The actual number in red should be (392.00+261.63)/2 = 326.815.
Note, this is a THEORETICAL concept based on the relationship of the Tonic and Dominant. The “axis” is the midpoint between the two. It is not the median between E and Eb, which would be 320.38 if this was actually the case. It is not. The axis of this THEORETICAL concept is the median between Tonic and Dominant, which is the result of (392.00+261.63)/2 = 326.815.
Sorry for the mistake, I appreciate the attention of those who felt compelled to complain and insult me based on this small error, keeping in mind that almost all of you doing so missed the very foundation of the median, which again, is based on the median between Tonic and Dominant. Thanks for watching!
So you're creating negative harmony from their insults?
@@davidmcauliffe8692 Bwahahahaha! Yes! :)
I figured that mismatch was just an error, but what about the fact that linear changes of pitch correspond to logarithmic changes of frequency? So the midpoint between two pitches isn't going to be half the sum of their frequencies.
I don't know what other people's complaints were but I can tell you that the average you are using (which is mean, not median, by the way) won't find you the midpoint between two pitches because pitch is not linearly related to frequency. For example if you took the mean of the frequencies of A4 and A6 you might expect to get A5, but you don't: A4 is 440hz, A5 is 880hz and A6 is 1760hz, they double each time. So the mean of A4 and A6 would be (440+1760)/2 = 1100 which is somewhere between C6 and C#6.
Either way the whole discussion seems pointless because this negative harmony concept is clearly a theory concerning the order of discrete pitch classes in the abstract and doesn't really have anything to do with exact frequencies.
You are exactly correct@@Ambidextroid , thanks for your input here. :)
This came recommended to me after I watched All-Star for the twentieth time in negative harmony
Same. All Star In Negative Harmony Looks Like An Emo Song.
Corrections/elaborations (as a music theory teacher):
13:25 Fyi, if you're going to label a scale out of it starting on C, people have been calling it C natural minor for centuries. It's not a fancy new scale pattern and would be disingenuous to imply so. All this method eventually does is find an inverted parallel natural minor when grouped with Major. When used with adjusted chords it just sometimes inverts chord quality. This idea can be a fun process for material generation, but it isn't anything new.
Brief aside: Imo, just using chords with common tones with the melody is a much simpler way of adjusting chords.
Consonance is the opposite of dissonance. You can have dissonant sounding harmonics (especially if it's distant). In standard notation, half flats/sharps and quarter flats/sharps do exist as well.
You can derive that building fourths are minor, while building fifths are Major since:
1. building on fourths outlines a natural minor scale (locrian if you go further)
2. building on fifths (with the same fundamental/starting note) outlines a Major pentatonic scale (lydian if you go further)
Also, there was a leap in logic going from an "axis" to "light and dark." Why is it potentially light or dark? The building on fourths/fifths (mentioned directly above) with the same fundamental (starting note) is essential to understand that way of thinking.
16:40 You mislabeled GMaj7 instead of the BbMaj7 as a substitute chord.
Lastly, check out serialism if you're that interested in categorizing pitch sets (for material generation). It's been done to excess there.
Light and dark just about the number of flats and sharps, major II V I decreases sharps (darkens, from the light side) while the VII IV I negative minor decreases flats (lightens, from the darker side). IF you consider the circle of fifths/fourths direction as whole keys
Thank you. I now understand negative harmony well enough to be sure I don't want to use it.
😭
Finally someone who really made an effort to explain this concept! Thank you very much! Subscribed!
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.
THIS is why I love the interwebs. I haven't had to wait long. TONS of people are cracking this and uploading thoughtful, creative videos, with comments sections that are illuminating. This stuff has lain around almost unnoticed for the proverbial four score, and within WEEKS of the name-drop, WE'RE OFF. Even if it does turn out to be isomorphic to something we already know, I haven't quite cracked that part of theory yet, so I get two explanations for the same thing. I SHOULD be able to get my tired, addled brain around the idea with that.*
Sincere thanks, Paul.
*er...
I've watched a bunch of videos on this topic and this is by FAR the clearest and the one that makes the most sense.
Congrats for managing to do that, and thank you.
Negative Harmony: instead of playing in Ionian mode, you're now in Lydian mode built on the 6th scale degree. There, I saved you 25 minutes
That's one way to look at it, but Levy's theory explains why that actually works. It's based on the concept of positive and negative, opposites, etc. Calling it another name doesn't change the concepts in the theory.
What do you mean? How does that tie in with chord and note substitions?
Lydian is the 4th degree of the major scale. Not the 6th
What Martin means is that you can play the Lydian mode of the sixth scale degree (actually, the flatted six in this theory). So, if you are in C you would play Ab Lydian. If you were in F you would play Db Lydian. Make sense?
You mean the Flatted 6th
Erm, this is also called "borrowing from the minor key". If you notice in the chart at 12:54, the "negative" chords all come from Eb-major, which has the parallel minor key of C-minor.
So, this is a nice "theory" for explaining "why" borrowing from the minor key might work, but the concept has been around for ages.. Turnarounds (to C) like Fm Ab7 Cmaj7 or Ab7 G7 Cmaj7 or Bb7 Ab7 G7 Cmaj7 or even extensions like Dm7b5 G7b9 Cmaj7 are all "borrowing notes from the C minor scale".. You can mix and match them depending on your preference of how heavy coloured you want your chords to be..
Yup. I think the author misunderstands; one wouldn't write a piece in 'negative harmony' as that doesn't really make sense. But, its most appropriate application is in changing the colour of a repeated section. Essentially it suggests that a perfect cadence and a minor plagal cadence (add6) have the same weight towards the key centre and could be interchanged for variety.
fps io 💯💯💯💯🔥
You're being overly fixated on an example instead of understanding the concept itself.
To all... THANK YOU! This has been a excellent discussion on music theory. Thank you for everyone that has been asking questions and contributing content. I've been trying to wrap my head around this concept, so last night I read Steve Coleman's essay. He describes negative harmony in a different way. I'm going to revisit my negative C major transposition to see what I've missed.
Perhaps to help everyone out, can someone take a stab at negative harmonizing Autumn Leaves on their own to see if it compares to my version? It is in G, the changes used in the video are:
|| A-7 | D7 | Gma7 | Cmaj7 | F#ø | B7 | E- | ||
Thanks again for your participation and interaction!
instaBlaster...
I watched two videos before this one and was thinking I'd never understand it. It's still wobbly for me, but this video actually helped me grasp the basic concept, so thank you so much for taking the time to do this. My third time was indeed a charm. Cheers.
I like this video a lot, but there is one thing wrong with it. Let's take the I in the negative C major scale, (that scale being G F Eb D C Bb Ab G) the notes are correct, but it's not a AbM7, It's a Cm(b)6, so the notes are C Eb G Ab not Ab C Eb G, this is because adding a 7th or not would in your case completely change the root of the chord and destroys the intended root note. Yes they contain the same notes, but it is important that in the scale the tonic chord reflects the tonic, an AbM7 though containing the same notes as a Cm(b)6 chord, function differently. And that process continues, the ii7 in the original C Major key is D F A C (Root of the chord a major second above the tonic, then ascends by thirds leaving D as the root), would be Bb D F G in the negative (Root of the chord a major second below the tonic, and reflecting the Dm chord over the negative axis leaving the Bb as the root).So it's important to specify that 7th chords become 6th chords when inverted to the negative and do not shift the root of the chord.
Thank you! This should be pinned
That kinda what I thought. The function of each chord (and each note) transfers over...
You could also think of it like the c major scale reflects with the c aeolian scale (natural minor). When each of the notes of the c major scale get reflected, you get all of the notes of the c aeolian scale, and going counter clockwise starting with the reflected DOMINANT (which is G-C), it actually makes up a c aeolian scale, and that scale works PERFECTLY with c minor (b6). If it were a C mixolydian scale, all the notes of its reflection would make up a Dorian, and then C Phrygian with C Lydian, and then C locrian with C locrian (it reflects with itself). Going with your example with D-7, if we started with the root and went up to the right, that would obviously make up a D Dorian scale, but if we reflected all of the notes of the D Dorian scale, we would get all of the notes of the Bb mixolydian scale, and the root would have to be Bb because the dominant of D is A, and the opposite of A is Bb. Thank y’all for listening to my Ted talk lololol😂😂
@@Kristian_Raices_ I don't believe I'm following (although it has been a few years haha), mode flipping into the negative looks like
*Positive* "Major"
Lydian
Ionian
Mixolydian
----Dorian----
Aeolian
Phyrigian
Locrian
*Negative* "Minor"
(negative Dorian is Dorian it's kinda like an axis)
EDIT: Since making the original comment, I now have a degree in music theory and history and this topic (Negative Harmony) was my senior thesis. If anyone ever wants to DM me questions or whatever I love talking about this sort of stuff!
Heya, you might have already noticed this, but the negative harmony version of C major is actually C major's parallel minor, starting on Lydian, and going backwards! Your table made that really clear, I feel like it's kind of a shortcut to finding the negative version of a key :)
I've tried to find lots of videos explaining negaive harmony and this is, by far, the best one I've found. Amazingly well explained, but not patronisingly slowly. Great job!
You actually made me understand "negative harmony"! You should make more videos like this. It seems you have a gift for explaining technical stuff the easy way.
15:37 you can also apply note substituons in melody. When you do it you will get completely different feeling. If you write the most happiest melody, you will get the most saddest one in negative version. So basically by using negative harmony, it is possible to compose two different melody by only creating one
Finally a digestible explanation of this much talked about "Negative Harmony". I find that a good deal of You tuber's just like to hear themselves talk and over complicate topics thinking this make for recondite scholastic. Thank you for keeping it simple.
Thank you, excellent teaching - what seemed complicated now understood! Thank you for making the video for us.
This is the best video to understand negative harmony. Thanks!
Thank you for this. I was trying to find some rhyme or reason behind negative harmony covers other than making major chords minor and vice versa. It's really cool when the melody is swapped for its negative counterpart as well.
thank you for your explanation, very clear and informative. I specially like the slightly offset circle of fifth!
this was a fantastic 10/10 explanation, but then you did the real book changes for autumn leaves and I was confused for like 10 minutes until I realized it was a different key lol
Yeah... I wanted something simple in a C or G to keep it close to the earlier charts. :) I'll be doing a follow up later this month probably. Thanks for the feedback!
Outstanding tutorial! Very impressive. Thank you so much for doing this. ✌🏾
Thanks for the explanation, kupo!! I understand it much better now, maybe not 100%, but through this video, I'm making progress!!
I can’t thank you enough for this video. This just opened up a door for me musically that I am so excited about I can’t sleep
This has to be the best and simplest explanation of negative harmonies ever...thank you so much! 🙏🏼
Clearest explanation of the subject that i’ve found. Thank you.
Wow, I'd never learned about this concept before. This explains some of the interesting chord changes I've found in songs that I've often wondered about (how did they come up with that?), from people like Brian Wilson, .Donald Fagen, and Burt Bacharach. I'm thinking that negative harmony options where used for some of these surprisingly odd chord movements that sound "right" , this is way cool!!
The comment section is negative harmonics.
I taught on negative harmony to my high school class a couple of weeks ago.
(After spending a weekend on understanding all this!! ;) )
Hey there. I've studied Levy's book and found no mention of this, maybe I missed something. The axis is not a mid-point between the C and G but C itself. I heard you saying you haven't read it so I strongly suggest you read it before paraphrasing the author. Howard's theory is that the overtones are found in nature while the undertones is found in the human "spirit", it resonates with us, thus while we may hear a C triad, our psyche may actually perceive simultaneously an Fmin. This is because E is a maj 3rd upwards for C and Ab is a maj 3rd downwards from C. This perception builds itself into a cadence with C maj gravitating towards Fmin and vice versa. If you alter a note from the cadence, say Cmaj -> Fmaj it creates movement as it is not a stationary cadence anymore, because now, Fmaj wants to resolve towards Cmin. The axis of rotation is the root itself. While these ideas presented by Jacob are very enlightening, it seems its another perspective on Levy's theory. L's idea is that while studying this concept you don't come up with chord progressions but simply relate harmony to the human spirit and psyche.
I completely agree. I've read the book twice since posting this video, the second time because I didn't find anything about the axis that Jacob Collier mentioned in his video. My video is more of an explanation of Collier's understanding of negative harmony. The personal conclusion I've reached is that negative harmony is just a theory that provided potentially interesting chord substations relating to modal interchange, but that it's an idea, not an actual thing. Harmony is based on harmonics, something that actually occurs in nature and can be reproduced.
Yes, Collier uses negative harmony in a way that preserves the tonic. If you used C as the mirror point, the chords would be from F minor. But he wants to use negative harmony to have new ways to get to the same tonic. Therefore he uses a different axis to make this possible. The drawback would be that a mirrored melody would be in G Phrygian instead of C Phrygian. In addition to this, he mirrors the chords extensions separately, so they're still extensions. And the basic triads still work nicely.
Paul, I really appreciate the effort that you have taken to assimilate this subject and make it easily understandable. I heard Collier on this and did not fully grasp how he was making the note substitutions and now I do!! Great Work!!
You can divide the octave across any one of twelve different axes and still produce negative harmony. Each just produces it in a different key.
To simply produce a negative version of a given chord sequence or melody, any division will produce exactly the same harmony, but each will produce a different transposition thereof. For some purposes, it may be preferable to chose the division that renders the parallel minor key to your major key original (or Vice versa). For other purposes, the relative key may serve better (either may represent a neat way to compose a B section, one that literally mirrors your A section, and which it turns out you’d already composed without realising it). The axis that falls halfway between the tonic and the dominant is specifically useful for swapping back and forth between your positive and negative chords.
Helping to expand my brain, Thank You Paul!
Finally! I Understood what it is "Negative Harmony" , thanks a lot Paul Croteau, great explanation.
Greetings from México
Wow....great presentation! I think I'm finally getting it! Thanx! I watched this video 3x....there is so much practical information in less than 20 min.!
This is the best presentation on this challenging topic. Yes...I watched the video several times, took 8 pages of notes, worked out the examples...but I'm really grasping the material from your video that s less than half the time of a standard college lecture. Thanx again!
Great video Paul! Perfectly explained and enjoyable to watch!
I received Levy's book for fathers day and am reading it now. I'll post an update once I understand this better. Thanks for all the great comments! :)
Now All Star - Smash Mouth in negative harmony makes more sense
lol
It all is.
why not subs the melody in negative ?
I think the issue here is Collier is not getting all of his information correct. If you look at what Steve Coleman is doing versus what Collier is doing, it's almost like they were reading two completely different books. I've been trying to impress this fact upon people because the difference in sound is tremendous. If you think of negative as static and positive as static, these super impositions are just going to change your key center, which is exactly why everyone is complaining about the "dissonance" (it's not really that dissonant if you're doing it correctly) and using a combination of the two, which ends up ultimately only moving between major and minor, adding some tritone subs, and minor third substitutions, which are all extremely common in jazz.
Here's the essay: m-base.com/essays/symmetrical-movement-concept/
Remember that negative harmony is "harmony," not "negative tonal centers." I think this speculation has sent everyone down a path (no pun intended) to compromise between the two instead of treating your ii V's as directional moves. And when this happens there is this tendency to "do what sounds better," which is a typical "I didn't transcribe this from anything" move.
Just an error I found @8:10 : in using equal temperament, finding the middle note requires you to use the logarithmic function and apply the two numbers in it.
The middle note, C, and G's frequencies are C=261.63, G=261.63 * 2^(7/12)=392, middle note is 261.63*2^(3.5/12) = 320.249 Hz
Added a pinned comment to explain the math error. Here is the summary:
In the key of C, the root C resonates at 261.65Hz. The dominant above it, G, resonates at 392 Hz. At this point I added 392 and 261.63, then divided by 2 to get the median. I showed this as 327.32 Hz in the video. This is when all hell recently broke loose for some reason. I have discovered my mistake: when I did the math, I fat-fingered 393 instead of 392 when determining the median. This is where the 327.32 comes from. (393+261.63)/2 = 327.32. The actual number in red should be (392.00+261.63)/2 = 326.815.
Note, this is a THEORETICAL concept based on the relationship of the Tonic and Dominant. The “axis” is the midpoint between the two. It is not the median between E and Eb, which would be 320.38 if this was actually the case. It is not. The axis of this THEORETICAL concept is the median between Tonic and Dominant, which is the result of (392.00+261.63)/2 = 326.815.
Both the negative and blended versions of autumn leaves here are just horrendous, especially since you dont adjust the melody.
I never comment on videos but this has to be the best explanation I have found on negative harmony, thank you.
Great video. I really enjoy your approaches to finding the axis. However, the chords subs are incorrect. If I may offer clarification about the parameters of negative reflection:
(very) Simply Put
1)All major chords become minor
2)All dominant chords become minor 6
3) Because the negative reflection of the major 1 chord is just minor
all negative harmonies can be calculated by using the V chord as the root of a descending phrygian scale against the original ascending Ionian ie
Positive (C major) Left
Negative ( G Phrygian) Right
C=G
D=F
E=Eb
F=D
G=C
A=Bb
B=Ab
So: C= C minor
G7 = Fm6
Hope this might help!
Daniel Murphy can you make a vídeo of this to understand it please, thanks!
Thanks for the video. I think one common example of a negative harmony substitution that everyone has heard is V - I becoming iv6 - I. Although you've written Dm7b5 here, the negative version of the V7 chord could also be written as iv6 (in C, Fm6). iv6 - I is a plagal cadence that is commonly used and sounds very strong, almost as strong as V - I. Jacob seems to associate positive harmony with perfect cadences and negative harmony with plagal cadences. That suggests that we might want to think of the -I chord as being Cm rather than Ab. Then V7 - I turns into a nice plagal Fm6 - Cm. Cm as the i chord makes even more sense considering that the notes in -C are really from the parallel minor, C aeolian.
Thank you! I finally have something of a grasp on what this concept is.
great video Paul. Bravo. Inspiring stuff!
It's one of the best videos I've ever seen about harmony and music theory basically..
Thank you for your work.. Keep it up.. ❤️
I appreciate your feedback!
excellent explanation! Thank you man
Thank you . Finally found a good explanation.
The 4th degree is called a subdominant because it is a dominant below the tonic not because it is slightly less dominant than the dominant. A fifth below C is an F so F is the subdominant.
You are an excellent teacher!!! Thanks for this clear explanation.
Keep up the good work.
Pretty cool. If you play a progression in C and then play the same thing right after using the substitute chords it's almost like an eerie call and response.
Maybe I'm missing something, but how is this any different from "modal interchange," simply borrowing chords from the parallel minor ("interchanging" between C major and C minor, two "modes" sharing the same "tonic")? Other than, of course, it (the "negative") giving you suggested "opposites" to "try" when trying to fabricate a progression, for songwriting.
Well if u took the six of c major (A) and compared it to the 6 of c minor (Ab) it doesnt match up as shown in the video where the "negative" A in c major is Bb
Thanks! Yeah, I understand all that... but still, really, it ONLY is generating chords between C major and C minor keys, right? That's what it seems... Which is... hilarious! Because I see this polluting the brains of many a theory student, lol. That said, if it gives someone a "replacement" chord in a way they (for whatever reason) wouldn't have arrived at by any other means, all good :-) Thanks Darius!
I agree, which supports the idea that this is just a theory, not an actual thing. :-)
Hey Dale! What the whole concept seems to me is just an explanation of "why a iv minor would want to resolve back to the tonic." What I feel Levy and Rusell talk about in their books is the idea that the gravity of every chord against the tonic remaining the same even if the "axis" or the "scale" is flipped over.
The whole jargon is borderline hilarious with so many people buying Levy's book now when people like the Beatles, Bowie and the Shadows were doing it in the 60's and I'm pretty sure they weren't thinking of the term negative harmony.
In other words, POLLUTION, haha! Thanks Aditya! Rad to read you here!
The C maj negative "scale" looks like a C natural minor scale starting on Ab going downwards
Very goodd video, lately I’ve been searching so much about all the techniques that Jacob uses, and it’s so hard to find good and well explained content speaking portuguese, but I’m giving my maximum to understand it all
Thank you very much!!!
For your information, Joseph Kosma was the composer of Autumn Leaves. Johnny Mercer wrote the English lyrics of the song.
take the triton from C ...Gb!... use it as the mirror...so you get the scale C Bb Ab G F Eb Db C...start with Cmaj and continue with the maj chords downwords to C....works for me in ANY scale...altered...-6...+5...
The strength of this system is that it relates to standard chromatic theory concepts while forcing the composer into harmonic areas which are not completely intuitive or easy to come by through experimenting with voice leading, enharmonic equivalents, chord substitutions, etc. It's easy to think it "sounds bad" if you're trying to force the music to stay in the original key, but it would be a cool way to transition to a new key, develop a theme, or just perform a chord substitution for dramatic effect.
It would be fun to play around with implementing negative harmony to a non-diatonic borrowed chord in a progression. Say you have a ii-V-I, substitute a minor v, then transition to the negative equivalent before resolving to wherever that takes you, which doesn't need to be in the original key.
If you're just thinking of using negative harmony for the occasional chord substitutions, yeah you could better explain it as a chromatic 3rd, borrowed chord, etc, but it seems like there is potential if you take a more compositional approach.
edit: much like set theory or serialism, the whole point is that the system gives you a way to find something you weren't looking for or would never find on your own in the first place.
edit 2: it would also be helpful to have some way of notating the "negativity" of a chord for the purpose of analysis and performance.
Very fascinating. I have heard this term "negative harmony" used but didn't know exactly what it meant...kind of brings to mind George Russell's lydian chromatic concept. Just a different way of organizing tonal structures
Great Explanation!
Now I understand how to play it, thank you so much!
think of it this way: now apart from 7 diatonic chords in C major you also have another 7 chords in Eb major. So, playing in C major you have extra options for unexpected harmonies and colors, pretty fun
I get what you saying, but how is this different from borrowing from the Eb key, or is it just the same but called negative harmony. Just trying to make sense of this in a physical playing way
@@pedroberoes49 to me it’s the same, but it tells you exactly What chord from Eb substitutes for each chord from C. However for me personally it’s not very practical and musical, it’s much better to find those alt chords manually, Even if you’re only restricted to Eb
@@pedroberoes49 I mean if you're using the system laid out in this video, all that you're really doing is borrowing chords from the parallel minor. All the chords in Eb major are really just C natural minor.
Clearest explanation on Negative Harmony out there. Did not get some bits by the end but i tried to follow and the most I could understand was this transposition thing but there was examples that did not seem to fit.
Man, you are amazing!!! thank you so much from Argentina
Brilliantly done! Thank you very much!
I Loved the video & I felt that it was the concept was clearly explained as opposed to other videos.
I think, to be more simple, we can say that the negative key is the bIII major key. For example like in the video, the negative key of C major is Eb major. But the Eb is starting at IV of C major key. And counting it backwards.
"Negative harmony" is otherwise known in traditional theory as "interval inversion." Why on earth would it be viewed as controversial? It's a common element of compositional technique dating back to the Renaissance.
They are not actually the same when you look at the origin of the theory. The entire concept is based on sonething called "undertones," which are supposed to be the opposite of "overtones." Overtones are a naturally occuring thing, while undertones are not. I consider the entire thing an exercise in creating something out of nothing to try and find new ways to approach music. Inversions, transpotition, retrograde, modal substitution, etc.... are all musical concepts based on changing notes or chords. Undertones don't exist, so the theory is basically useless. Thanks for commenting!
@@YoPaulieMusic "Undertones" do exist, however:
en.wikipedia.org/wiki/Undertone_series
I didn't know James Woods had a music education TH-cam Channel. Fantastic stuff!
Great video, super instructive! I wonder about the harmonic content as a way to understand the consonance (literally the interacting frequencies). To my ear the "pure negative" is dissonant, your version does rescue it a bit.
Thank you so much. Extraordinary explanation!
After watching 10 videos or so I finally get to understand some of it.
Glad that you liked the content. :)
The explanation "G is the dominant so we take it as the counterpart of the tonic C" still is arbitrary, but the axis circle makes sense. It would be possible to actually use G as the zero-point, or D, or any other note. Using G as the zero-point, G minor triad would sub for C major triad. I think this concept is worth generalizing and not restricting to only the axis between third and minor third.
This is just a modal interchange (C major and Cminor) but with some pretty concepts to make it seem complicated.
No, its not, because each chord has his own substitution. It works with non diatonic chords too, for example the secundary dominants follows the cicle of fourths (in C: G7 becomes Fm6; D7 becomes Bbm6 A7 becomes Ebm6). You couldnt do it only with modal intechange
What an absolutely fantastic lesson! Thanks!
wow this is the clearest and most detailed explanation I have found about negative harmony on youtube, thank you, I subscribe to your channel :)
Great tutorial. But I think there is a mistake. The frequency of the "axis" should be the geometric mean √(ab) instead of arithmetic mean (a+b)/2. That is to say, the axis = square root of (392Hz × 261.63Hz) = .... = square root of (the product of frequencies of any two symmetric notes) = 320.25Hz. Because the frequencies of each note on keyboard is ordered as a geometric sequence instead of arithmetic sequence.
A couple of people have brought up the math situation regarding the axis. In every case, the frequency still falls between the 3rd and flatted third of the key, so there is no real change to the method of finding the axis. In C it is still between E and Eb. :) Thanks for taking the time to comment, I appreciate it!
Omg this helped soon much! Question: how come you didn't switch the melody of Autumn Leaves as well? Thanks
Stunning Teacher!
Thank you for this! I was worried it would be too long but I was actually surprised that 18 mins already passed by. Great concise and coherent explanation!
Yes because 18 minutes is an eternity.
7:58 Talking about linear midpoints between frequencies is a little suspect given that pitch is a logarithmic scale. The perceived midpoint between two pitches is not the midpoint between the corresponding frequencies.
It's also irrelevant because it's a theoretical concept as a way to show a non-existent midpoint for a non-existent physio-acoustic concept. :)
@@YoPaulieMusic While it isn't a big deal, I think using correct math matters, you used the arithmetic mean instead of the geometric mean. It just happened in this case to give you a value in the correct range this time. Say we have a note at 400 hz, we go up two octaves to 1600 hz, if we use the arithmetic mean to find their midpoint we'll get (400+1600)/2=1000, but one octave up from 400 hz is 800 hz
If we instead use the geometric mean we'll get sqrt(400*1600)=800 hz
The value at the timestamp should then be sqrt(392*261.63)=320.248 hz
Well, correct math always matters if you care about math,@@paulfoss5385 . :) But in this case we are talking about Western-based musical theory concepts and the goal is to find where on the piano keyboard the split point is. There is plenty of room for mathematical variance... thanks for commenting!
@@YoPaulieMusic First of all, you made a good video.
What I care about is that you'll be able to find note midpoints consistently in the future. The arithmetic mean happened to land in the relevant range this time, but it won't always, as in the example I gave.
You can't dismiss math as irrelevant while you're in the process of using it. That you are trying to dismiss it suggests that embarrassed and are being slightly passive aggressive, which I think is an understandable response for a creator being subjected to scrutiny from thousands of strangers, but there's no reason for embarrassment here, they don't teach the geometric mean in school and the situations where it is the correct average to use.
Thanks@@paulfoss5385. I don't mind the constant flow of people discussing the mathematical mean, vs average, etc. There are actually several different takes on the concept within the comments, I would estimate there are at least three or four different theories on what that mysterty mid point should be. Composers that want to try to usw this theorhetical concept will never need to know the specific frequency between E and Eb, they will just need to know that the approximate split point is between E and Eb (in the example from the video). There is some frustration that people are choosing to focus on this mathematical situation instead of the larger overall concept/theory. :) I appreciate the dialogue.
Very Clear explanation. Thank you Paul!
Best video that talks about this clearly
That was an amazing well paced progressive explanation. Thanks a lot!
This is very well done, and shows how to arrive at the substitute chords. Based on watching another video it only works well (meaning sounds good) when certain negative chords are substituted for their positive counter part in a given chord progression. This is obviously dictated by musical taste. At least your video gives a clear explanation of what chords to try as this is different from tritone substitution.
Great teachings for such an interesting subject of negative harmony! Mathematics in music is amazingly cool!
"Now youre probably wonder why im gonna need all this notes for, after all, i build up negative C major chords for 12 hours. But to awnser that, we need to talk about pararell universes"
9:18 "tominant and dominant" XD
Great explanation, thank you!
sent here after Gian’t Steps negative harmony
well explained, thank you!
I think the calculation of the midpoint should be in notes, not in hertz, because the mapping of notes to hertz is not linear. That gives 3.5 notes above C, or the midpoint between Eb and E - same answer, but sounder reasoning I believe.
wait... in 15:28 there is no point of negative harmony substitution if it is not applied to the melody as well. If you paint a tree, then mirror the branches to its roots and then superpose the leaves what do you have? a mess
I think you can do it either way. Negative Harmony just provides chord substitutions for your given melody. You have the choice of changing the melody, but it is not required.
I'm open to making changes if I've made a mistake. Can you find a problem with the method/explanation? What sounds random?
You need to mirror the melody as well, or it will just sound out of tune. It's not ment to just substitute the chords like you do.
Hello Paul, from my opinion, I don’t think there is any mistake, it is just that after translating all the chords into their negative, then the melody is misplaced, it would need to be mirrored as well. As an observation, in the case of dominants, for instance, G7->C translated to its negative version would be Fm6->C instead of Dø->C. G minor Phrygian is the negative scale of C major Ionian; the scale is Fm with the base on the 6th for its substitution, as well the plagal harmonic resolution, that's why in many cases if we keep the melody as it was, the scale doesn't correspond to its negative version, however, we can't say it is a mistake of course it depends of the context. "Giant Steps" sounds very well with some negative substitutions over the melody.
Paul Croteau I don't find any problem yet in theory explanation, but if you applied that into a song, make sure you made an axis melody too. Like C major ionian ascending scale into G minor phrygian descending scale with the same rhythmic. But this is actually very helping me out, so congrats, you got a new subscriber! 👍
Thank you mann i never thought id understand this concept..
Nice presentation, but I do not think "reversing" the chords of "Autumn Leaves" while keeping the melody the same worked at all.
As other points out, you are just rewriting Ionian to Aeolian in the end, so going by the whole "negative" concept seems overly complicated and counterintuitive.
I completely agree. I did that in order to illustrate the concept... I think Negative Harmony is a gimmick at best.
Exactly. Conman.
I'm confused - he starts off by saying that, in the key of C, the axis point is between Eb and E. OK, so far so good, but then he draws a circle of fifths which shows the axis dividing C and G. So which is it?
Go to 6:23 in the video. The harmonic midpoint is between the Tonic (C) and Dominant (G). This puts it somewhere between E and Eb.
Now i am able to make negative harmony covers
If I want to use my new powers for evil, I will.