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!

This came recommended to me after I watched All-Star for the twentieth time in negative harmony

Finally someone who really made an effort to explain this concept! Thank you very much! Subscribed!

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

Thank you. I now understand negative harmony well enough to be sure I don't want to use it.

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.

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.

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.

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.

Thank you, excellent teaching - what seemed complicated now understood! Thank you for making the video for us.

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

Clearest explanation of the subject that i’ve found. Thank you.

This has to be the best and simplest explanation of negative harmonies ever...thank you so much! 🙏🏼

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!

wow this is the clearest and most detailed explanation I have found about negative harmony on youtube, thank you, I subscribe to your channel :)

Thank you so much. Extraordinary explanation!

Thank you! I finally have something of a grasp on what this concept is.

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!

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!!

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.

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...

Outstanding tutorial! Very impressive. Thank you so much for doing this. ✌🏾

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.

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!

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.

Most comprehensive explanation of the concept I found so far!

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!!!

Stunning Teacher!

What an absolutely fantastic lesson! Thanks!

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 Explanation! Now I understand how to play it, thank you so much!

I never comment on videos but this has to be the best explanation I have found on negative harmony, thank you.

thank you for your explanation, very clear and informative. I specially like the slightly offset circle of fifth!

Incredible walk-through and very interesting reading suggestions.

Thanks for the explanation! Finally I understood it

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.. ❤️

Great video Paul! Perfectly explained and enjoyable to watch!

Absolutely excellent video!

Best explanation and demonstrstion yet! Thanks

Helping to expand my brain, Thank You Paul!

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.

I didn't know James Woods had a music education KZfaq Channel. Fantastic stuff!

This explanation is so clear! We thanks.

Thanks for the explanation, kupo!! I understand it much better now, maybe not 100%, but through this video, I'm making progress!!

This is the best video to understand negative harmony. Thanks!

That was an amazing well paced progressive explanation. Thanks a lot!

The comment section is negative harmonics.

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

great video Paul. Bravo. Inspiring stuff!

excellent explanation! Thank you man

Perfect explanation. Much help thank you!

U explained it so beautifully Thxx a lot!!!!

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.

Brilliantly done! Thank you very much!

Thank you so much!! Very exciting stuff - gonna use it for my own...

Thanks a lot. I agree with them all. Yours is the best explanation on this. No more mysteries about it!

9:18 tonimant and dominant :) Great video! Thanks for the explanation!

You are an excellent teacher!!! Thanks for this clear explanation. Keep up the good work.

Thanks for this video brother! Awesome awesome.

I taught on negative harmony to my high school class a couple of weeks ago. (After spending a weekend on understanding all this!! ;) )

Now All Star - Smash Mouth in negative harmony makes more sense

This is a fantastically clear explanation of negative. thank you so much

well explained, thank you!

I Loved the video & I felt that it was the concept was clearly explained as opposed to other videos.

Great teachings for such an interesting subject of negative harmony! Mathematics in music is amazingly cool!

THANK YOU SOOOO MUCH🙏🙏

*VERY* helpful thanks.

Thank you! This made so much sense.

Thank you so much! This is very well explained

Man, you are amazing!!! thank you so much from Argentina

Great explanation, thank you!

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

thanks, very clear!!

Both the negative and blended versions of autumn leaves here are just horrendous, especially since you dont adjust the melody.

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..

excellent video!!!

Best video that talks about this clearly

Thank you . Finally found a good explanation.

Thanks a lot man! Excelent lesson!

Finally! I Understood what it is "Negative Harmony" , thanks a lot Paul Croteau, great explanation. Greetings from México

it made me finally understand it!!! thank you!!

Very clearly explained, though I'll forget it all by the morning. Thanks. BTW - Bartok had his own way of understanding harmony. Wrote a paper about it once, but forgot that too.

The C maj negative "scale" looks like a C natural minor scale starting on Ab going downwards

Thanks! I learned a lot.

Thank you mann i never thought id understand this concept..

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

GOLD ! Thank you

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

thank you for sharing!!!

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

Very Clear explanation. Thank you Paul!

Such a great lesson Finally understand

Excellent vid thank you!

this is awesome! thanks

After watching 10 videos or so I finally get to understand some of it.

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.

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!!

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! :)

sir, can you plz clear my doubt what chord will be used for Minor chord like (CM7 {AbM7} ) but what will be used for Em,Am,Dm ? ________IS THIS CORRECT_________ For (E7) we are using (F7) then for (Em) we'll use (Fm) ???

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.