The Furthest Distance Between Two Chords

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What does it mean for two chords two be far apart? How do we even measure that? Well, there's lots of different approaches that each give their own answers, but one of my favorites is a motion that really hasn't been examined very deeply, one that I got to invent my own name for: The Exochord. It's a cool, dramatic sound that works a lot better than it feels like it should, and the story of why it's so far away is a really fun one. Check it out!
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7 сен 2024

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Комментарии : 204

@12tone 5 лет назад

UPDATE: This apparently does have a name! Scott Murphy described it as the Tonnetz Pole. There's still been very little written about it, but if you do want to learn more that's the term to search. I'm sticking with Exochord, though, it's a lot more fun to say. ORIGINAL POST: To be clear, I'm not claiming to be the first one to come up with this. Heck, I doubt I'm even the first one to name it: There's lots of writings about Neo-Riemannian theory out there, and I can't say I've read all of them. I did check with another theorist friend to confirm that at least I wasn't the only one who hadn't encountered a name for the movement, and as far as I can tell most high-level NRT writers are more interested in unifying structures like Hexatonic Cycles and Weitzmann Regions than exploring random outliers anyway, but I know better than to claim "first" on basically any idea, especially one that just falls right out of the system like this. Someone else undoubtedly got here first, it's just I have no idea who, or what they called it.

@Lordcamilli 5 лет назад

This relationship also appears on the Harmonic major which gives you a IVm-V7-I. Also on some other exotic scales. The interesting thing happens when you add a 4th note, which really opens up possibilities for those relationships. Great video. Can you make one for NRT with 7ths?

@markusreuter 5 лет назад

Composer Daniel Schell uses the term "Salto" in his "Musique Optimale", defined as the number of half-steps to go from one chord to another (in terms of closest possible voice-leading). So maybe call this one "Salto 5"? :-)

@leonardobuccoleri7582 5 лет назад

Hey! Could you guys please make a video about harmonic relationships between main keys of different songs in an album?

@WheeljacksScoreVideos 5 лет назад

I loved the Autobot logo you drew; any reference to transformers gets my attention better :sweat_smile:

@Zyborggian 5 лет назад

IVE BEEN WANTING A VIDEO LIKE THIS FOREVER I USE THIS CHORD PROGRESSION ALL THE TIME THANK YOU.

@AlanKey86 5 лет назад

The 1 chord's connected to the... 3 chord The 3 chord's connected to the... 5 chord The 5 chord's connected to the... 3 chord Now hear the name of the lord! (Amen cadence)

@josephkarl2061 5 лет назад

I won't be able to get that tune out of my head all day now... 😂

@DancingRain 4 года назад

1,3,5,3... Does that in some way or another spell out YHWH?

@AlexKnauth 5 лет назад

(6:42) I actually think that sounds fine. The Gm chord doesn't sound weird, it just sounds like the start of a "downer" modulation, like the kind in a musical-theater song that starts out happy but then someone comes in with some bad news, but still fits in fine

@Simoran 5 лет назад

You know what, that's a good point. I really thought it sounded strange before you made me think of a musical theater idea behind it, and then I pictured it perfectly.

@forgetful9845 5 лет назад

Yeah I think it would work well in a song if after the Gm hit, a really sad melody started playing with the tonic on Gm.

@mykhedelic6471 5 лет назад

Okay, but how many intervals to Kevin Bacon?

@IaCthulhuFthagn 5 лет назад

Or indeed to Paul Erdős?

@metaltom2003 5 лет назад

Six. Definitely six. LOL

@otesunki 3 года назад

Six.

@danatronics9039 5 лет назад

2:11 these two chords remind me of Take on Me... such a small part of the song but so iconic

@wyattstevens8574 Год назад

I can totally hear an F#m after the C#m! You're right: "Take... on..."

@johnfoster7762 5 лет назад

And here I thought it was just the chord that was a tritone away. I have learned something entirely new today, thank you. Do you have any journals or anything to recommend for learning more of this type of stuff? I'm in school for business so I don't have direct access to academic sources on music theory, but I've picked up the basics of stuff like Neo-Riemannian theory by now and I want to begin learning at a higher level. I'm probably a little weird in that these ideas actually really help my creativity when composing, I love those "outside" sounds and I'm always looking for new ways to be harmonically interesting. It's also just super cool how deep you can take simple ideas in music theory.

@12tone 5 лет назад

If you're looking for journals, MTO-SMT is probably my favorite. It's the online publication for the Society for Music Theory. It can get pretty technical, but they cover a lot of really interesting and obscure things.

@alex_evstyugov 5 лет назад

6:41 that's the most important word in the whole video: "context". 6:35 that's the second most important word: "familiar". Recently I've been writing in the style of Chopin a lot, and when you played A to Gm it sounded so unremarkable to me I didn't even shrug. And as you went on to explain, you don't even need to be Chopin, just having an occasional listen to The Four Chords on the radio will suffice. That's why A to Eb actually sounds more distant than A to Gm, as witnessed elsewhere in the video. It's basically the exact same thing, but it's much less common. Still a lovely progression, though. Frankly, I believe at this point in time in Western music, to find the most distant chord we have to think microtonal, or at least quarter tones. Edit: I think it was in the "Full of Noises" book that Thomas Ades mentioned some piece where the composer actually created a context in which the *tonic* chord sounded horribly out of place. It's like plain boring C major, and it's your tonic, but hearing it makes you physically ill. I can't remember the composer or the piece right now, and I'm browsing the book as we speak but can't find that bit. Maybe someone else can help out.

@shanok3 5 лет назад

Anyone pls find it out

@lidaco 5 лет назад

Commenting cuz I'm curious about the answer as well

@NathanQED 5 лет назад

In Béla Bartók's opera Bluebeard's Castle, there's a fortissimo C major chord played by the full orchestra and soprano upon the opening of the fifth door, and it's incredibly powerful and unnerving, in the context of the strange tonal landscape that came before it. Here's an interesting article about it written by a Chicago Symphony violist: csosoundsandstories.org/how-one-chord-builds-to-the-astonishing-power-of-bluebeards-castle/

@dwilliams4142 5 лет назад

This is awesome! There are several recurring themes in mathematics very concerned with questions exactly like this. Most commonly in topology and abstract algebra (modules). You could truly devote a lifetime studying these transformations for kinds of closest and farthest relationships. Super fun!

@TheSantiago52 8 месяцев назад

Has encontrado literatura que explore estas relaciones?

@JulianDoe 5 лет назад

Wait, wait, wait...What? oh no, this is another episode of 12tone that I have to watch at half speed :D well done,man really interesting!

@infinitefretboard 5 лет назад

So that's why the phrygian half cadence sounds so badass!

@MrvlZmb 3 года назад

The exochord and its most distant major triad without a third chord for context sound perfectly fine in the bridge and fade out of “Kashmir”, where they imply Phrygian Dominant.

@PhaseControlDNB 5 лет назад

5:35, hey, Vsauce, Michael here :D

@mrdjchasm 5 лет назад

Hahaha so true.

@kunzangrangdrol 5 лет назад

I found this interesting because recently I came upon this same major/minor triad combination from a whole different angle, which I wont go into. But I'd like to share one usage that I particularly like. Start with this lydian chord, Major7flat5. Let's use EbM7b5, or Eb, G, A & D. Now, use a Major triad with the Major7 of the chord as a root, or play a DMaj triad in all inversions over the EM7b5 chord. For the minor a whole step below, do the same but play the minor chord on what would be the sixth of the Maj7b5 chord, or in our case, play a cmi in all inversions over EbM7b5. (The c minor triad is of course part of the EbM7b5 but here it is more about a melodic line and should be inertwined with the D Major triad and played above the EbM7b5 chord.) Next experiment and intertwine them in all inversions over the EM7b5 chord. The EM7b5 chord is best left in root position, or 2nd inversion, but you can invert that as well for interest. The sonorities are very interesting. For more harmonic variations try using the two chord combination and 'borrow' notes from a Bb Bebop Major scale, or a D Lydian Dominant scale, and with any other associated scales (try the c melodic minor scale over the EbM7b5 chord once in a while, then go back to the Dmaj/cmi combo, etc., etc., etc.)

@paulc778 5 лет назад

This occurs in "Music to Watch Girls By", in the main verse - it goes from Am to B major, which is an absolutely bonkers chord change to solo over. (And obviously later in the piece, once its changed key, Bbm to C major).

@xeoxeon2615 5 лет назад

Looks like you could map that hexagonal network of chords around a sphere, where opposite poles would be each other’s exochords. Neat. I’d buy that!

@shaman9 5 лет назад

(7:08) fascinating result indeed. shout out to euler's identity!

@mcaron00 5 лет назад

Lots of Klezmer songs use the I and the bvii. As you pointed out, it's built around the 5th mode of the harmonic minor. Some call it the Lydian dominant scale. I could be wrong but I think it's fairly common in folk music from around the Agean sea.

@iantaakalla8180 2 года назад

It turns out that the Snif City Hotel Theme has that exact movement of F -> Ebm, so it turns out there is an accessible usage of this song. (But it comes off of a remix of Snif City which feels like it would be close but instead would have Fm -> Ebm, but at least they both seem to have Fm -> F#). (Also, The Bloodless from Hades has this. I guess a whole minor chord step down is a common Phrygian movement).

@maxonmendel5757 5 лет назад

A# minor. We're done here In all seriousness, I spent a couple hours last night building triads up from the root So I iii V vii II and so on, just switching quality and going up a third. I found some crazy patterns and eventually arrived at 24 unique chords: one for each chromatic note as major and minor. Its fascinating because when you make a chart with each if the modes from most sharps (lydian) to most flats (locrian), and then check off if a mode has a particular chord (lydian has a II chord for example, and ionian instead had a ii chord) you get to see the modes cascade into each other, morphing from one to the next. But after 24 chords, you arrive back at a major root. Its cyclical (I derived it from the circle of fifths btw.) from what I can tell according to this, the bV triad is furthest from the I triad. For reference, that's the Ebmaj against the Amaj you mentioned at the top of the video

@elliottmanley5182 5 лет назад

In order to draw all the major and minor chords and complete all the connecting hexagons, the diagram will have to be embedded on the surface of a torus. The patterns of hexagon descibe helixes wrapping around the torus. Beautiful. I collaborated on this subject in a chapter of the book "Patterns of Eternity" which seems to be selling for outrageous sums on Amazon now!

@GammaFn. 5 лет назад

Hey, I paused the video before you showed the chord, and I came up with the same answer, for the same reason! I actually found the Tonnetz on a Wikipedia dive, so I think of things in terms of that torus instead of the PLR torus. They're equivalent, just exchanging faces for vertices and vice versa. This mathematician approves.

@HanBurritoz 5 лет назад

It is also amazing to use in tone rows, when you also want to keep it sound more consonant. Like Fm - Gm - A - B triads use all 12 notes of the harmonic scale.

@idhott 5 лет назад

I think Mahler used this in his second symphony for the “death shriek” in the third movement! It goes from some kind of c chord (chromatic bassline under it, not sure if it’s major) to a massive b flat minor chord that sends chills down your spine. I always wondered what made it so jarring until I went over to my keyboard, figured out the chords, then remembered this video.

@Raalezor 5 лет назад

this was super fascinating! I found this relationship looking at subdominant chords in stepwise modal interchange (nrt is a bit beyond my understanding lmao) - you can use this down a whole step and change chord quality (specifically major to minor like in this video) in two places, the lydian I to the phrygian bvii or equally the ionian IV to the locrian biii. What intrigued me about this relationship is that when the major chord is played with a 9, #11 and 13 (like a lydian I), and the down-a-whole-step minor with a 9, 11 and 13 (like a dorian i), the movement may be extreme (and I might have to watch this video 7 more times to understand why) but it has the effect of preserving the major chord's first and fifth degree in the 9 and 13 of the down-a-whole-step minor chord. So its a movement that contains both an exorchord and a 1-5 anchor, it takes both the biggest step possible and stands totally still

@TacoDude314 5 лет назад

By interpreting them as scales instead of chords and "forgetting" the root note, this graph reduces to a square grid because all the down-right (A->F#mi) are just changes in the root. I bet you could get a neat effect by having a "rootless" melody which moves between the scales in the square grid, playing over chords which move between the nodes of the original hexagonal grid. Say the melody and chords start on A. The melody can move to Ami, C#mi, F#, or D while the chords can move to Ami, C#mi, or F#mi. We'll say the melody moves to F# and the chords to Ami. From there the melody can move to F#mi, Bbmi, Eb, or B while the chords can move to C, A, or F. No clue how good this would sound but it seems interesting.

@TypingHazard 5 лет назад

This whole thing reminds me of something I noticed a long time ago about the Circle of Fifths, where if you treat the keys as major chords and then put their relative minors between the keys/chords/whatever you have this neat representation of how triads or keys can relate to one another and if you just travel this circle linearly (A maj -> C#min -> E maj - G#min -> B -> D#min etc etc) you can sneakily play your way through every key without ever sounding like you made a sudden obvious key change. It's always just kind of been a cute observation and not really a substantial system, just sort of an amorphous music-y idea thing v0v but this aspect of Neo-Riemannian Theory you've shared looks like a much more evolved understanding of these relationships. I think I will endeavor to learn more about this stuff. One thing that stuck out to me right away is that other theories might contextualize these two chords to be pretty closely related, for example it's not uncommon to use a minor IV chord as a substitute for a V in jazz - so in your A to Gmin example, if we're in D then these are harmonically similar chords. Also IIRC doesn't that whole negative harmony thing make a ivmin6 chord out to be complementary to the V7? Interesting that all these models would imply such different proximities between chords

@djdm2603 5 лет назад

I was expecting this to be on hexachords, but I am always happy to be surprised.

@ADarkandStormyNight 4 года назад

Well Schoenberg in his structural functions in harmony would call it a Superstrong progression. Root movement a second apart. When he discusses his concept of regions it is relatively far apart from the Tonic so there is some overlap here. He justifies his terminology in a similar way, so I believe you would find some relative concepts there if you poke around, but because he focuses on harmonic function and equivalence a lot of harmonies that would be distant in this context are just functioning as something close to the home key. Like in this case, although he would consider the progression a superstrong one, it is also just the minor subtonic chord functioning as a subdominant or dominant depending on context. Anyway, his concept of regions does address this relationship to an extent.

@ohwhen7775 5 лет назад

My interpretation: The ii chord is distant because the minor 3rd of the ii is the 4th/IV of the root, and there's no 4th/IV in the harmonic series relative to the root/fundamental, and the one that's remotely close is around 51 cents sharp, so not quite the same note. For CGE going to DAF, the F and E are chromatic and AFAIK there's no chromatics in the harmonic series either, which further outline the significance of the harmonic distance between them. This places F in the key of C to be inherently plagal, it's on the left side of the circle of 5ths, E way over on the right side, and within the harmonic series. F is also responsible for the b6 interval in A Aeolian. Thus (partly) proving JC's theory about 4ths being inherently more minor feeling than just using "chromatics" for dissonance, such as a minor add9 chord, which is barely minor to begin with given it has two intervals from the right side of the circle of 5ths before it even has 1 from the left side (the m3rd). bvii relative to I is distant because the chord family is plagal on plagal, the root itself is plagal DESPITE the fact that there's a b7th in the harmonic series (31 cents flat but it's there). So what gives? The harmonic series of the *major triad* is what gives, not just the root note. Because the first harmonic that's different from the fundamental is the 5th, that has to apply to A, E, *and* C#, making the 5th of that C# a G#, which is the maj7th in A, this means that even though there's no chromatic in overtone series, the maj7 *feels* more at home to us than the b7th because we express major tonality in the form of the Maj triad (& its inherent harmonics) in a lotta western music that we're used to by now. ... This makes G feel more outside than G# to A, add to that the m3rd of G is Bb which is way outside of A being chromatic, the D is diatonic to A in the major scale but still chromatic to C# and therefore on left side of CoF being the 4th/IV too. Relative major of that being a maj triad a tritone away, I'm pretty sure the tritone is the furthest you can get. But AEC# to BbEbF is also distant and shares no similarities. I'm done for now, gotta sleep.

@hosemarino 5 лет назад

From what I understand it's the bvii minor within the major scale (which uses the natural vii diminished, so flattening it makes it a normal m7 chord instead of being a diminished (half diminished seventh))

@benjammin3829 5 лет назад

I really like that method for laying out the diagram! Using the "pyramid" diagram can get hard to manage at the lower levels.

@sazarod 5 лет назад

You can play a hijaz scale very nicely over a chord progression like A - Gm. Hijaz is Phrygian with a major third, and a mode of harmonic minor.

@ToneZoneStudios 5 лет назад

God bless you for making these videos my friend. You have a talent for explaining these complex ideas very elegantly. Thank you!

@amj.composer 3 года назад

I use that a lot when messing around with Phrygian! It's a lot of fun

@ronmor2004 5 лет назад

I've actually used this progression a lot because it sounds amazing, it can really change the mood of a piece very effectively. Btw, it sounds equally as awesome even if the tonic is minor.

@pathagas 5 лет назад

I loooove neo-Riemannian theory! Read a few research papers that use it and thought it was amazing. Love how it works in a hexatonic scale.

@Tarikrptls 5 лет назад

Related to that harmonic minor approach: In Flamenco music where we tend to play phyrgian #3 or at least resolve to a major I b9, a minor bVII sounds pretty good and close. It has some inherent bitterness, but iwe use it a lot! (Amazing videos btw

@FelipeTellez 5 лет назад

Phrygian Dominant Scale on A....Gmin is the subtonic....another fun way to think about it =)

@JonBoa 4 года назад

Can you make another Harmony video about the advanced techniques you mentioned in your video “The Trick To Writing Harmony Lines” (Voice Leading, Tensions, Contrary Motion, and Secondary Melodies)?

@MarsLos10 5 лет назад

Wow SO INTERESTING thanks for sharing this concept man

@dyjhjhy 5 лет назад

Led Zeppelin used those two chords in the Kashmir, I have always been fascinated with this sound. great video!!

@Ozarka741 5 лет назад

To me, the distance between these two chords in particular as well as the fact that they coexist in minor so well suggests that negative harmony's claim that they are negative versions of each other is true. You mentioned that the reason we don't think twice about hearing them in minor is that we've grown accustomed to them, and you may be right to take a nurture stance, but I would tend to lean toward nature because of things like the universality of the pentatonic scale and the apparent relationship between music and the harmonic series. Plus I'm holding out hope that we'll be able to find other sets of chords (triadic or otherwise) that exhibit a natural tonic, subdominant, and dominant relationship while being superficially different to traditional tonal harmony.

@Ozarka741 5 лет назад

If we were to find chords with similar acoustical relationships, it may not necessarily mean that they would sound like tonic, subdominant, and dominant; those functions may be inherent in I-IV-V or they may be learned. I suspect that the answer is neither fully nature nor fully nurture, which I hope would mean that on some fundamental level they would have the same functions relative to each other, but the superficial difference would make them unique. On the other hand, it could be that if we found chords with similar relationships that they would sound to us like random chords. I can't say for sure which would be the case.

@Al59redux 5 лет назад

I would have said A to Eb, as major o minor they don't share any note. But sometimes these two chords may appear in sequence and sound smoothly, if the first works as VIb and the second as V/V (v.g., Dbm / A / Eb7 / Ab7 / Dbm).

@lyavainBergen 5 лет назад

Now we are talking really cool music language! Loved most of your other videos but this one is really like scientific. Good shot!

@Classic_H_Radio 5 лет назад

Another way to arrive at this conclusion would be using Negative Harmony (made popular by Jacob Collier). In the Key of D, A is the V chord, but the "negative V" is the minor IV, which would be Gm. So, within their shared key center, they're mirrored opposites of one another.

@SchildBeats 5 лет назад

yes or just say its the negative doubledominant (the minor IV of the minor IV) so Gm goes to Dm goes to A major :) actually sound great if used with fitting notes :)

@mrsaxobeat6891 4 года назад

Interestingly, you can show that there must be one and only one distant chord through the topology of a dodecahedron. Only one corner is 5 away from a certain other one. This means that the Neo-Riemann series is symmetric too

@fitzdraco 5 лет назад

So I'm not sure how to ask this, but the middle of the video seems like it has something more useful then the furthest chord. Is there a way to use that diagram to do some kind of modal interchange without using a key? I guess I'm asking is there a way to use to use those diagrams to do modal interchange and such without worrying about key?

@12tone 5 лет назад

Absolutely! That's largely why this system was invented: To show how you could move through a non-tonal harmonic space in an ordered way. I'm not sure it's quite the same as modal interchange, but it's a good analogy!

@chrisharrison809 5 лет назад

You’re pretty brilliant man. Thanks for making these

@thescarymoosh 5 лет назад

In Ashkenazi Klezmer music, which permeates the Eastern European folk landscape, the I - bvii motion such as A - Gm is extremely common for tunes played in the phrygian dominant mode, also called "freygish" or "ahava raba". Examples: Nakhes fun kinder ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-A5Xa0h0od34.html Yesterday is buried ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE--7d9NNwxIjQ.html, Baym rebns sude ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-TzUl0GXEeXE.html

@dirtbagdeluxe 5 лет назад

Making a networks of chord values like this makes me think of the Stradella bass system on the accordion. Now I'm imagining how to combine the two

@Hecatonicosachoron 5 лет назад

Have you realised that the graph of triads at 3:30 is a torus? A hexagonal tiling of a torus to be exact.

@abramthiessen8749 5 лет назад

I had. It was an abandoned project of mine to try and make a wireframe Neo-Riemannian torus. I have also drawn a map of chords extended to 4 notes (major and minor 7ths) and including sus chords. It doesn't change things much but it does add more kinds of movements.

@Hecatonicosachoron 5 лет назад

Abram Thiessen For the 24 triads it should be fairly easy, it could be a fun construction, although folding the tiling into a torus will get a bit messy. One could write a composition based on the Hamiltonian paths of the graph, although it would sound a bit strange as you would be forced to move to the fourth and fifth only via the mediants... it would also have too regular and repeating harmonic rhythm

@thedistinguished5255 5 лет назад

Wow that's so cool

@IcarusRuthven 5 лет назад

I see the hexagonal tiling, but what makes it a torus?

@Hecatonicosachoron 5 лет назад

@Knight Icarus if you extend it long enough it starts repeating, which you can get if the whole structure folds into itself. Hexagonal, triangular and square tilings also tile a flat torus because it's... well, flat.

@Bug4566 5 лет назад

You're like Vihart but for music theory nerds. I love this

@matthewjamestaylor 5 лет назад

In the other direction this is great cadential material. D major to G major to G minor to A major. Great video. Cheers.

@mgrocki 5 лет назад

I feel like stylistically, our musical interests may differ, although I recall you're a metalhead at heart? Anyway, I LOVE these videos. Keep it up! (PS... this video is starting to look alot like Organic Chemistry... 4:50!)

@tompw3141 5 лет назад

aromatic chords, perhaps?

@iantaakalla8180 2 года назад

When you can smell a set of six chords for some reason

@Guerin78 5 лет назад

Not at all the chord I would have guessed, considering it's available via mode mixture (it's the diatonic VII chord of Phrygian and Locrian). My guess would have been the major triads a semitone away--everything else is available through mode mixture, chromatic mediants, or--in the case of the bVminor, as the relative minor of a chromatic mediant.)

@maurowindholz5880 5 лет назад

Hi 12tone! Would there be such a thing as the exokey? That is, the key that's the furthest away from another key. Might it be the same relation as the exochord, i. e., the minor key that is a whole tone below the reference major key? If so, have you ever notice how Eric Clapton's Layla explores exactly this relation??? The verse is in E major and the chores in Dm!!!! Please comment o that!!! Your videos are awesome.

@thealientree3821 5 лет назад

If you add Diminished triads (still possible in all modes related to Major), what will happen?

@12tone 5 лет назад

I'm not sure! Most of the more elaborate Neo-Riemannian models that I know of focus on adding augmented triads instead, as a sort of in-between for the relative transformation. I'll look into it, though, that could be interesting!

@tubatalabal 3 года назад

I'm guessing the discussion of intrinsic vs. positional function ultimately comes from Caplin's work, which I've never been able to get my hear around. If you ever get around to that, I'm all ears.

@alexthuene2806 5 лет назад

i LOve these videos dude

@Sonic_Time_Traveler 5 лет назад

Could you consider the idea of making a video on different analysis styles?

@CarlosGonzalez-mp9re 5 лет назад

I didn't make a deep analysis of this issue, but I usually consider the farthest chord or mode the same chord or mode but a tritone away (This way you usually get the biggest number of alterations from one to another). With modes or scales with a tritone is funny because they end up having the same root if you change the mode. For example, a Lydian mode a tritone away of the original, is the same as a Locrian mode with the original root.

@CarlosGonzalez-mp9re 5 лет назад

At first I thought too, of a different kind of chord a tritone away of the original as A and Ebm. But playing I felt it weird but natural, and I noticed that the third of the second chord is a note from the original key, and the fifth is very related to the root so the only real "new" note was the root, which was also fine, because the new chord worked well as a chromatic step. I use it a lot in sweep picking or another chord progressions because as a chromatic step, is very tonal, but the perfect fifth although is justified by the harmonic series, is very out of the key and it gives a very atonal sound although is a very tonal progression. It's weird but I like it.

@firebrain2991 5 лет назад

that last bit about how "it's weird there's only one minor chord that is the furthest away" reminds me of the "hairy ball theorem" in mathematics

@konungredocsil657 5 лет назад

If ya want a song where you could this type of theory to analyze it, check out take a bow by Muse. I think they use this idea of chord closeness in that song.

@AmandaKaymusic 5 лет назад

Thank you. Great clip.

@ARZiehm 5 лет назад

The viib - I chord vamp, or in every film soundtrack "The exotic desert" chord change (See prince of persia or the mummy soundtracks)

@mayday777 4 года назад

For some reason it has a Western Film feel to it.It also reminds me something from an anime I think Attack on Titan or Full metal alchemist.

@tearlach47 5 лет назад

I'm surprised that there's only a single answer with the method you used. I would've thought that a few would've been equidistantly far apart in this kind of a system, but it seems not.

@petercampanelli1062 4 года назад

"Talkin' About The Good Times" by The Pretty Things uses this exact progression on the chorus

@MartijnHover 5 лет назад

A Turkish musician once taught me a scale that goes 1 b2 3 4 5 b6 b7 and that goes over an A Gm chord progression. No idea what that scale is called. It's sort of Phrygian, I guess.

@rayhairston7582 5 лет назад

Great information

@nicholasmackelprang8385 5 лет назад

That chord progression can be voice led smoothly with step movement in every voice if it is done in four part harmony.

@MaemiNoYume 5 лет назад

there's another place where this happens... kinda... Db major is the neopolitan chord for C major. What's the relative minor of Db major? Bb minor. If you are in a simple progression like: Fmaj7, Emin7, Dmin7, you can usually insert Dbmaj7 after Dmin7 and then go to C major. What if you extend this even more and insert the Bb minor after the Db major? I tested, and it felt pretty good for my ears.

@Al59redux 5 лет назад

Sounds nice, but the C in the end, after the Db - Bbm, tends to sound to me as a V and send me back to F.

@MaemiNoYume 5 лет назад

@@Al59redux yes. F fits really well after the Bbm, far better than C. But if you use Bbm7 instead of just Bbm, the 7th can go down one half-step to be the 5th of C, so it will be better than just Bbm. It's natural that F fits better because F is closer to Ab major than C is (in the circle of fifths).

@Perom83 5 лет назад

I hear Gm, sometimes in brazillian music, as Em7b5/G . So, Gm A7 Dm, its like a IIm7b5 V7 Im

@vidaofficial7483 5 лет назад

Very cool concept.

@Dulceria-La-Princesita 5 лет назад

HEY! Those are some good looking bananas, dude.

@JSGH-JOE 5 лет назад

Awesome... thank you!

@jamescastelli 5 лет назад

I'm glad you mentioned A and Gm being the V and iv in D harmonic minor, but it seems to me that even ignoring that, when limiting yourself to the key of A Major where a sudden Gm sounds strange, one of the tones (D) is at least in the key of A Major, so arguably isn't the most "distant" chord, if one can be found that has no noted from the A Major scale. You first mentioned Ebm, which, if you respell it as D#m, obviously has an F# in common with the key of A Major. Ah, but Eb MAJOR has no notes in common with either the chord OR key of A Major. Similarly, the relative chord to Eb Major: C minor, is similarly situated, so perhaps the minor quality would make it sound more distant from a major triad. So basically you have a tritone substitution going on. Why don't you consider this angle?

@12tone 5 лет назад

I did consider that, but like I said it's a question of how you measure furthest. If you're looking at key centers, then A and Eb major are direct opposites on the circle of 5ths and thus the most distant, but in this case I was more concerned with non-tonal chord relationships so comparing the notes back to an imagined key center wasn't really relevant.

@jamescastelli 5 лет назад

@@12tone Hmm, okay, well it seems odd to regard "chords constructed within diatonic hierarchies" without any relationship to that. Sure, pop music today has all but stripped chords of their once important "function." I would still argue that it sounds more "alien" to alternate between A and Eb major chords than between A and Gm. Since neither pairs of chords share any tones, the aural effect combined with the fact that neither chord contains any other notes from anywhere in the other chord's KEY should elevate my interpretation. Especially if music is a subjective/associative experience, it seems odd to base your analysis solely on an arbitrary paper-hopping method.

@dastuffz 5 лет назад

this video is awesome

@martinepstein9826 3 года назад

Why Riemannian? Something to do with Riemannian metric? Come to think of it, if you draw a connected graph and define the distance between two nodes as the smallest number of edges you can traverse to get from one to the other you do get a metric space. It's not clear to me how this theory describes our experience of harmony. You say the exochord *would* sound weird but our exposure to harmonic minor made us adapt to it. How do you know? Obviously one could test this by raising a child in total isolation from Yngwie Malmsteen records but that would be unethical.

@tubatalabal 3 года назад

Because, as he says in the video, it was developed by music theorist Hugo Riemann. Nothing to do with math or Bernhard Riemann.

@fridaychen8 3 года назад

Could Exochords be more distant if found in different tuning systems?

@xyshomavazax 2 года назад

Minor secondary subdomminant? Altered plagal cascade?

@blakeingraham3983 5 лет назад

Could you apply this same process to more than just major and minor chords? For example, what chord is the farthest away from Bbsus6 or Fadd9?

@Paul_K_ 5 лет назад

before watching the full video for your reasoning, my answer for the furthest chord from A major is E#/F minor, just based on my personal framework.

@uritibon17 5 лет назад

Brings to mind the leap between A major and G minor in Prokofievs first movement of the second piano sonata between the first theme to the bridge - very jarring (my teacher wanted it to sound like a punch to the head, to me it just looks like one of those coarse movie cuts from a lively scene to a bleak one)

@benjaminmargulies1853 8 месяцев назад

The B flat in G minor is a tritone away from the E in A major

@sewbernard 5 лет назад

Idk man it sounds like ive heard this exact thing in warcraft and lotr before so it sounds pretty good to me, except it never resolved back to the A

@igoletacdvc 5 лет назад

What would be the furthest key change?

@2li678 5 лет назад

Interesting perspective. It doesn't SOUND that distant to me, though. They sound (and look) like neighbors. I think for it to sound distant the root would have to be a fourth to a fifth away... but maybe that's just my ear as a folk musician.

@Teemu_V 5 лет назад

This is some amusing theorizing, but I find it odd claiming that the judgement for the so called exo-chord is based on Neo-Riemannian chord spheres. A minor chord a semitone below a major chord has many smooth uses even in traditionally functional music. That's how Yesterday begins. The chord is a part of ii / V chord progression in relative minor. Other usages may refer to either Lydian qualities or tonical ambiguity between I and V or other scale degrees. These practical uses for this chord don't convice me that this chord would somehow possess the title of exo-chord. By the way, exo-chord is a fine name altogether!

@12tone 5 лет назад

Yesterday starts with a major chord going to a minor chord that's a half-step below. The exochord relationship I'm describing here is a whole step.

@Teemu_V 5 лет назад

@@12tone My mistake. Good job.

@mcaeln7268 4 года назад

I feel like if we tried hard enough, we could make a kind of ball out of this and use as a physical model for composers

@tubatalabal 3 года назад

It's called the Tonnetz. If you look in your favorite app store, you'll no doubt find several Tonnetz apps. Topologically, though, it's a torus, not a ball.

@t71024 5 лет назад

Interesting graph. Can you continue forever and tile an infinite plane with it? In other words, is it geometrically flat?

@12tone 5 лет назад

It is! It's actually a version of one of the most important structures in Neo-Riemannian Theory, the Tonnetz! It's usually shown wrapped around a torus to make the repetitive nature clear, but yes, it tiles perfectly well too.

@SSGranor 5 лет назад

Don't quote me on this; but, I believe that the existence of a unique exochord (or, Tonnetz pole, as 12tone mentions it's called in the pinned comment) is basically equivalent to the fact that the pattern tiles infinitely.

@aqiiiiiiiil 5 лет назад

I thought you gonna play Paranoid Android for a second there, in the beginning.

@Rainer67059 5 лет назад

A piano player can play two chords at once one with each hand. Anyone who composes for piano or another keyboard instrument must consider the limited reach of the hands of the piano player. On the one hand the notes played with one hand musn't be too far apart. On the other hand, the chords played with the two hands musn't be too far apart either but they can be rather far apart. Just how far? Now I'm gonna start to watch the video to find out.

@Tabu11211 5 лет назад

Super cool!

@joenormanmusic 5 лет назад

Can you do AWOLNATION’s Sail???

@mentalitydesignvideo 5 лет назад

Easy: contrabass and piccolo. Whatever they play, it's the most distant.

@mayday777 4 года назад

So the exochord is either vii or bV?

@v0Xx60 5 лет назад

I know its not exactly that, but that diagram of chord relationships reminds me of a tonnetz, the positions of everything is even largely the same.

@12tone 5 лет назад

It actually is! Well, one version. It's what happens if you take a normal tonnetz and connect the chords instead of the notes. I've often seen it called a Chickenwire Tonnetz 'cause it uses hexagons instead of triangles.

@v0Xx60 5 лет назад

@@12tone That's really cool! I actually use a tonnetz frequently as a reference when noodling on guitar. I really like having the clear visual of the relationships between notes. I'm going to have to look into this more expanded version for future use. Amazingly informative as always!