I have been playing guitar for over 30 years now and nobody has ever explained it this way to me. I feel like my minds eye has been opened wide and now I can see all the patterns in my head without even looking at a guitar fretboard. For the people who find this complicated and confusing, just remember that our brains are wired a certain way to help us learn and in my case, I’m a pattern type of person and I have always seen this pattern on my feet board but the only thing I needed to know open my mind was the key to decipher it’s meaning. Thank you so much for this gift. I will like, subscribe, and share.

i’ve playing guitar for 52 years (really) and i have a degree in music theory and composition. i was mesmerized and lost at the same time. MIND BLOWN. Better watch it again.

This has changed my life completely, I am now a mathmusician

Why didn't I have a teacher like you when I was a kid! This is amazing!

At around minute 7, I was feeling the tug to disagree because of the major-3rd interval between the 4th and 5th strings of any standard tuning (regardless of how high or low you have 'standard' tuning). You do explain the semitone shift a minute later, but I feel that it is understated, as the results have big consequences, and those consequences are *enormous blessings to fingerstyle players* . I wonder if I'm unique in that I see chords and CAGED system patterns -- not a Cartesian coordinate system. I still like this video because it explains note relationships perfectly well but only while strings are *tuned fourths apart* . Food for thought.

Wow, this is what I was looking for. I am a beginner playing the guitar, and also an electronic engineer for 40 years. Everything in electronics is mathematically based, this is the only way to really understand the mysteries of electronics. I knew the guitar fret board had to have a mathematical definition on how the fret notes are positioned on the neck. I feel a lot better now knowing there is some method to the madness. I'm still studying this video as I still have a few things to comprehend, nevertheless this video is a wonderful insight on this subject. Thanks so much for the details, I needed it.

This is above my understanding...I need a drink 😅😅😅

I´m really happy that this was not the first video I've encountered when learning guitar.

I am glad a number of people interested in guitar found this helpful. I viewed it as a colorful way to make learning guitar more confusing. Thanks for your efforts, Mike.

I have been playing for 20 years have a degree in jazz and followed what you were saying but it infinitely made guitar more complicated 😂. Scales and modes/ recognizing intervals works just fine for me

I’ve been recently sorting through the joys of music theory and I found this video most insightful!! Thank you and keep up the fantastic work. This is the depiction of the higher dimensions we engage with as music lovers. Awesome content!

This is not necessarily helpful for teaching guitar but in revealing geometry behind music theory it’s pretty spectacular. The animations are incredible! I’ve always been intrigued by the mathematical foundation of music but I have a hard time articulating it to others. This video will be mucho shared

Mike, you are the Christopher Nolan of music theory videos! For a second, you brought me to a musical tesseract and unlocked a new dimension! Thank you for this mind-blowing mathematical lecture in musical physics.

I find that what helps me most with the guitar is to simply view the neck and fretboard as a piece of lumber with strings stretched over it.

Thanks for this incredible lecture! I grew up playing the classical guitar and have just picked up the electric guitar, where for the first time I'm conscious of the patterns to learning scales and using movable chords. It's made me more excited about this beautiful instrument. Your explanations have only helped me process and brought me clarity to what I've been observing.

Bro.. 🤜🏼🤛🏼 You win the best fretboard theory video I have ever seen. Its been 36 years of picking random covers out by ear.. I’m turning myself into a music theory, geek to figure it out. Now I love music theory, the traditional method, or the active listening method, I have never thought to related to a Taurus, my mind is blown.

Muscle memory, intervals, chord shapes and good ears.

I studied with Pat Martino in 1982 for 6 lessons. He was pointing these concepts back then. Good stuff.

To me this explanation is making the whole thing more complicated. I rely on the major/minor scale and intervals to navigate my way around the fret board

Mendeleev Presented to The Royal Society, a Thesis which shows that the Periodic Table of Elements is in Octave Format, so We are All, and Everything is Condensed Energetic Music. Tolkien even includes "The Three Themes of Music" which Illuvatar "gives" to the Airnur to Sing, which in turn, brings all things into existence, providing the structure, and phenomena of reality.

U lost me at hello!

Holy moly. Three of my favorite subjects in one video: music, math and color theory. My brain is doing back flips!

This blows my mind! This will definately be totally usless.

My engineer mind LOVES this! After years of playing, last year I stumbled onto seeing the circle of 4ths or 5ths going across the strings at a given fret, and suddenly could know where the notes were within a key, relative to the root. Your observations gave me more insight into the repeating nature of the patterns for all the notes in a key... and merging that with my knowledge of the CAGED patterns... the light bulb is flickering on... THANK YOU!

You've got no idea how happy I'm am to have found your channel! I'm both a math and music nerd lol, this was like eating fries with ice cream, the perfect pair. Thanks a lot!

An old feller told me once......."When in doubt, move up two frets" LOL!

Very interesting, without knowing the concept of guitar theory, I had told a friend of mine whom is a lead guitarist that he was a color man, it was what I felt he brought to the band, so from a layman point of view to your explanation an agreement of understanding that makes this so very true, it's like a creative singer that feels this color and responds accordingly, like it was fait that brought this conversation, a language of it own that everyone can see as the hear, just down right spiritual, in fact in the Bible when God's people would go to war the tribe of Judah went first, the name Judah means praise. It's a God thing and you are a intelligent feller. Really enjoy your presentation.

That was an incredible video. The time and effort and vision to build that and succinctly present those concepts is amazing!

I’m tone deaf AND color blind… I wanted to learn guitar. I feel a little discouraged right now

Holy cow, you just made 10 years of my life make total sense today, thanks❤

My brother played bass professionally for over 33 years and he only used his ear to learn the songs. That did limit his options career-wise. Music and mathematics are connected. Sound, vibration and frequency are built into human DNA. It's why music is such a powerful medium. Thanks.

Very well explained. I will try to use the method. After 35 years of struggling with tin ear this will improve my right hand dramatically.

I’m an engineer(electrical) by degree so the math part all makes sense. But my struggle in the past has been approaching the guitar like a mathematical tool. Not only does it force me to slow down to think (way too much) about what is going on, but it causes me to constantly review the fretboard patterns to make sure I’ve got the math right. Although I think this information is useful from a theory perspective, for me it would kill the pleasure and my skill in playing guitar. As one guitarist said to me, you can think the music or you can feel the music. When I get on my bike it’s total feel, as it should be. Now I have to retrain my mind (from years of abuse as an engineer) to begin feeling the music again. Thanks Mike George for this information as I found it fascinating.

Been playing guitar since I was 12 (70 now) - and never saw or realized this. As Ben Eller would say - "this is why you suck at guitar" LOL

Very good material, your introduction of n-dimensional topology as applied to the guitar and music in general is new to me, and fascinating. Since I'm a former data guy the fretboard has looked like a matrix/vector to me for a long time. A song looks like the (usually) cyclical audible expression of a series of vector transformations over/through a period of time. And the series for a given instrument and piece of music can be (and usually is) stacked and synced with the series - the musical "parts" - of others, to produce more complex performances. Bla bla. Linear algebra. Why this all works this way, and why music can engender psychological states in human listeners, beats me. Neato. Now you have me thinking about n-dimensional toroidal vectors and transformations along the time dimension. Hmm. Thank you, Mike.

9:46 “Holy Torus, Neo, that was incredible! 👍🏾🎶

I actually found the information useful. I had noticed years ago that the fretboard on a horizontal plane (box type) was based on the circle of 5ths. My excellent guitar teacher at the time was unaware of that fact. Has it made me a better guitar player? Probably not, but I put the blame on the the player (myself), where it belongs. It is fascinating though: if one can unlock the fretboard and ALL of the other intricacies of becoming a great musician, that's when the fun really begins! It's still work for me.......

I need therapy, only 4 minutes in and there was a overloaded circuit breaker in my head, in a good way, you delivered

This is an amazing video with great visuals. Much, much, MUCH appreciated!

fascinating way to think about the fretboard, thank you for opening my eyes to this!

You're the greatest contemporary talant in music I ever know!!! 💖💖💖

Wow! What an amazing insight into the fret board! Very informative! Great teaching!

This is certainly interesting especially from a compositional standpoint. And if improvisers have a compositional approach perhaps this might work. But the guitar in standard tuning is arranged to make it easy to form chords. This kind of explains the second and third string ( b and g) being in a third, while the rest of the tuning is in fourths. I think seeing the patterns as chords give it context even if you are playing in scalar fashion. But anyway, we can agree that the guitar is fascinating. I do like the thinking in colors approach. Worth exploring.

Thanks, Mike, This is the first time that I've seen these patterns laid out like this. Now, the trick, I guess, is bridging these patterns to practical application. I have begun visualizing the fretboard in terms of scale degrees in relation to the tonic in hopes of being able to quickly play any scale or mode just by knowing which scale degrees comprise it. Been working on the natural minor (Aeolian) - so now I'm thinking 1,2,b3,4,5,b6,b7 rather than trying to memorize a pattern (if that makes any sense). Although a pattern does emerge, I'm not trying to memorize per se. I think it's pretty cool how the half step patterns emerge - it feels like it's the half steps that give the scale/mode their feel. I'm rambling... anyone thanks again. - Cheers

Mind-Blowing is certainly the proper terminology. Awesome!

This is not a “how to play guitar” video. It is describing math and is not for everyone. After almost 40 years of playing guitar and bass I found this very interesting. I have been working with perfect 4ths tuning with the idea that I may try 8 string guitar at some point and want to keep the relationships the same. Anyway, very interesting take and great effort on the graphics: subscribed!

When he said St. Vincent, I spit out my cornflakes from laughter.

Choose blue note or bluegrass - Morpheus

Grateful for creating and for sharing this. Amazing how maths and music can be taught in one shot. Thank you for the idea and for the time you spent to make it available.

Love it. What you have discovered is that the guitar fretboard is (almost) ISOMORPHIC with 12-tone equal temperament -- that is, that both are generated by (a) stacking tempered perfect fifths and then (b) adding and/or subtracting octaves. See Wikipedia's articles on "Isomorphic keyboard," "Dynamic Tonality," and the papers in their references. Good work!

Someone said that "music is numbers in motion". How true it is. Also, this is the best lesson I've seen on this subject. Thanks for posting. SL

This is a fantastic explanation of the guitar fretboard, note relationships and music theory in general. Truly mind blowing and helpful! Thanks Mike!

Thank you. you took something complicated, the guitar fret board notes, and make it Extremely Complicated.

Hell! I flunked freshman Algebra and had to go to summer school! Thanks Miss “P” (name hidden to prevent a lawsuit) Now I’m totally screwed 53 years later!

10:02 ... “You will remember nothing!” ;) ... intriguing presentation,thanks mucho

Most interesting. And clearly explained. Thank you. I expect to be studying this for a while. There's a lot of info in these patterns! Thank you for organizing this body of work. Cheers, Dk

Here is how you make this practical: LEARN YOUR GOD DAMN INTERVALS!!! There is no way around it. No matter how much of a revelation you think this video is, it will not provide any shortcuts to understanding the fretboard. You simply have to spend lots of time and brain power drilling the patterns of the fretboard into your brain, both visually and aurally. Even though it takes time, learning your intervals, especially learning to hear your intervals, will pay dividends for as long as you listen to, play, and internalize music. If this is new territory for you, start out with octaves! Memorize the main shapes used to play octaves between the following pairs of strings: E-D; A-G; D-B; G-E; E-G; A-B; and D-E! Start with that and don't move on until you have them under your fingers and can move them around all over the place. Then do (in approximately this order): fifths/fourths, major/minor thirds, half/whole steps between different strings (I'm assuming you have a handle on those when played on the same string), tritones, major/minor sevenths, and major/minor sixths, before moving on to larger intervals like ninths, tenths, etc. That said, just getting comfortable within an octave takes a long time (months, if not years if you're being truly rigorous with yourself), and I cannot overstate how far that alone will get you. It will take you very, very far. If you're not yet sold on committing time to this, I will say that for me the primary benefits have been: Being able to play melodies/motifs/other musical ideas by ear, instantly. It also allows me to improvise in a way in which I'm not guessing what notes will come out of the instrument-- I know exactly what I'm going to play before I play it, which means being able to fluidly convert my internal musical ideas into awesome lines in real time. To me, it is one of the most satisfying forms of self expression that being a musician can provide. One thing that this video overlooks (among others), is the exception to the rule which is the B string. You have to learn the patterns on and between each string, and that means learning the shapes for the normal strings, as well as intimately understanding the way in which those shapes change when the B string is involved. That is why I believe this level of abstraction can be detrimental, because it overlooks the fact that the guitar (typically) only has 6 strings (as opposed to an arbitrarily large number) and that it is not completely tuned in perfect fourths. I will say, the math behind music is absolutely incredible, and this video doesn't begin to scratch the surface of it. I would recommend someone like 3blue1brown for that. For the physics of music, checkout Science and Music by James Jeans if you really want a revelation.

I’ve played the guitar since 4th grade. This video made me totally confused about the guitar fretboard.

LOVE LOVE LOVE THIS. Bruh - keep it coming.

it was irrelevant how you mentioned this is connected with mathematics with no underlying principles in trig or algebra. you brought up the idea of a Cartesian plane but didn't explain your unites or explain your functions numerically (polynoamil or quadratic function). what you are doing is creating graphic designs with elementary school colors showing us a cool design for guitarest to look at there fret board but this has nothing to do with mathematics. there's no rigor. but i loved the vids epic man keep up the good work and keep playing. love it

Yeah this is easy enough, but what if we convert the notes by using logarithmic transformation? We can then take square roots of any note and any octave to inform our fingers where to go and get there ten times faster?

On my umteenth viewing of this and still learning more. Now I can alter some basic chords and get a sound i anticipate. I'm on the road to improvisation.

Geez, way to make music as fun as math. Forget this, I'm gonna go jam some tunes and enjoy myself.

Now I’m more confused. It was fun seeing how you broke this down, though. I just think about all of this complexity and it kind of intimidates me. Perhaps one day I will finally learn to play the guitar.

Very cool man! Keep the vids coming🤘

Mind blown

Those are some great insights. I think I'll have to watch this a couple more times to really understand what's happening though.

This was such a great video! I'm taking a geometry of music course this semester and I will be sure to try to learn more about this in class!

I was confused about the fretboard before. But after watching this video I’m _really_ f***ing lost! 😵‍💫

A string is a chromatic scale, East and West. A fret is a segment of the circle if fifths, North & South. Wow.

Mike decided to simplify guitar by incorporating analytical geometry. Boss.

My eyes are as glazed as a donut.

I have wondered all my life why I cannot play the guitar... now I know exactly why. It's in a language that my brain cannot comprehend. Every time I find 2 or three notes that sound good together, they are in a different pattern everywhere else on the fingerboard. Even these color coded hints make no sense to me. So, I'll just keep on building great guitars and let YOU GUYS play them.

Thanks for being up front Mike, [Mind Blowing Mathematics] As a hack guitarist, it was confusing for me and I assume most others. But it was interesting as I watched the whole video. Thank you!

Great visualization framework to help navigate the fretboard, in my opinion. If you are musically trained and/or can already navigate the fretboard fluidly good on you, this is obviously not something you need. I’ve been playing guitar as a hobby for two decades and still appreciate tools like this one and find them helpful to improve my skills in new ways. Thanks for the video!

I'm working on essentially this type of thing for my blog at the moment. I don't expect to solve much but I'm building some basic terminology and systems for describing and analysing the fingering of guitar music on the fretboard. It's turning out to involve a reasonable amount of vectors, group theory, stats and combinatorics, made harder by the fact that quite a few of the exogenous mathematical rules have to come from the limitations hand/guitar anatomy and playing technique necessarily imposes. I'm starting with quite a few limitations to the model, and can then build in extra techniques

Damn, man, only 34,800 subscribers? Your channel is seriously underestimated!

Its interesting to use colors, but ultimately unhelpful outside of Modern or Serial music of some sort. When you eventually know the notes and intervals etc, the colors aren't going to be used. I think its best to go from using dots to numbers, assuming the dots are necessary in the first place. Perhaps the color system can be helpful in getting the point across that the numbers themselves arent Math anymore than the letters are words, but are place holders for a certain frequency or pitch. Music Theory often has several names for things that depend on how its being looked at. Adding colors seems to add another layer of confusion in something we're all trying to unify and generally sounds like a bad idea if taken too seriously by the student.

I memorize the fretboard like this, except I do it a bit simpler. I only keep track of root, third and fifths and figure out the rest on the fly. And I find the root with the circle of fifths.

This video is absolutely awesome! 🤘🤘

This is the sort of thing that some minds really connect with....and for others it is just another "oh crap, an even more complicated set of facts to confuse myself with".

Simply WOW!

Learning guitar, and also being into color painting, I found your videos very interesting. Thanks a lot this make a lot of s'e'nse and is definitely useful. This is also a ,very rare, case wher "mind-blowing in a YT video is not a cheap click bait.

I very much doubt that this specific conceptual framework is the secret of the maestros you cited.

Wow that really makes things clear !

This reminds me the book "A Geometry of Music" by Dmitri Tymoczko, applied to guitar logic. Excellent video. Greetings from Bogotá, Colombia.

Interesting take...however I'm colourblind...so there's that. Also I'm not sure that translating music theory (for guitar) into yet another language would be any easier than just learning the theory/fretboard...which is really only half the battle anyways.

I was worried there for a second I'm happy you got to the major 3rd shift between strings 3 and 2 great video

Loved it! Fascinating.

This is dope. Love it.

The torus by the way is the geometric representation of space-time, aka the dimension we exist in. The hyperboloid is the exact opposite of a torus, and represents creation, or the center of all potential. It's the opposite of space-time where there is no existence, and no change. Rest. This is the dimension where new music comes from. Once it is played, it becomes actualized and this process takes place within the torus.

Simply mind blowing

great method I wish I would have had this 20 years ago. I learned all my interval relationships which give the same out come but I believe this would have been quicker. I love the math behind it

Great explanation.. However, everything is shattered when you go to standard tuning which distorts the nice matrix

These kinds of ideas need to be contemplated.

Was hoping to find a new teaching tool. Nope. I was instantly lost. I'm a classically trained guitarist and this turned the fret board into a complete mystery.

I LOVE this!

This is fantastic. Ive had a music theory and a guitar class in highschool, and this is method is one I understood so well. It has taken me years to somewhat understand the circle of fifths. Using color has made it so much simpler for me to understand. Amazing stuff. Keep it up.

in that case (because you made such a video) I have something for you that you absolutely should discuss, for our common good :D 1 - Triadic Chromatic Approach (Garzone) 2 - Twelve-Tone Improvisation (John O'Gallagher) 3 - GMC Generic Modality Compression (Mick Goodrick) +bonus 4 - Pat Martino Multiple Substitutions Demonstration (wtf is this?????)

Awesome!!!