The Guitar Fretboard's Mind-Blowing Mathematics

The guitar fretboard is filled with secret patterns ... that are hiding in plain sight. In this video, I show you how to uncover them so you can master the instrument.
And ... you'll see how the guitar offers a glimpse into the higher dimensions. (For real.)
If you'd like to see more videos like this, please LIKE and SUBSCRIBE. And if you know someone who needs to see this, be sure to SHARE it with them. I want to know what you think, so please COMMENT.
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[@juanmedina3867]

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.

[@Fake_Jesus]

Right?! I feel exactly the same way! The sky is the limit now.

[@buddyboy66]

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.

[@Fake_Jesus]

I'm spending time on just this video until the patterns become part of me.

[@rubbingandracing]

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

[@circulode4tas48]

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

[@Fake_Jesus]

I wish it would have been the first.

[@patrickdarby-sheehan5368]

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

[@mattkanter1729]

Cheers !

[@Fake_Jesus]

It's not above you. Just take one relationship at a time and explore it all over the fretboard. It will take time. You'll get it!

[@TheKingG2010]

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

[@Fake_Jesus]

I feel the same way

[@namvet9881]

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.

[@Mdjagg]

Lol

[@williamhogge5549]

If you like confusing, check out Pat Martinos take on parent chords etc. Its technically correct, but you'll need aspirin before you're done. Lol

[@timhallas4275]

The geometry of music is like the algebra of cooking. The best bread uses the fewest ingredients and you never measure them::: The magic is in the hands of the baker.

[@franciscoacosta1667]

Keep lost in the fretboard. If not, watch the video again. He is basicly explaining simetrical intervals between diferent strings and freets

[@namvet9881]

Thank you for that, I appreciate it!@@franciscoacosta1667

[@brianbergmusic5288]

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.

[@LeeGee]

Can't you see both?

[@brianbergmusic5288]

@@LeeGee You could if you are like Tom Quayle who chooses to use all 4ths tuning: kzbin.info/www/bejne/gpbQh4pmf914iLs

[@vinny5004]

Agreed. I’m a mathematician and guitar player, and it was an interesting exercise, with limited usefulness when in standard tuning. Also, good guitar players have simply memorized the fretboard as second nature from lots of practice and experience. That intuition is ingrained in their minds, not some color matrix or even conscious labeling of notes and intervals. Also, knowing the position and pattern of internals on the guitar is essential and much simpler than what is presented here.

[@landshark7154]

B/E string shift ruined the party 😮

[@paulmitchell5349]

Muscle memory, intervals, chord shapes and good ears.

[@Pedro_MVS_Lima]

And arpeggios...

[@daedalusjones4228]

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.

[@fredclarke801]

Don't forget the frets! (LOL)

[@levous2]

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

[@w1o2l3f4i5e]

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

[@graemethorne4540]

Yeah sure is more confusing 🤣

[@mtmcb]

Transposing the color spectrum to the fretboard - and then adding the 'shift' for the two bottom strings - screwed up any hope of following an already difficult pattern, at least for me.

[@cfdwarrior]

@@mtmcb As a beginner...my brain exploded while watching this!

[@austyndrums1993]

It's important to know the notes on the fret board. Just period. How would know where your root is when you're playing? If you in any way have memorized the low e strings notes to assist in finding your root then you in fact have half assed learned the notes. Now match them to the other strings. Just do it. Why you cheaping out, don't you want to be a better player.

[@mtmcb]

@@cfdwarrior 48 years playing, here. I do try to improve, and am always grateful for what I CAN do. Improving alot, I think, requires time. When I first started playing at 17 y.o., it was no big deal to put in 3 hours per day. I was/am very good with the little I know. I'm not EVH, that's for sure. Back then (1970's) you learned from your friends, practicing, and maybe guitar lessons. I know some people have more inherent talent than others, but I will quickly add that if you truly enjoy the instrument, you will always get better at it, and yes, whatever point you're at, you will always improve by the "you get out of it what you put into it" principle. Scales are needful, even if only from a conceptual background understanding of what you are playing, but I find them difficult to deal with 'on the fly'. Intervals, on the other hand, are very useful when playing melody, and the shorter intervals become intuitive after time. I would say, finally, that the single best concept for my own improvement has been that of the "CAGED" system. It can become very easy to use while improvising or simply looking for a better position to play, when you are constructing a song.

[@justinreed8792]

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

[@franciscoacosta1667]

Those are intervals... Are You sure You have a degree? Or... Just trying to sound like You know what you're talking about?

[@justinreed8792]

@@franciscoacosta1667 yes i make a living as a music teacher I definitely know what I’m talking about. This may be helpful for some but i just don’t need this kind of patterns to understand or explain guitar well

[@fyodordostoevsky9671]

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!

[@Joehawk6]

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.

[@Thomas-yb6nq]

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.

[@sharonemanuel-ip5703]

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.

[@drbocca]

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.

[@pmomalley]

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

[@jamesfarrington9030]

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

[@TheSkillkeeper]

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

[@kmwwrench]

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

[@NabanilSanyal]

Me too

[@michaelyork4554]

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.

[@kaseysimons128]

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

[@Sont256]

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

[@joaol.galdino8738]

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!

[@Mixmenfuck223]

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

[@MichaelJamesGallagherAuthor]

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.

[@vicentesolivelles7815]

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.

[@13flaws18]

Very cool man! Keep the vids coming🤘

[@petehatch]

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

[@mikegeorge360]

I'm glad it helps!

[@donk.2070]

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

[@fys9110]

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

[@garrycole8909]

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

[@tracerammo]

This video is absolutely awesome! 🤘🤘

[@mikegeorge360]

Thanks! Music is a beautiful thing, right?

[@ATAsgard1]

LOVE LOVE LOVE THIS. Bruh - keep it coming.

[@mgusa9372]

Mind-Blowing is certainly the proper terminology. Awesome!

[@davedonner2983]

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!

[@HealthySkepticism777]

How long you been playing??

[@xolapower]

Loved it! Fascinating.

[@seanfullerton1695]

Wow that really makes things clear !

[@ConorBreakell]

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!

[@nickefgen9219]

Great video thank you for posting it

[@wyatt8791]

<a href="#" class="seekto" data-time="586">9:46</a> “Holy Torus, Neo, that was incredible! 👍🏾🎶

[@peterbroderson6080]

Yes many thanks, very helpful

[@DANTHETUBEMAN]

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

[@michaelbaudin]

Impressive. Thank you very much for the lesson!

[@2goofybrothers]

Love the visuals of the patterns. Subscribed.

[@mikegeorge360]

Awesome! Thank you - and welcome. 🤘

[@yourbandisabusiness]

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

[@mikegeorge360]

Thanks for your feedback. And cheers!

[@camiloops.official]

Awesome ❤

[@awittypilot8961]

VERY interesting....not sure how to apply on the fly but definitely cool. Rock on!

[@user-tq6hj8bh9y]

Great video , thank you!

[@aisa2112]

Excellent analysis across various disciplines.

[@artemi-music]

thanks for the video

[@johnsteele7201]

"mind blowing" is an understatement!

[@user-pp3ku8sh5v]

Simply mind blowing

[@JudgeFredd]

Excellent explanations

[@mikedonnellan4937]

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.

[@breeze787]

Your right! You blew my mind.

[@williamcurington1017]

Great take on it. Seen this before but I love your presentation.

[@waylonbailey3989]

This is dope. Love it.

[@miketierney7510]

This finally reaches me. This makes sense. Thanks!

[@user-uk6ko7iw4r]

Amazing and fascinating🔥🔥🎸🎸

[@ericwei-cmsh]

Simply WOW!

[@petewiseman]

Yes. I will apply this over the next three years 👍

[@laughingwar3063]

Awesome!!!

[@FlaschDJ]

These kinds of ideas need to be contemplated.

[@melarrow6202]

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.

[@arbarb7204]

Excellent visual 🤙🏼🤙🏼🤙🏼

[@martham9980]

I LOVE this!

[@jitterjive4711]

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

[@mikegeorge360]

Yes, this does make sense. Not memorizing the pattern that emerges, per se, but focusing on the underlying intervals themselves. It's a deeper understanding. Very cool. You're totally right -- bridging these patterns to practical application is the key. To put theory into practice. The "Fretboard Geometry" playlist dissects these patterns a bit more, so you really know all intervals at the atomic level -- to then build any pattern from there (scales, modes, chords, progressions). If you're interested, there's much more in the Community on the practical application of all this (link in the video notes).

[@andercoyote4170]

Jitterjive, I have been thinking in this same way! recently began approaching scales and the fretboard from the perspective of scale degrees.

[@Pedro_MVS_Lima]

That makes perfect sense.

[@tigerscott2966]

great video. thanks.

[@charlierussell7887]

<a href="#" class="seekto" data-time="602">10:02</a> ... “You will remember nothing!” ;) ... intriguing presentation,thanks mucho

[@jamesrogers5277]

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

[@linnhudson4908]

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.

[@rubbersole79]

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

[@fattmusiek5452]

This video was nuts man

[@gizmoser]

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!

[@alnorman4802]

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

[@Giranii]

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.

[@mikegeorge360]

Thank you so much, Norman. And I'm glad it's making sense.

[@tigerscott2966]

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.

[@samratdhamale]

An eye opener..

[@JamesJones101]

Great video!

[@reubennb2859]

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

[@mikegeorge360]

This sounds cool.

[@LiveWireVodou]

Great stuff, thank you!🙏 Now I want to here some of your music 🎸

[@Tom-fb4gz]

You are amazing. Thank you for that!

[@shanelondon1907]

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

[@uptopmikep7065]

Very colorful.

[@Fake_Jesus]

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.

[@yamahajapan5351]

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?

[@grtntgod]

Superb

[@tonygonzalez958]

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

[@howardfriedly3235]

Well that was clear as mud.

[@Racosz]

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

[@rexbenemerito1943]

You are one of a kind. I would say near genius. Thanks for the enlightenment.

[@juansarmiento2022]

Mind blowing video.

[@farleyshaw7018]

My mind is blown now

[@conanladler3472]

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

[@mikegeorge360]

Thanks!

[@estebanmarin002]

Amazing

[@NabanilSanyal]

This is brilliant....

[@Psychodermia]

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