Fretboard Math

LorenFL

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I'm not quite ready to REALLY start learning the fretboard, though I know I should, and I do want to.

I poke around Here from time to time and experiment with different scales. Really, more playing with different sounds than paying attention to what notes I'm playing or in what key. Trying to get some of the more common scales (particularly blues and pentatonics, but I find that the Egyptian and Chinese/Japanese scales are simple and fun to play with) into my head for improvisational purposes, and just to amuse myself.

I picked up the basic "box" patterns of pentatonic and blues scales pretty early on (9 years ago), now I'm trying to expand on them to extend my "runs" into the correct notes.

Now, what I just noticed is that there's some obvious simple MATH on the fretboard. I've done a lot of reading and watched a lot of tutorial videos, and nobody's EVER mentioned this. I feel a little annoyed at MYSELF for not seeing it before, but perhaps even more annoyed that nobody's teaching this.

What the heck am I talking about? Well, for instance, the one that just jumped out at me is that the "shapes" of the notes in a particular key/scale repeat on the fretboard. And not only that, but that repeated shape includes EXACTLY the same notes (perhaps octave-shifted). Mathematically, related to that idea... Any note on two bottom strings (any scale, any key) you can move left 3 frets and down two strings and find the same note! Simple math! Good to know!

So, any shape on the E and A strings that you move to the other two strings and down the neck by 3 frets is exactly the same set of notes.

Yeah, I know, it's all basic musical math. But, SHORTCUTS... they can really amplify the learning curve. Heck, if I can learn HALF the fretboard and get the other half by simple relative math... I've done something.

Alright, that being said... what other simple mathematical shortcuts am I missing? Simple obvious connections that make it easier to learn to play beyond the first 4 frets.
 

LorenFL

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Oh yeah, worthy of note: I'm playing in Low G. So, not only does the math work, but it SOUNDS right, too.

And, yes, I used to play chess... and I was/am a Tetris wizard.
 

clear

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Interesting observation.

This "fretboard math" you mentioned is really apparent on the guitar, and it is taught in beginner guitar lessons (in fact, tuning the guitar uses the fact that the 5th frets of each string is the same note as the open string below, except for the B string). I think the reason it isn't mentioned with the uke is that most ukes are tuned gCEA; which makes the "math" less useful.
 

LorenFL

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Yeah, that's true. That's why I mentioned that I'm Low G.

And the uke strings can be tuned relative to each other by remembering that the strings are 5 and 4 frets apart. (more math) 5 frets up on the G is C, 4 frets up on the C is E, and 5 frets up on the E is A. But, that's slightly harder to remember and work with than the "down two strings and over three frets" rule. (and that rule works because the 5/4 relationship repeats)

I'm just wondering what the more experienced players have noticed that might be similar. How does this relate to that... using simple "math".
 

clear

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Oh yeah, worthy of note: I'm playing in Low G. So, not only does the math work, but it SOUNDS right, too.

And, yes, I used to play chess... and I was/am a Tetris wizard.

I play chess too; and I used to play TETRIS as well.

I remember back when I used to play the TETRIS arcade machines and would be disappointed if I don't get a large group of viewers. I loved it when I create a traffic jam in the arcades.
 

LorenFL

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Okay, this one's not quite "math", but it is an example of going from what you know... applying a known change to it to get something else.

https://coolukulele.com/learning-ukulele-chord-shapes/

What bugs me about stuff like this, and this one is no exception, is that they generally assume that you know stuff! Makes it really hard for a beginner who isn't aware of what part of the equation they don't know yet.

For this particular page, what you sort of need to know is basic chord theory. I mean, I guess you could just go through the motions without knowing that. But, I like to know!
 

tm3

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Great thread, and great tips!

Maybe I'm enthralled because I'm a former tournament chess player. Long before barre chords and blues scales my study was the King's Indian Defense, the Pirc, and the Torre.
 

ripock

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tm3,

I tend to focus on shapes which are the practical applications of the math of the strings.

E.g., barreing the four strings is a m7, barreing the first three is a minor chord, barreing the last three strings is a major chord, going diagonally on all strings is a maj7 chord, going diagonal on the lower three strings is a major chord.

I've actually built up a whole way of making chords based on the mathematics of the fret board. You take any chord quality that you care about--for example the minor 6 chord. Then you figure out how to play it with a root on the g string, on the c string, on the e string and on the a string. It is a lot of work, but when you're done you don't have 4 chords. You have 48 chords because you can now slide each of those four chords anywhere on the fretboard and play any of the 12 keys.
 

LorenFL

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I've been thinking about trying to learn the fretboard again lately. I haven't done it, of course. But, I've been thinking about it.

New Uke coming this week... hopefully, that will inspire me to do more than my usual noodling around.
 

ripock

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what worked for me were modes. You take for example the C major scale, or C Ionian in mode-speak. Then learn the D Dorian, which are the same seven notes played from D to D instead of c to c. Then learn the E Phrygian, again the same notes as the C Ioniian but played from E to E. You keep doing this 'til you get to the B Lokrian. What you are doing is playing the same notes: c,d,e,f,g,a,b, but you're playing them higher and higher on the fret board. As long as you stay aware of what notes you're playing, it will help you learn the fret board. For instance, if you're playing G mixolydian on the 7th fret, you're playing the same notes as the C major scale; you're just playing them higher on the fret board. The trick is to stay mindful of what note you're playing regardless of what mode you're in. Eventually you will know by experience where the C's are, where the D's are, etc.
 

tm3

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tm3,

I tend to focus on shapes which are the practical applications of the math of the strings.

E.g., barreing the four strings is a m7, barreing the first three is a minor chord, barreing the last three strings is a major chord, going diagonally on all strings is a maj7 chord, going diagonal on the lower three strings is a major chord.

I've actually built up a whole way of making chords based on the mathematics of the fret board. You take any chord quality that you care about--for example the minor 6 chord. Then you figure out how to play it with a root on the g string, on the c string, on the e string and on the a string. It is a lot of work, but when you're done you don't have 4 chords. You have 48 chords because you can now slide each of those four chords anywhere on the fretboard and play any of the 12 keys.

That is pretty slick! I'll have to work with it some to try to get my head around it.
 

ripock

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I am just adding some more things that worked for me personally in learning the fret board.

First of all, I want to mention that something that didn't work for me: flash cards. I made flash cards of all the frets and they did do their job. I quizzed myself so that I could (and still can) tell you what notes are on any of the frets. However, that knowledge didn't translate to musical knowledge or fretboard math for me.

The thing that brought a lot of it together for me was getting a personal relationship with a note. For me, it started with the B on the 11th fret. I liked the sound of it and I went to it a lot. In terms of fretboard math. I used that B in the scale of which it was a part. I mindfully played the B and was conscious of what notes I played around the B in the scale. In that way I started learning the notes around the B in the scale. Then I started to move either horizontally or vertically on the fretboard and moved to another scale, but the B was still a part of it.

I am currently smitten with the D# on the 6th fret. I am going to go to that D# because I like and I am going to explore things around that d# and thereby I am going to become really acquainted with the area of the fretboard.

Okay. That's it for now. This works for me and my overall ukulele life. I don't know if it would work for someone who is more geared toward playing covers of established songs. However, I do just submit it in case it could be of use.