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Thread: Fretboard Math

  1. #1
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    Default Fretboard Math

    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.
    What could possibly go wrong?

  2. #2
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    Default

    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.
    What could possibly go wrong?

  3. #3
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    Default

    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.

  4. #4
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    Default

    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".
    What could possibly go wrong?

  5. #5
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    Default

    Quote Originally Posted by LorenFL View Post
    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.

  6. #6
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    Default

    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!
    What could possibly go wrong?

  7. #7
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    Default

    I wrote a bit about this here: https://liveukulele.com/lessons/techniques/octaves/. Cool hack that makes some things easier to visualize.

    Re: fretboard math, I've always thought this video is brilliant: https://www.youtube.com/watch?v=L6E-HNioxHk&t=2s.

  8. #8
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    Looks like I have some things to review this evening. Thanks!
    What could possibly go wrong?

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