(Microtonal theory) 19 subset of 31 ET critique?

Discussion in 'Music Theory, Lessons & Techniques' started by Winspear, Jun 10, 2019.

  1. Winspear

    Winspear Tom Winspear Vendor

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    Hi guys, I'm getting closer to my dream of having a 31 guitar and am wondering if some of you usual suspects here would share your thoughts on this fretting idea. I'm asking for you to imagine what you'd think about playing this.

    I'm wanting to simplify a 31 EDO fretboard tuned in 4ths to make it less cramped, more playable, easier to navigate. Utilizing straight frets - I'm open to fretlets in future but not right now. Along one string, I've removed the least useful intervals resulting in a subset of 19. That is, chromatic scale with #/b accidental differentiation, and an Fb and Cb - much like 19 EDO. Read the C string in my diagram to see this most clearly.

    On a keyboard, it's a great tuning, most of its modes are solid.
    However, the lack of factors of 31 mean there is absolutely no way to tune a guitar or create a similar scale that will result in this subset being isolated. That is to say, each string produces the scale in its own key - all 31 notes exist on the fretboard still rather than just 19, and not all intervals are available from all locations.

    Ontop is the image is a full 31 board. Below is the 19 subset.

    My first thoughts were that this is chaos and my reduction idea is useless. On closer inspection though, I'm not so sure.

    -Tuned in 4ths, every fret has barres available with your usual 4th, b7, m3, etc
    -There are only two frets that have no 5th available to be fingered anywhere
    -There are only two frets that have no 310c m3 available - these frets have the 890 M6 inversion available. 310+1 octave is available as a barre of course
    -There are five frets that have no M3 available, nor an octave higher - these frets have the 813 m6 inversion available.
    -There are nine frets that have no 271c m3 available, nor an octave higher
    -There are ten frets that have no 348c neutral 3rd available, nor an octave higher
    -Seven frets have only the sharp major 7th version available. All of these do have the 425 major 3rd or neutral 3rd available to use with it.

    So what do you think, would the less cramped fretboard be worth it for these limitations and mental complications for you? My main concern is confusion and less strength for modulation, but a full 31 board is equally intimidating in other ways. This does seem quite logical to approach, as if you use the sharper of each paired fret to create a 12 note chromatic scale, these frets have most of the options available (the flatter of the pairs are the less versatile).

    Why not 19 EDO? Whilst its triads are great, I much prefer the m9 and M7 of 31 - M7 of 19 is a real problem for me. I also like that 31 has a harmonic 7th, neutral 3rd, and flat m3 as options. The 39c trill is fun too. Though certainly the complications of this subset fretting have me considering 19 EDO as an alternative more than I ever have before.
     

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  2. ixlramp

    ixlramp SS.org Regular

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    Oh man ...
    On the tappistry forum i'm messing about with designing a Just Intonation fretboard but only using full-width frets, it's so complex, so i sympathise.

    Must it be all-4ths tuning? A CGCGCG type tuning (or an open tuning that octave-repeats) will help make more intervals usable across the whole fretboard.

    If some of the frets are still as close as they would be in full 31EDO, there's no fret spacing advantage, it's only as good as the most cramped frets.

    About fretlets, these can be quite easy to create, cut a full width slot and add a trimmed fret (you probably know this).
     
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  3. Winspear

    Winspear Tom Winspear Vendor

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    I considered it. I thought I'd gone off such tunings years ago but I tried again lastnight and it's quite fun to play and fits me better than it used to. The mapping looks good for sure! That said, you're right about the spacing advantage - it just looks more approachable having some small 'option' frets and a number of nice wider ones. I do think barring would be the biggest problem for small frets so I'm cautious about that tuning, but it is appealing. I'll have to make sure the scale length can handle both types of tuning I think :)
     
  4. ixlramp

    ixlramp SS.org Regular

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    I don't want to influence you too much because i would normally encourage you to research, then follow your intuition, however since you asked ...

    Personally i would consider the limitations and complexity to be worse than the issues of a full 31EDO fretboard.
    The close frets exist with either, and the complications of the limitations may be as difficult as navigating the full 31EDO.
    I suspect i would change my mind about the intervals i chose later.
    If i wanted to change open tuning later it would make the interval choice non-optimal. Being stuck in one tuning is scary for me.
    I would go full 31 on a very long scale, maybe even 34", and maybe tune in 3rds to reduce interval stretches.
    Full 31EDO would also be far more sellable to a microtonalist if you ever wanted to sell it.

    From my 24EDO guitar (25" scale) i have found that closer frets make wider string spacing helpful. It made me realise that the standard large distance between frets compensates in some ways for close string spacing. So i suggest making spacing at the nut larger than the typical 7mm.
     
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  5. Winspear

    Winspear Tom Winspear Vendor

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    Cool! I'm pretty much in agreement honestly! I'm absolutely going to finish prototyping full 31 first - my brain just got going on "what if it's too much" once I held the slotted fretboard blank. I think you're right it'll be worth getting used to though.
    Bass scale 3rds is an idea I've had for later too (though it would bug me so much that it skips over the octave slightly rather than repeating like 12 :lol:) , that would be a fun instrument! I'll keep that in mind about the nut, I can see that might make sense - gets it feeling closer to the upper half of a regular 12 board for example.
     
  6. Winspear

    Winspear Tom Winspear Vendor

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    What do you think about how to break up the upper octave? I don't consider all 31 an option beyond the octave if I want to enjoy playing haha. Alternating fret removal results in all 31 note available (though with some awkward position shifts, each note existing on alternate strings etc). Alternatively I could use a 12 note subset to remove the more unusual accidentals, but only have around 13/14 notes of the 31 available. Either method will involve some micro bending often I am sure.
     
  7. ixlramp

    ixlramp SS.org Regular

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    My personal biased opinion is that it isn't worth doing for similar reasons.
    It would be difficult to decide where to transition as you don't know how your technique will develop and how far up full 31EDO will be playable.
    The best transition point will also depend on the music played. For example when playing slowly full 31EDO is not a problem, you can roll up onto a fingertip, but fast playing would need a lower transition point.

    I would just not play the high frets much, and accept that when i do i will have to play slower and more precisely, and be rather limited.
    I would tune the highest string (a D'Addario NYXL .007 or .008) as high as possible to compensate.
    Personally, i would probably not have a 2 octave neck for a shorter, stronger neck.
     

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