Study in Microtonality and Lutherie – two

I’ve been carving and assembling over the past few weeks, encountering hurdles which are probably typical for someone new to lutherie. I’ve had to work out kinks in my design, and, on numerous occasions, I’ve approached steps which were just too difficult to perform without tools that I didn’t have. Presently, I’m working on the instrument’s neck, and I have decided that this will be a prototype guitar. I will spare my serious labour and attention for a time when I am well-versed in the field.

This post is just a catch-up on the materials I’ve collected. I gave myself to intensive research so that I might spend well, work comfortably, and find myself as prepared as I could be for each step, and I think that a quick post on these efforts is rather necessary.

I am including three images. Two are of the workspace that I assembled in my living room. You can see that I have a very stable workbench. Above it, on the pegboard, I keep carving, sawing, clamping, measuring and gluing equipment. I keep power tools on a shelf beneath the bench, and, in the small cabinet, I keep electronic supplies, jigs, fastening hardware, and diagrams. The shelf near the ceiling is for sewing equipment, but I included it in the picture because I have been using the workbench as a sewing table, and for other purposes which a desk may serve.

I want to make it clear that many hours, often spread out over weeks, went into collecting information on most of the tools, the selections available to me, the pricings, the personal opinions and preferences of every-day luthiers, etc. I could tell brief stories about most of the woodworking instruments, but they would be radically dull. Appreciate that such stories might exist.

The third picture is of my library which houses my music literature apart from scores, sheet music, and lead sheets. I purchased about half of it for this project. AlthoughI have given some time to becoming acquainted with this material, it is really a single book which has proven itself indispensable (at the least, for this leg of the project), titled rather simply, Guitarmaking (Tradition and Technology).


  1. JP,
    I see that guitar with the odd fretboard there. I don’t think I’ll ever totally understand the math behind what you’re doing, but do you have any notes or drawings you used to design that guitar? I’m just curious to see how you go about measuring where to put the frets and what they do.

    – B

  2. jrwallace says:

    Distances between pitches are described with ratios. When the distances between pitches are identical, said distances are described by the same ratio. What’s confusing about this is the reason why ratios are used in this way. The human ear interprets sound differently than it behaves: I find this hard to describe and it isn’t necessary for you to understand in order for me to answer your question – yet, the reason is that what the ear understands to be a linear behavior can be mapped within a logarithmic function. Don’t worry about it. Just understand that when it comes to a string physically producing a sound, string length ratios must be equivalent in order to produce pitches separated by what seem like equal distances.

    I can use this to explain how a guitar is fretted normally. Think of it like this: Consider the distance from the nut (the end of the fretboard by the head of the guitar) to the bridge (where the strings start on the body). Call this distance Y. Now consider the small distance from the nut to the fret closest to the nut and call this distance X. We can then define ratio X/Y (or Y/X – in this scenario it doesn’t matter). This is what we’re calling the string length ratio. To keep it consistent down the neck, we next define Y as the distance between fret one and the bridge, and we define X as the distance between fret one and fret two. Et c.

    This works fine on paper, but not to precision in real life, so small tweaks should be made. However, the tweaks are so small, they aren’t worth talking about in this setting.

    When it comes to microtonal guitars, one simply works with different ratios. There’s a ton of complicated math behind the tuning systems. And it is unbelievably complicated to choose which ratios should be applied to certain strings – much like running a math equation across several chalkboards. Yet the translation of these ratios to the fretboard is still done with simple ratio math. The ratio which one desires between two pitches is translated into the ratio of the distance between two frets and the bridge.

    I know this is complicated. I expect it’s hard to follow. Here’s what’s important:

    – it can be argued that the ear hears sound differently than it behaves on paper, and, consequently, we use proportions rather than ruler measurements to describe what we call music

    – we also use proportions to calculate string length and column length (that’s the term for wind, brass, and reed instruments) when building instruments

    – in building microtonal instruments which share designs with traditional instruments, it is often inconvenient that the traditional instrument is designed for twelve tones whereas the microtonal instrument could be designed for any multitude of tones

    When building the odd fretboard you mentioned, I overlay about six microtonal fretting designs on top of each other. When one fret interferred with another, I had to pick which one I felt was most important.