Re: JI frets all the way across...

>
> I'm interested in how you did a JI fretboard with frets that go all the
way
> across. If you have strings tuned to different notes, then you would have
a
> different set of ratios with each string. In effect you would have alot
> more ratios at your disposal. Say you have a string tuned to what well
> call 1/1 and it has a fret for 5/4 (for example) . If you have another
> string 3/2 to the first string that same fret will make a 15/8 with the
> first string. If you have a string tuned 5/4 to the first, that same fret
> gives 25/16 and a string tuned 16/9 to the first string gives a 10/9. If
> you have a fret that makes a 7-linit ratio with the 1/1 string, say 7/5,
> then the other strings give -21/20, 7/4 and 112/45 (sic). While the 7/4
is
> useful, I wonder about how often the other two would come in handy. So I
> guess you would have to be careful how you tune the strings, or maybe
those
> way out intervals sound cool?

Well, yes -- you do end up with different sets of ratios on each string,
depending on how you tune the strings to each other. That's either a
blessing or a curse, and often both. Sometimes it is annoying if you're
trying to play in a particular scale and the only way to get the note
you're looking for is to jump way up or down somewhere on a different
string. I have found that some melodies which would be pretty simple on a
more standard guitar can be inhumanly difficult on mine if I want to use
the specific just pitches.

On the other hand, I like to try different types of things (e.g. 5-limit
diatonic, Archytas enharmonic, harmonic series, Wilson hexanies, etc.) and
when I designed it I didn't see any point in requiring a specific pitch set
on every string when I didn't even know what kinds of scales I might want
to explore sometime. I have found that tuning the strings to
1/1-3/2-2/1-8/3-3/1-4/1 gives a pretty flexible set of pitches with low
ratios most of the time (since any ratio is only being multiplied by 3 or
1/3), so it's good for general purpose playing, and gives reasonable access
to several common scales. Recently I've been playing with the strings
tuned to 2-3-4-5-6-7 harmonic series segment, which gives me at least
marginal fingerings for a few Wilson hexanies and some other weird harmonic
stuff. So I only see the point of the partial fretlets scheme if you have
a specific pitch set and string tuning that you want to lock into.

It's also worth mentioning that even the bigger-numbered ratios are
certainly consonant with *something*, if not necessarily to 1/1. (Assuming
low prime limits.) Your hypothetical 25/16 is consonant to the 5/4 and
your 112/45 is consonant to the 16/9, for example. Not every possible
pitch is always played against the 1/1, so even *if* you wish to avoid
dissonant complex ratios, there is still some context to use any of them in
a consonant way, depending on how you are moving around. Strangely, when I
am randomly improvising I often find myself semi-consciously calculating
the ratios between notes in anticipation of what might sound good. It is
surprising how instinctive this can become.

> With partial frets, especially ones that are only one string wide, you
have
> to be careful about pulling the string off the edge of the fret, but its
> not really a problem.

I suppose it depends on what type of music you're trying to play...

kp

I have some questions about guitars in general.

Is there any particular reason why guitar strings are generally placed
strictly in order of descending pitch? Would there be anything
particularly wrong with having two strings next to each other with a large
ratio in pitch, like 3:1?

Is there any particular benefit of having frets continue at least part
way across the fretboard even if they don't go all the way across?

-Bram

(enjoying the pencil and paper exercise of figuring out frettings, and
dreaming that he might have the free time to work on a real one someday)

> Is there any particular reason why guitar strings are generally placed
> strictly in order of descending pitch?

Well, lessee... The bridge adjustment can be approximated by a slanted,
straight piece if the open-string pitches are more or less monotonic. But
that's a secondary concern I suppose.

If you have a completely consistent interval between the strings, as you
would on a violin or mandolin (P5), or most of the strings of a guitar (P4),
it's a little easier to transpose fingering patterns of various scales and
chords.