Re: adventures in JI guitar

Dante-
Nice work. Looks like your thinking was pretty similar to mine when I
constructed a JI electric. I did not have a lot of specific ideas about
scales, etc but I wanted to have a guitar with a good selection of basic
just intervals. Thus the fret spacing on my JI guitar is quite pragmatic
-- not necessarily an ideal selection of all the intervals I would ever
want, but with a pretty conservative choice of frets that don't get too
physically close to each other for playability. Now that I've had a couple
of years to play with it I might have some improvements to make next time
around.

Interesting idea to use wire for frets. I wouldn't have thought of that.
Do you think it works as well as regular frets for playability? Has anyone
else done a JI guitar using partial "fretlets" instead of going all the way
across (like I did)? I am interested in how people have done this.
Besides gluing pieces of wire, you could cut a slot all the way across and
then just refill the unused portion after installing each fretlet.
Personally I prefer the full frets method.

Is David Canright's guitar article still online somewhere? That was a
primary inspiration for getting me started on a JI guitar. Also, if you
haven't checked it out already, read John Starrett's refretting guide on
his web page. I'm currently using it as my main reference in refretting a
Stratocaster to 22ET. I'm finally getting to the final stages of this
project. I've had too much Life going on the past few months, but recently
I've had a bit more time to work on this. All that remains now is final
fret filing. Hopefully in the next couple of weeks...

hooyah,
kris peck

>From: "Kris Peck" <kpeck@wavetech.net>
>
>Dante-
>Nice work. Looks like your thinking was pretty similar to mine when I
>constructed a JI electric. I did not have a lot of specific ideas about
>scales, etc but I wanted to have a guitar with a good selection of basic
>just intervals. Thus the fret spacing on my JI guitar is quite pragmatic
>-- not necessarily an ideal selection of all the intervals I would ever
>want, but with a pretty conservative choice of frets that don't get too
>physically close to each other for playability. Now that I've had a couple
>of years to play with it I might have some improvements to make next time
>around.
>
>Interesting idea to use wire for frets. I wouldn't have thought of that.
>Do you think it works as well as regular frets for playability? Has anyone
>else done a JI guitar using partial "fretlets" instead of going all the way
>across (like I did)? I am interested in how people have done this.
>Besides gluing pieces of wire, you could cut a slot all the way across and
>then just refill the unused portion after installing each fretlet.
>Personally I prefer the full frets method.
>

Hi Kris-

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?

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 also thought of cutting a slot all the way and then filling in the unused
portion. The thing is the fret positions sometimes only differ by a mm or
two from string to string and that is too close to cut slots for each. On a
guitar with adjustable saddles for each string it might be possible to get
the fret positions lined up, but something tells me that, even if you got
the fret position for 2/1 or 3/2 lined up, some of the higher ratios would
still be in slightly different spots on different strings. I feel like this
should be mathematically demonstrable, but I'm not sure how.

dante

Kris wrote:
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?

****

I believe it may be quite practical to have frets going all the way across
in a JI guitar. I have been considering the following arrangement which
when combined together creates a kind of matrix guitar. Please let me know
what you think, as I have not yet fully thought it through.

Two guitars would be required (perhaps a double necked electric?):

#1
Strings tuned, lowest to highest, 1/1 5/4 3/2 7/4 9/4 11/4
Frets placed to correspond to subharmonics 24 to 12 (or any other mode of
the subharmonic series)
Fret 0 =1/1, 1= 24/23, 2=12/11, 3=8/7, 4= 6/5.....11=24/13, 12=2/1

This instrument would allow harmonic 11 limit bar chords to be played on
each of the intervals of the subharmonic series, and would allow
subharmonic scales to be played on each string.

#2
String tuned, lowest to highest, 1/1 8/5 4/3 (or 3/2?) 8/7 32/9 32/11
Frets placed to correspond to harmonics 8 to 16 or perhaps 12 to 24.

This instrument would allow subharmonic 11 limit bar chords to be played on
each of the intervals of the harmonic series, and a harmonic series on each
string.

With each instrument, other scales derived by playing scales across the
neck, and other chords by playing something other than a bar chord.

Feedback Please!

Darren Burgess
South East Just Intonation Society
Gainesville FL

> Has anyone
> else done a JI guitar using partial "fretlets" instead of going all the way
> across (like I did)?

Interchangeable-fingerboard guitars by Novatone (previously Intonation
Systems, subsequently Mark Rankin) used partial frets.

It's striking that there seem to be two trends in just guitars and these
reflect two different ideas about just intonation.

The first attempts to play music with traditonal voice leading, but in just
intonation. This would seem to lead inevitably to broken frets and/or very
small distances between frets.

The second is more related to the world of Hawai'ian/slide guitar playing,
voice leading is here a minor consideration. Cross sets (the Partchian
diamond is one such set) are built between the open string and the frets.
Both could be harmonic or subharmonic, or one could be harmonic and the
other subharmonic.

An interesting little problem is how, given a slide guitar with six
strings, could one maximally accomodate both otonal and utonal chords?

Ignoring octave registration, here are some obvious possibilities with
complete tetrads and useful non-harmonic tones on neighboring strings:

7/4 - 1/1 - 3/2 - 5/4 - 15/8 - 15/14

7/4 - 3/2 - 5/4 - 1/1 - 5/3 - 10/7

3/2 - 5/4 - 1/1 - 7/4 - 7/5 - 7/6

4/3 - 8/5 - 1/1 - 8/7 - 10/7 - 12/7

Here is a possibility with otonality complete through 9 and a 1-3-5-9
utonality

7/4 - 5/4 - 1/1 - 3/2 - 9/8 - 9/5

> 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.

I think I understood Rod Poole to say that the solves that problem by not
tuning the strings to "different notes". That is, they're all octaves apart.

As an earlier reply suggested though, having different notes on each string
isn't necessarily a problem.

Gary Morrison wrote:

>
> I think I understood Rod Poole to say that the solves that problem by not
> tuning the strings to "different notes". That is, they're all octaves apart.

Rod Poole frets his guitar to a 13-limit 17 tone scale. From that he expands the
tuning by ALL types of open string tunings.
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com