A new era in JI guitar design!

Move over Jon Catler. :-)

I hate to sound immodest, but I'd hate it even more if this stuff was
ignored just because I'm not patenting it or charging money for it.

An aim of many of my posts to the tuning list over the years has been to
try to heal the split in many people's minds between what they think of as
"JI" and what they think of as "temperaments". Many thanks to all those who
have supported this effort.

There is no sharp boundary between the two. A temperament _is_ JI if it
_sounds_ like JI when you listen to it (as opposed to looking at the
numbers). I coined the terms "wafso-just" and "microtemperament" for this
purpose. A microtemperament _is_ JI.

I also suggest that a tuning involving small whole-number ratios, that are
tuned too precisely, (e.g. on an electronic instrument) such that no beats
are discernible on even the longest duration notes), may _not_ be JI.

I have previously championed the use of microtemperaments to make more JI
intervals available with the same number of notes, but here is a new
application of microtemperaments: making continuous-fret guitars feasible
for JI scales, without being forced to have tiny spacings between frets or
intervals as big as a fifth between adjacent strings (with its attendant
lack of playable chords).

Below I give the open string tuning and fretting for a guitar for Erv
Wilson's "Pascal" scale,. As mentioned by Kraig Grady, this is a
1,3,7,9,11,15 Eikosany plus 1*7*15/3 and 3*9*11*3. The JI resources of this
22 note scale are awesome. Now here is a guitar for it that has only 22
frets per octave, no fret spacing smaller than 30 cents, and no open-string
step wider than a perfect fourth (3:4) or narrower than a minor third (5:6).

This also represents the debut of a brilliant new 15-limit microtemperament
discovered recently by Graham Breed. It has a period of 1/3 octave and a
generator of approximately 83.02 cents (or 11/159 octave). Or equivalently
the generator may be considered to be a 316.98 cent minor third. This
linear temperament has 15-limit JI intervals that deviate by no more than
2.8c from the strict ratio!

Notes are named below using the usual product-of-factors notation. This
scale can also be named consistently using 72-EDO notations although
actually tuning it to 72-EDO would introduce much larger deviations from
the 15-limit ratios.

Extrascalar (i.e. non-Pascal) notes are shown as "x". Most of these will
also have (multiple) useful product-of-factors interpretations but I
haven't worked them out.

Notes missing from some strings are shown as m(...). About a third of these
differ by only 7.5 cents from the nearby extrascalar note.

Notes corresponding to the next open string are shown -...- whether fretted
or missing.

Pascal guitar, by Dave Keenan 6-Aug-2001

open string steps
317c 384.9c 498.1c 317c 384.9c
5:6 4:5 3:4 5:6 4:5

1*7*15/3 1*3*7 1*7*15 1*7*15/3 1*3*7 1*7*15 nut 0.0c

7*11*15 7*9*11 1*3*9 7*11*15 7*9*11 1*3*9 1fr 52.8c

3*9*11 x 3*9*11*3 3*9*11 x 3*9*11*3 2fr 105.7c
m(1*3*15) m(1*3*15)

1*7*11 9*11*15 3*7*11 1*7*11 9*11*15 3*7*11 3fr 166.0c

3*7*15 3*7*9 7*9*15 3*7*15 3*7*9 7*9*15 4fr 203.8c

1*11*15 1*9*11 3*11*15 1*11*15 1*9*11 3*11*15 5fr 286.8c

-1*3*7- 3*9*15 1*7*9 -1*3*7- 3*9*15 1*7*9 6fr 317.0c

m(7*9*11) m(7*9*11)
-m(1*7*15)- -m(1*7*15)-
x x 1*3*11 x x 1*3*11 7fr 400.0c

1*3*15 1*3*9 1*9*15 1*3*15 1*3*9 1*9*15 8fr 437.7c

m(9*11*15)m(3*9*11*3) m(9*11*15)m(3*9*11*3)
x x -1*7*15/3- x x 1*7*15/3 9fr 498.1c
m(3*7*9) m(3*7*9)

x 3*7*11 7*11*15 x 3*7*11 7*11*15 10fr 550.9c

m(7*9*15) m(7*9*15)
1*9*11 x 3*9*11 1*9*11 x 3*9*11 11fr 603.8c

m(3*9*15) m(3*9*15)

x 3*11*15 1*7*11 x 3*11*15 1*7*11 12fr 664.2c

1*7*15 1*7*9 3*7*15 1*7*15 1*7*9 3*7*15 13fr 701.9c

m(1*3*9) m(1*3*9)

x 1*3*11 1*11*15 x 1*3*11 1*11*15 14fr 784.9c
3*9*11*3 3*9*11*3
x 1*9*15 1*3*7 x 1*9*15 1*3*7 15fr 815.1c

3*7*11 x 7*9*11 3*7*11 x 7*9*11 16fr 867.9c
m(1*7*15/3) m(1*7*15/3)
m(7*9*15) m(7*9*15)

x 7*11*15 1*3*15 x 7*11*15 1*3*15 17fr 935.8c

3*11*15 3*9*11 9*11*15 3*11*15 3*9*11 9*11*15 18fr 988.7c

1*7*9 x 3*7*9 1*7*9 x 3*7*9 19fr 1018.9c

m(1*7*11) m(1*7*11)

m(3*7*15) m(3*7*15)
1*3*11 x 1*9*11 1*3*11 x 1*9*11 20fr 1101.9c

1*9*15 x 3*9*15 1*9*15 x 3*9*15 21fr 1139.6c

m(1*11*15) m(1*11*15)

1*7*15/3 1*3*7 1*7*15 1*7*15/3 1*3*7 1*7*15 8ve 1200.0c

Regards,
-- Dave Keenan
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

> I also suggest that a tuning involving small whole-number ratios,
> that are tuned too precisely, (e.g. on an electronic instrument)
> such that no beats are discernible on even the longest duration
> notes), may _not_ be JI.

What's your reasoning for that again?

> This also represents the debut of a brilliant new 15-limit
> microtemperament discovered recently by Graham Breed. It has a
> period of 1/3 octave and a generator of approximately 83.02
> cents (or 11/159 octave). Or equivalently the generator may be
> considered to be a 316.98 cent minor third. This linear
> temperament has 15-limit JI intervals that deviate by no more
> than 2.8c from the strict ratio!

Did I miss info on this?

-Carl

--- In tuning@y..., carl@l... wrote:
> > I also suggest that a tuning involving small whole-number ratios,
> > that are tuned too precisely, (e.g. on an electronic instrument)
> > such that no beats are discernible on even the longest duration
> > notes), may _not_ be JI.
>
> What's your reasoning for that again?

I think Dave is going to have to take that back. It may not be
musical, but it sure is JI.
>
> > This also represents the debut of a brilliant new 15-limit
> > microtemperament discovered recently by Graham Breed. It has a
> > period of 1/3 octave and a generator of approximately 83.02
> > cents (or 11/159 octave). Or equivalently the generator may be
> > considered to be a 316.98 cent minor third. This linear
> > temperament has 15-limit JI intervals that deviate by no more
> > than 2.8c from the strict ratio!
>
> Did I miss info on this?
>
See <tuning-math@yahoogroups.com>.

>>> I also suggest that a tuning involving small whole-number ratios,
>>> that are tuned too precisely, (e.g. on an electronic instrument)
>>> such that no beats are discernible on even the longest duration
>>> notes), may _not_ be JI.
>>
>> What's your reasoning for that again?
>
> I think Dave is going to have to take that back. It may not be
> musical, but it sure is JI.

Maybe he wants to call it "synthesis"...

>>> This also represents the debut of a brilliant new 15-limit
>>> microtemperament discovered recently by Graham Breed. It has a
>>> period of 1/3 octave and a generator of approximately 83.02
>>> cents (or 11/159 octave). Or equivalently the generator may be
>>> considered to be a 316.98 cent minor third. This linear
>>> temperament has 15-limit JI intervals that deviate by no more
>>> than 2.8c from the strict ratio!
>>
>> Did I miss info on this?
>>
> See <tuning-math@y...>.

I'm on that list, Paul, as you know. The only things I could think
of were Graham's temperament catalog thread, and his automatically
generated temperament thread. I went to the corresponding web pages,
which nearly killed me since they don't seem to be attached to his
main site, and could find no reference to the scale mentioned above.

-Carl

Carl wrote:

> I'm on that list, Paul, as you know. The only things I could think
> of were Graham's temperament catalog thread, and his automatically
> generated temperament thread. I went to the corresponding web pages,
> which nearly killed me since they don't seem to be attached to his
> main site, and could find no reference to the scale mentioned above.

Sorry about it not being connected up. I did update the index a couple of
weeks ago, but forgot to upload it. I'll try to remember this time.

The temperament Paul mentioned is in both lists. It's called
"multiple-29" in the catalog, and comes at the top of the 15-limit list.
It might be good with two keyboards each tuned to 29-equal. I've already
shown how 29 notes do make sense on 7+5. However, I don't have a good
enough dual-keyboard setup to try it myself, so usual caveats apply. It
looks like a nifty temperament if you have a keyboard to fit it.

Graham

> The temperament Paul mentioned is in both lists.

D'oh!

> It's called "multiple-29" in the catalog, and comes at the top
> of the 15-limit list. It might be good with two keyboards each
> tuned to 29-equal. I've already shown how 29 notes do make sense
> on 7+5. However, I don't have a good enough dual-keyboard setup
> to try it myself, so usual caveats apply. It looks like a nifty
> temperament if you have a keyboard to fit it.

Looks like the bit I'm missing is the "period" terminology...

-Carl

--- In tuning@y..., graham@m... wrote:
> Carl wrote:
>
> > I'm on that list, Paul, as you know. The only things I could
think
> > of were Graham's temperament catalog thread, and his automatically
> > generated temperament thread. I went to the corresponding web
pages,
> > which nearly killed me since they don't seem to be attached to his
> > main site, and could find no reference to the scale mentioned
above.
>
> Sorry about it not being connected up. I did update the index a
couple of
> weeks ago, but forgot to upload it. I'll try to remember this time.
>
> The temperament Paul mentioned is in both lists. It's called
> "multiple-29" in the catalog, and comes at the top of the 15-limit
list.
> It might be good with two keyboards each tuned to 29-equal. I've
already
> shown how 29 notes do make sense on 7+5. However, I don't have a
good
> enough dual-keyboard setup to try it myself, so usual caveats
apply. It
> looks like a nifty temperament if you have a keyboard to fit it.

Graham, are you sure this is the one? This is the temperament that
Dave Keenan mentioned (I didn't mention any) and Carl was asking
about:

"This also represents the debut of a brilliant new 15-limit
microtemperament
discovered recently by Graham Breed. It has a period of 1/3 octave
and a
generator of approximately 83.02 cents (or 11/159 octave). Or
equivalently
the generator may be considered to be a 316.98 cent minor third. This
linear temperament has 15-limit JI intervals that deviate by no more
than
2.8c from the strict ratio!"

So is the period 1/3 octave or 1/29 octave?

--- In tuning@y..., carl@l... wrote:
> > I also suggest that a tuning involving small whole-number ratios,
> > that are tuned too precisely, (e.g. on an electronic instrument)
> > such that no beats are discernible on even the longest duration
> > notes), may _not_ be JI.
>
> What's your reasoning for that again?

Whether or not you call it JI is beside the point. The point really is
that, when the notes of a chord are _phase-locked_ to small
whole-number ratios, you don't get a chord, you get a timbre. You can
get total cancellation of some partials. And hey, to me, it sounds
boring.

> > This also represents the debut of a brilliant new 15-limit
> > microtemperament discovered recently by Graham Breed. It has a
> > period of 1/3 octave and a generator of approximately 83.02
> > cents (or 11/159 octave). Or equivalently the generator may be
> > considered to be a 316.98 cent minor third. This linear
> > temperament has 15-limit JI intervals that deviate by no more
> > than 2.8c from the strict ratio!
>
> Did I miss info on this?

Graham probably hasn't taken much notice of it himself, yet. See
http://x31eq.com/temper.html
When you've read the page, click on the "15-limit" link near the top
and scroll down 'til you see "11/53, 83.0 cent generator", the fourth
temperament in the list.

-- Dave Keenan

The main tools we needed for practical JI guitar design, that were missing
until very recently, were _good_ _linear_ _microtemperaments_. i.e. they
must have few generators per interval, they must be linear and they must
have errors less than about 3 cents. Here are my suggestions, for octave
based scales.

Period Gen Max gens Max err Name
5-limit 1 oct 317.0 c 6 1.4 c kleismic
7-limit 1 oct 116.6 c 13 2.4 c miracle
9-limit 1 oct 316.8 c 22 2.7 c kleismic?
11-limit 1/2 oct 183.2 c 30 2.4 c ?
13-limit 1/3 oct 83.0 c 48 2.8 c ?
15-limit 1/3 oct 83.0 c 48 2.8 c ?

There are a number of others which may be better if you are willing to go
up to 3.3 c errors.

Period Gen Max gens Max err Name
5-limit 1/2 oct 105.2 c 6 3.3 c diaschismic
9-limit 1 oct 116.6 c 19 3.3 c miracle
11-limit 1 oct 116.6 c 22 3.3 c miracle

I selected these from Graham Breed's
http://x31eq.com/temper.html

For scales which do not use all the odd numbers up to a given limit, (such
as 'Pascal' which is 15-limit without 5s or 13s), there are probably other
optimum choices, which Graham could undoubtedly find for us if he felt so
inclined.

-----------------
The Pascal guitar
-----------------
There were some errors in the previous Pascal Guitar diagram. Notably I
failed to show some missing notes in the critical region near the nut.
There are 3 missing notes in the critical region, all on the 1*3*7 strings.

The biggest problem with this design is that 9*11*15 and 3*9*15 are
completely missing from the low octave, since they only appear on the
1*7*15 strings.

Pascal guitar, by Dave Keenan 7-Aug-2001

open string steps
317c 384.9c 498.1c 317c 384.9c
5:6 4:5 3:4 5:6 4:5

1*7*15/3 1*3*7 1*7*15 1*7*15/3 1*3*7 1*7*15 nut 0.0c

7*11*15 7*9*11 1*3*9 7*11*15 7*9*11 1*3*9 1fr 52.8c

3*9*11 x 3*9*11*3 3*9*11 x 3*9*11*3 2fr 105.7c
m(1*3*15) m(1*3*15)

1*7*11 x 3*7*11 1*7*11 x 3*7*11 3fr 166.0c
m(9*11*15) m(9*11*15)
3*7*15 3*7*9 7*9*15 3*7*15 3*7*9 7*9*15 4fr 203.8c

1*11*15 1*9*11 3*11*15 1*11*15 1*9*11 3*11*15 5fr 286.8c

-1*3*7- x 1*7*9 -1*3*7- x 1*7*9 6fr 317.0c
m(3*9*15) m(3*9*15)

m(7*9*11) m(7*9*11)
-m(1*7*15)- -m(1*7*15)-
x x 1*3*11 x x 1*3*11 7fr 400.0c

1*3*15 1*3*9 1*9*15 1*3*15 1*3*9 1*9*15 8fr 437.7c

m(9*11*15)m(3*9*11*3) m(9*11*15)m(3*9*11*3)
x x -1*7*15/3- x x 1*7*15/3 9fr 498.1c
m(3*7*9) m(3*7*9)

x 3*7*11 7*11*15 x 3*7*11 7*11*15 10fr 550.9c

m(7*9*15) m(7*9*15)
1*9*11 x 3*9*11 1*9*11 x 3*9*11 11fr 603.8c

m(3*9*15) m(3*9*15)

x x 1*7*11 x x 1*7*11 12fr 664.2c
m(3*11*15) m(3*11*15)
1*7*15 1*7*9 3*7*15 1*7*15 1*7*9 3*7*15 13fr 701.9c

m(1*3*9) m(1*3*9)

x 1*3*11 1*11*15 x 1*3*11 1*11*15 14fr 784.9c
m(3*9*11*3) m(3*9*11*3 )
x x 1*3*7 x x 1*3*7 15fr 815.1c
m(1*9*15) m(1*9*15)

3*7*11 x 7*9*11 3*7*11 x 7*9*11 16fr 867.9c
m(1*7*15/3) m(1*7*15/3)
m(7*9*15) m(7*9*15)

x 7*11*15 1*3*15 x 7*11*15 1*3*15 17fr 935.8c

3*11*15 3*9*11 9*11*15 3*11*15 3*9*11 9*11*15 18fr 988.7c

1*7*9 x 3*7*9 1*7*9 x 3*7*9 19fr 1018.9c

m(1*7*11) m(1*7*11)

m(3*7*15) m(3*7*15)
1*3*11 x 1*9*11 1*3*11 x 1*9*11 20fr 1101.9c

1*9*15 x 3*9*15 1*9*15 x 3*9*15 21fr 1139.6c

m(1*11*15) m(1*11*15)

1*7*15/3 1*3*7 1*7*15 1*7*15/3 1*3*7 1*7*15 8ve 1200.0c

When I get time, I may draw up a diagram for Pete McRae's Pascal guitar for
comparison. As described by Kraig, this has open strings:

2:3 3:4 3:4 8:9 3:4
D# A# D# G# A# D#
1*7*11 3*7*11 1*7*11 1*7*11/3 3*7*11 1*7*11

with the full 22 notes on the 1*7*11 strings. I notice that 1*7*11/3 (G#)
is not a note of the scale. Is this correct Kraig?

Regards,
-- Dave Keenan
-- Dave Keenan
Brisbane, Australia
http://dkeenan.com

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
> Period Gen Max gens Max err Name
> 5-limit 1 oct 317.0 c 6 1.4 c kleismic
> 7-limit 1 oct 116.6 c 13 2.4 c miracle
> 9-limit 1 oct 316.8 c 22 2.7 c kleismic?
> 11-limit 1/2 oct 183.2 c 30 2.4 c ?
> 13-limit 1/3 oct 83.0 c 48 2.8 c ?
> 15-limit 1/3 oct 83.0 c 48 2.8 c ?

The linear microtemperament above, with 1/3 oct period and 83.0c
generator (as used for the Pascal guitar design) could be called
"triple-kleismic". 1200/3 - 83.0 = 317.0 c

But that 11-limit one still has me beat.

-- Dave Keenan

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:
> Hi Dave and everybody,
>
> I lost track of the miracle thread a while back, so I'm not sure
> whether anyone has noticed this or whether or not it would be
> relevant... but on the face of it, it seems to me to be a way to
link
> the Sims' (et al) 12-tet and sixthtones mindset with the 7/72
> generator.
>
> This is because the 72-tet miracle generator can also be derived as
> either a 1D Pythagorean diatonic remapping

You mean a linear temperament?

> or as a 2D syntonic 5-limit

You mean a planar temperament?

> by letting P = 1200/6.

No, it's still linear.
Ok.

> 18, [12, 30], 42, 72, ...

If I use a generator of 116.7 c with a period of 1/6 octave I get MOS
cardinalities of
12, (18), 30, (42), 72, ...

> Here's the 2D example in rounded cents:
>
> 147----64---181
> / \ / \ / \
> / \ / \ / \
> 83-----0---117----34
>
> So this is direct 2:3 = 7/72 remapping.

I'm sorry I don't understand how this was generated or what its raison
d'etre.

> Anyone see a use for this pertaining to the miracle by way of 72-tet
> thread... it certainly seems a nice conceptual way to frame some
> aspect of it?

Hmm. Sextuple-miracle. You need 8 generators per chain to get a
1:3:5:7:9:11? Like this

^
p
e +-+-9-+-+11-+-+-+
r 7-+-1-+-+-+-+-+-3
i +-+-+-+-+-+-+-5-+
o +-+-+-+-+-+-+-+-+
d +-+-+-+-+-+-+-+-+
s +-+-+-+-+-+-+-+-+
generators>

If you wanted to ignore 7s, or 7s and 3s, or 7s, 3s and 5s it could be
useful, otherwise it looks like too many notes (with any kind of
symmetry). But certainly something to add to the bag of tricks. Thanks
Dan.

You might have to spell out more of what you had in mind.

So no-one wants to talk about JI guitars? <sigh>

--Dave Keenan

--- In tuning@y..., "D.Stearns" <STEARNS@C...> wrote:

/tuning/topicId_unknown.html#26791

> Hi Dave,
>
> <<I'm sorry I don't understand how this was generated or what its
> raison d'etre.>>
>
>
> It's a syntonic (or Pythagorean) diatonic remapping where:
>
> (LOG(N/D))*((1200/6)/LOG(2/1))
>
> What caught my attention was the relationship between the Sims'
> sixthtone thinking and the miracle generator... I just happened to
> notice this while I was working on something else.
>

But, isn't this why we were notating "miracle" in 72-tET??... or I
must be missing the entire point... (??)

_________ _______ ________
Joseph Pehrson

Dan Stearns suggests a movable fret guitar--something
already invented by a German firm. John Schneider
showed me his copy on my xenharmonic visit to SoCal in
Nov. '98. There's also a replaceable fretboard guitar
made by a someone in California, which could serve the
same purpose.

I wrote down the contact info for the manufacturers
somewhere, but will my co-conspirator Kris Peck or one
of the rest of ya will recall the details?

__________________________________________________
Do You Yahoo!?
Make international calls for as low as $.04/minute with Yahoo! Messenger
http://phonecard.yahoo.com/

----- Original Message -----
From: Harold Fortuin <harold_fortuin@yahoo.com>

> Dan Stearns suggests a movable fret guitar--something
> already invented by a German firm. John Schneider
> showed me his copy on my xenharmonic visit to SoCal in
> Nov. '98. There's also a replaceable fretboard guitar
> made by a someone in California, which could serve the
> same purpose.
>
> I wrote down the contact info for the manufacturers
> somewhere, but will my co-conspirator Kris Peck or one
> of the rest of ya will recall the details?

You can also go fretless and use nylon string for frets.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

I've been following this thread eagerly though with the usual difficulty when it comes to maths.
Have any conclusions been reached? If so would it be possible to put these up as a webpage? The
emails don't do justice to fretboard diagrams. I'm considering having a guitar refretted to a JI
system and the Blackjack and Eikosany both come to mind. Does anyone have the fret measurements
for, say, a 65cm classical guitar string length for either of these (or other) systems?

Best Wishes.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> So no-one wants to talk about JI guitars? <sigh>
>
> --Dave Keenan

I think your work in this area is too important and complex for just
this list. Why not write an article for Xenharmonikon?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> --- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> > So no-one wants to talk about JI guitars? <sigh>
> >
> > --Dave Keenan
>
> I think your work in this area is too important and complex for just
> this list. Why not write an article for Xenharmonikon?

Thanks Paul and Alison. It seems I mistook a lack of discussion for a
lack of interest, but it now seems it is simply a lack of
disagreement. I hope that using microtemperaments to make JI guitars
feasible, seems inevitable now. But I agree with Dan; it needs some
testing in practice. I don't have the resources. I may build _one_
(prob. Blackjack) but I'm not a "real" guitarist. It would be great if
some others were willing to take the risk and have one built (or set
some up using movable frets, or fretless with nylon strings for
frets).

For Alison's (and others') benefit, can someone give some web pages
that tell you how to turn cents into actual millimeters for fretting a
particular guitar? From memory I think John Starrett, Charles Lucy,
Graham Breed or Heinz Bohlen might have such info on their sites.
I'd start here
http://www-math.cudenver.edu/~jstarret/microtone.html
You can get to the others from there.

Regards,
-- Dave Keenan

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> For Alison's (and others') benefit, can someone give some web pages
> that tell you how to turn cents into actual millimeters for
fretting a
> particular guitar?

It's very simple. String length is inversely proportional to
frequency. Dave, you can work out the rest from that.

Caution: The above is only approximately true. For a near-JI guitar,
it would make sense to make small corrections for the increased
tension necessary to get the string down to the fret. The details
will depend on how high you set your action and what material your
strings are made of. Dante Rosati put his frets in by ear and you can
see how they depart from the "theoretical" approximation referred to
above. They don't go straight across the fingerboard. Part of this is
usually taken account on real guitars by having a slanted bridge, but
most guitars are still sharp for notes fretted on the first fret, and
considerably less so on the second fret. A small adjustment to the
positions of both the nut and bridge can usually solve the problem
completely for all intents and purposes. But this process may be
covered under Buzz Feiten's patent . . .

<snip>
> Thanks Paul and Alison. It seems I mistook a lack of discussion for
a
> lack of interest, but it now seems it is simply a lack of
> disagreement. I hope that using microtemperaments to make JI guitars
> feasible, seems inevitable now. But I agree with Dan; it needs some
> testing in practice. I don't have the resources. I may build _one_
> (prob. Blackjack) but I'm not a "real" guitarist. It would be great
if
> some others were willing to take the risk and have one built (or set
> some up using movable frets, or fretless with nylon strings for
> frets).
>
> For Alison's (and others') benefit, can someone give some web pages
> that tell you how to turn cents into actual millimeters for fretting
a
> particular guitar? From memory I think John Starrett, Charles Lucy,
> Graham Breed or Heinz Bohlen might have such info on their sites.
> I'd start here
> http://www-math.cudenver.edu/~jstarret/microtone.html
> You can get to the others from there.
>
> Regards,
> -- Dave Keenan

Yes, Dave, I do have such info here:
http://www-math.cudenver.edu/~jstarret/guitar.html

I am interested in building a Blackjack guitar. I have a fretless just
waiting for an interesting idea. Can you fill me in privately on the
details of the scale?

John Starrett

<snip> A small adjustment to the
> positions of both the nut and bridge can usually solve the problem
> completely for all intents and purposes. But this process may be
> covered under Buzz Feiten's patent . . .

...which is no problem. The only problem would be if one tried to
*sell* a guitar without paying a royalty. Also, the patent may cover
only 12tet.

Good day to you David!

As always your post in regards to "A new era in JI guitar design" was
amazing. Thank you for sharing your knowledge with the world!

Please check the following link:

http://www.mbay.net/~anne/david/frets/index.htm

this particular person (who also is named "David")is very
knowledgable in the field of fretting guitars using JI. I've emailed
him quite a few times and he has helped me a lot. He's a great
contact!

You may want to check his home page for other areas of JI interest as
well.

Take care
Wally

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
> Move over Jon Catler. :-)
>
> I hate to sound immodest, but I'd hate it even more if this stuff
was
> ignored just because I'm not patenting it or charging money for it.
>
> An aim of many of my posts to the tuning list over the years has
been to
> try to heal the split in many people's minds between what they
think of as
> "JI" and what they think of as "temperaments". Many thanks to all
those who
> have supported this effort.
>
> There is no sharp boundary between the two. A temperament _is_ JI
if it
> _sounds_ like JI when you listen to it (as opposed to looking at the
> numbers). I coined the terms "wafso-just" and "microtemperament"
for this
> purpose. A microtemperament _is_ JI.
>
> I also suggest that a tuning involving small whole-number ratios,
that are
> tuned too precisely, (e.g. on an electronic instrument) such that
no beats
> are discernible on even the longest duration notes), may _not_ be
JI.
>
> I have previously championed the use of microtemperaments to make
more JI
> intervals available with the same number of notes, but here is a new
> application of microtemperaments: making continuous-fret guitars
feasible
> for JI scales, without being forced to have tiny spacings between
frets or
> intervals as big as a fifth between adjacent strings (with its
attendant
> lack of playable chords).
>
> Below I give the open string tuning and fretting for a guitar for
Erv
> Wilson's "Pascal" scale,. As mentioned by Kraig Grady, this is a
> 1,3,7,9,11,15 Eikosany plus 1*7*15/3 and 3*9*11*3. The JI resources
of this
> 22 note scale are awesome. Now here is a guitar for it that has
only 22
> frets per octave, no fret spacing smaller than 30 cents, and no
open-string
> step wider than a perfect fourth (3:4) or narrower than a minor
third (5:6).
>
> This also represents the debut of a brilliant new 15-limit
microtemperament
> discovered recently by Graham Breed. It has a period of 1/3 octave
and a
> generator of approximately 83.02 cents (or 11/159 octave). Or
equivalently
> the generator may be considered to be a 316.98 cent minor third.
This
> linear temperament has 15-limit JI intervals that deviate by no
more than
> 2.8c from the strict ratio!
>
> Notes are named below using the usual product-of-factors notation.
This
> scale can also be named consistently using 72-EDO notations although
> actually tuning it to 72-EDO would introduce much larger deviations
from
> the 15-limit ratios.
>
> Extrascalar (i.e. non-Pascal) notes are shown as "x". Most of these
will
> also have (multiple) useful product-of-factors interpretations but I
> haven't worked them out.
>
> Notes missing from some strings are shown as m(...). About a third
of these
> differ by only 7.5 cents from the nearby extrascalar note.
>
> Notes corresponding to the next open string are shown -...- whether
fretted
> or missing.
>
> Pascal guitar, by Dave Keenan 6-Aug-2001
>
> open string steps
> 317c 384.9c 498.1c 317c 384.9c
> 5:6 4:5 3:4 5:6 4:5
>
> 1*7*15/3 1*3*7 1*7*15 1*7*15/3 1*3*7 1*7*15 nut
0.0c
>
>
> 7*11*15 7*9*11 1*3*9 7*11*15 7*9*11 1*3*9 1fr
52.8c
>
>
> 3*9*11 x 3*9*11*3 3*9*11 x 3*9*11*3 2fr
105.7c
> m(1*3*15) m(1*3*15)
>
>
> 1*7*11 9*11*15 3*7*11 1*7*11 9*11*15 3*7*11 3fr
166.0c
>
> 3*7*15 3*7*9 7*9*15 3*7*15 3*7*9 7*9*15 4fr
203.8c
>
>
>
>
> 1*11*15 1*9*11 3*11*15 1*11*15 1*9*11 3*11*15 5fr
286.8c
>
> -1*3*7- 3*9*15 1*7*9 -1*3*7- 3*9*15 1*7*9 6fr
317.0c
>
>
> m(7*9*11) m(7*9*11)
> -m(1*7*15)- -m(1*7*15)-
> x x 1*3*11 x x 1*3*11 7fr
400.0c
>
> 1*3*15 1*3*9 1*9*15 1*3*15 1*3*9 1*9*15 8fr
437.7c
>
>
> m(9*11*15)m(3*9*11*3) m(9*11*15)m(3*9*11*3)
> x x -1*7*15/3- x x 1*7*15/3 9fr
498.1c
> m(3*7*9) m(3*7*9)

>
> x 3*7*11 7*11*15 x 3*7*11 7*11*15 10fr
550.9c
>
> m(7*9*15) m(7*9*15)

> 1*9*11 x 3*9*11 1*9*11 x 3*9*11 11fr
603.8c
>
> m(3*9*15) m(3*9*15)

>
> x 3*11*15 1*7*11 x 3*11*15 1*7*11 12fr
664.2c
>
> 1*7*15 1*7*9 3*7*15 1*7*15 1*7*9 3*7*15 13fr
701.9c
>
>
> m(1*3*9) m(1*3*9)

>
> x 1*3*11 1*11*15 x 1*3*11 1*11*15 14fr
784.9c
> 3*9*11*3 3*9*11*3

> x 1*9*15 1*3*7 x 1*9*15 1*3*7 15fr
815.1c
>
>
> 3*7*11 x 7*9*11 3*7*11 x 7*9*11 16fr
867.9c
> m(1*7*15/3) m(1*7*15/3)

> m(7*9*15) m(7*9*15)

>
> x 7*11*15 1*3*15 x 7*11*15 1*3*15 17fr
935.8c
>
>
> 3*11*15 3*9*11 9*11*15 3*11*15 3*9*11 9*11*15 18fr
988.7c
>
> 1*7*9 x 3*7*9 1*7*9 x 3*7*9 19fr
1018.9c
>
> m(1*7*11) m(1*7*11)

>
> m(3*7*15) m(3*7*15)

> 1*3*11 x 1*9*11 1*3*11 x 1*9*11 20fr
1101.9c
>
> 1*9*15 x 3*9*15 1*9*15 x 3*9*15 21fr
1139.6c
>
> m(1*11*15) m(1*11*15)

>
> 1*7*15/3 1*3*7 1*7*15 1*7*15/3 1*3*7 1*7*15 8ve
1200.0c
>
> Regards,
> -- Dave Keenan
> -- Dave Keenan
> Brisbane, Australia
> http://dkeenan.com

Hi David

Here is David Canwright's home page:

http://www.mbay.net/~anne/david/.

Lot's of great links to "fretting in JI"

Regards
Wally

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
> Move over Jon Catler. :-)
>
> I hate to sound immodest, but I'd hate it even more if this stuff
was
> ignored just because I'm not patenting it or charging money for it.
>
> An aim of many of my posts to the tuning list over the years has
been to
> try to heal the split in many people's minds between what they
think of as
> "JI" and what they think of as "temperaments". Many thanks to all
those who
> have supported this effort.
>
> There is no sharp boundary between the two. A temperament _is_ JI
if it
> _sounds_ like JI when you listen to it (as opposed to looking at the
> numbers). I coined the terms "wafso-just" and "microtemperament"
for this
> purpose. A microtemperament _is_ JI.
>
> I also suggest that a tuning involving small whole-number ratios,
that are
> tuned too precisely, (e.g. on an electronic instrument) such that
no beats
> are discernible on even the longest duration notes), may _not_ be
JI.
>
> I have previously championed the use of microtemperaments to make
more JI
> intervals available with the same number of notes, but here is a new
> application of microtemperaments: making continuous-fret guitars
feasible
> for JI scales, without being forced to have tiny spacings between
frets or
> intervals as big as a fifth between adjacent strings (with its
attendant
> lack of playable chords).
>
> Below I give the open string tuning and fretting for a guitar for
Erv
> Wilson's "Pascal" scale,. As mentioned by Kraig Grady, this is a
> 1,3,7,9,11,15 Eikosany plus 1*7*15/3 and 3*9*11*3. The JI resources
of this
> 22 note scale are awesome. Now here is a guitar for it that has
only 22
> frets per octave, no fret spacing smaller than 30 cents, and no
open-string
> step wider than a perfect fourth (3:4) or narrower than a minor
third (5:6).
>
> This also represents the debut of a brilliant new 15-limit
microtemperament
> discovered recently by Graham Breed. It has a period of 1/3 octave
and a
> generator of approximately 83.02 cents (or 11/159 octave). Or
equivalently
> the generator may be considered to be a 316.98 cent minor third.
This
> linear temperament has 15-limit JI intervals that deviate by no
more than
> 2.8c from the strict ratio!
>
> Notes are named below using the usual product-of-factors notation.
This
> scale can also be named consistently using 72-EDO notations although
> actually tuning it to 72-EDO would introduce much larger deviations
from
> the 15-limit ratios.
>
> Extrascalar (i.e. non-Pascal) notes are shown as "x". Most of these
will
> also have (multiple) useful product-of-factors interpretations but I
> haven't worked them out.
>
> Notes missing from some strings are shown as m(...). About a third
of these
> differ by only 7.5 cents from the nearby extrascalar note.
>
> Notes corresponding to the next open string are shown -...- whether
fretted
> or missing.
>
> Pascal guitar, by Dave Keenan 6-Aug-2001
>
> open string steps
> 317c 384.9c 498.1c 317c 384.9c
> 5:6 4:5 3:4 5:6 4:5
>
> 1*7*15/3 1*3*7 1*7*15 1*7*15/3 1*3*7 1*7*15 nut
0.0c
>
>
> 7*11*15 7*9*11 1*3*9 7*11*15 7*9*11 1*3*9 1fr
52.8c
>
>
> 3*9*11 x 3*9*11*3 3*9*11 x 3*9*11*3 2fr
105.7c
> m(1*3*15) m(1*3*15)
>
>
> 1*7*11 9*11*15 3*7*11 1*7*11 9*11*15 3*7*11 3fr
166.0c
>
> 3*7*15 3*7*9 7*9*15 3*7*15 3*7*9 7*9*15 4fr
203.8c
>
>
>
>
> 1*11*15 1*9*11 3*11*15 1*11*15 1*9*11 3*11*15 5fr
286.8c
>
> -1*3*7- 3*9*15 1*7*9 -1*3*7- 3*9*15 1*7*9 6fr
317.0c
>
>
> m(7*9*11) m(7*9*11)
> -m(1*7*15)- -m(1*7*15)-
> x x 1*3*11 x x 1*3*11 7fr
400.0c
>
> 1*3*15 1*3*9 1*9*15 1*3*15 1*3*9 1*9*15 8fr
437.7c
>
>
> m(9*11*15)m(3*9*11*3) m(9*11*15)m(3*9*11*3)
> x x -1*7*15/3- x x 1*7*15/3 9fr
498.1c
> m(3*7*9) m(3*7*9)

>
> x 3*7*11 7*11*15 x 3*7*11 7*11*15 10fr
550.9c
>
> m(7*9*15) m(7*9*15)

> 1*9*11 x 3*9*11 1*9*11 x 3*9*11 11fr
603.8c
>
> m(3*9*15) m(3*9*15)

>
> x 3*11*15 1*7*11 x 3*11*15 1*7*11 12fr
664.2c
>
> 1*7*15 1*7*9 3*7*15 1*7*15 1*7*9 3*7*15 13fr
701.9c
>
>
> m(1*3*9) m(1*3*9)

>
> x 1*3*11 1*11*15 x 1*3*11 1*11*15 14fr
784.9c
> 3*9*11*3 3*9*11*3

> x 1*9*15 1*3*7 x 1*9*15 1*3*7 15fr
815.1c
>
>
> 3*7*11 x 7*9*11 3*7*11 x 7*9*11 16fr
867.9c
> m(1*7*15/3) m(1*7*15/3)

> m(7*9*15) m(7*9*15)

>
> x 7*11*15 1*3*15 x 7*11*15 1*3*15 17fr
935.8c
>
>
> 3*11*15 3*9*11 9*11*15 3*11*15 3*9*11 9*11*15 18fr
988.7c
>
> 1*7*9 x 3*7*9 1*7*9 x 3*7*9 19fr
1018.9c
>
> m(1*7*11) m(1*7*11)

>
> m(3*7*15) m(3*7*15)

> 1*3*11 x 1*9*11 1*3*11 x 1*9*11 20fr
1101.9c
>
> 1*9*15 x 3*9*15 1*9*15 x 3*9*15 21fr
1139.6c
>
> m(1*11*15) m(1*11*15)

>
> 1*7*15/3 1*3*7 1*7*15 1*7*15/3 1*3*7 1*7*15 8ve
1200.0c
>
> Regards,
> -- Dave Keenan
> -- Dave Keenan
> Brisbane, Australia
> http://dkeenan.com

--- In tuning@y..., "Wally" <earth7@o...> wrote:
> Hi David
>
> Here is David Canwright's home page:
>
> http://www.mbay.net/~anne/david/.
>
> Lot's of great links to "fretting in JI"
>
> Regards
> Wally

David Canright also has a way of skewing lattices so that height
corresponds exactly to pitch. More people should be making their
lattices do this (it's very hard with ASCII, though). Canright's
music is really nice, too.

--- In tuning@y..., "John Starrett" <jstarret@c...> wrote:
> Yes, Dave, I do have such info here:
> http://www-math.cudenver.edu/~jstarret/guitar.html

Thanks for that John.

> I am interested in building a Blackjack guitar. I have a fretless
just
> waiting for an interesting idea. Can you fill me in privately on the
> details of the scale?

In case others are interested, and missed it last time, here it is
again publically.

http://dkeenan.com/Music/Miracle/BlackjackGuitar.gif

If you want more info, don't hesitate to ask more specific questions.

-- Dave Keenan

--- In tuning@y..., earth7@o... wrote:
> Please check the following link:
>
> http://www.mbay.net/~anne/david/frets/index.htm
>
> this particular person (who also is named "David")is very
> knowledgable in the field of fretting guitars using JI. I've emailed
> him quite a few times and he has helped me a lot. He's a great
> contact!

Thanks for the kind words Wally. In future it would be best if you
didn't quote the entire post that you are replying to, particularly
when it is a long one full of numbers.

David Canright is to be applauded for sharing his work in this area.
But I hope we have now passed the era when a guitar designed for an 8
note JI scale has 49 fretlets to the octave! (a worst case).

Paul Erlich used the term "near-JI" for the guitars I'm proposing. But
I disagree. I think they are simply JI. I hope we got beyond the
simple idea that JI = rational some time ago. If anyone thinks they
have a rationally tuned guitar, they are fooling themselves.

Of course JI = rational is a very good first approximation, kind of
like we still teach kids that electrons orbit around the nucleus
of an atom like planets around the sun. But that model isn't gonna do
you much good if you want to design a laser. For that you need quantum
mechanics, where unfortunately the math is a lot harder.

-- Dave Keenan

on 8/10/01 2:57 AM, tuning@yahoogroups.com at tuning@yahoogroups.com wrote:

> From: "Dave Keenan" <D.KEENAN@UQ.NET.AU>

>>> So no-one wants to talk about JI guitars? <sigh>
>>>
>>> --Dave Keenan

> Thanks Paul and Alison. It seems I mistook a lack of discussion for a
> lack of interest, but it now seems it is simply a lack of
> disagreement.

Hello Dave,

I haven't added anything to the discussion, as I'm not really qualified in
the scale construction dep't, but I am quite interested in what you're
designing. I have one of the interchangeable fretboard systems, still trying
to find a guitar to install it onto, and would be quite interested in having
a blackjack fretboard.

Seth

--
Seth Austen

http://www.sethausten.com
emails: seth@sethausten.com
klezmusic@earthlink.net

----- Original Message -----
From: Dave Keenan <D.KEENAN@UQ.NET.AU>

> David Canright is to be applauded for sharing his work in this area.
> But I hope we have now passed the era when a guitar designed for an 8
> note JI scale has 49 fretlets to the octave! (a worst case).

Have you ever played such an instrument?

> Paul Erlich used the term "near-JI" for the guitars I'm proposing. But
> I disagree. I think they are simply JI. I hope we got beyond the
> simple idea that JI = rational some time ago. If anyone thinks they
> have a rationally tuned guitar, they are fooling themselves.

?

> Of course JI = rational is a very good first approximation

An approximation? I thought it IS the definition.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

----- Original Message -----
From: Dave Keenan <D.KEENAN@UQ.NET.AU>

> I may build _one_
> (prob. Blackjack) but I'm not a "real" guitarist.

I missed this one. Ignore my previous question.

> It would be great if
> some others were willing to take the risk and have one built (or set
> some up using movable frets, or fretless with nylon strings for
> frets).

I want to keep my fretless dedicated to to being fretless,
but I do have an old acoustic that has needed a fret job
for 19 years. It never seemed worth the $$$, but I've
been thinking of making it fretless. I'll order some fret nippers
to pull the frets and find out what kind of wood putty to use
this afternoon. I don't mind experimenting on this guitar.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

Dave Keenan wrote:

> Thanks Paul and Alison. It seems I mistook a lack of discussion for a
> lack of interest, but it now seems it is simply a lack of
> disagreement. I hope that using microtemperaments to make JI guitars
> feasible, seems inevitable now. But I agree with Dan; it needs some
> testing in practice. I don't have the resources. I may build _one_
> (prob. Blackjack) but I'm not a "real" guitarist. It would be great if
> some others were willing to take the risk and have one built (or set
> some up using movable frets, or fretless with nylon strings for
> frets).

I'm keen to try out the Blackjack and it's good to see interest from others. Perhaps in a few
years there will be a cult "Blackjack School". Movable frets are difficult, nylon strings tricky
and a fixed fret refret the easiest for me. Thanks Dave and all the others for your fine efforts
in this field of research. Over here this will truly bring the word of God to the pagans.

Best Wishes.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
>
> Paul Erlich used the term "near-JI" for the guitars I'm proposing.
But
> I disagree. I think they are simply JI.

Nah . . . JI has more wolves than the tunings you're using.

Never mind. I spent some time looking into this whole
72-tet-blackjack-canasta-miracle bit and think I
understand what DK was saying.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

----- Original Message -----
From: David Beardsley <davidbeardsley@biink.com>

> ----- Original Message -----
> From: Dave Keenan <D.KEENAN@UQ.NET.AU>
>
> > David Canright is to be applauded for sharing his work in this area.
> > But I hope we have now passed the era when a guitar designed for an 8
> > note JI scale has 49 fretlets to the octave! (a worst case).
>
> Have you ever played such an instrument?
>
> > Paul Erlich used the term "near-JI" for the guitars I'm proposing. But
> > I disagree. I think they are simply JI. I hope we got beyond the
> > simple idea that JI = rational some time ago. If anyone thinks they
> > have a rationally tuned guitar, they are fooling themselves.
>
> ?
>
> > Of course JI = rational is a very good first approximation
>
> An approximation? I thought it IS the definition.
>
>
> * David Beardsley
> * http://biink.com
> * http://mp3.com/davidbeardsley
>
>
>
>
> You do not need web access to participate. You may subscribe through
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>
>
>

--- In tuning@y..., Harold Fortuin <harold_fortuin@y...> wrote:
> Dan Stearns suggests a movable fret guitar--something
> already invented by a German firm. John Schneider
> showed me his copy on my xenharmonic visit to SoCal in
> Nov. '98. There's also a replaceable fretboard guitar
> made by a someone in California, which could serve the
> same purpose.
>
> I wrote down the contact info for the manufacturers
> somewhere, but will my co-conspirator Kris Peck or one
> of the rest of ya will recall the details?

Hi Harold (and company)-
I just checked my files and located the nice color brochure you
passed on to me a couple years ago after your California trip. I
think you got this from either John Schneider or Rod Poole? It's for
Walter Vogt's system, which has the flexible frets adjustable for
each string. The contact information states:

"Please address your inquiry for expert modification of your
instrument or for a new high-quality master guitar incorporating the
new fretboard to:

Herve R. Chouard
Fellererstr. 2
D- 85 354 Freising
Tel. privat: 0 8161 / 6 7748
Workshop: 0 8161 / 9 4952 "

I have no idea whether this information is current or valid at this
time. Also you mention the interchangeable fretboard guitar, which I
assume is the Mark Rankin system. I don't have his address handy but
I've seen it posted on this list several times in the past. One of
these days I would love to try out the interchangeable fretboard
system, since that's about as close as you can get to a "programmable
tuning table" for acoustic instruments!

kp