Blackjack guitar fretting spreadsheet

Here's an Excel97 spreadsheet for calculating fret positions for a
Blackjack guitar refret. It can easily be adapted for any tuning.

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

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

--- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
> Here's an Excel97 spreadsheet for calculating fret positions for a
> Blackjack guitar refret. It can easily be adapted for any tuning.
>
> http://dkeenan.com/Music/Miracle/BlackjackGuitar.xls
>
> Regards,
> -- Dave Keenan
> Brisbane, Australia
> http://dkeenan.com

Hi Dave. I will check this out. I have seen your page with the
Blackjack Guitar Proposal, and I am studying my options for the
targetted guitar. I have a bass that is also free of frets and needs a
new identity, so as soon as my time frees up (Neil's new 31 and some
work related stuff must be finished first) I will begin serious
planning. I hope you don't mind if I pick your brain a little then.

--- In tuning@y..., "John Starrett" <jstarret@c...> wrote:
> --- In tuning@y..., David C Keenan <D.KEENAN@U...> wrote:
> > Here's an Excel97 spreadsheet for calculating fret positions for a
> > Blackjack guitar refret. It can easily be adapted for any tuning.
> >
> > http://dkeenan.com/Music/Miracle/BlackjackGuitar.xls
> >
> > Regards,
> > -- Dave Keenan
> > Brisbane, Australia
> > http://dkeenan.com
>
> Hi Dave. I will check this out. I have seen your page with the
> Blackjack Guitar Proposal, and I am studying my options for the
> targetted guitar. I have a bass that is also free of frets and
needs a
> new identity, so as soon as my time frees up (Neil's new 31 and
some
> work related stuff must be finished first) I will begin serious
> planning. I hope you don't mind if I pick your brain a little then.

Dave, when you came up with this fretting, did you assume that the
center of symmetry of the blackjack scale would be the best "tonic"
for the scale? As we have seen, there are other notes that have more
consonant connections with neighboring notes in the lattice, and thus
could better serve as "tonics".

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Dave, when you came up with this fretting, did you assume that the
> center of symmetry of the blackjack scale would be the best "tonic"
> for the scale?

No. There was no consideration of any tonic whatsoever.

The aim was purely to maximise playable 11-limit chords (as stacks of
thirds or fourths), while ensuring that melodically there were no gaps in
the scale in the critical region between the nut and the position
corresponding to the pitch of the next string.

Nice bonuses were
(a) All strings have an actual fret corresponding to the pitch of the next
string, to facilitate tuning.
(b) Outside the critical region, "parasitic" notes introduce some JI
diatonics (major minor and Arabic). The few frets involved could be
tempered to meantone without greatly affecting the blackjack scale.

> As we have seen, there are other notes that have more
> consonant connections with neighboring notes in the lattice, and thus
> could better serve as "tonics".

Sure. Which do you favour? How do you see this affecting the guitar design?

Here is tablature for all eight available 4:5:6:7 chords in the reference
scale (no parasitic notes). Most have more than one position shown. Some of
these can also be seen to generalise to barre-chords for playing in other
positions.

The notation below is based on the point of symmetry being "D" and "4", so
the chain of generators is:
D> E[ F< F#v G Ab^ A> B[ C< C#v D Eb^ E> F] G< G#v A Bb^ B> C] D<
4> 5> 6> 7> 8> 9> 0 1 2 3 4 5 6 7 8 9 0< 1< 2< 3< 4<

Open strings are Eb^ G< Bb^ D F] A
5 8 1< 4 7 0<

B[sm7
_ _ _ _o_
| | | | | |
|_|_|_@_|_| 11fr
|_|_|_|_|_|
| | | | | |
@_|_@_|_|_|
|_@_|_|_|_|

C<sm7
_o_ _ _ _
|_|_|_|_|_@
| | | | | |
|_|_|_|_@_|
|_|_@_@_|_|

_ _ _ _ _
|_|_|_|_@_| 7fr
| | | | | |
|_|_|_@_|_|
|_@_|_|_|_|
|_|_@_|_|_|

C#vsm7
_ _ _ _ _
|_|_|_|_|_@ 3fr
| | | | | |
|_|_|_|_@_|
|_|_@_@_|_|

_x_ _ _ _
+_+_+_+_+_+ 3fr
| | | | | |
|_|_|_|_@_|
|_|_@_@_|_|

Dsm7
_ _ _ _ _
|_|_|_|_|_@ 5fr
| | | | | |
|_|_|_|_@_|
|_|_@_@_|_|

_ _ _o_ _o
|_|_|_|_@_|
| | | | | |
|_|_|_|_|_|
|_|_@_|_|_|
| | | | | |
|_@_|_|_|_|
@_|_|_|_|_|

Eb^sm7
o_x_ _ _ _
|_|_|_|_|_@ 7fr
| | | | | |
|_|_|_|_@_|
|_|_@_@_|_|

o_ _ _ _ _
| | | | | |
|_|_|_+_+_+ 2fr
|_|_|_|_@_|
| | | | | |
|_|_|_|_|_|
|_|_@_|_|_|
| | | | | |
|_@_|_|_|_|

E>sm7
_ _ _o_ _
|_|_|_|_|_|
| | | | | |
@_|_@_|_|_|
|_@_|_|_|_|
| | | | | |
|_|_|_|_|_?
|_|_|_|_?_|

_ _ _ _ _
| | | | | |
|_|_|_+_+_+ 4fr
|_|_|_|_@_|
| | | | | |
|_|_|_|_|_|
|_|_@_|_|_|
| | | | | |
|_@_|_|_|_|

F]sm7
_ _ _ _o_
| | | | | |
|_|_|_@_|_| 2fr
|_|_|_|_|_|
| | | | | |
@_|_@_|_|_|
|_@_|_|_|_|

G<sm7
_ _ _ _ _
| | | | | |
|_|_|_@_|_| 4fr
|_|_|_|_|_|
| | | | | |
@_|_@_|_|_|
|_@_|_|_|_|

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