Re: A Meantone guitar design (was: An Eikosany guitar design)

I decided I had better see what happens when I apply this design method,
developed thru the Blackjack and Eikosany guitar designs, to something more
familiar or closer to home. Meantone.

Until now, I didn't think it was possible to make a 12-of-meantone guitar
with only 12 continuous frets per octave and no missing notes. But here it
is for an Eb to G# tuning. I've shown cents for it as a subset of 31-EDO,
but it will work for any meantone. Extra-scalar notes are shown in
parenthesis.

D F# B D F# B nut 0c

Eb G C Eb G C 1fr 116c

E G# C# E G# C# 2fr 194c

F A D F A D 3fr 310c

(Gb) Bb Eb (Gb) Bb Eb 4fr 426c

G B E G B E 5fr 503c

(Ab) C F (Ab) C F 6fr 619c

A C# F# A C# F# 7fr 697c

Bb D G Bb D G 8fr 813c

B (D#) G# B (D#) G# 9fr 890c

C E A C E A 10fr 1006c

(Db) F Bb (Db) F Bb 11fr 1123c

D F# B D F# B 8ve 1200c

And here's 19-of-meantone for a Gb to B# tuning.

F A D F A D nut 0c

F# A# D# F# A# D# 1fr 77c
Gb Bb Eb Gb Bb Eb 2fr 116c

G B E G B E 3fr 194c

G# B# E# G# B# E# 4fr 271c
Ab C F Ab C F 6fr 310c

A C# F# A C# F# 7fr 387c
(Bbb)Db Gb (Bbb)Db Gb 8fr 426c

Bb D G Bb D G 9fr 503c

B D# G# B D# G# 10fr 581c
(Cb) Eb Ab (Cb) Eb Ab 11fr 619c

C E A C E A 12fr 697c

C# E# A# C# E# A# 13fr 774c
Db F Bb Db F Bb 14fr 813c

D F# B D F# B 15fr 890c

D# (Fx) B# D# (Fx) B# 16fr 968c
Eb G C Eb G C 17fr 1006c

E G# C# E G# C# 18fr 1084c
(Fb) Ab Db (Fb) Ab Db 19fr 1123c

F A D F A D 8ve 1200c

Now for homework, some interested person might like to try their hand at
using this method to design a guitar for one of the other linear
temperaments in Graham's catalog.
http://x31eq.com/catalog.htm

I'm happy to answer questions.

I'm interested to see the optimal 22 of paultone (diaschismic). You could
treat it as having a generator of 110c with a half-octave period (a chain
of 11 notes per period). But there's not a lot of point to this, since
22-EDO is so close.

You could try 17 of Schismic (perfect fourths), 17 of neutral-thirds, 19 of
Magic (major thirds), 19 of Kleismic (minor thirds). Gee I wish Graham
Breed would include the MA optimal generator for each temperament, in his
catalog. :-)

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