Quattro NOT 11tet

> From: John Starrett <jstarret@math.cudenver.edu>
>
> The 11 pitches in your scale are evenly spaced, but the
> distance from the octave fret to the first fret
> above the octave is larger than 1/2 the distance from the nut
> to the first

Ahh... With the proper bridge placement, the fret spacing gets
logarithmically smaller to the point where it converges on 0 right at the
bridge. True 11tet would do the same thing. The Quattro in question would
converge about a half inch beyond the bridge. Oops!

This kind of bridge twiddling will not yield equal temperaments, but it
could provide a wealth of fractal scale resources, no?

Here's a comparison of the fret measurements between true 11tet and a
bridge-adjusted 12tet to give 11 tones in the first octave. I used a 100
inch scale in my calculator because it was a nice round number.

TRUE 11TET

measured from nut
0.00 inches 0.00 cents C
6.10 inches 109.00 cents C# +9
11.83 inches 218.00 cents D +18
17.21 inches 327.00 cents D# +27
22.26 inches 436.00 cents E +36
27.01 inches 545.00 cents F +45
31.46 inches 654.00 cents G -46
35.64 inches 763.00 cents Ab -37
39.57 inches 872.00 cents A -28
43.26 inches 981.00 cents Bb -19
46.72 inches 1090.00 cents B -10
50.00 inches 1200.00 cents C +0
53.05 inches 1309.00 cents C# +9
55.92 inches 1418.00 cents D +18
58.61 inches 1527.00 cents D# +27
61.13 inches 1636.00 cents E +36
63.50 inches 1745.00 cents F +45
65.73 inches 1854.00 cents G -46
67.82 inches 1963.00 cents Ab -37
69.79 inches 2072.00 cents A -28
71.63 inches 2181.00 cents Bb -19
73.36 inches 2290.00 cents B -10
75.00 inches 2400.00 cents C +0

12tet adjusted for 11 notes in the first octave

0.00 inches
5.97 inches
11.60 inches
16.92 inches
21.93 inches
26.67 inches
31.14 inches
35.36 inches
39.34 inches
43.10 inches
46.65 inches
50.00 inches 1200 cents
53.16 inches
56.14 inches
58.96 inches
61.62 inches
64.13 inches
66.49 inches
68.73 inches
70.84 inches
72.83 inches
74.71 inches
76.48 inches
78.16 inches
79.74 inches

---
Glen Peterson
30 Elm Street North Andover, MA 01845
(978) 975-1527
http://www.OrganicDesign.org/Glen/Instruments

> [Glen Peterson, TD 306.17]
>
>> From: John Starrett <jstarret@math.cudenver.edu>
>>
>> The 11 pitches in your scale are evenly spaced, but the
>> distance from the octave fret to the first fret
>> above the octave is larger than 1/2 the distance from the nut
>> to the first
>
> Ahh... With the proper bridge placement, the fret spacing gets
> logarithmically smaller to the point where it converges on 0
> right at the bridge. True 11tet would do the same thing. The
> Quattro in question would converge about a half inch beyond the
> bridge. Oops!

Just wanted to point out again that in my post about Ivor Darreg's
18-tET guitar with moveable bridge, I was careful to say that
it provided *pseudo*-17- and -19-tET'. Ivor knew that moving
the bridge did not give exact 17- and 19-tET (while the guitar
was fretted to *exactly* 18-tET), but it was close enough for
him that he found the 3-instruments-in-one to be useful.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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