more graphs (temperaments)

[Ron Koval]

Hi all-

More from Jorgensen-

Previously, I posted with some graphs for Well temp. tunings, showing the 
symmetry of the widths of thirds based on the circle of fifths.

Today, I'll show some skewed tunings.  First, one that most have heard 
of...Vallotti-Young:

(width of major thirds built on shown note; 13.7=ET, each period=1/2 cent)
pure..........................ET.....................
C :............*
G :............*
D :............*
A :....................*
E :...........................*
B :...................................*
F#:...........................................*
Db:...........................................*
Ab:...........................................*
Eb:...................................*
Bb:..........................*
F :...................*
C :...........*

this tuning shares some qualities of meantone with well tuning in that there 
are keys that have the same width thirds in a row, then the familiar curve 
travels through the other keys.  Notice that this tuning favors the sharp 
keys over the flat keys.


Next, look at the equal beating Printz, which favors the flat keys:
pure..........................ET...........

C :*
G :.................*
D :.........................*
A :.................................*
E :.......................................*
B :.......................................*
F#:...........................................*
Db:...........................................*
Ab:...........................................*
Eb:.........................*
Bb:.............*
F :.....*
C :*

Here's my stab a mild meantone....still seems tougher tolerances are needed 
if the lines are going to be straight after tuning. Much easier to tune to a 
curve and actually get a curve!

offsets from ET tuning
c  2
c#-2
d  0
d# 3
e  0
f  2
f#-2
g  1
g# 1
a  0
a# 2
b -1
pure...........................ET..............

C :.......................*
G :.......................*
D :.......................*
A :.......................*
E :.............................*
B :...................................*
F#:...................................*
Db:...................................*
Ab:.............................*
Eb:.......................*
Bb:.......................*
F :.......................*
C :.......................*


Now, back to tuning!

Ron Koval



(graphman)
________________________________________________________________________
Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com