Jorgensen Analyses EBVT

[Ron Koval]

Bill,

Thanks for the update.  Are you sure of those numbers?

Quick review for those that missed it:

Graphing temperaments in ascii involves going around the circle of fifths 
and graphing the width of the major third of the listed note.  ET thirds are 
around 14 cents from pure.  So, a meantone may look something like this: 
(smoothest for most at the expense of some)

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

And a well temperament may look something like this:(smooth progression)
............................ET
C.........*
G...............*
D...................*
A...........................*
E...................................*
B.......................................*
F#.........................................*
C#......................................*
Ab..................................*
Eb..........................*
Bb..................*
F...............*
C.........*


But the numbers you posted graph like this:
............................14 cents

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


Other Equal beating temperaments show non-smoothness when graphed, but I've 
not seen something with this much up and down in any of the records.  Now I 
know that these are just the cents width of the major thirds, not 
considering beats, or any of the other intervals.  The beatgraph does show 
many equal beating intervals, as well as a smooth progression of the m3-M3 
beat speed found in many of the Equal beating temperaments.  The B is set 
right at ET width, though it has the harshest 5th, so it may sound rougher 
than it graphs. There are many instances of the m3 in a chord beating twice 
as fast as the M3, or the 6th and m3 having double beating.  Non-standard, 
but interesting just the same.  I'll try tuning it soon.

Ron Koval





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