Re: Band Organ Just Tuning
By Robbie Rhodes
You quoted from the letter from Jim Spriggs:
> The problem that you posed regarding "meantone tuning" for the
> Wurlitzer 150 has led to, I believe, a serendipitous solution. The
> solution is de Caus' "just" tuning scale, which for the Wurlitzer is
> ideal. The 150 can only play in the keys of "C" and "G", the latter
> only occasionaly being used. This makes it possible for all of the
> chords normally used (tonic, dominant, and subdominant) to be totally
> without beats (eureka!). Much more information will follow. It would be
> well worth tuning the 150 in that fashion. I might write an article for
> the Bulletin on it if you find that it really sounds better.
Great! That's just the conclusion I reached after staring at the real frequencies. In the table below I have _assumed_ a value for the D# so that it is zero-beat in the C-minor chord. I hope that this is confirmed when you hear from Jim Spriggs. The last two columns, "de Caus frequency", may be multiplied by the standard pitch to get the actual frequencies. For example, for the best match with the equally tempered scale based on A = 440 Hz, the note C may be adjusted to zero-beat with a tuning fork at C = 261.63 Hz (which is 0 cents deviation from the A440 standard).
note Equal de Caus de Caus de Caus
cents cents freq freq
C 0 0 1.0 1/1
C# 100 71 1.04167 25/24
D 200 204 1.125 9/8
D# 300 (315.5) 1.2 6/5
E 400 386 1.25 5/4
F 500 498 1.3333 4/3
F# 600 590 1.40625 45/32
G 700 702 1.5 3/2
G# 800
A 900 884 1.66667 5/3
A# 1000
B 1100 1088 1.875 15/8
Because the "de Caus just tuning" is designed for zero beats, it is very simple to tune "by ear". Here is the algorithm:
1. Strike the tuning fork, adjust C for zero-beat.
2. Sound C, adjust G, and then E, all for zero-beat. (the tonic chord) (Then re-check that C and G are zero-beat.)
3. Sound C and G, adjust D# for zero-beat. (tonic minor chord)
4. Sound G, adjust D, and then B, all for zero beat. (dominant chord)
5. Sound D, adjust F# for zero-beat
6. Sound C, adjust F, and then A, all for zero-beat. (subdominant chord)
7. Sound A, adjust C# for zero-beat.
I am eager to hear the "before and after" comparison recording of your Wurlitzer 150 organ. Steve Goodman tells me that "this is the way it ought to be tuned!"
Cheers,
Robbie Rhodes |
(Message sent Thu 28 Nov 1996, 05:30:52 GMT, from time zone GMT-0800.) |
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