Re: Band Organ Just Tuning
By Robbie Rhodes
I wasn't able to meet face-to-face with Fritz Gellerman when I visited in Florida, but we had a pleasant telephone conversation about this subject, and the tuning scale in Digest 961122. I have added the column "Equal Temperment Tuning", and in the last column is shown the difference when compared to the "de Caus" Just Tuning Scale:
note Equal deCaus diff.
cents cents cents
C 0 0 0
C# 100 71 - 29
D 200 204 + 4
D# 300
E 400 386 - 14
F 500 498 - 2
F# 600 590 - 10
G 700 702 + 2
G# 800
A 900 884 - 16
A# 1000
B 1100 1088 - 12
C 1200 1200 0
____
sum: - 77
There are 9 notes per octave in this organ scale, therefore the average difference is -77 / 9 = -8.56 cents.
If this tuning scale were applied to a piano, the piano tuner would have to consider the effect upon the net tension of the piano strings, which would be reduced in tuning the piano "flat" from its normal (Concert) pitch. With organ pipes this means that most of the tuning stoppers or slides must pulled out, and so new problems might arise.
The net effect can be minimized if 8.5 cents is added to the de Caus scale:
note Equal deCaus diff.
cents cents cents
C 0 8.5 + 8.5
C# 100 79.5 - 21.5
D 200 212.5 + 12.5
D# 300
E 400 394.5 - 5.5
F 500 506.5 + 6.5
F# 600 598.5 - 1.5
G 700 710.5 + 10.5
G# 800
A 900 892.5 - 7.5
A# 1000
B 1100 1096.5 - 3.5
C 1200 1208.5 + 8.5
____
sum: - 1.5
average difference = -1.5 / 9 = -0.17 cents.
The "tables of cents" given above would be used with a modern electronic tuning device, while the old-time organbuilder would probably "count the beats" in the time-honoured tradition. Thus, for completeness, the tables should be expanded to also show the absolute frequencies, and the resulting beat frequencies.
I'll do this later -- I just got home after spending a long sleepless night in the Dallas-Ft. Worth airport, where the first storm of the winter canceled my flight home!
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| Robbie Rhodes |
| Return-Path: rrhodes@foxtail.com |
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(Message sent Mon 25 Nov 1996, 22:22:29 GMT, from time zone GMT-0800.) |
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