HammondWiki - Diff: GearRatio

Differences between version 9 and previous revision of GearRatio.

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Newer page: version 9 Last edited on May 30, 2016 9:53 pm. by
Older page: version 8 Last edited on May 30, 2016 8:32 pm. by
@@ -1,21 +1,23 @@
-The difference in the number of teeth between the DrivingGear''''s and the DrivenGear''''s is the *gear ratio*: 
+The difference in the number of teeth between the [Driving Gears| DrivingGear] and the [Driven Gears| DrivenGear] is the *gear ratio*. With the driving gears rotating at a fixed speed of 20 revolutions per second, the difference in the number of teeth between the two gears means that the driven gears, and the tonewheels connected to them, will spin at at a speed set by the gear ratio. Since the relationship between semitones is the twelfth root of two and gears can only have an integral number of teeth, Hammond selected gear ratios that were as close as possible to the correct values. With the number of "teeth" on the [Tonewheels|ToneWheel] doubling every octave, the minimum number of different gear ratios needed is twelve : 
  
 <verbatim> 
 Note Driving Driven Ratio 
 C 85 104 0.817307692 
 C# 71 82 0.865853659 
 D 67 73 0.917808219 
-D# 105 108 .972222222 
-E 103 100 1.030000000  
-F 84 77 1 .090909091  
-F# 74 64 1 .156250000  
-G 98 80 1 .225000000  
-G# 96 74 1 .297297297  
-A 88 64 1 .375000000  
-A# 67 46 1 .456521739  
-B 108 70 1 .542857143  
+D# 70 72 .972222222 
+E 69 67 1.029850746  
+F 54 99 .545454545  
+F# 37 64 .578125000  
+G 49 80 .612500000  
+G# 48 74 .648648649  
+A 66 96 .687500000  
+A# 67 92 .728260870  
+B 54 70 .771428571  
 </verbatim> 
+  
+In the patent organ, Hammond had shown two octaves of 16 toothed tonewheels, with different gear ratios for the second set of tonewheels.  
  
 Note that these ratios produce a very close *approximation* of the equal tempered scale. They are *NOT* exact. These ratios are used in each of the first seven octaves. The octave produced is dependent on the number of teeth on the ToneWheel''''s. In 60 Hz organs, the motor turns at 1200 RPM / 60Hz or 20 revolutions per second. The lowest octave has tonewheels with 2 teeth. The first 7 tones in the highest octave (C through F#) are produced by tonewheels with 192 teeth. For these 7 tones to be correct with only 192 teeth, they use the gear ratios for notes F through B. 
  
 The formula to calculate the exact frequency produced is: 

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