Just Hammond: Difference between revisions
Table 1 inserted |
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<math>n_2=\frac{Z_1}{Z_2}\cdot n_1</math> | <math>n_2=\frac{Z_1}{Z_2}\cdot n_1</math> | ||
Table 1: Pairings of Gearwheels / Resulting Ratios and Intervals | |||
{| class="wikitable" | |||
! rowspan="3" style="text-align: center;" | Pitch | |||
Class | |||
! colspan="2" style="text-align: center; font-weight:bold;" | | |||
HAMMOND<br> | |||
Organ<br> | |||
Mechanical<br> | |||
Gearing<br> | |||
! colspan="2" style="text-align: center;" | | |||
Gear Ratio<br> | |||
(cancelled)<br> | |||
! rowspan="2" | | |||
! rowspan="2" style="text-align: center;" | | |||
Conversion<br> | |||
of raw<br> | |||
ratio to<br> | |||
interval<br><br><br> | |||
! rowspan="2" style="text-align: center;" | | |||
Deviation<br> | |||
from<br> | |||
12tone equal<br> | |||
temperament<br> | |||
(12edo)<br><br> | |||
! rowspan="2" style="text-align: center;" | | |||
Intonation<br> | |||
(Note A renders<br> | |||
standard pitch,<br> | |||
if (A) is<br> | |||
rotating<br> | |||
@20 rev./sec) | |||
|- | |||
| style="text-align: center;" | (A) | |||
| style="text-align: center;" | (B) | |||
| style="text-align: center;" | (C) | |||
| style="text-align: center;" | (D) | |||
|- | |||
| style="text-align: center;" | driving | |||
Z1[teeth] | |||
| style="text-align: center;" | driven | |||
Z2[teeth] | |||
| colspan="2" style="text-align: center;" | <br>Fraction | |||
| style="text-align: center;" | Ratio | |||
(C)/(D) | |||
| style="text-align: center;" | <br>[cents] | |||
| style="text-align: center;" | <br>[cents] | |||
| style="text-align: center;" | <br>[cents] | |||
|- | |||
| style="text-align: center;" | C | |||
| style="text-align: right;" | 85 | |||
| 104 | |||
| style="text-align: right; " | 85 | |||
| 104 | |||
| style="text-align: center;" | 0.8173077 | |||
| style="text-align: right; " | -349.26 | |||
| style="text-align: center;" | -49.26 | |||
| style="text-align: center;" | -0.576 | |||
|- | |||
| style="text-align: center;" | C# | |||
| style="text-align: right; background-color:#cbcefb;" | 71 | |||
| 82 | |||
| style="text-align: right; background-color:#cbcefb;" | 71 | |||
| 82 | |||
| style="text-align: center;" | 0.8658537 | |||
| style="text-align: right;" | -249.37 | |||
| style="text-align: center;" | -49.37 | |||
| style="text-align: center;" | -0.684 | |||
|- | |||
| style="text-align: center;" | D | |||
| style="text-align: right; background-color:#cbcefb;" | 67 | |||
| style="background-color:#cbcefb;" | 73 | |||
| style="text-align: right; background-color:#cbcefb;" | 67 | |||
| style="background-color:#cbcefb;" | 73 | |||
| style="text-align: center;" | 0.9178082 | |||
| style="text-align: right;" | -148.48 | |||
| style="text-align: center;" | -48.48 | |||
| style="text-align: center;" | 0.200 | |||
|- | |||
| style="text-align: center;" | D# | |||
| style="text-align: right;" | 105 | |||
| 108 | |||
| style="text-align: right;" | 35 | |||
| 36 | |||
| style="text-align: center; background-color:#ffffff;" | 0.9722222 | |||
| style="text-align: right;" | -48.77 | |||
| style="text-align: center;" | -48.77 | |||
| style="text-align: center;" | -0.088 | |||
|- | |||
| style="text-align: center;" | E | |||
| style="text-align: right; background-color:#cbcefb;" | 103 | |||
| 100 | |||
| style="text-align: right; background-color:#cbcefb;" | 103 | |||
| 100 | |||
| style="text-align: center;" | 1.0300000 | |||
| style="text-align: right;" | 51.17 | |||
| style="text-align: center;" | -48.83 | |||
| style="text-align: center;" | -0.145 | |||
|- | |||
| style="text-align: center;" | F | |||
| style="text-align: right;" | 84 | |||
| 77 | |||
| style="text-align: right;" | 12 | |||
| style="background-color:#cbcefb;" | 11 | |||
| style="text-align: center;" | 1.0909091 | |||
| style="text-align: right;" | 150.64 | |||
| style="text-align: center;" | -49.36 | |||
| style="text-align: center;" | -0.681 | |||
|- | |||
| style="text-align: center;" | F# | |||
| style="text-align: right;" | 74 | |||
| 64 | |||
| style="text-align: right; background-color:#cbcefb;" | 37 | |||
| 32 | |||
| style="text-align: center;" | 1.1562500 | |||
| style="text-align: right;" | 251.34 | |||
| style="text-align: center;" | -48.66 | |||
| style="text-align: center;" | 0.026 | |||
|- | |||
| style="text-align: center;" | G | |||
| style="text-align: right;" | 98 | |||
| 80 | |||
| style="text-align: right;" | 49 | |||
| 40 | |||
| style="text-align: center;" | 1.2250000 | |||
| style="text-align: right;" | 351.34 | |||
| style="text-align: center;" | -48.66 | |||
| style="text-align: center;" | 0.020 | |||
|- | |||
| style="text-align: center;" | G# | |||
| style="text-align: right;" | 96 | |||
| 74 | |||
| style="text-align: right;" | 48 | |||
| style="background-color:#cbcefb;" | 37 | |||
| style="text-align: center;" | 1.2972973 | |||
| style="text-align: right;" | 450.61 | |||
| style="text-align: center;" | -49.39 | |||
| style="text-align: center;" | -0.707 | |||
|- | |||
| style="text-align: center; font-weight:bold;" | A | |||
| style="text-align: right;" | 88 | |||
| 64 | |||
| style="text-align: right; background-color:#cbcefb;" | 11 | |||
| 8 | |||
| style="text-align: center;" | 1.3750000 | |||
| style="text-align: right;" | 551.32 | |||
| style="text-align: center;" | -48.68 | |||
| style="text-align: center; font-weight:bold;" | 0.000 | |||
|- | |||
| style="text-align: center;" | A# | |||
| style="text-align: right; background-color:#cbcefb;" | 67 | |||
| 46 | |||
| style="text-align: right; background-color:#cbcefb;" | 67 | |||
| 46 | |||
| style="text-align: center;" | 1.4565217 | |||
| style="text-align: right;" | 651.03 | |||
| style="text-align: center;" | -48.97 | |||
| style="text-align: center;" | -0.285 | |||
|- | |||
| style="text-align: center;" | B | |||
| style="text-align: right;" | 108 | |||
| 70 | |||
| style="text-align: right;" | 54 | |||
| 35 | |||
| style="text-align: center;" | 1.5428571 | |||
| style="text-align: right;" | 750.73 | |||
| style="text-align: center;" | -49.27 | |||
| style="text-align: center;" | -0.593 | |||
|} | |||
(Purple colored cells contain prime numbers) | |||