Just Hammond: Difference between revisions
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This article features just intervals created by the mechanical tonegenerator of the classical Hammond B-3 Organ model. | This article features just intervals created by the mechanical tonegenerator of the classical Hammond B-3 Organ model. | ||
==Design of the Hammond B-3’s Tonegenerator== | ==Design of the Hammond B-3’s Tonegenerator== | ||
Since 1935 the Hammond Organ Company’s goal was to market electromechanical organs<ref>Webressource https://en.wikipedia.org/wiki/Hammond_organ (retrieved December 2019)</ref> with 12-tone equally tempered (12edo) tuning. The mechanical tonegenerator of the Hammond B-3 Organ is based on a set of | Since 1935 the Hammond Organ Company’s goal was to market electromechanical organs<ref>Webressource https://en.wikipedia.org/wiki/Hammond_organ (retrieved December 2019)</ref> with 12-tone equally tempered (12edo) tuning. The mechanical tonegenerator of the Hammond B-3 Organ is based on a set of twelve ''different pairings'' of gearwheels that make (12*4) ''driven'' shafts turn. The corresponding ''driving'' gearwheels are mounted on a common shaft and turn all at the same rotational speed ''n<sub>1</sub>''. Certain gears reduce, others increase rotational speed.<ref>Detailed photos of a similar M-1 tonegenerator are provided by https://modularsynthesis.com/hammond/m3/m3.htm (retrieved December 2019)</ref> | ||
For every chromatic pitch class four driven shafts are installed. Pure octaves are generated by dedicated ''tonewheels'' (with 2, 4, 8, 16, 32, 64 or 128 high and low points on their edges) that rotate with the driven shafts. Each high point on a tone wheel is called a ''tooth''. When the gears are in motion, magnetic pickups react to the tonewheels’ passing teeth and generate an electric signal that can be amplified and transmitted to a loudspeaker. | |||
For each pair of gearwheels the ratio of rotational speed ''n<sub>2</sub>''/''n<sub>1</sub>'' is determined by the inverse ratio of the gearwheels’ integer teeth numbers Z<sub>1</sub> and Z<sub>2</sub>: | For each pair of gearwheels the ratio of rotational speed ''n<sub>2</sub>''/''n<sub>1</sub>'' is determined by the inverse ratio of the gearwheels’ integer teeth numbers Z<sub>1</sub> and Z<sub>2</sub>: | ||
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<math>\frac{Z_1}{Z_2}=\frac{n_2}{n_1}</math> | <math>\frac{Z_1}{Z_2}=\frac{n_2}{n_1}</math> | ||
To calculate the rotational speed ''n<sub>2</sub>'' of the driven | To calculate the rotational speed ''n<sub>2</sub>'' of the driven shafts we write | ||
<math>n_2=\frac{Z_1}{Z_2}\cdot n_1</math> | <math>n_2=\frac{Z_1}{Z_2}\cdot n_1</math> | ||
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== Tuning == | == Tuning == | ||
The whole set of frequency ''ratios'' is fixed by the design of the gear mechanism. The driving shaft’s (A) rotational speed ''n<sub>1</sub>'' determines the instrument’s (master-)tuning. Rotating at exactly 1200 rpm (20 rev./sec), the pitch of note A equals precisely 27.500 Hz or one of its doublings. Therefore the instrument aligns note A with a concert pitch of 440.0 Hz. | The whole set of frequency ''ratios'' is fixed by the design of the gear mechanism. The driving shaft’s (A) rotational speed ''n<sub>1</sub>'' determines the instrument’s (master-) tuning. Rotating at exactly 1200 rpm (20 rev./sec), the pitch of note A equals precisely 27.500 Hz or one of its doublings. Therefore the instrument aligns note A with a concert pitch of 440.0 Hz. | ||
<math>f_\text{A}=20.0/\text{s}\cdot\frac{88}{64}\cdot(2^4)=440.0/\text{s} = 440.0 \text{ Hz}</math> | <math>f_\text{A}=20.0/\text{s}\cdot\frac{88}{64}\cdot(2^4)=440.0/\text{s} = 440.0 \text{ Hz}</math> | ||