Just Hammond: Difference between revisions
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Table 1: Pairings of Gearwheels / Ratios and Intervals | Table 1: Pairings of Gearwheels<ref>Gearing details were taken from http://www.goodeveca.net/RotorOrgan/ToneWheelSpec.html (retrieved Dec 29, 2019) | ||
The German Wikipedia provides the same technical information (in German): https://de.wikipedia.org/wiki/Hammondorgel#Tonerzeugung (retrieved Dec 29, 2019) | |||
The ''HammondWiki'' publishes a second, alternative set of gear ratios with slightly deviating pitch class “E”. Certain other pitch classes are shifted by pure octaves. http://www.dairiki.org/HammondWiki/GearRatio (retrieved Dec 29, 2019)</ref> / Ratios and Intervals | |||
{| class="wikitable" | {| class="wikitable" | ||
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(Note A renders<br> | (Note A renders<br> | ||
standard pitch,<br> | standard pitch,<br> | ||
if (A) is<br> | if shaft (A) is<br> | ||
rotating<br> | rotating<br> | ||
@20 rev./sec) | @20 rev./sec) | ||
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== Just Intervals == | == Just Intervals == | ||
When we associate ''“ratios of the gearwheels’ integer teeth numbers”'' with ''“frequency ratios between partials”'' we realize an intrinsic ''just interval'' determined by integer teeth numbers within such mechanical gear - even without turning the shafts! Although the Hammond Organ pretends to generate a 12edo scale, the instrument in fact creates a high prime limit just scale. | When we associate ''“ratios of the gearwheels’ integer teeth numbers”'' with ''“frequency ratios between partials”'' we realize an intrinsic ''just interval'' determined by integer teeth numbers within such mechanical gear - even without turning the shafts! Although the Hammond Organ pretends to generate a 12edo scale, the instrument in fact creates a high prime limit just scale. | ||
== 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 (which equals 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. | |||
<nowiki><math>f_A=20.0/\textup{sec}\cdot\frac{88}{64}\cdot(2^4)=440.0/\textup{sec} = 440.0\textup{ Hz}<\math></nowiki> | |||