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. | |||
==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 12 pairs of gearwheels that make twelve ''driven'' shafts turn. The corresponding twelve ''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> | 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 12 pairs of gearwheels that make twelve ''driven'' shafts turn. The corresponding twelve ''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> | ||
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The supplemental note B establishes an additional prime factor. We find the matching pattern of partials for this sus4-chord (1442:1925:2160) farther up in the harmonic series, where this chord spans the boundary between the 11<sup>th</sup> and the 12<sup>th</sup> octave. | The supplemental note B establishes an additional prime factor. We find the matching pattern of partials for this sus4-chord (1442:1925:2160) farther up in the harmonic series, where this chord spans the boundary between the 11<sup>th</sup> and the 12<sup>th</sup> octave. | ||
==== Example 3: Mapping all of the | ==== Example 3: Mapping all of the tonegenerator's pitchclasses ==== | ||
The full set of the Hammond Organ’s intervals resides surprisingly far up in the Harmonic Series: | The full set of the Hammond Organ’s intervals resides surprisingly far up in the Harmonic Series: | ||
* The '''44th''' '''octave starts''' at partial #(2<sup>43</sup>), just below the set of partials determined by the Hammond Organ’s tonegenerator | * The '''44th''' '''octave starts''' at partial #(2<sup>43</sup>), just below the set of partials determined by the Hammond Organ’s tonegenerator | ||
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== Discussion and General Applicability == | == Discussion and General Applicability == | ||
No doubt - the evidence that a cluster of 12 simultaneously ringing semitones from a Hammond Organ is allocated around the 45<sup>th</sup> octave of the harmonic series is of limited practical | No doubt - the evidence that a cluster of 12 simultaneously ringing semitones from a Hammond Organ is allocated around the 45<sup>th</sup> octave of the harmonic series is of limited practical use. Nevertheless the method of prime factorization can be applied to arbitrary '''intervals, chords or scales built from rational intervals''' to identify their position in the harmonic series. Simply replace the gear-ratios by just intervals of interest. | ||
==References== | ==References== | ||
<references /> | <references /> | ||
== See also… == | == See also… == | ||
Dismantling the tonegenarator of a scrapped H-Series Hammond Organ [8:47 min] | * Dismantling the tonegenarator of a scrapped H-Series Hammond Organ [8:47 min] https://www.youtube.com/watch?v=7Qqmr6IiFLE | ||
https://www.youtube.com/watch?v=7Qqmr6IiFLE | * An artist’s perception: Tony Monaco demonstrates how to apply the tonegenerator’s features of a Hammond Organ [31:10 min] https://www.youtube.com/watch?v=5CG81_Y8SvY | ||
An artist’s perception: Tony Monaco demonstrates how to apply the tonegenerator’s features of a Hammond Organ [31:10 min] | ** @ 4:48 min: ''“…these sounds are in there”'' | ||
* @ 4:48 min: ''“…these sounds are in there”'' | ** @ 5:40 min: ''“16 foot, biggest pipes, the deepest sounds – they come from the foot”'' | ||
* @ 5:40 min: ''“16 foot, biggest pipes, the deepest sounds – they come from the foot”'' | |||