Just Hammond: Difference between revisions

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~~[THIS PAGE IS A WORK IN PROGRESS...]~~

The 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==

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==== Example 1: Mapping a single interval====

In this example we map the combination of a Hammond Organ’s note E and a higher note A ~~(a fourth up)~~ to the harmonic series.

In this example we map the combination of a Hammond Organ’s note E and a higher note A to the harmonic series.

Table 2: ~~The~~ fourth E-A

Table 2: Mapping the fourth E-A

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==== Example 2: Mapping a chord ====

Adding an upper fifth (note B), the second example illustrates how to map the sus4-chord E-A-B to the harmonic series.

Adding an upper fifth (note B), the second example illustrates how to map the resulting sus4-chord E-A-B to the harmonic series.

Table 3: sus4-chord E-A-B

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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 11th and the 12th octave.

==== Example 3: ~~Hammond - full scale~~ ====

==== Example 3: Mapping all of the tonegenarator's pitchclasses ====

Table 4: ~~Full~~ set of ~~pitchclasses~~

The full set of the Hammond Organ’s intervals resides surprisingly far up in the Harmonic Series:

* The '''44th''' '''octave starts''' at partial #(243), just below the set of partials determined by the Hammond Organ’s tonegenerator

* The '''45th''' '''octave''' starts '''right within the derived set of partials''' and starts at partial #(244)

Table 4: The full set of intervals' position in the Harmonic Series

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! rowspan="3" style="text-align: center;" |

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| style="text-align: center;" | (C)

| style="text-align: center;" | (D)

| ~~rowspan~~="2" ~~colspan~~="16" style="text-align: center; background-color:#cbcefb;" |

| colspan="16" rowspan="2" style="text-align: center; background-color:#cbcefb;" |

... of Column (D)

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[...~~WILL BE CONTINUED]~~

== Discussion and General Applicability ==

No doubt - the evidence that a cluster of 12 simultaneously ringing semitones from a Hammond Organ is allocated around the 45th octave of the harmonic series is of limited practical relevance. 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==

== See also… ==

Dismantling the tonegenarator of a scrapped H-Series Hammond Organ [8:47 min]

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]

* @ 4:48 min: ''“…these sounds are in there”''

* @ 5:40 min: ''“16 foot, biggest pipes, the deepest sounds – they come from the foot”''

https://www.youtube.com/watch?v=5CG81_Y8SvY

@@ Line 1: / Line 1: @@
-[THIS PAGE IS A WORK IN PROGRESS...]
 The 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==
@@ Line 220: / Line 218: @@
 ==== Example 1: Mapping a single interval====
-In this example we map the combination of a Hammond Organ’s note E and a higher note A (a fourth up) to the harmonic series.
+In this example we map the combination of a Hammond Organ’s note E and a higher note A to the harmonic series.
-<u>Table 2</u>: The fourth E-A
+<u>Table 2</u>: Mapping the fourth E-A
 {| class="wikitable"
@@ Line 305: / Line 303: @@
 ==== Example 2: Mapping a chord ====
-Adding an upper fifth (note B), the second example illustrates how to map the sus4-chord E-A-B to the harmonic series.
+Adding an upper fifth (note B), the second example illustrates how to map the resulting sus4-chord E-A-B to the harmonic series.
 <u>Table 3</u>: sus4-chord E-A-B
@@ Line 402: / Line 400: @@
 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: Hammond - full scale ====
+==== Example 3:  Mapping all of the tonegenarator's pitchclasses ====
-Table 4: Full set of pitchclasses
+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 '''45th''' '''octave''' starts '''right within the derived set of partials''' and starts at partial #(2<sup>44</sup>)
+<u>Table 4</u>: The full set of intervals' position in the Harmonic Series
 {| class="wikitable"
 ! rowspan="3" style="text-align: center;" | <br><br><br>
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 | style="text-align: center;" | (C)
 | style="text-align: center;" | (D)
-| rowspan="2" colspan="16" style="text-align: center; background-color:#cbcefb;" |
+| colspan="16" rowspan="2" style="text-align: center; background-color:#cbcefb;" |
 ... of Column (D)<br><br><br><br>
 | rowspan="2" style="text-align: center;" |
@@ Line 737: / Line 737: @@
 |}
-[...WILL BE CONTINUED]
+== 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 relevance. 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 />
+== See also… ==
+Dismantling the tonegenarator of a scrapped H-Series Hammond Organ [8:47 min]
+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]
+* @ 4:48 min: ''“…these sounds are in there”''
+* @ 5:40 min: ''“16 foot, biggest pipes, the deepest sounds – they come from the foot”''
+https://www.youtube.com/watch?v=5CG81_Y8SvY