Just Hammond: Difference between revisions

Line 195:

The whole set of frequency ''ratios'' is fixed by the design of the gear mechanism. The driving shaft’s (A) rotational speed ''n1'' 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.

== Mapping Hammond’s Rational Intervals to the Harmonic Series ==

Line 216:

== Mapping Hammond’s Rational Intervals (cont.): Examples ==

The following examples illustrate how to map intervals or chords to the harmonic series.

Table 2: ~~Mapping a single interval~~

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

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

Table 2: Fourth E-A

{| class="wikitable"

Line 298:

Line 302:

|}

~~In this first example we map the combination of a Hammond Organ’s note E and a higher note A (a fourth up) to the harmonic series.~~ The resulting interval E-A appears between partial # 206 and partial # 275. Thus the frequency ratio is (275:206), which equals 500.14 cents.

The resulting interval E-A appears between partial # 206 and partial # 275. Thus the frequency ratio is (275:206), which equals 500.14 cents.

~~Table 3~~: ~~Supplement of an upper note "~~B"

==== Example 2: Supplementing a Fifth ====

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

{| class="wikitable"

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

Line 394:

Line 400:

for orientation only

|}

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.

~~The second example illustrates how to map the resulting sus4-chord to the harmonic series~~.

==== Example 3: [...WILL BE CONTINUED] ====

~~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.

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

==References==

@@ Line 195: / Line 195: @@
 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.
-<math>f_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>
 == Mapping Hammond’s Rational Intervals to the Harmonic Series ==
@@ Line 216: / Line 216: @@
 == Mapping Hammond’s Rational Intervals (cont.): Examples ==
 The following examples illustrate how to map intervals or chords to the harmonic series.
-<u>Table 2</u>: Mapping a single interval
+==== Example 1: Mapping a single interval====
+In this first example we map the combination of a Hammond Organ’s note E and a higher note A (a fourth up) to the harmonic series.
+<u>Table 2</u>: Fourth E-A
 {| class="wikitable"
@@ Line 298: / Line 302: @@
 |}
-In this first example we map the combination of a Hammond Organ’s note E and a higher note A (a fourth up) to the harmonic series. The resulting interval E-A appears between partial # 206 and partial # 275. Thus the frequency ratio is (275:206), which equals 500.14 cents.
+The resulting interval E-A appears between partial # 206 and partial # 275. Thus the frequency ratio is (275:206), which equals 500.14 cents.
-<u>Table 3</u>: Supplement of an upper note "B"
+==== Example 2: Supplementing a Fifth ====
+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
 {| class="wikitable"
 ! rowspan="3" style="text-align: center;" |<br><br><br>
@@ Line 394: / Line 400: @@
 for orientation only
 |}
+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 second example illustrates how to map the resulting sus4-chord to the harmonic series.
+==== Example 3: [...WILL BE CONTINUED] ====
-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.
-[...WILL BE CONTINUED]
 ==References==
 <references />