Just Hammond: Difference between revisions

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

The following examples illustrate how to map intervals or chords to the harmonic series. ~~In the first example we map the combination of a Hammond Organ’s note E and a higher note A (a fourth up):~~

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

Table 2: Mapping a single interval

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

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

| ~~rowspan~~="2" ~~colspan~~="5" style="text-align: center; background-color:#cbcefb;" |

| colspan="5" rowspan="2" style="text-align: center; background-color:#cbcefb;" |

...of Column (D)

| rowspan="2" style="text-align: center;" |

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| style="text-align: center;" | 9.6

|-

| colspan="3" |

Multiply -------->

to find (D)'s least

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|}

The resulting interval E-A appears between partial # 206 and partial # 275.~~ ~~

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~~ frequency ratio is (275:206), which equals 500.14 cents.

Table 3: Supplement of an upper note "B"

~~Amending~~ an upper note B~~, the next example illustrates how to map the resulting sus4-chord to the harmonic series.~~

{| class="wikitable"

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

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

| ~~rowspan~~="2" ~~colspan~~="6" style="text-align: center; background-color:#cbcefb;" |

| colspan="6" rowspan="2" style="text-align: center; background-color:#cbcefb;" |

...of Column (D)

| rowspan="2" style="text-align: center;" |

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|}

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

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]

@@ 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. In the first example we map the combination of a Hammond Organ’s note E and a higher note A (a fourth up):
+The following examples illustrate how to map intervals or chords to the harmonic series.
 <u>Table 2</u>: Mapping a single interval
@@ Line 241: / Line 241: @@
 | style="text-align: center;" | (C)
 | style="text-align: center;" | (D)
-| rowspan="2" colspan="5" style="text-align: center; background-color:#cbcefb;" |
+| colspan="5" rowspan="2" style="text-align: center; background-color:#cbcefb;" |
 ...of Column (D)<br><br><br><br>
 | rowspan="2" style="text-align: center;" |
@@ Line 279: / Line 279: @@
 | style="text-align: center;" | 9.6
 |-
-| colspan="3"  |
+| colspan="3" |
 Multiply --------><br>
 to find (D)'s least<br>
@@ Line 298: / Line 298: @@
 |}
-The resulting interval E-A appears between partial # 206 and partial # 275.<br>
+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 frequency ratio is (275:206), which equals 500.14 cents.
+<u>Table 3</u>: Supplement of an upper note "B"
-Amending an upper note B, the next example illustrates how to map the resulting sus4-chord to the harmonic series.
 {| class="wikitable"
@@ Line 325: / Line 323: @@
 | style="text-align: center;" | (C)
 | style="text-align: center;" | (D)
-| rowspan="2" colspan="6" style="text-align: center; background-color:#cbcefb;" |
+| colspan="6" rowspan="2" style="text-align: center; background-color:#cbcefb;" |
 ...of Column (D)<br><br><br><br>
 | rowspan="2" style="text-align: center;" |
@@ Line 397: / Line 395: @@
 |}
+The second example illustrates how to map the resulting sus4-chord to the harmonic series.
+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]