Just Hammond: Difference between revisions

Line 220:

==== 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.

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.

Table 2: ~~Fourth~~ E-A

Table 2: The fourth E-A

{| class="wikitable"

Line 234:

! colspan="5" style="text-align: center;" |

Prime

Factorization~~...~~

Factorization

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

Ascending

Line 258:

1+(ln(P)/ln(2))

|-

| colspan="2" style="text-align: center;" | Fraction

| colspan="2" style="text-align: center;" |Fraction

(C)/(D)

|-

Line 302:

|}

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 appears between partial # 206 and partial # 275. Thus the frequency ratio is (275:206), which equals 500.14 cents.

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

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

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

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

Table 3: sus4-chord E-A-B

Line 318:

! colspan="6" style="text-align: center;" |

Prime

Factorization~~...~~

Factorization

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

Ascending

Line 342:

1+(ln(P)/ln(2))

|-

| colspan="2" style="text-align: center;" | Fraction

| colspan="2" style="text-align: center;" |Fraction

(C)/(D)

|-

Line 402:

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: [...WILL BE CONTINUED] ~~====~~

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

Table 4: Full set of pitchclasses

{| class="wikitable"

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

Pitch

Class

! colspan="2" style="text-align: center;" |

HAMMOND

Gear Ratio

(canceled)

! colspan="16" style="text-align: center;" |

Prime

Factorization

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

Ascending

Partial Numbers of

an Overtone Scale

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

Partial Found

in Octave #

|-

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

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

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

... of Column (D)

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

Recalculated

Numerator =

Partial #

P=LCM *(C)/(D)

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

Counted from

1/1:

Octave# =

1+(ln(P)/ln(2))

|-

| colspan="2" style="text-align: center;" |Fraction

(C)/(D)

|-

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

| style="text-align: right; background-color:#ffffff;" | 85

| style="font-weight:bold; background-color:#ffffff;" | 104

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

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center; background-color:#cbcefb;" | 13

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 15,003,356,791,500

| style="text-align: center;" | 44.8

|-

| style="text-align: center;" | C#

| style="text-align: right; background-color:#ffffff;" | 71

| style="font-weight:bold; background-color:#ffffff;" | 82

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

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center; background-color:#cbcefb;" | 41

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 15,894,517,438,800

| style="text-align: center;" | 44.9

|-

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

| style="text-align: right; background-color:#ffffff;" | 67

| style="font-weight:bold; background-color:#ffffff;" | 73

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center; background-color:#cbcefb;" | 73

| style="text-align: center;" | 16,848,249,818,400

| style="text-align: center;" | 44.9

|-

| style="text-align: center;" | D#

| style="text-align: right; background-color:#ffffff;" | 35

| style="font-weight:bold; background-color:#ffffff;" | 36

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

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center; background-color:#cbcefb;" | 3

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 17,847,130,301,000

| style="text-align: center;" | 45.0

|-

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

| style="text-align: right; background-color:#ffffff;" | 103

| style="font-weight:bold; background-color:#ffffff;" | 100

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

| style="text-align: center; background-color:#cbcefb;" |

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

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 18,907,759,758,888

| style="text-align: center;" | 45.1

|-

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

| style="text-align: right; background-color:#ffffff;" | 12

| style="font-weight:bold; background-color:#ffffff;" | 11

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center; background-color:#cbcefb;" | 11

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 20,025,870,883,200

| style="text-align: center;" | 45.2

|-

| style="text-align: center;" | F#

| style="text-align: right; background-color:#ffffff;" | 37

| style="font-weight:bold; background-color:#ffffff;" | 32

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

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 21,225,337,107,975

| style="text-align: center;" | 45.3

|-

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

| style="text-align: right; background-color:#ffffff;" | 49

| style="font-weight:bold; background-color:#ffffff;" | 40

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

| style="text-align: center; background-color:#cbcefb;" |

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

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 22,487,384,179,260

| style="text-align: center;" | 45.4

|-

| style="text-align: center;" | G#

| style="text-align: right; background-color:#ffffff;" | 48

| style="font-weight:bold; background-color:#ffffff;" | 37

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center; background-color:#cbcefb;" | 37

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 23,814,549,158,400

| style="text-align: center;" | 45.4

|-

| style="text-align: center; font-weight:bold;" | A

| style="text-align: right; background-color:#ffffff;" | 11

| style="font-weight:bold; background-color:#ffffff;" | 8

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

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 25,240,941,425,700

| style="text-align: center;" | 45.5

|-

| style="text-align: center;" | A#

| style="text-align: right; background-color:#ffffff;" | 67

| style="font-weight:bold; background-color:#ffffff;" | 46

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

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center; background-color:#cbcefb;" | 23

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 26,737,439,929,200

| style="text-align: center;" | 45.6

|-

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

| style="text-align: right;" | 54

| style="font-weight:bold;" | 35

| style="text-align: center; background-color:#cbcefb;" |

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

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center; background-color:#cbcefb;" | 7

| style="text-align: center; background-color:#cbcefb;" |

| style="text-align: center;" | 28,322,303,106,240

| style="text-align: center;" | 45.7

|-

| colspan="3" |

Multiply -------->

to find (D)'s least

common multiple

(LCM)

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 2

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 3

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 5

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 7

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 11

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 13

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 23

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 37

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 41

| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 73

| style="text-align: center; font-weight:bold;" |

18,357,048,309,600

(LCM)

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

45.1

Decimal printed

for orientation only

|}

[...WILL BE CONTINUED]

==References==

@@ Line 220: / Line 220: @@
 ==== 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.
+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.
-<u>Table 2</u>: Fourth E-A
+<u>Table 2</u>: The fourth E-A
 {| class="wikitable"
@@ Line 234: / Line 234: @@
 ! colspan="5" style="text-align: center;" |
 Prime <br>
-Factorization...
+Factorization
 ! style="text-align: center;" |
 Ascending<br>
@@ Line 258: / Line 258: @@
 +(ln(P)/ln(2))
 |-
-| colspan="2" style="text-align: center;" | Fraction
+| colspan="2" style="text-align: center;" |Fraction<br>
 (C)/(D)
 |-
@@ Line 302: / Line 302: @@
 |}
-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 appears between partial # 206 and partial # 275. Thus the frequency ratio is (275:206), which equals 500.14 cents.
-==== Example 2: Supplementing a Fifth ====
+==== Example 2: Mapping a chord ====
-The second example illustrates how to map the resulting sus4-chord E-A-B to the harmonic series.
+Adding an upper fifth (note B), the second example illustrates how to map the sus4-chord E-A-B to the harmonic series.
 <u>Table 3</u>: sus4-chord E-A-B
@@ Line 318: / Line 318: @@
 ! colspan="6" style="text-align: center;" |
 Prime<br>
-Factorization...
+Factorization
 ! style="text-align: center;" |
 Ascending<br>
@@ Line 342: / Line 342: @@
 +(ln(P)/ln(2))
 |-
-| colspan="2" style="text-align: center;" | Fraction
+| colspan="2" style="text-align: center;" |Fraction<br>
 (C)/(D)
 |-
@@ Line 402: / Line 402: @@
 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: [...WILL BE CONTINUED] ====
+==== Example 3: Hammond - full scale ====
+Table 4: Full set of pitchclasses
+{| class="wikitable"
+! rowspan="3" style="text-align: center;" | <br><br><br>
+Pitch<br>
+Class
+! colspan="2" style="text-align: center;" |
+HAMMOND<br>
+Gear Ratio<br>
+(canceled)
+! colspan="16" style="text-align: center;" |
+Prime <br>
+Factorization
+! style="text-align: center;" |
+Ascending<br>
+Partial Numbers of<br>
+an Overtone Scale
+! style="text-align: center;" |
+Partial Found<br>
+in Octave #
+|-
+| style="text-align: center;" | (C)
+| style="text-align: center;" | (D)
+| rowspan="2" colspan="16" style="text-align: center; background-color:#cbcefb;" |
+... of Column (D)<br><br><br><br>
+| rowspan="2" style="text-align: center;" |
+Recalculated<br>
+Numerator =<br>
+Partial #<br>
+P=LCM *(C)/(D)
+| rowspan="2" style="text-align: center;" |
+Counted from<br>
+/1:<br>
+Octave# =<br>
++(ln(P)/ln(2))
+|-
+| colspan="2" style="text-align: center;" |Fraction<br>
+(C)/(D)
+|-
+| style="text-align: center;" | C
+| style="text-align: right; background-color:#ffffff;" | 85
+| style="font-weight:bold; background-color:#ffffff;" | 104
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 13
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 15,003,356,791,500
+| style="text-align: center;" | 44.8
+|-
+| style="text-align: center;" | C#
+| style="text-align: right; background-color:#ffffff;" | 71
+| style="font-weight:bold; background-color:#ffffff;" | 82
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 41
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 15,894,517,438,800
+| style="text-align: center;" | 44.9
+|-
+| style="text-align: center;" | D
+| style="text-align: right; background-color:#ffffff;" | 67
+| style="font-weight:bold; background-color:#ffffff;" | 73
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 73
+| style="text-align: center;" | 16,848,249,818,400
+| style="text-align: center;" | 44.9
+|-
+| style="text-align: center;" | D#
+| style="text-align: right; background-color:#ffffff;" | 35
+| style="font-weight:bold; background-color:#ffffff;" | 36
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 3
+| style="text-align: center; background-color:#cbcefb;" | 3
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 17,847,130,301,000
+| style="text-align: center;" | 45.0
+|-
+| style="text-align: center;" | E
+| style="text-align: right; background-color:#ffffff;" | 103
+| style="font-weight:bold; background-color:#ffffff;" | 100
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 5
+| style="text-align: center; background-color:#cbcefb;" | 5
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 18,907,759,758,888
+| style="text-align: center;" | 45.1
+|-
+| style="text-align: center;" | F
+| style="text-align: right; background-color:#ffffff;" | 12
+| style="font-weight:bold; background-color:#ffffff;" | 11
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 11
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 20,025,870,883,200
+| style="text-align: center;" | 45.2
+|-
+| style="text-align: center;" | F#
+| style="text-align: right; background-color:#ffffff;" | 37
+| style="font-weight:bold; background-color:#ffffff;" | 32
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 21,225,337,107,975
+| style="text-align: center;" | 45.3
+|-
+| style="text-align: center;" | G
+| style="text-align: right; background-color:#ffffff;" | 49
+| style="font-weight:bold; background-color:#ffffff;" | 40
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 5
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 22,487,384,179,260
+| style="text-align: center;" | 45.4
+|-
+| style="text-align: center;" | G#
+| style="text-align: right; background-color:#ffffff;" | 48
+| style="font-weight:bold; background-color:#ffffff;" | 37
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 37
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 23,814,549,158,400
+| style="text-align: center;" | 45.4
+|-
+| style="text-align: center; font-weight:bold;" | A
+| style="text-align: right; background-color:#ffffff;" | 11
+| style="font-weight:bold; background-color:#ffffff;" | 8
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 25,240,941,425,700
+| style="text-align: center;" | 45.5
+|-
+| style="text-align: center;" | A#
+| style="text-align: right; background-color:#ffffff;" | 67
+| style="font-weight:bold; background-color:#ffffff;" | 46
+| style="text-align: center; background-color:#cbcefb;" | 2
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 23
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 26,737,439,929,200
+| style="text-align: center;" | 45.6
+|-
+| style="text-align: center;" | B
+| style="text-align: right;" | 54
+| style="font-weight:bold;" | 35
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 5
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" | 7
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center; background-color:#cbcefb;" |
+| style="text-align: center;" | 28,322,303,106,240
+| style="text-align: center;" | 45.7
+|-
+| colspan="3" |
+Multiply --------><br>
+to find (D)'s least<br>
+common multiple<br>
+(LCM)
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 2<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 2<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 2<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 2<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 2<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 3<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 3<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 5<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 5<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 7<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 11<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 13<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 23<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 37<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 41<br><br><br><br>
+| style="text-align: center; font-weight:bold; background-color:#cbcefb;" | 73<br><br><br><br>
+| style="text-align: center; font-weight:bold;" |
+,357,048,309,600<br><br>
+(LCM)<br><br>
+| style="text-align: center;" |
+.1<br><br>
+Decimal printed<br>
+for orientation only
+|}
+[...WILL BE CONTINUED]
 ==References==
 <references />