Just Hammond: Difference between revisions
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<u>Table 1 | <u>Table 1</u>: Pairings of Gearwheels<ref>Gearing details were taken from http://www.goodeveca.net/RotorOrgan/ToneWheelSpec.html (retrieved Dec 29, 2019) | ||
The German Wikipedia provides the same technical information (in German): https://de.wikipedia.org/wiki/Hammondorgel#Tonerzeugung (retrieved Dec 29, 2019) | The German Wikipedia provides the same technical information (in German): https://de.wikipedia.org/wiki/Hammondorgel#Tonerzeugung (retrieved Dec 29, 2019) | ||
The ''HammondWiki'' publishes a second, alternative set of gear ratios with slightly deviating pitch class “E”. Certain other pitch classes are shifted by pure octaves. http://www.dairiki.org/HammondWiki/GearRatio (retrieved Dec 29, 2019)</ref> / Ratios and Intervals | The ''HammondWiki'' publishes a second, alternative set of gear ratios with slightly deviating pitch class “E”. Certain other pitch classes are shifted by pure octaves. http://www.dairiki.org/HammondWiki/GearRatio (retrieved Dec 29, 2019)</ref> / Ratios and Intervals | ||
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| style="text-align: right;" | 35 | | style="text-align: right;" | 35 | ||
| 36 | | 36 | ||
| style="text-align: center | | style="text-align: center;" | 0.9722222 | ||
| style="text-align: right;" | -48.77 | | style="text-align: right;" | -48.77 | ||
| style="text-align: center;" | -48.77 | | style="text-align: center;" | -48.77 | ||
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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. In the first example we map the combination of a Hammond Organ’s note E and a higher note A (a fourth up): | ||
<u>Table 2 | <u>Table 2</u>: Mapping a single interval | ||
{| class="wikitable" | {| class="wikitable" | ||
! rowspan="3" style="text-align: center;" | | ! rowspan="3" style="text-align: center;" | <br><br><br> | ||
<br><br><br>Pitch<br> | Pitch<br> | ||
Class | Class | ||
! colspan="2" style="text-align: center;" | | ! colspan="2" style="text-align: center;" | | ||
HAMMOND<br> | |||
Gear Ratio<br> | Gear Ratio<br> | ||
(canceled) | (canceled) | ||
! colspan="5" style="text-align: center | ! colspan="5" style="text-align: center;" | | ||
Prime <br> | |||
Factorization... | |||
! style="text-align: center;" | | ! style="text-align: center;" | | ||
Ascending<br> | Ascending<br> | ||
Partial Numbers of<br> | Partial Numbers of<br> | ||
an Overtone Scale | an Overtone Scale<br> | ||
! | ! style="text-align: center;" | | ||
Partial | Partial Found <br> | ||
in Octave | in Octave | ||
|- | |- | ||
| style="text-align: center;" | (C) | | style="text-align: center;" | (C) | ||
| style="text-align: center | | style="text-align: center;" | (D) | ||
| rowspan="2" colspan="5" style="text-align: center | | rowspan="2" colspan="5" style="text-align: center; background-color:#cbcefb;" | | ||
...of Column (D)<br><br><br><br> | |||
| rowspan="2" style="text-align: center;" | | | rowspan="2" style="text-align: center;" | | ||
Recalculated<br> | Recalculated<br> | ||
Numerator<br> | Numerator =<br> | ||
=<br> | Partial# <br> | ||
P=LCM *(C)/(D) | |||
| rowspan="2" style="text-align: center;" | | |||
Counted <br> | |||
from 1/1:<br> | |||
Octave# =<br> | |||
1+(ln(P)/ln(2)) | |||
|- | |- | ||
| colspan="2" style="text-align: center;" | Fraction | | colspan="2" style="text-align: center;" | Fraction | ||
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|- | |- | ||
| style="text-align: center;" | E | | style="text-align: center;" | E | ||
| style="text-align: right | | style="text-align: right;" | 103 | ||
| style="font-weight:bold | | style="font-weight:bold;" | 100 | ||
| style="background-color:#cbcefb;" | 2 | | style="background-color:#cbcefb;" | 2 | ||
| style="background-color:#cbcefb;" | 2 | | style="background-color:#cbcefb;" | 2 | ||
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|- | |- | ||
| style="text-align: center;" | A | | style="text-align: center;" | A | ||
| style="text-align: right | | style="text-align: right;" | 11 | ||
| style="font-weight:bold | | style="font-weight:bold;" | 8 | ||
| style="background-color:#cbcefb;" | 2 | | style="background-color:#cbcefb;" | 2 | ||
| style="background-color:#cbcefb;" | 2 | | style="background-color:#cbcefb;" | 2 | ||
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|- | |- | ||
| colspan="3" style="font-weight:bold;" | | | colspan="3" style="font-weight:bold;" | | ||
Multiply | Multiply -----><br> | ||
to find (D)'s least<br> | to find (D)'s least<br> | ||
common multiple (LCM) | common multiple<br> | ||
| style="font-weight:bold; background-color:#cbcefb;" | 2<br><br><br> | (LCM) | ||
| style="font-weight:bold; background-color:#cbcefb;" | 2<br><br><br> | | style="font-weight:bold; background-color:#cbcefb;" | 2<br><br><br><br> | ||
| style="font-weight:bold; background-color:#cbcefb;" | 2<br><br><br> | | style="font-weight:bold; background-color:#cbcefb;" | 2<br><br><br><br> | ||
| style="font-weight:bold; background-color:#cbcefb;" | 5<br><br><br> | | style="font-weight:bold; background-color:#cbcefb;" | 2<br><br><br><br> | ||
| style="font-weight:bold; background-color:#cbcefb;" | 5<br><br><br> | | style="font-weight:bold; background-color:#cbcefb;" | 5<br><br><br><br> | ||
| style="text-align: center; font-weight:bold;" | 200<br> | | style="font-weight:bold; background-color:#cbcefb;" | 5<br><br><br><br> | ||
<br>(LCM) | | style="text-align: center; font-weight:bold;" | | ||
| style="text-align: center;" | 8.6 | 200<br><br> | ||
(LCM)<br><br> | |||
Decimal printed<br> | | style="text-align: center;" | | ||
for orientation only | 8.6<br><br> | ||
(Decimal printed<br> | |||
for orientation only) | |||
|} | |} | ||