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The difference between piano and Hammond organ timbre: the harmonic series explained

In the videos at the right the harmonic series is explained. The text below explains how both instruments handle this phenomenon.

The Piano

The piano uses strings that have a regular structure, which will emit regular waves. Our ears experience that as a musical tone.¹ The same thing happens when blowing air, plucking a string or striking a drumhead. Piano strings all differ in length, tension, thickness and density which will give them the frequencies belonging to them. However, you are not hearing one basic tone. You are hearing a whole series of tones when you strike only one key. This is known as the harmonic series, or overtone series. The lower the fundamental tone, the more audible the overtones are. From the video demonstration we can conclude that this series of waves consist of the root and then waves that are:

2x the frequency of the root

3x the frequency of the root

4x the frequency of the root

5x the frequency of the root, etc.

The higher the root, the less audible the overtones get for our human ears. This will result in the root being more clear and present.

The Hammond organ

The Hammond organ was designed to create sounds as close to pure sine waves as possible. A pure sine wave has no overtones at all and can be reproduced by synthesis only. A Hammond organ has two keyboards, called manuals. Above the upper manual there are the aforementioned 38 drawbars, pullout switches comparable to the stops of a pipe organ.² For each manual there are two sets of nine drawbars available, assigned to the reverse coloured preset A# and B keys on the left side, plus two drawbars for the bass pedals.

Each drawbar, which makes a connection from the key to the corresponding tone wheel, emits a sine wave, so the organ player creates tones by making all kinds of combinations of pulling in or out the drawbars. We call those “drawbar settings”, which are expressed from left to right in the numbers 0 till 8. The classic Jimmy Smith setting is notated as 888000000. The combination of drawbar settings is enormous, since they are adjustable in nine steps and there are nine of them for every key. Plus because of can turn them to your liking, it’s inevitable that the tones you play will not follow the harmonic series. However, the tones that are emitted by pulling the drawbars will follow a pattern close to the natural harmonic series from the third drawbar onwards.

Drawbar Harmonic

16’ sub

5 1/3’ fundamental + 5^th

8’ fundamental

4’ octave

2 2/3’ octave + 5^th

2’ 2 octaves

1 3/5’ 2 octaves + 3^rd

1 2/3’ 2 octaves + 5^th

1’ 3 octaves

Take notice that the 16’ drawbar (sub) will be experienced as the actual root, as soon as that drawbar is pulled out and that the 1’ drawbar should be two octaves and a minor 7^th according to the harmonic series. However, drawbars follow the same principle as the pipes of a church organ, hence the symbols in feet on them. The ninth drawbar with the 1’ sits three octaves above the fundamental, just like the ninth stop of a pipe organ.

Foldback

Harmonic foldback is used to reduce the required number of pitches at both ends of the keyboard. It affects the 3rd and subsequent harmonics at the top, and the sub-fundamental harmonic at the bottom. The diagram below shows the effect of the harmonic foldback on the top and bottom notes of the keyboard. The lowest note has its sub-fundamental folded back, even though the tone generator goes low enough, represented by the width of the grey bars. At the top, there are five tones which ‘go off the top’ of the generator and are folded back onto the top octave provided. Notice that this means that if you play the top C, it actually includes two of the same tones (tones 80 and 85) three times over. In theory the full 5 octaves of the B3 keyboard would require 61 basic tones, plus 3 octaves above for harmonics and one octave below for the sub-fundamental harmonic. This gives a total of nine octaves, or 61+36+12 = 109 tones. Since there are only 91 tones available, the need for foldback is clear.³

Before we dive into spectrograms

All the Hammond organ’s tonewheels responsible for the tones “A” are set to divisions of A=440 Hz. The formula for making a tone on a Hammond organ shows clearly how simple it is to get to 440 Hz, where F stands for frequency, M for motor speed (revs per second), T for the amount of teeth and R for gear ratio.

F = M * T * R

A=440 therefore equals 20 revs per second * 16 teeth * the gear ratio (88/64) = 440

All other tonewheels and gear ratios couldn’t be made to exactly follow equal-temperament, nor exact harmonics of each other, but are close to both. See the table at the right.⁴

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