Companion page for a paper presented at the 14th International Conference on Digital Audio Effect (DAFx-11), Paris, France, September 19–23, 2011
The Hammond organ is an early electronic musical instrument, which was popular in the 1960s and 1970s. This paper proposes computationally efficient models for the Hammond organ and its rotating speaker system, the Leslie. Organ tones are generated using additive synthesis with appropriate features, such as a typical fast attack and decay envelope for the weighted sum of the harmonics and a small amplitude modulation simulating the construction inaccuracies of tone wheels. The key click is realized by adding the sixth harmonic modulated by an additional envelope to the original organ tone. For the Leslie speaker modeling we propose a new approach, which is based on time-varying spectral delay filters producing the Doppler effect. The resulting virtual organ, which is conceptually easy, has a pleasing sound and is computationally efficient to implement.
Notes on the Demo Files
The organ model
The example timbre described in the paper is used. Each note is generated with four sine oscillators whose frequencies are one (1), two (2), three (3), and eight (8) times the fundamental in the “high” pitch examples, and half (0.5), one (1), one and a half (1.5) and eight (8) times the fundamental in the “low” pitch examples. The generated harmonics are either “perfect”, which means that they are exact multiples of the fundamental, or “imperfect”, which means that they are rounded to closest frequency in the equal tempered scale (affects only the components that are 1.5 and 3 times the fundamental). The relative amplitudes of the components are (from the lowest to the highest) 1, 0.2, 0.2, and 0.1. In addition, the key click is generated with an additional sine oscillator whose frequency is six (6) times the fundamental (rounded, if required) and whose relative amplitude is 0.2 and which has a separate amplitude envelope. Furthermore, the tone wheel disk imperfections are modeled as a small amplitude modulation for every frequency component. The component amplitudes are modulated by sinusoids whose frequency is 5 Hertz, whose amplitude is 0.05, and whose phases depend on the MIDI number of the components.
In the following tables, the following short-hand notation is used to denote different cases:
The Leslie model
The model parameters given in the paper are used. The proposed model two operation modes that correspond to the slow and fast rotation speeds of the Leslie speaker. The rotation frequencies are two (2) and six (6) Hertz for the bass unit in the slow and fast rotation speed modes, respectively. For the treble unit, the rotation frequencies are 0.1 Hz higher than those of the bass unit.
The key click effect, imperfect harmonics, and imperfect tone wheels are used in all examples given below.
Rotation speed switch
A sustained C major chord with the rotation speed mode switched
The demo song played through the Leslie model
Updated on Wednesday September 21, 2011