# Modal Processor Effects Inspired by [PERSON] Tonewheel Organs
## 1 Introduction  
The [PERSON] tonewheel organ is a classic electromechanical musical instrument, patented by [PERSON] in 1934 [1]. Although it was intended as an affordable substitute for church organs [2], it has also become widely known as an essential part of jazz (where it was popularized by [PERSON]), R & B and rock music (where the [PERSON] playing of [PERSON] of Emerson, Lake & and Palmer and [PERSON] of Deep Purple is exemplary). The most popular model is the Hammond B-3, although many other models exist [3]. The sound of the [PERSON] organ is rich and unusual. Its complexity comes from the [PERSON] organ's unique approach to timbre and certain quirks of its construction. In this article, we describe a novel class of modal-processor-based audio effects which we call the \"Hammondizer\". The Hammondizer can imprint the sonics of the [PERSON] organ onto any sound; it mimics and draws inspiration from the architecture of the [PERSON] tonewheel organ. We begin by describing the architecture and sonics of the [PERSON] tonewheel organ alongside related work on [PERSON] organ modeling. The [PERSON] organ is essentially an additive synthesizer. Additive synthesizers create complex musical tones by adding together sinusoidal signals of different frequencies, amplitudes, and phases [4]. In the [PERSON] organ, 91 sinusoidal signals are available. These sinusoids are created when \"tonewheels\"--ferromagnetic metal discs--spin and the pattern of ridges cut into their edges is transduced by electromagnetic pickups into electrical signals, a technique originated in [PERSON]'s late-19 th century instrument, the Telharmonium [5]. [PERSON] organ tonewheel pickups have not been studied much in particular, but modeling and simulation of electromagnetic pickups ingeneral is an active research area [6; 7; 8; 9; 10]. Any nonlinearities in a pickup model will cause bandwidth expansion and add to the characteristic sound of the [PERSON] organ. In the case that this bandwidth expansion would go beyond the Nyquist limit, alias-suppression methods become relevant [11; 12; 13; 14]. These 91 tonewheels are tuned approximately to the twelve-tone equal-tempered musical scale [15]--In scientific pitch notation, the lowest-frequency tonewheel on a [PERSON] organ is tuned to C1 (\(\approx\)32.7 Hz) and the highest-frequency tonewheel is tuned to F#7 (\(\approx\)5919.9 Hz) [16]. The lowest octave of tonewheels do not form sinusoids, but more complex tones that have strong 3 rd and 5 th harmonics, making them closer to square waves than sine waves [15]. Some aficionados have pointed to crosstalk between nearby tonewheel/pickup pairs as an important sonic feature of the [PERSON] organ [17; 18]. The tone of the [PERSON] organ is set using nine \"drawbars\". Unlike traditional organs, where \"stops\" bring in entire complex organ sounds, the [PERSON] organ's drawbars set the relative amplitudes of individual sinusoids in a particular timbre. These nine sinusoids form a pseudo-harmonic series summarized in Table 1[19]. This pseudo-harmonic series deviates from the standard harmonic series in three ways: (1) each overtone is tuned to the nearest available tonewheel; (2) certain overtones are omitted, especially the 6 th harmonic, which would be between the 8 th and 9 th drawbar); and (3) new fictitious overtones are added (the 5 th and sub-octave). The raw sound of the [PERSON] organ tonewheels is static. To enrich the sound, [PERSON] added a chorus/vibrato circuit [20]. Earlier models used a tremolo effect in place of the chorus/vibrato circuit [21]. The sound was further enriched by an electro-mechanical spring reverb device [22]. Although [PERSON] did not originally approve of the practice, it became customary to play [PERSON] organs through a Leslie speaker, an assembly with a spinning horn and baffle that creates acoustic chorus and tremolo effects. The Leslie speaker has been covered extensively in the modeling literature.