# Modal Processor Effects Inspired by [PERSON] Tonewheel Organs
## 5 Results and Discussion
### Pitch Processing Examples  
In this section, we demonstrate the Hammondizer's drawbar tone controls (Figure 9), its frequency range (Figure 10), and crosstalk and vibrato processing (Figure 11). Figure 9 shows spectrograms of a pure tone input signal and versions processed with the Hammondizer. The input signal (Figure 9a) is a 1.75-second-long sine wave tuned to middle C (C3, \(\approx\)261.63 Hz). The output signal (Figure 9b) shows five different Hammondized versions of the input signal. Each of the five versions uses a different registration; the vibrato, crosstalk, and distortion were disabled. The different Hammond organ registrations shown in these results are given in Figure 8. Figure 9b uses the first five registrations of Figure 8 in order. Figure 8: Various Hammond organ registrations and their names. (**a**) 008000000 fundamental; (**b**) 447000000 \"bassoon\"; (**c**) 803600000 \"mellow-Dee\"; (**d**) 006070540 “clarinet”; (**e**) 668848588 “shoutin”; (**f**) 888888888 \"all out\"; (**g**) 88800008 “whistle stop”; (**h**) 888800000 \"[PERSON]\". The C3 sine wave is tuned very close to the center frequency of mode \(w=455\). Knowing that the Hammondizer uses the matrix \(\boldsymbol{\Gamma}(\boldsymbol{r}(t))\) to drive output modes that are offset from each analysis mode by the length-9 column \(\boldsymbol{o}\) (recall Table 1 and Equation (1)), we expect that an input consisting of a single sinusoid will in general create output signals with nine sinusoidal components (recall Equation (11)) near modes \((287,553,455,623,721,791,847,889,959)\). However, since \(\boldsymbol{\Gamma}(\boldsymbol{r}(t))\) is a function of the registration \(\boldsymbol{r}(t)\), the output behavior is heavily dependent on the registration. Notice that the 008000000 registration does not affect the signal much beyond a slight lengthening due to the decay time of the modes near C3. Since each \(r(t)\) except \(r_{3}(t)\) is zero, only one sinusoid comes out. The second setting, \"bassoon\" (447000000) produces three sinusoids in response to the input sinusoid, since it has three non-zero \(r(t)\)s. The amplitude of each sinusoid depends on its corresponding drawbar setting (recall Table 2). The \"bassoon,\" \"mellow-Dee,\" and \"shoutin\" registrations have non-zero first drawbar settings--notice that they produce energy an octave below C3. The \"shoutin\" \" and \"all out\" registrations have no non-zero drawbar settings--notice that the individual sine wave of the input has driven nine sine waves in the output, and that their relative amplitudes reflect the \"shoutin\" \" and \"all out\" registrations (668848588 and 888888888, respectively). Figure 10 shows spectrograms of a sinusoidal input signal and its Hammondized response. The input signal (Figure 10a) is a series of nine 0.5-second-long sine waves, generated at octave intervals from C0 (\(\approx\)32.70 Hz) and to C8 (\(\approx\)8372.02 Hz). The Hammondized output (Figure 10a) used the 668848588 (\"shoutin\" \") registration, and the vibrato, crosstalk, and distortion were disabled. In a broad sense, the Hammondizer imprints the \"shoutin\" \" partial structure onto the input sinusoids. Note, however, that since the Hammondizer does not have any modes outside the 40 Hz to 5120 Hz frequency range, the C0 and C8 inputs generate little output, though transients in the C0 sinusoid produce a ghostly \"whoosh\" sound. Figure 9: (**a**) C3 sine wave input and (**b**) Hammondized version with five different registrations. The Hammondizer crosstalk and vibrato components are now explored using the pure tone input of Figure 9a. In Figure 11a, the effect of crosstalk is illustrated using the \"clarinet\" registration with vibrato and distortion disabled. Crosstalk amplitudes of \(-\infty\), \(-24\), \(-18\), \(-12\), and \(-6\) dB are simulated. Note the increased presence of energy in adjacent notes with increased crosstalk amplitude. In Figure 11b, the effect of vibrato is studied using a \"whistle stop\" (888000008) registration, with crosstalk and distortion disabled.