* fR2 = 3fo can be indicative of 2nd formant (resonance) tuning in the male passaggio in classical singing when producing an /ɑ/ vowel . The formula displayed in the middle panel is in compliance with .
 Ritzerfeld, W. G. J. and Miller, D. G. (2017) ‘Formant Tuning and Feedback in the Male Passaggio’, Journal of Voice, 31(4), pp. 506.e7-506.e17. doi: 10.1016/j.jvoice.2016.10.006.
 Titze, I. R. et al. (2015) ‘Toward a consensus on symbolic notation of harmonics, resonances, and formants in vocalization’, J Acoust Soc Am, 137(5), pp. 3005–3007.
Idea: JBH, CTH
The sonified PAS7 logo can be displayed with any software that generates a spectrogram from a sound file (e.g., Praat or VoceVista). In other words, to view the logo, load the sound file and display it as a spectrogram.
When viewing in Praat, change the "Spectrogram Settings ..." to the following values for best results:
- View range: 0 -- 5000 Hz
- Window length: choose anything in the range of 0.1 to 0.3 seconds, according to your taste
- Dynamic range: 40 dB
The possiblity for various FFT window size settings (in Praat termed the "window length") highlights a fundamental issue of a spectrogram: In analogy to Heisenberg's uncertainty principle, a choice has to be made: One can either maximize the temporal resolution (at the cost of worsening the spectral resolution) or the spectral resolution (at the cost of worsening the temporal resolution).
Adjusting the dynamic range of the spectrogram (a feature often overlooked when visualizing the spectral contents of a sound) will change the color brightness of the displayed logo.
The PAS7 logo was designed by Kristen Murdaugh. The sonification was achieved by taking the color intensity values of each pixel in the grayscale logo image and useing these to scale the time-varying amplitudes of a bank of sine wave oscillators. In particular, the x-axis of the image was mapped onto the temporal axis of the resulting sound, and the y-axis of the image was mapped onto the spectral axis (ranging from 0 to 5000 Hz) of the oscillator bank. The sonification algorithm was implemented by CTH in the Python programming language.