Supporting document AIMC 2022

Appendix A: Production Strategies

A.1

A.2

A.4

A.5

Appendix B: Harmonic variation in sinusoidal synthesis

Let \( a_i \) be the amplitude of the \( i \)-th harmonic as inferred from the CQT frame (the fundamental being \( a_1 \)). Furthermore, let \( \lambda \in [0, \lambda_{max}] \) be the desired strength of the harmonic variability (we use \( \lambda_{max} = 10 \)). Lastly, weight coefficients \( w_i \) are defined such that \( w_1 = 0.8 \) , \( w_2 = 0.9 \) , and \( w_{>2} = 1.0 \) , countering the tendency of the non-linearity to over-emphasize the lowest harmonics. The non-linear amplitude is defined as: \[ s_i = \sigma(\lambda a_i w_i), \] where \( \sigma \) is the softmax function. The final amplitude is a weighted combination of the original amplitude and the non-linear amplitude: \[ v_i = (1-\frac{\lambda}{\lambda_{max}}) a_i + \frac{\lambda}{\lambda_{max}} s_i \]

Appendix C: Heterophony between Bass Lines

C.1

"Bass C1" + "Bass C2" before effects
"Bass C1" + "Bass C2" after effects

C.2

"Bass D1" + "Bass D2" before effects
"Bass D1" + "Bass D2" after effects

Appendix D: Examples of simultaneous pitches within bass lines

Example 1: The Cure, ``The Holy Hour''

The song ``The Holy Hour'' by British band The Cure is the first track on their 1981 album ``Faith'', released with Fiction Records. The song starts with a 16-beat long solo bass part. Audition of the extract suggests two melodic lines. The bottom-most line is likely to correspond to the notes that were actually played on the instrument. The line is transcribed as a score show below. The top-most line is perceived as continuously varying pitch. The figure below the score shows that the perceived played notes are partially detected by the deep convolutional neural network-based, pitch estimation model CREPE [Kim et al., 2018].

The third figure shows a Short-Term Fourier Transform of the extract, along with the perceived played notes. One feature of STFT is a sliding comb filter on the higher frequencies. Flanging is an audio effect produced by mixing two identical signals together, one signal delayed by a small and gradually changing period. The sliding comb filter is likely to be generated by a Flanger. One stimulus used in pitch perception is iterated rippled noise. Such a stimulus is generated by delaying a random noise by some amount and adding the delayed noise back to the undelayed noise in an iterative process [Yost, 2009]. The comb filter generated by a Flanger may therefore prompt perceived gradually changing pitch in the result. The last figure shows how the autocorrelation-based pitch estimation model MirPitch [Lartillot, 2008] interprets part of the resonances produced by the comb filter as pitch.

The extract from ``The Holy Hour'' is generated by one instrument, on which one note is played. Still, two simultaneous melodic lines can be identified. The first line originates from the notes that are actually played, the second line originates from the sliding comb filter. It is difficult to transcribe pitch from the second line as a score, as the pitch values evolve continuously.

Example 2: Judas Priest, ``Bloodstone''

The song ``Bloodstone'' by British band Judas Priest is the fourth track on their 1982 album ``Screaming for Vengeance''. The bass track is available to the authors through the ``Rock Band'' game franchise of Sony Interactive. The score below shows a transcription of the bass track from 1'10 to 1'15. The transcription features two staves. The bottom stave shows the notes that are perceived as actually played. The top stave shows notes that are perceived in addition to those actually played. The figure below the score shows the short-term Fourier transform of the audio corresponding to the transcribed bass track. Examination of the transform shows that 1) the fundamental is missing, and 2) the additional perceived notes generally correspond to harmonics 6 and 7. In this case the difference in perceived pitches seems to coincide to with the up- and downward motion of the plectrum plucking the string, where the higher pitches coincide with the upward motion. A possible explanation for this is the difference in string tension during the plucking action. This effect is present in guitar playing as well. Furthermore, the equalization of the track may make the effect more pronounced.

Example 3: Faith no More, ``Epic''

This example is from the song ``Epic'' by American band Faith No More. ``Epic'' is the second single from their 1990 album ``The Real Thing''. The bass track is available to the authors through the ``Rock Band'' game franchise. The score below shows a transcription of the two simultaneous perceived melodic line in the bass track from 1'58 to 2'05. The pitch in the top stave is always one octave above the pitch in the bottom stave, and the parts are exactly synchronised. We believe this to be a consequence of doubling the original bass part with a distorted version of the same part.

Appendix E

E.1

Track Solo 1 (bars 82–83) Section 2 (before effects)
Track Solo 1 (bars 82–83) Section 2 (after effects)

The following figures show the short-time spectra at positions indicated by the numbered vertical lines in the transcription. Some observations about the selected spectral slices:

• In all the slices, odd harmonics are more salient than even ones. This is due to the artists' preferred choice of odd/even sonification control (see paper).
• In all the slices, the fundamental is missing, and the lowest harmonic is odd. This is due to the weighting of the lowest harmonics as part of the "harmonic variation" sonification control (see paper).
• In slices 1, 2, 3, 5, 7 and 8, the additional perceived pitch value corresponds to harmonic 3. In slice 6, it corresponds to harmonic 5. In slices 4 and 9, it doesn't correspond to a harmonic.
• In slices 2, 3, 5, 7, 8 and 9, the additional perceived pitch value corresponds to the loudest formant. In slices 1, 4 and 6, other formants which are not the fundamental are louder.