## 4 Results  
### ISI Histogram  
Figures 2 and 3 show six examples of ISI histograms, each consisting of adjacent time intervals, where each interval is an integration over the cochlea spike output in this interval. Five of these six examples were used in the listening test, only the top plot of Figure 2 is presented as a single-note example to exemplify the pitch theory and the salience of pitch over timbre discussed above. This single-note example is a single-line saxophone melody. It appears that at all time intervals there is only one strong peak. Aurally, this peak follows the played melody very well. To verify this perception, in Figure 4 an excerpt of Figure 2's top plot is shown. It shows the whole time but is restricted to the area of large peaks. The continuous curve overlaying the ISI histogram plot is the result of an autocorrelation calculation using the plain sound time series as input. With 50 ms intervals the autocorrelation of the sound time series is calculated, and the interval between the autocorrelation beginning and the first autocorrelation function peak is taken as the fundamental periodicity. This is an established method for detecting \(f_{0}\) in single melodies, and has, e.g., been applied to analyse intonation of Cambodian Buddhist _smot_ chanting [43]. Both functions, the autocorrelation and the ISI histogram, align very well. Therefore, the largest peak in the ISI histogram can be used for \(f_{0}\) extraction in single melody lines. Still, we are interested in multi-pitch perception. Therefore, a second example is that of a synthetic sound, a string pad, playing a two-note interval of four octaves and a major third (sound 28, #2-a#6), with two fundamental frequencies at \(f_{1}=93\) Hz and \(f_{2}=1762\) Hz. This sound is particularly interesting, as both pitches were perceived separately (see results of listening test below). Indeed, the two pitches are clearly represented as major peaks in the ISI histogram. In this plot, and the following, the expected peaks are indicated by solid lines starting from the top down to 0.7 of the plot's height. The precise frequencies were calculated using a Morelet wavelet transform of the original sounds. The third example is a Myanmar large buckle gong (sound 23). Its fundamental frequency is at \(f_{1}=126\) Hz. Additionally, the next two partials at \(f_{2}=199\) Hz and \(f_{3}=252\) Hz are indicated in the plot in Figure 2's middle plot too. Such a gong has a basically inharmonic spectrum; still, many percussion instruments are carved such that the overtone spectrum is tuned with the gong. In an interview with a gong builder in Yangon during a field trip, the instrument maker explained that he hammers the gong in such a way as to tune the third partial to the fifth of the fundamental. Indeed, the gong is tuned very precisely. The relation \(f_{3}/f_{2}=2\) is a perfect octave, \(f_{2}/f_{1}=1.58\) is nearly a perfect fifth. In the ISI histogram, the lowest partial \(f_{1}\) is the strongest periodicity, \(f_{2}\) and \(f_{3}\) are nearly not present. Still, there is a residual around 63 Hz, the octave below \(f_{1}\), and two lighter ones two and three octaves below. Indeed, we would expect a residual pitch to appear around 63 Hz, which is actually there. The wavelet transform does not show any energy below \(f_{1}\) of this gong. Therefore, this gong is similar to Western church bells, where the hum note is a residual [47]. The ISI histogram at \(f_{1}\) is also blurred, which most probably is caused by the beating of the gong, which is not perfectly symmetric, causing degenerated modes. Three other examples are shown in Figure 3. All are two-note intervals played on a classical guitar and all have the same low note g3 with a lowest partial at 193 Hz (called \(f_{1}\) here to compare with the second note with the lowest partial at \(f_{2}\)). Three intervals are shown: the octave at the top, a fifth in the middle, and a major seventh at the bottom.