Figure 1
Consonance and dissonance curves drawn by Helmholtz, Partch, and Erlich (modified from Sethares (2004: 85–90)).
Figure 2
Melodic nucleus and the possible melodies for Hüseyni makam (modified from Bayraktarkatal and Güray (2023:18)),4 along with the notation of the Hüseyni makam pitches (below).
Figure 3
Details of the proposed methodology steps.
Figure 4
Orientational and positional figures6 (Öztürk, 2014: 144–155).
Figure 5
Tree representation of A–B–C pitches in a hierarchical order of superiority.
Figure 6
Determination process of the central pitch(es) to which each pitch is hierarchically connected.
Figure 7
Entropy values obtained as a result of applying Erlich’s model and a sample illustration for two pitch pairs.
Figure 8
Melodic figures of Hüseyni Sofyan Şarkı.
Figure 9
Relative hierarchy tree of Hüseyni Sofyan Şarkı.
Table 1
Event‑based entropy calculation for Hüseyni Sofyan Şarkı.
| Event | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Pitch | r | d | d | n | n | ç | n | h | h | e | g | m | g | a | h |
| Central pitch | d | h | h | h | d | h | h | h | h | h | h | h | h | h | h |
| Freq. ratio | 0.89 | 0.67 | 0.67 | 0.89 | 1.33 | 0.79 | 0.89 | 1.00 | 1.00 | 1.11 | 1.19 | 1.33 | 1.19 | 1.11 | 1.00 |
| Freq. ratio (cent) | 204 | 702 | 702 | 204 | 498 | 408 | 204 | 0 | 0 | 181 | 294 | 498 | 294 | 181 | 0 |
| Entropy | 3.39 | 0.96 | 0.96 | 3.39 | 1.83 | 4.00 | 3.39 | 0.00 | 0.00 | 3.53 | 3.86 | 1.83 | 3.86 | 3.53 | 0.00 |
| Cumulative entropy | 3.39 | 4.35 | 5.30 | 7.91 | 11.91 | 15.30 | 0.00 | 0.00 | 3.53 | 7.38 | 9.21 | 13.06 | 16.59 | 0.00 | |
Table 2
Calculation steps for event 4.
| Calculation Step | Reference Visualization | |
|---|---|---|
| 1 | Fourth pitch (event 4) of the melody = neva (n) Frequency of neva = 440 Hz | Figure 10 (Part A) |
| 2 | The pitches hierarchically connected to the neva pitch = dügah (d) and hüseyni (h) Frequency of dügah (d) = 330 Hz Frequency of hüseyni (h)= 495 Hz | Figure 10 (Part B) |
| 3 | Freq. ratiodügah = Interval (cent)dügah = | Figure 10 (Part C) |
| 4 | Freq. ratiohüseyni = Interval (cent)hüseyni = | Figure 10 (Part D) |
| 5 | Entropydügah = 1.83 Entropyhüseyni = 3.39 | Figure 10 (Part E) |
| 6 | Entropyaverage = | |
| 7 |
Figure 10
Visualizations for the calculation steps for event 4.
Figure 11
Event‑based entropy and cumulative entropy graphs for Hüseyni Sofyan Şarkı.
Figure 12
Time‑based entropy graph for Hüseyni Sofyan Şarkı.
Figure 13
Comparison of the cumulative entropies of Hüseyni Sofyan Şarkı and Hüseyni Peşrev.14