X:

^{^}m:

̶  ^

2-1. Encoding the Modal Notations of the Melodic Figures (X_n^my)

X_n:

^{^}my:

The compound notation '^my' in the schematic code signifies the relative positioning of key modal elements within a melodic figure, particularly the šahed, trichord, and anchor tone. It is through the interactions of attraction and repulsion among these elements that the melodic contour, referred to as māyeh, is established.

The position of the šāhed, denoted by the variable '^m' as a generic1 degree number in the schematic notation Xn^my, signifies its placement within the cycle 'Xn' in relation to the anchor tone.

X_n^my

SAHED POSITION

MODAL CIRCLE

CYCLE

MAYEH

̶ 

2. Foundations of the Proposed Theoretical Model

y:

SUMMARY

This diagram summarizes all the components of the modal notations for melodic figures and presents the corresponding annotations, as follows:

• Maqām
• Melodic Figure
• Circle
• Cycle
• Māyeh
• Melodic Model

In the schematic notation Xn^my, the lowercase 'y' denotes the configuration of the trichord and the position of the Šāhed tone within it, which can manifest in the following ways:

• a (○●●): 
  The modal trichord consists of three adjacent tones, with šāhed being the first or lowest tone.
  
  
• b (●○●):
  The modal trichord consists of three adjacent tones, with šāhed being the middle tone.
  
  
• c (●●○): 
  The modal trichord consists of three adjacent tones, with šāhed being the last or highest tone.
  
  

• e (●x○●):
  The modal trichord consists of three non-adjacent tones chosen from a sequence of four contiguous tones within the cycle, with the šāhed being the second highest tone. The excluded tone is located between the two lower tones of the trichord.
  
  
• f (●●x○):
  The modal trichord consists of three non-adjacent tones chosen from a sequence of four contiguous tones within the cycle, with the šāhed serving as the highest tone and the excluded tone being  its lower adjacent one.

MELODIC MODEL

2-2. Overview of Circles and Cycles (X_n)

This section presents the modal circles used in the corpus of Persian music, along with their associated cycles. It features segmented circles that illustrate the octave's division within each modal circle, with a clockwise direction indicating the cycles. Additionally, the interval pattern for each cycle is identified, starting from its anchor tone, denoted by the number '1', through the chromatically precise use of Arabic numerals. Numerals without accidentals signify major or perfect intervals, while the inclusion of accidentals modifies these intervals, either enlarging or diminishing them as required.

To the next section