Intiqāl (Modulation)

DiArMaqAr implements the first algorithmic interpretation of Sāmī al-Shawwā's (1946) modulation guidelines, enabling systematic exploration of intiqālāt (modulation practices) networks that were previously documented only in prose.

Overview

Unlike Anglo-European modulation theory, Turkish makam theory, or contemporary Arabic theoretical approaches, Al-Shawwā's method employs specific conditions based on maqām degree relationships within the Persian-Arab-Ottoman note naming framework.

Historical Context

Sāmī Al-Shawwā, a revered Cairo-born, Aleppine violinist, provided unique guidelines for maqām modulation in his 1946 work Al-Qawāʿid al-Fannīya fī al-Mūsīqa al-Sharqīya wa al-Gharbīya (The Artistic Principles of Eastern and Western Music).

Key Principle: Modulation should occur through specific maqām degree relationships while maintaining "good disposition" (ḥusn al-taṣarruf) and avoiding abrupt transitions that would be "hard on the ear" (ṣaʿb ʿalā al-udhun).

This approach emphasizes melodic connection rather than harmonic compatibility, reflecting the fundamentally melodic nature of maqāmic practice.

Theoretical Foundation

The 24-Tone Classification System

Al-Shawwā classified a 24-tone system into three categories based on the Persian-Arab-Ottoman note naming framework:

1. Aṣlīya or Ṭabīʿīya (Original/Natural): Represented as "n"

   • These are stable, consonant maqām degrees that form the foundation of maqām structure which are whole tones and three-fourths tones.

2. Anṣāf (Half-notes, sing. niṣf): Represented as "h" (niṣf, half)

   • These represent the half-tones

3. Arbāʿ (One-fourth notes, sing. rubʿ): Represented as "q" (rubʿ, quarter)

   • These represent one-fourth tones, reflecting our understanding of Arabic maqām theory dividing a whole tone into four unequal parts (not equal divisions)

The Shawwā Function

Implemented as: sh(n): N → {"n", "h", "q", "/"}

This function evaluates the validity of proposed modulations based on the specific classification of individual note names within the 24-tone system. The function returns "n" for natural/original notes, "h" for half-notes (anṣāf), "q" for quarter-notes (arbāʿ), and "/" for notes outside Al-Shawwā's theoretical framework.

Modulation Rules

The algorithm evaluates multiple cases for valid transitions:

1. Tonic Correspondence

Modulation between maqāmāt sharing the same tonic (qarār). Al-Shawwā opens his guidelines by requiring that every maqām rest its qarār "on one of the seven original «natural» notes, or on a niṣf of the seven anṣāf" — so the tonic must be classified as an "original" note ("n") or a half-note ("h"). A quarter-note ("q") tonic falls outside his framework.

2. Third-Degree Modulation

Transition where the third degree of the source maqām becomes the tonic of the target, valid only when:

• The third degree is classified as an "original" note (aṣlīya/ṭabīʿīya, represented as "n")

3. Alternative Third-Degree Modulation

If the standard third degree is invalid, Al-Shawwā permits using an anṣāf (half-note, represented as "h") maqām degree immediately below it, provided:

• It is the sixth pitch class from the fundamental (qarār) maqām degree of the source maqām according to the 24-tone list
• It maintains a distance of two pitch classes from the preceding maqām degree within the source maqām

4. Fourth and Fifth-Degree Modulation

Transitions using the fourth or fifth maqām degrees of the source maqām as the tonic of the target. Al-Shawwā attaches no condition of their own to these degrees. The only constraint is his opening principle that every maqām rests its qarār on an original note or on a niṣf, and a pivot works by hosting the target's qarār — so the fourth or fifth degree must be classified "n" or "h". A "q" (rubʿ) degree can host no qarār.

5. Sixth-Degree Modulation (No Third)

When both the third degree and its alternative are invalid, modulation may occur through the sixth maqām degree, provided:

• It is the sixteenth or seventeenth pitch class from the tonic of the source maqām
• It remains an "original" maqām degree (aṣlīya/ṭabīʿīya, represented as "n")

6. Sixth-Degree Modulation (Between Naturals)

The sixth maqām degree may also be used when it is a half-note ("h") lying between two "natural" maqām degrees — al-Shawwā's example is ʿajam over dūgāh in maqām al-bayyāt, "a niṣf confined between two natural notes, ḥusaynī and awj". Unlike rule 5 this is not a fallback: bayyāt's third degree is perfectly valid.

Algorithmic Implementation

The modulate.ts function implements these rules using Al-Shawwā's specific 24-tone classification system as the reference framework.

Process:

1. Evaluates source maqām's maqām degrees according to Al-Shawwā's classification
2. Tests each modulation rule against potential target maqāmāt
3. Generates list of valid modulation pathways
4. Creates interactive networks showing relationships

Using Modulation Analysis

Via REST API

# Get modulation analysis for a maqām (example: principle maqām used in adhān)
curl "https://diarmaqar.net/api/maqamat/maqam_hijaz?tuningSystem=ibnsina_1037&startingNote=yegah&includeModulations=true&pitchClassDataType=cents"

# Response includes:
# - Valid modulation targets
# - Modulation type (third-degree, fourth-degree, etc.)
# - Network relationships

Research Applications

The implementation of the Shawwā algorithm enables:

Modulation Network Analysis

• Interactive lists: All valid modulation pathways from any maqām
• Network visualization: Structural relationships between maqāmāt
• Hub identification: Central maqāmāt serving as modulation hubs
• Cluster analysis: Groups of closely related modes

Quantitative Analysis

• Pattern recognition: Systematic modulation structures
• Comparative studies: How modulation possibilities vary across tuning systems
• Theoretical investigation: Validation against historical practices

Compositional Applications

• Systematic exploration: Discover modulation pathways
• Traditional frameworks: Informed by historical theory
• Creative practice: Contemporary composition grounded in tradition

Limitations and Context

The modulation algorithm:

• Represents one theoretical perspective (Al-Shawwā 1946)
• Is historically accurate to documented approach
• Could benefit from incorporating additional frameworks
• May be supplemented by audio analysis of recorded performances

Future enhancements could integrate:

• Modulation analysis from audio recordings
• Additional theoretical frameworks
• Performance practice documentation
• Contemporary compositional approaches

Next Steps

• Explore Taṣwīr (Transposition) capabilities
• Learn about Maqāmāt structure
• Understand Bibliographic Sources
• Review Research Applications