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 "2p" (two parts)

   • These represent the half-tones

3. Arbāʿ (One-fourth notes, sing. rubʿ): Represented as "1p" (one part)

   • 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", "1p", "2p", "/"}

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, "2p" for half-notes (anṣāf), "1p" 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), provided the tonic is classified as an "original" note (aṣlīya/ṭabīʿīya, represented as "n").

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 "2p") 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.

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 lies between two "natural" maqām degrees within the source maqām.

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 "http://localhost:3000/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

Via TypeScript Library

import { modulate } from '@/functions/modulate'

// Get valid modulations from source maqām
const modulations = modulate(sourceMaqam, allMaqamat, tuningSystem)

// Each modulation includes:
// - Target maqām
// - Modulation type
// - Maqām degree relationship
// - Classification validation

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