Tanāghīm (Tuning Systems)

Tanāghīm (tuning systems, singular: tanghīm) are the foundational layer of Arabic maqām theory in DiArMaqAr. They provide the pitch framework upon which all other musical structures are built.

What is a tanghīm?

A tanghīm is an ordered sequence of pitch classes within an octave. These pitch classes can be expressed through various mathematical representations, all relative to the first pitch class.

Mathematical Representations

Frequency Ratios (Fractions):

• Example: 1/1, 9/8, 4/3, 3/2, 16/9
• All ratios are relative to 1/1 (the reference pitch)

Cents Values:

• Example: 0, 203.9, 498.0, 702.0, 996.1
• All values are relative to 0 cents (the reference pitch)

String Lengths / Fret Divisions:

• Historical measurement approaches used in medieval treatises
• Converted to other formats for computational use

Reference Frequency and Note Names

To render a tanghīm sonically, two additional pieces of information are needed:

1. Reference Frequency: The absolute frequency (in Hz) assigned to the first pitch class
2. Note Names: Mapping to the Persian-Arab-Ottoman note naming convention

These associations are documented in historical sources and reflect either theoretical standardization or performance practice traditions.

Historical Sources

DiArMaqAr integrates tanāghīm spanning over 1,000 years of documented theory and practice, from medieval theorists like al-Kindī (874), al-Fārābī (950), and Ibn Sīnā (1037), through modern sources including the Cairo Congress Tuning Committee (1932) and al-Ṣabbāgh (1950), to contemporary approaches (Allami 2022-2025).

Each tanghīm includes complete bibliographic attribution with source references and page numbers where applicable.

Extended Range System

In DiArMaqAr, tanāghīm are expanded across multiple registers to support comprehensive musical analysis:

• Lower register: qarār qarār or qarār prefixes
• Main register: Standard note names
• Upper register: Standard note names (higher range)
• Extended upper register: jawāb or jawāb jawāb prefixes

This expansion is essential for:

• Jins and maqām analysis across full ranges
• Transposition calculations
• Modulation pathway exploration
• Authentic representation of Arabic theory

Starting Note Conventions

Tanāghīm follow different starting note conventions based on their historical sources:

Oud-based systems start on ʿushayrān, reflecting oud tuning in perfect fourths (e.g., al-Kindī, al-Fārābī, Ibn Sīnā).

Monochord/sonometer systems start on yegāh or rāst, reflecting theoretical measurement approaches (e.g., Cairo Congress 1932).

The starting note affects available maqāmāt, transposition possibilities, and modulation characteristics.

Mathematical Conversion

Each pitch class is automatically converted to multiple formats including frequency ratios, cents, absolute frequencies, MIDI values, string lengths, and cents deviations from 12-EDO reference notes.

Using Tanāghīm

Via REST API

# Get all available tuning systems (full metadata per tanghīm)
curl http://localhost:3000/api/tuning-systems

# There is no GET /api/tuning-systems/{id}; use list + idName, or pitch classes / maqāmāt in context:
curl "http://localhost:3000/api/tuning-systems/alfarabi_950g/ushayran/pitch-classes?pitchClassDataType=cents"

Via TypeScript Library

import { TuningSystem } from '@/models/TuningSystem'
import { getTuningSystemPitchClasses } from '@/functions/getTuningSystemPitchClasses'

// Create tuning system instance
const tuningSystem = new TuningSystem(tuningSystemData)

// Get all pitch classes
const pitchClasses = getTuningSystemPitchClasses(tuningSystem, 'ushayran')

Bibliographic Attribution

Every tanghīm includes:

• Source citation: Complete bibliographic reference
• Page references: Specific pages where the system appears
• Creator attribution: Historical theorist or modern scholar
• Publication year: Temporal context
• Commentary: Contextual notes by Dr. Khyam Allami

This transparent provenance enables:

• Scholarly verification
• Academic citation
• Further research
• Understanding of theoretical evolution

Next Steps

• Learn how tanāghīm relate to Ajnās
• Explore Taṣwīr (Transposition) capabilities
• Understand Starting Note Conventions