---
url: /docs/guide/tuning-systems.md
description: Understanding tanāghīm (tuning systems) and their role in Arabic maqām theory
---

# 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

```bash
# Get all available tuning systems (full metadata per tanghīm)
curl https://diarmaqar.net/api/tuning-systems

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

## 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](/guide/ajnas/)
* Explore [Taṣwīr (Transposition)](/guide/taswir/) capabilities
* Understand [Starting Note Conventions](/guide/theoretical-framework/#starting-note-conventions)