Foundations
Tuning Systems
Holdrian commas, 53-TET, Pythagorean tuning, and the gap between theory and practiced intonation.
- 01Pythagorean Tuning: How Stacked Fifths Built an OctaveThe ancient method of tuning by pure fifths, the comma it produces, and the mathematical accident that connects it to the 53-tone system of Turkish makam theory.
- 02Holdrian Commas and 53-TET: The Mathematics of Ottoman TuningHow the 53-tone equal temperament system and Holdrian commas became the theoretical language of Turkish makam intonation.
- 03Comma Calculations: Practical Math for the 53-Tone SystemHow to convert between Holdrian commas, cents, and frequency ratios — with worked examples building a Rast scale and verifying against Pythagorean tuning.
- 04Setar Tuning: Dastgah-Specific Kouk for the Persian SetarHow Persian setar players retune their strings to match different dastgahs, and why the kouk shapes the instrument's resonant character.
- 05Just Intonation: Tuning by Pure RatiosThe tuning system built on small-integer frequency ratios — why its intervals sound pure, the fundamental problems that prevent it from scaling, and its quiet relevance to Middle Eastern modal music.
- 06Moteghayyer: The Mutable Pitches of Persian Classical MusicHow specific scale degrees in Persian dastgah music shift their intonation depending on melodic context — a structural feature that distinguishes the dastgah system from both Western tonality and Turkish makam.
- 07Three Pitch Systems Compared: 53-TET, 24-TET, and Just IntonationHow the Turkish 53-comma system, the Arabic quarter-tone grid, and ratio-based just intonation each model Middle Eastern intervals — where they agree, where they diverge, and why no single framework captures what performers actually do.
- 08The Tuning Debate: AEU, Yarman-79, and Alternative FrameworksWhy the dominant 53-comma system remains contested, what the alternatives propose, and what computational pitch analysis reveals about how musicians actually play.
- 09Arabic Tuning Theory: 24-TET and the Quarter-Tone GridHow the 24-tone equal temperament system became the standard framework for Arabic maqam theory — its relationship to Turkish 53-comma and Persian flexible approaches, and what it captures and misses.
- 10Tuning the Oud and Cümbüş: Families, Not a StandardA practical guide to tuning the oud and cümbüş: the Turkish and Arabic tuning families, the courses-and-bam system, how to tune by ear, and why the internet's most popular cümbüş tuning has no traceable source.
- 11Practical Tuning: From Theory to the Instrument in Your HandsHow musicians in the makam and dastgah traditions actually tune their instruments — by ear, by harmonics, by beating, and despite the limitations of electronic tuners built for a twelve-note world.