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Arab tone system
View on WikipediaThe modern Arab tone system, or system of musical tuning, is based upon the theoretical division of the octave into twenty-four equal divisions or 24-tone equal temperament, the distance between each successive note being a quarter tone (50 cents). Each tone has its own name not repeated in different octaves, unlike systems featuring octave equivalency. The lowest tone is named yakah and is determined by the lowest pitch in the range of the singer. The next higher octave is nawa and the second tuti.[1] However, from these twenty-four tones, seven are selected to produce a scale and thus the interval of a quarter tone is never used and the three-quarter tone or neutral second should be considered the characteristic interval.[2]

By contrast, in the European equally tempered scale, the octave is divided into twelve equal divisions, or exactly half as many as the Arab system. Thus, when Arabic music is written in European musical notation, a slashed or reversed flat sign is used to indicate a quarter-tone flat, a standard flat symbol for a half-tone flat, and a flat sign combined with a slashed or reversed flat sign for a three-quarter-tone flat, sharp with one vertical line for quarter sharps, standard sharp symbol (♯) for a half-step sharp, and a sharp with three vertical lines for a three-quarter-tone sharp. A two octave range starting with yakah arbitrarily on the G below middle C is used.[3]
In practice, much fewer than twenty-four tones are used in a single performance. All twenty-four tones are individual pitches differentiated into a hierarchy of important pitches—pillars—which occur more frequently in the tone rows of traditional music and most often begin tone rows, and scattered less important or rarely occurring pitches (see tonality).[4]
The specific notes used in a piece will be part of one of more than seventy modes or maqam rows named after characteristic tones that are rarely the first tone (unlike in European-influenced music theory where the tonic is listed first). The rows are heptatonic and constructed from augmented, major, neutral, and minor seconds. Many different but similar ratios are proposed for the frequency ratios of the tones of each row and performance practice, as of 1996, has not been investigated using electronic measurements.[5]
The current tone system is derived from the work of Farabi (d. 950 CE) (heptatonic scales constructed from seconds), who used a 25-tone unequal scale (see tetrachord), and Mikha'il Mishaqah (1800–1888) who first presented the 24-tone equal-tempered division.[6] Some strict traditionalists and musicians also use a 17-tone set, rejecting the 24-tone division as commercial.[7]
See also
[edit]References
[edit]- ^ Touma, Habib Hassan (1996). The Music of the Arabs, p.17-18, trans. Laurie Schwartz. Portland, Oregon: Amadeus Press. ISBN 0-931340-88-8.
- ^ Touma (1996), p.23.
- ^ Touma (1996), p.24.
- ^ Touma (1996), p.24-25
- ^ Touma (1996), p.18.
- ^ Touma (1996), p.19.
- ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems. CRC PRess. p. 102.
Arab tone system
View on GrokipediaOverview and Historical Context
Definition and Core Principles
The Arab tone system serves as the foundational tuning framework in Arabic music, defined as a microtonal system that theoretically divides the octave into 24 equal parts known as quarter tones, each spanning approximately 50 cents—a unit of pitch interval where the full octave measures 1200 cents.[5] This contrasts sharply with the Western 12-tone equal temperament, which uses semitones of 100 cents each, limiting expressive nuance in intervals smaller than a semitone.[5] The system's adoption of 24-tone equal temperament emerged in the 19th century, influenced by interactions with Western music theory, and was further debated at the 1932 Cairo Congress of Arab Music, which proposed it as a theoretical standard.[5] At its core, the Arab tone system emphasizes flexible intonation to enable expressive melodic variation, allowing performers to adjust pitches slightly beyond fixed theoretical positions for emotional depth and contextual suitability.[2] This principle is rooted in early theoretical treatises, such as those by Al-Farabi (d. 950 CE), who explored intricate pitch divisions to capture the subtleties of musical sound.[5] While the system provides a structured basis for composition and improvisation, its practical application prioritizes aural intuition over rigid adherence to equal divisions. The Arab tone system builds upon Pythagorean tuning principles, originally derived from ratios of pure intervals like the perfect fifth, but adapted to incorporate microintervals that enrich modal structures.[6] Theoretically permitting 24 distinct pitches per octave, it accommodates a range of 17 to 22 tones in actual usage, varying by maqam—the melodic modes constructed on this tonal foundation.[5][7] This adaptability ensures the system's enduring relevance in Arabic musical traditions.Origins in Islamic Golden Age Music Theory
The Arab tone system emerged from a synthesis of ancient Greek Pythagorean principles, Persian modal structures, and Byzantine melodic practices, which were systematically integrated and formalized during the 8th to 13th centuries under the Abbasid Caliphate in Baghdad. This period of intellectual flourishing saw scholars adapt and expand upon these diverse traditions to create a theoretical framework for Arabic music, emphasizing interval ratios and scale divisions that distinguished it from contemporaneous European systems.[8][9] A pivotal institution in this development was the House of Wisdom in Baghdad, established in the 9th century under Caliph al-Ma'mun, where Greek musical treatises by authors such as Aristoxenus, Euclid, Ptolemy, and Nichomachus were translated into Arabic alongside Persian and Byzantine texts. These translations not only preserved ancient knowledge but also facilitated its reinterpretation through an Islamic lens, enabling theorists to blend mathematical acoustics with practical performance elements derived from regional traditions. Scholars like Hunain ibn Ishaq contributed directly to these efforts, laying the groundwork for subsequent Arabic innovations in tone classification.[8] Early systematization began with Al-Kindi (d. 873 CE), who provided foundational descriptions of musical intervals in works like Risala fi khubr ta’lif al-alhan, drawing on Greek concepts to analyze sound production and tetrachord structures within an Arabic context. Building on this, Al-Farabi (d. 950 CE) offered a more comprehensive classification in his Kitab al-musiqi al-kabir, detailing various scale systems and modes based on Greek influences, including detailed classifications of intervals and consonances. The culmination of these medieval advancements came with Safi al-Din al-Urmawi (d. 1294 CE), whose Kitab al-Adwar introduced the influential 17-tone model, arranging tetrachords and pentachords to generate maqams while refining interval ratios for greater precision.[8][10][9][11] This theoretical foundation evolved into the modern 24-tone system during the 19th and 20th centuries, with significant refinements under Ottoman patronage that emphasized lute fretting and modal elaboration, followed by Egyptian scholars who standardized quarter-tone intervals for broader accessibility. The 1932 Cairo Congress of Arab Music further debated these developments, proposing the 24-tone equal temperament as a potential unifying framework while incorporating Western influences, though without full consensus. However, the proposal faced opposition from traditionalists advocating for preservation of variable intonation, resulting in no binding consensus but influencing subsequent theoretical and educational approaches.[12][13][5]Theoretical Framework
Octave Division and Scale Structure
The Arab tone system theoretically divides the octave, defined by a frequency ratio of 2:1 and equivalent to 1200 cents, into 24 equal parts to accommodate microtonal intervals inherent in traditional Arabic music theory. Each subdivision, known as a quarter tone, measures 50 cents, calculated as cents, establishing a framework of 24-tone equal temperament that serves as a foundational grid for pitch organization.[14] This division, formalized in 19th-century treatises such as Mikha'il Mishaqa's Risālat al-mūsīqī (ca. 1840), provides a systematic nomenclature for intervals smaller than the Western semitone while allowing for flexible intonation in performance.[15] The scale structure builds hierarchically upon seven primary notes analogous to the Western diatonic scale, which are then expanded through microtonal inflections to fill the 24-tone continuum. Neutral seconds, spanning 150 cents or three quarter tones, function as common building blocks within this organization, bridging the primary tones with subtle variations that enrich melodic contours.[14] Larger intervals derive from multiples of the quarter tone: a whole tone approximates 200 cents (four quarter tones), and a semitone equals 100 cents (two quarter tones), enabling precise mapping of scalar progressions. This quarter tone scale forms a complete cyclic system across the octave, where enharmonic equivalents—pitches occupying the same position but bearing multiple names based on contextual usage—underscore the system's adaptability to diverse melodic paths. Such equivalences, for instance, allow a single 50-cent interval to be denoted differently depending on its scalar role, reflecting the theoretical emphasis on relational pitch classes rather than absolute fixed tuning.[14]Fundamental Intervals and Their Ratios
The Arab tone system employs a set of fundamental intervals that form the building blocks of its scales and modes, derived primarily from historical theoretical traditions and adapted in modern practice to a 24-tone equal temperament per octave. This system divides the octave into 24 approximately equal steps, each nominally 50 cents, though performers introduce slight variations for expressive and modal purposes. Unlike fixed Western equal temperament, these intervals allow flexibility, with quarter tones ranging from 45 to 55 cents to accommodate regional and contextual intonation differences.[16][5] Key intervals include the quarter tone, the smallest distinct step, measuring about 50 cents with an approximate ratio of , though traditional approximations sometimes reference \sqrt{{grok:render&&&type=render_inline_citation&&&citation_id=4&&&citation_type=wikipedia}}{2} \approx 1.0293 in equal divisions. The small second, around 100 cents (ratio ), functions as a diatonic semitone, while the neutral second spans 150 cents (ratio ), providing a three-quarter tone quality essential for melodic contour. The whole tone is typically 200 cents (Pythagorean ratio ), and the minor third measures 300 cents (just ratio ), both foundational to tetrachord constructions in maqam. From Pythagorean tuning, the limma (small semitone) is approximately 90 cents (), adapted for microtonal contexts, and the buzurg (large whole tone) is about 204 cents, derived from stacked apotomes in theoretical treatises. These ratios, while idealized, are realized with acoustic variations in performance to enhance modal flexibility.[17][15] The following table outlines the 24 positions within the octave in the standard equal-tempered Arab system, with cumulative cent values from the tonic and common interval names where applicable. Positions are numbered from 1 (unison) to 25 (octave), reflecting the 1932 Cairo Congress standardization for notation and instrumentation.| Position | Cents | Common Name/Interval |
|---|---|---|
| 1 | 0 | Unison |
| 2 | 50 | Quarter tone |
| 3 | 100 | Small second (semitone) |
| 4 | 150 | Neutral second (three-quarter tone) |
| 5 | 200 | Whole tone |
| 6 | 250 | Augmented second |
| 7 | 300 | Minor third |
| 8 | 350 | Neutral third |
| 9 | 400 | Major third |
| 10 | 450 | Augmented third |
| 11 | 500 | Perfect fourth |
| 12 | 550 | Augmented fourth (sharp fourth) |
| 13 | 600 | Diminished fifth |
| 14 | 650 | Augmented fourth |
| 15 | 700 | Perfect fifth |
| 16 | 750 | Augmented fifth |
| 17 | 800 | Minor sixth |
| 18 | 850 | Neutral sixth |
| 19 | 900 | Major sixth |
| 20 | 950 | Augmented sixth |
| 21 | 1000 | Minor seventh |
| 22 | 1050 | Neutral seventh |
| 23 | 1100 | Major seventh |
| 24 | 1150 | Augmented seventh |
| 25 | 1200 | Octave |
