Weighing Diverse Theoretical Models on Turkish Maqam Music Against Pitch Measurements: A Comparison of Peaks Automatically Derived from Frequency Histograms with Proposed Scale Tones

Abstract

Since the early 20th century, various theories have been advanced in order to mathematically explain and notate modes of Traditional Turkish music known as maqams. In this article, maqam scales according to various theoretical models based on different tunings are compared with pitch measurements obtained from select recordings of master Turkish performers in order to study their level of match with analysed data. Chosen recordings are subjected to a fully computerized sequence of signal processing algorithms for the automatic determination of the set of relative pitches for each maqam scale: f0 estimation, histogram computation, tonic detection + histogram alignment, and peak picking. For nine well-recognized maqams, automatically derived relative pitches are compared with scale tones defined by theoretical models using quantitative distance measures. We analyse and interpret histogram peaks based on these measures to find the theoretical models most conforming with all the recordings, and hence, with the quotidian performance trends influenced by them.

Acknowledgement

Barış Bozkurt and M. Kemal Karaosmanoğlu are partially supported by Scientific and Technological Research Council of Türkiye, TÜBİTAK (Project No: 107E024). We would like to also thank Ali Cenk Gedik for his help in construction of the audio database.

Notes

¹Also cf. ‘diatonic genus’, ‘chromatic genus’ and ‘enharmonic genus’ in Tonalsoft Encyclopedia of Microtonal Music-Theory by Joseph Monzo, and compare with Ibn Sina, ca. 1030/2004.

²This scale is constructed via a chain of 4 fifths up and 12 fifths down from the tone of origin.

³This would imply Saba Zamzama instead of Saba. Note, that Zamzama is synonymous with a half-tone + whole-tone + half-tone diminished tetrachord in modern Arabic Maqam music theory.

⁴We have chosen Zirafkand and Rahavi for demonstration purposes, because they are two rare maqams that Urmavi gives both the genera and the edvar for.

⁵Natural diatonic or ‘whole’ tones (tam perdeler) in contrast to half-tones (nim perdeler). These are the only indications Kantemir and later Ottoman theorists provide for the distances between perdes. Notice the similarity between maqam names and perde names. A perde is named after a maqam because it is a crucial functional degree for that maqam.

⁶The Western note-names are those used by Yalçın Tura.

⁷An instrumental–vocal form of composition meant for music education that demonstrates many maqams one after the other.

⁸We have been informed by our second reviewer Dr. Albrecht Schneider that this comma of 22.64151 cents is wrongly attributed to William Holder. It was actually discovered by a Belgian Engineer named Jean Galle as reported by Marin Mersenne in 1637. Nicolaus Mercator gave a more mathematically precise description of the said comma in 1660. We also observe that Alexander J. Ellis calls the 53-tone equal temperament yielding this artificial comma‘Mercator's cycle’ (Helmholtz, 1877, pp. 328–329, 436). ‘Mercator's cycle’ appears afterwards in Isaac Newton's unpublished manuscripts dated 1664–65 and William Holder's treatise of 1684. (cf. Barbieri, 2008). We reproduce this information with permission of and special thanks to our reviewer Dr. Schneider who was generous enough to disclose his identity (emails dated 26 March and 29 April 2009). Due to the fact that this comma is known widely in Turkish Maqam music circles as the Holderian comma despite attempts to call it other names (cf. Uysal, 2001, pp. 49, 60, 122, 144 [‘uygun’], and Aksoy, B. Makam in Tan im ina Doğru. Musıkişinas, 7. İstanbul, 2000, pp. 70–87 [‘minik’, suggested by Mildan Niyazi Ayomak]), and since William Holder partook in the promulgation of it, we shall keep referring to it as the Holderian comma (Hc) in our study.

⁹The first person to employ 1/8 tones to explain modern Turkish genera and maqams is Edward J. Hines. Through personal communication, the second author has learned that Mr. Hines has chosen 48-tone equal temperament to notate maqams as early as 1989 (Hines, 2009; through private email communication with the second author, 3 May 2009). This information was obtained after the main body of the article was completed; hence, Mr. Hines' approach was not included in the manuscript.

¹⁰For a synopsis of the role of the 24-tone Pythagorean tuning and theory in light of events and ideologies that led to the ban on the education of Turkish Maqam music instruments and the prohibition of Alla Turca broadcasts during 1934–1936, cf. Yarman (2009).

¹¹Initially, a short-hand for the demonstration of comma, limma, apotome and minor tone positions within the whole-tone.

¹²Cf. Signell, 1977; also Zannos, 1990: ‘Using a limited number of degrees is a theoretical concession which inevitably results in disregarding certain details of intonation.’

¹³Admittedly, the utilization of 12-tone equal temperament or a sibling tuning in keyboard and fretted instruments in Classical/Contemporary Western music is not in the least unacceptable, namely, one can perform a piece written for trombone or violin on a piano without grossly misrepresenting or distorting the intended music, whereas, fretting the tanbur or affixing mandals on a qanun strictly according to the 24-tone Yekta–Arel–Ezgi–Uzdilek tuning will be disastrous for Maqam music performance; namely, this tuning scheme will grossly misrepresent or distort the intended music, particularly for maqams or modulations to Saba, Uşşak, Hüzzam, Karcığar, etc., where the margin of error for certain tones is very narrow.

¹⁴For example, Zannos (1990) acknowledges: ‘The key problem of the diatonic species is a very old one: the position of the degree segah (vou) … Today, some schools prefer a higher position, some a lower one …’

¹⁵Metallic levers arrayed across the diagonal side of the qanun that serve to alter vibrating lengths of the courses on the fly by an amount foreordained at the time of their installation.

¹⁶Where Karl Signell measures intervals between perdes fretted by tanbur virtuoso Necdet Yaşar not defined in AEU theory.

¹⁷Where Gülçin Yahya takes the total percentage of each counted perde executed in an ud taksim (improvisations) of Yorgo Bacanos using Steinberg WaveLab (we do not know how she ascertains a perde's frequency) and compares that to the percentage of note lengths in her hand-transcriptions of that taksim. This operation demonstrates either the failure of the ear (or at least the author's ear) to determine correct note durations, or the hazard of incorrectly identifying a perde's frequency value for comparison with its heard counterpart, or both.

¹⁸A step toward this direction has already been taken by the third author in his novel publication of a Turkish Music Multimedia Encyclopedia called ‘Mus2okur’ (www.musiki.org).

¹⁹It is common practice to use the Holderian comma (Hc) as the smallest intervallic unit in Turkish Maqam music theoretical parlance. To facilitate comparisons with other models, we also use the Holderian comma unit in our figures and tables.

²⁰The ratio of a schisma is 32805:32768. It is an miniscule interval of 2 cents attained by subtracting 5 octaves from a stack of 8 pure fifths plus 1 pure major third.