General

Musical Mathematics, 2010, Cris Forster, Chronicle Books, ISBN 0811874079.

Covers Ancient Greek, Indian, Indonesian, Middle-Eastern, Chinese, European and Contemporary Scales, including detailed analysis and explanation of source documents. Sections on instrument building and physics. The best general reference on tuning published to date, and destined to become a legendary scholarly work.

Tuning and Temperament: A Historical Survey, 1951, J. Murray Barbour, Michigan State College Press; 2004 reprint, Dover Books, ISBN 0486434060

Western Historical

Tuning, 1991, Owen Jorgenson, Michigan State University Press, ISBN 0-87013-290-3

This well-known large red book is a comprehensive collection of every western 12 note octave-repeating scale used in western music during the common practice period, such as meantones and well-temperaments. Each scale listed with cents values, piano tuning directions, and historical notes. I like this book but some early music mavens have issues with it. Sewn binding and acid-free paper. Out of print.

Indonesia

Music in Bali: A Study in Form and Instrumental Organization in Balinese Orchestral Music, 1966, Colin McPhee, Yale University Press; 1976 paper reprint, Da Capo Press, ISBN 0-30670-7780

Still the best book on Balinese gamelan but hard to find. Great discussion of Balinese music theory. Includes measurements made in the 1930s of pelog and slendro tunings of many Balinese gamelans. Out of print. Used copies are going for $725.

Music in Java, 1934, 1949 (2ed.), 1973 (3ed.), Jaap Kunst, Kluwer Academic Publishing, ISBN 9-02471-5199, Two Volume set.

Includes measurements of pelog and slendro tunings of many Javanese gamelans. Out of print. $300 used.

India

Bharata’s Vina, 2010, Cristiano M.L. Forster, Musical Mathematics, section 11.20 (World Tunings→Indian Music→Ancient Beginnings), Chronicle Books, ISBN 0811874079.

Ramamatya’s Vina, 2010, Cristiano M.L. Forster, Musical Mathematics, section 11.32 (World Tunings→Indian Music→South India), Chronicle Books, ISBN 0811874079.

Intonation in North Indian Music: A Select Comparison of Theories with Contemporary Practice, 1982, Mark Levy, Biblia Impex Private Limited, New Delhi.

Excellent review of all well known historical mathematical theories about ancient and North Indian intonation, followed by the first detailed methodological measurements of intonation and pitch gestures from a century of recordings by masters of the art. Establishes that asserted-but-not-proven theories do not describe actual practice; dynamic sur not fixed sruti is the basis of actual practice; and intonation is consistent within a given performer’s work with each specific raga, but not performer to performer or raga to raga. Levy studied under N. A. Jairazbhoy at UCLA and this thesis extended previous published research by Jairazbhoy by doing more detailed measurements than were previously possible. Essential reading.

Assessing The Tuning Of Sung Indian Classical Music [pdf], 2011, Joan Serrà, Gopala K. Koduri, Marius Miron and Xavier Serra, Int. Soc. for Music Information Retrieval Conf. (ISMIR)

Important. Histograms of free intonation vocal interval use in Hindustani and Carnatic music shows that North Indian Hindustani contemporary practice has converged on Western 12tET tuning. This is likely due in part to the use in the last century of equal tempered Harmoniums during vocal practice and solo accompaniment. In Carnatic music, there is found a more varied pitch use, and strong evidence of just intonation in the thirds. Consistent with all previous studies, neither tradition empirically shows evidence of a theoretical structure of 22 fixed ratio srutis supporting intonations used in performance.

Application of Pitch Tracking to South Indian Classical Music [pdf], 2003, A. Krishnaswamy, Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

Krishnaswamy’s initial foray into intonation analysis. Introduces use of three different methods of pitch tracking and relative results, autocorrelation having the most detail. Jumps into analysis of recorded performance. Finds 12 fixed notes, but some with considerable numbers of inflected variants, and particular pitch shapes associated with gamaka.

Pitch Measurements versus Perception of South Indian Classical Music [pdf], 2003, A. Krishnaswamy, Proceedings of the Stockholm Music Acoustics Conference (SMAC).

Krishnaswamy’s second paper, continuing his intonation research. Theoretical foundations not based on evidence are bound to have problems. Many gamakams are fundamental aspects of intonation, not ornamentation because they are required to be executed in a specific form, and without them the performance would be wrong. Poor intonation is readily identified, but nuances of intonation vary considerably between performers and between ragas. Pitch inflections are studied in detail; atomic concepts of inflected intervals, transient notes, and transient inflexions are proposed.

On the Twelve Basic Intervals in South Indian Classical Music [pdf], 2003, A. Krishnaswamy, Audio Engineering Society (AES) 115th Convention.

Inflexions and Microtonality in South Indian Classical Music [doc], 2004, A. Krishnaswamy, Proceedings of Frontiers of Research on Speech and Music (FRSM), Annamalainagar, India.

Historical survey of sruthi theory including Bharatha. Microtones are used in Carnatic music, including inflexions of pitch between fixed pitches. The exact values of constant pitches used vary between performers and ragams, for example the preferred intonation of the major third can vary up to 64 cents, depending on which performer. In addition to this though, there are other pitches used.

Multi-Dimensional Musical Atoms in South Indian Classical Music [pdf], 2004, A. Krishnaswamy (CCRMA), Proceedings of the 8th International Conference of Music Perception and Cognition (ICMPC), pp. 401-404.

Microtones in Carnatic music are not fixed pitch. Existence of exactly 22 srutis not supported by previous research. Master musicians skeptical of popular fixed pitch theories, stress actual performance as the true musical reality. Summary and integration of previous research. Fancy color graphs and diagrams.

Analysis of Gamakams of Carnatic Music using the Computer, 2002, M. Subramanian, Journal of Sangeet Natak Akademi, New Delhi, Vol.XXXVII, No.1, pp. 26-47.

Inspired by previous pitch analysis work by N. A. Jairazbhoy, Subramanian analyzes expressive dynamic pitch use (gamaka) in vocal performance of Raga Mayamalavagowla, using published CDs as source material. He finds in practice use of intervallic values ranging outside that predicted by conventional theory.

Carnatic Ragam Thodi - Pitch Analysis of Notes and Gamakams, 2007, M. Subramanian, Sangeet Natak, Vol XLI, No.1, 2007 pp. 3-28

Analysis of intonation in the popular Ragam Thodi, finding less use of fixed pitch than in other ragams. Thodi is a ragam where the mood is governed not by notes themselves, but the particular way the notes are intoned.

The ‘Maya’ of Pitch and Frequency, 2008, M. Subramanian, Music Research

“The frequencies of notes do not decide everything in a musical system like Carnatic Music which is heavily phrase oriented and in which movements between and around notes take a lion’s share compared to steady notes.” (summary quoted from MusicResearch.in)

On the Applicability of the Ancient Śruti Scheme to the Current Fixed-Tonic, Variable-Interval Mēla System [pdf], 2010, Madhu Mohan Komaragiri, Journal of the Madras Music Academy, 2010, Vol. 81, pages 135–143. Chennai, India.

On Some Adaptations of Western Concepts of Intonation to South Indian Music [pdf], 2010, Madhu Mohan Komaragiri, Journal of the Indian Musicological Society, Pages 66–75, Volume 40, 2009–2010, Mumbai, India.

Synopsis of the Doctoral Dissertation “Pitch Analysis in Karṇāṭaka Music — An Examination of Intonation and Modern Theories of 22 Śruti-s” [pdf], 2005, Madhu Mohan Komaragiri, Madras University, India.

An Empirical Study of Intonation in Raga Kalyani [pdf], 2005, Komaragiri, Madhu Mohan, Proceedings of the international symposium “IT-to-Mass: Speech and Music” Pages 65-68. FRSM–2005, Jan 6–7. Bhubaneswar, India.

Microtonality in South India: Not So Modal, 2000, Rafael Reina, Annual Magazine of the Foundation for Microtonal Music, Huygens-Fokker.

Pitch and melody use in Indian music is much more sophisticated than in the west. Reina explains four melody techniques used in Carnatic music which he has borrowed for use in his own compositions.

Central Asia

Central Asia, 130 Years of Russian Dominance, A Historical Overview, 3ed, 1994, Edward Allworth (editor), Duke University Press, ISBN 0-8223-1521-1

Chapter 15, Musical Tradition and Innovation, by Johanna Spector, is an excellent 50 page overview on music of the region, including specific details of instruments and charts of tunings used.

Middle-East

The Dastgāh Concept in Persian Music, 1990, Hormoz Farhat, Cambridge University Press, ISBN 0521542065 (pbk. 2004)

Al-Kindi’s ‘Ud, 2010, Cristiano M.L. Forster, Musical Mathematics, section 11.45 (World Tunings→Arabian, Persian, and Turkish Music), Chronicle Books, ISBN 0811874079.

Al-Farabi’s ‘Uds, 2010, Cristiano M.L. Forster, Musical Mathematics, section 11.53 (World Tunings→Arabian, Persian, and Turkish Music), Chronicle Books, ISBN 0811874079.

Africa

The Soul of Mbira: Music and Traditions of the Shona People of Zimbabwe, 1978, 1981, Paul F. Berliner, The University of Chicago Press, ISBN 0226043797 (pbk. 1993)

Contemporary Directions

Genesis of a Music, 2ed., 1974, Harry Partch, Da Capo Press, ISBN 0-306-80106-X pbk.

The place to get started thinking about just intonation and instrument building.

Tuning, Timbre, Spectrum, Scale, 2ed., 2004, William A. Sethares, Springer, ISBN 1852337974.

Essential book on the interactions between harmonic and inharmonic overtones of sounds, and tuning systems.

The Bohlen-Pierce Scale, Max V. Mathews and John R. Pierce, reprinted pg 165-173, Current Directions in Computer Music Research, 1989, MIT Press, ISBN 0-262-13241-9

The first published discussion of this well-known nonoctave scale.

A Theory of Equal-Tempered Scales, Kees van Prooijen, Interface vol. 7 no. 1, June 1978, pp. 45-56

Possibly the earliest paper discussing a general theory of nonoctave equal temperaments.

Tuning in to Wendy Carlos, Connor Cochran and Wendy Carlos, Electronic Musician, November 1986

Interview with Wendy Carlos about her work with tuning.

Three Asymmetric Divisions of the Octave, Wendy Carlos, Pitch, 1989

Technical article about the discovery and properties of three new nonoctave scales: Carlos Alpha, Beta and Gamma.

Five is Not an Odd Number: An Exploration of the Benefits of Equal Divisions of the Octave That Are Divisible by 5 [pdf], Igliashon Jones, 2010, City of the Asleep.

Evaluation of the musical intervals available and properties of equal temperaments that divide the octave into a multiple of 5 number of steps.