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Tone and Tuning Systems

21st Annual Congress of the Gesellschaft für Musiktheorie (GMTH)

Musik-Akademie Basel / Hochschule für Musik (FHNW)

01.-03. Oktober 2021

Music is played with certain intonations, and instruments are tuned. Music notation is built on the basis of tone systems and tuning systems, and music theory and practice likewise develop upon these foundations. Conceptions of and reflections on tone and tuning systems can be found in all cultures and are subject to historical processes. Despite the great importance of such systems, too rarely is serious thought given to their fundamentals, including note names, the sequence of whole tones and half tones, the clefs, etc.

The ancient Greek theory of tetrachords, the music of the Middle Ages, the vieltönig (“multitonal”) chromatic and enharmonic systems of the 16th and 17th centuries, the meantone temperament of the Baroque era, 19th-century approaches to the tuning of pure fifths and pure thirds, and the microtonal concepts of the 20th and 21st centuries—none of these can be represented on the standard twelve-key piano any more easily than the music of many non-Western cultures around the world.

The possibility of musical thought depends on the tone system. And some issues cannot be reconciled without certain internal tensions. The relationship between a mode of musical thought and the underlying tuning system can be fruitfully contradictory if the music expresses other things that the systematics and nomenclature of the tone system suggest. Tuning systems are directly linked to the physical fundamentals of music—that is, the acoustics and conditions for generating sound—and are in many respects the province of music theory. This furthermore extends into performance practice and instrument making.

The 21st annual GMTH congress in Basel invites participants to rethink such questions in this central area of music theory. A wide range of topics and research areas is encouraged. The keynote addresses are not directly assigned to the sections of the congress and are intended to illuminate the topic of the congress from different perspectives. The event will feature the following keynote speakers: the composer Catherine Lamb, the music theorist Alexander Rehding, and the Arabic and Turkish music theory specialist Michalis Cholevas. The campus of the Musikakademie Basel with the University of Music (FHNW), comprising the Classical Institute, the Schola Cantorum Basiliensis, and the Jazz Campus, offers a wide range of resources for this endeavour: special instruments are available on which almost all issues relating to the congress’s theme can be presented acoustically (particular mention should be made of a unique reconstruction of Nicola Vicentino’s Arciorgano). In addition, resident research departments and lecturers are among the most accomplished specialists in these areas of study.

The Sections of Congress

The contents of the sections are intentionally not sharply distinguished from each other. Contributions that build bridges between the following sections are possible and welcome.

Systematising Tone systems arrange tones in various ways. Tuning systems define a configuration of the pitches, usually with particular tunable instruments in mind. Both are often based on systematics that explain interval categories according to mathematical principles, and which are at the same time integrated into the context of the performance and notational practice of a certain period or cultural area. What is the relationship between an established tone system, its tuning rules and the praxis of making music? Which musical ideas can be articulated in which systems, and which contradictions between idea and system are possible? What is the relationship between melodic thinking and harmony? How does a musical idea or shape react in different systems? Which utopian tone systems or tuning rules would open up new perspectives?

Teaching Tone systems and tunings need to be understood and heard. Which tools can be used in teaching them? Which visualizations support the understanding of such systems? To what extent are representations of tone systems (such as the gamut, hexachordal theory and the Guidonian hand) spatializations of audible phenomena, and what potentials and problems are associated with them? What influence do the learned spatial structures of tone systems have on music making? How can tuning phenomena be brought to the ear in teaching situations? Which media and databases can support the pedagogical exploration of such questions in detail?

Performing Tone systems and tunings are realized in performances of music. With what questions are the players confronted? What tone system do they select? Under which criteria do they look at notations and performance practice? Why is a different intonation often chosen for the performance of a particular musical detail? What improvements to instruments could help with the performance? How can vocal ensembles rehearse, for example, the enharmonics of Vicentino and his successors, or microtonal contemporary music? How is the relationship between equally tuned pitches and purely tuned intervals represented in performance?

Perceiving The ear is our most direct conduit for the perception of tuning systems—more visceral than any intellectual debate, it offers holistic impressions that trigger feelings in us. What do we perceive? Obviously, when listening to tuned sounds, a variety of parameters overlap. For example, in the acoustic phenomenon of beating, timbre and rhythm are as relevant as pitch. How can such constellations be described? What is their significance for music? Which theories and analytical methods lend themselves to a holistic approach?

Illustrating The complex position of tone and tuning systems between mathematical definition, historical derivation, and questions of implementation in practice sometimes leads to very complicated descriptions. Visualizations can help here. There are numerous historical and modern examples: physical instruments (such as the monochord) as well as digital media can be used both to illustrate and simulate the sounds. This section is devoted to the question of how such concepts can be applied and what alternatives exist for representations of such systems. Which keyboards and which software can be used for the simulation? Where is there a need for new developments?

Free section


  • Individual papers: 20 min. presentation + 5 min. discussion.
  • Panels: 90 min. (a series of lectures of variable length with or without discussion).
  • Book presentations: 20 min. including discussion; by arrangement: please send proposals directly to the congress management team.
  • Workshops; by arrangement: please send proposals directly to the congress management team.

Submission and organization

All applications had to be submitted by May 30th, 2021.

Individual lectures:

  • Abstracts (max. 2,000 characters including spaces).
  • Biographical information (max. 1,000 characters including spaces).


  • Brief description of the concept and individual contributions (a total of max. 4,000 char- acters including spaces).
  • Biographical details of all those involved (max. 1,000 characters each, including spaces).

The conference languages and the languages of the abstracts are German, English, French, and Italian.

The selection of contributions is done by a double-blind peer review. You will receive a notification on the result of your submission by July 15th, 2021 at the latest.

Contact and further information

For general questions please write to:

Congress website:

Congress management: Moritz Heffter, Johannes Menke, Florian Vogt, Caspar Johannes Walter

We are currently assuming that the congress can be held as in-person in the city of Basel. In the worst-case scenario, however, online formats are also being considered. Further information will follow on the congress website in due time.