Absolute Pitch Standards: Method and Music

As noted by Martin West, the development, and systematic use, of an elaborate notation system like the Greek one ‘presupposes a fixed standard of pitch. Otherwise there would be no reason to choose one key rather than another for a given piece of music, and far fewer symbols would be needed’.
It is, of course, unlikely that ‘a specific standard was maintained everywhere at all times without error; but any fluctuation seems to have been small’ (West 1992, 273–4).

In keeping with this, we occasionally hear about the use of pitch pipes (epitonion, tonarium) on the part of voice trainers. These pipes were ‘presumably a kind of flute’ (West 1992, 114), i.e. reedless pipes that could provide a reliable, and absolute (apotomon), starting point for musical performances. 

But is it possible to identify, at least approximately, the pitch standard adopted by the Greeks?

Recent scholarship has made substantial progress on this question, following in the footsteps of Martin West. Since 2010, in particular, a number of publications that have a bearing on the issue of absolute pitch, among others, have been produced by Stefan Hagel (see esp. Hagel 2010a, 2020b, 2014) as well as myself (Lynch 2022a, 2022b, 2024).

Given that these publications cover a lot of complex material, it is sometimes hard for readers to identify how our evaluation of the evidence at times rests on different principles and methodologies, leading us to propose different reconstructions of the Greek harmonic system and its relationship to the musical documents as well as  ancient instruments.

This paper, therefore, provides a summary of the approaches that Hagel and I have adopted in addressing the question of absolute pitch, followed by more detailed discussions of the two approaches and their implications for the interpretation of ancient instrument finds, for the benefit of readers who wish to delve more deeply into this issue. 

These of course are, and remain, matters of interpretation. Precisely for this reason, however, it is important to be as clear as possible with regard to the rationales and implications of the two approaches.

Summary

– My approach (Lynch 2023, 2024a) is based on the evidence provided by the Koilē flute, which suggests a standard concert pitch of ~432 Hz. 

– Hagel developed an iconography-based statistical method that led him to identify a standard pitch of  ~490 Hz (Hagel 2010a).

– This is a difference of about a tone at most (221 cents), and therefore well within historical ranges of variation (Ellis 1880, 305), even though we reached these estimates by very different methods. Both options are also consistent with the general range identified by West (1992, 276).

– Hagel’s assessment entails a potential variation of ±97 cents, making his reference pitch potentially just over a semitone higher than the Koilē flute (490 Hz–97 cents = 463.3 Hz, ~121 cents higher than 432Hz).

– Hagel’s range of variation widens to ±132 cents at 99% confidence level, making the lowest boundary ~454 Hz, i.e. 86 cents higher than 432Hz.

– In my view, this is a remarkably positive result. If scholars who have studied these issues carefully, and have very different views on other matters, reached estimates that are so close to each other, then it must be roughly correct. Given that we are looking at music that was performed over 2000 years ago, it is amazing that such a tight estimate could be reached at all!