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The temperament test: can you hear the difference between historical and modern tunings?

In this article I explained why the ubiquity of modern equally-tempered tuning means that we don't hear baroque music the way its composers did, even when the notes are notionally the same. That there is a difference between historical and modern tunings is undeniable. What is contestable, perhaps, is how significant the difference is, when applied to real instruments, and heard by 'ordinary' listeners (i.e., not professional tuners).

To answer this question properly would require an exhaustive survey, with large numbers of people listening to many of pieces of music of dfferent genres, on large numbers of instruments in many different environments. If anybody wants to fund such a research program, please call me. In the meantime, I offer the following do-it-yourself listening test.

The test

On this page are links to eight MP3 files. I would have liked to supply something better than MP3, or at least at a higher bitrate, but I have to pay for my Web bandwidth, so I can't. Each of these files contains a rendition of exactly the same piece of music — the opening Aria from Bach's Goldberg Variations. No real instruments were harmed in the making of these recordings — they started with a MIDI transcription from the score, and were 'played' into MP3 format by the Timidity++ software. What makes Timidity interesting here — apart from the fact that it's free — is that you can specify a table of note pitches for all the notes on the keyboard. So I've taken four tuning schemes, and run the application through eight times — once for each scheme in the original key of G, and once in the key of A. The tunings were ordinary modern equal temperament, Young's 1999 well-tempered system, quarter-comma meantone, and just (i.e., pure) intonation.

Why two different keys? Well, one of the arguments in favour of equally-tempered tuning is that all keys are equally good (or bad). While equal-tempering may not be optimal in the key of G, it should be no less optimal in any other key. I do have renditions in keys other than G and A major, but there's only a certain amount of room on the Web server. But the method for generating these recordings is straightforward, I will happily describe it to anybody who wants to know. I suspect that some more sophisticated synthesis application, such as PianoTeq, have built-in facilities for this, anyhow.

In my recordings I used a piano sample rather than something more baroque, for the simple reason that I couldn't be sure that any of the harpischord, etc., samples available were tuned 'correctly' (i.e., equally tempered, as the software requires). If the original samples were tuned in some historical way, then the process of correcting them from assumed equal-tempering to historical temperament would have had completely unpredictable results. As it is, we rely on the source instrument being tuned to perfect ET, without octave stretches and all the other clever things that modern tuners employ. I did run the tests with pure tones, that is, mathematically correct sinewaves of exact pitches, and I can't say that my own findings were very different. But other people's might be.

A comment might be in order about what 'just' or 'pure' intonation means in this context. We can't tune a real instrument to pure intervals (that is, pitch ratios that are based on divinding small integers, such as 3/2, 5/4, 4/3, etc), at least not in more than one key. If we could, there would be no such thing as temperament. But with a software synthesizer we can retune instantly, so we can recalculate new key pitches for any key we want to use, and still remain 'just'. So in my recordings the just turning is correct for the key of G on the G recording, and correct for the key of A on the A recording.

The samples

Here are the files:

In the original key of G major:

Transposed to A major:

The results

It would be interesting to know whether other people can distinguish these recordings and, if so, which they prefer. They sound slightly different to me, so I'm sure to a professional tuner they would be quite distinguishable. Certainly other people who have listened told me that there were audible differences, but there was no consensus on which they preferred.

What is most striking to me is the difference between just intonation and any of the other systems. After the just tuning, the others all just sound, well, out of tune. And that's odd because I play the piano, and I'm used to the sound of equal temperament. It's really only possible to get a piano tuned justly using software — I can't imagine that anybody is going to spend the time and effort tuning a real piano in such a way that it can only be played in one key.

One final point: it's easy to tune a piano that exists only in a computer, and when it's tuned it stays in tune indefinitely. If only that were so for real instruments! The difference between the different temperaments in my tests were quite subtle, and I'm not sure I would hear them unless I was actively listening for them. And that raises what, to me, is an interesting question: is there an audible difference between temperaments in a real instrument tuned by a real tuner, in a real environment were instruments don't stay perfectly in tune? My tests can't answer that question one way or the other. But I wonder...

Copyright © 1994-2013 Kevin Boone. Updated May 14 2010