• Music articles
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
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.
Here are the files:
In the original key of G major:
Transposed to A major:
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...