The High Third
from Lies My Music Teacher Told Me, page 70
In case you are getting the impression that I think I have it
out, let me assure you that I havent. Every book needs a
bit of mystery.
Heres ours. The numbers indicate that the fifth partial
(scale step 3) is lower
than the tempered major third. Yet, I have observed that many
musicians (particularly string players and singers) seem to prefer
that is higher than the tempered third when the fifth of the chord
also sounding. Evidently, there is more happening here than just
simple partials. Here's an opportunity for cutting-edge research.
Before you read more below about this fascinating topic, listen
to this audio clip to find out whether you hear something
move up or down in pitch. First listen for the overall effect.
Then play it again and listen with more attention to individual
pitches in the chord.
to listen - (Wave
this clip you will hear two pitches initially, then a third pitch
enters. Finally, the initial two pitches drop out leaving the
third pitch sounding alone. Do you hear the single pitch at the
end of the clip change when the others drop out? If so, do you
hear the pitch go up or down?
to listen - (Wave,
(Theses audio clips were created by Paul
a very knowledgeable musician
and theorist whom I met on the Yahoo Tuning List,
where a number of
experienced tuning experts participated in a search for a
mathematical explanation for the high third.)
before you read further, tell us by email
what you heard. Are you a musical performer? If so, it will be
helpful to know your performance medium (instrument, voice) and
the number of years of experience. Well post the results
(anonymously, of course) as they are received. It should at least
be interesting, and perhaps informative.
Now, heres the story.
began to wonder about the mysterious high third quite
a number of years ago while teaching my entry-level college choir
to sing in tune. Once the group could sing a pure unison, I demonstrated
the perception of basic acoustic fifths and thirds and then asked
the singers to tune these over a sustained fundamental (root)
pitchG over C, then E over C, for example. The idea was
to seek the best tuning by moving the pitch (G or
E) up or down ever so slightly until it locked with
the fundamental pitch (C).
of the lesson was to show that intervals tuned by ear
are not the same intervals when played on a keyboard. Once a well-tuned
interval was sounding vocally, our accompanist tapped the corresponding
pitch on the keyboard for comparison. The contrast in pitch was
clearly audible. The vocal intervals sounded clean and in
tune. The piano intervals sounded somewhat cloudy
and less focused.
As would be expected (according to the math of acoustics), the
pianos perfect fifth (G) was slightly lower than the singers
perfect fifth and the pianos major third (E) was clearly
higher than the singers major third. The Harvard Dictionary
of Music states that the few cents difference in the acoustic
(singers) fifth and the tempered (pianos) fifth is
not noticeable to the human ear. Our young singers, who likely
had never even heard of the Harvard Dictionary, had no trouble
hearing the discrepancy.
exercise can be performed by most anyone using a bit of patience
and some careful listening, and I suggest you try it yourself.
to bring up the appropriate exercises from Natural Ear
Training in a new browser window. Be sure to move your
vocal pitch very slightly up or down to the best
tuning in order to experience acoustic tuning.)
the singers could securely tune the major third and perfect fifth
separately to the sounding root (two simultaneous pitches, in
each case), I asked them to sing all three pitches simultaneously,
creating a C major chord. We first tuned the basses to a piano
reference pitch (C below middle C). Then the tenors added a well-tuned
fifth (G above the basses C). The sopranos and altos then
added the third (E above middle C).
When everything sounded homogenous, I asked the accompanist to
tap on the piano each of the sung pitches to check for discrepancy.
The basses were still sounding a solid C. The tenors were still
providing a fifth slightly above the pianos G. However,
the sopranos and altos were singing a third that was higher
than the pianos E, yet, the chord sounded pure and in
Apparently, the presence of a well-tuned fifth had caused the
third to be tuned much higher than when the third was tuned to
the root alonethat is, without the fifth. This curious turn
of events prompted me to consult outside help to find out whether
there is an acoustical (mathematical) explanation for this phenomenon.
I was aware of Yahoos Tuning List, an on-line
email conversation among the most experienced music/math experts
anywhere. I described my problem to the microtonalists
there, and to my delight many of them rolled up their theoretical
sleeves and went to work. After about three months of exchanging
ideas, crunching numbers and testing theories, no clear-cut solution
Some felt the effect was simply a learned stylistic preference.
To me, this didnt seem to jibe with the fact that my choir
consisted almost entirely of novice singers. It also didnt
explain why the learned preference wasnt sung
when the fifth wasnt sounding.
Others felt the effect was likely a psychoacoustic phenomenon.
They suspected that the actual pitches being sung were in accord
with acoustic norms, and that the ear created some sort of illusion
of the third appearing higher. I thanked everyone for their help
and left it at that. I had known for many years that experienced
singers as well as string and wind players frequently performed
and acknowledged the high third. In fact, I remember
being startled when I discovered that the acoustic facts didnt
support the major third I grew up with. This seemed to me to support
the idea that the high third was indeed a learned preference,
but it still bothered me that I had consistently observed it being
preferred by my novice singers.
About a year after my first Tuning List visit, I returned with
new evidence. It occurred to me to record the tuning lesson at
the beginning of a new semester and ask the tuning gurus to analyze
electronically the pitches being sung. Here is the audio clip
I posted for their consideration (a bit fuzzy sounding here, but
I think you'll get the idea)..
to listen: (Wave,
3.36mb) or (Mp3,
basses get their pitch (C) from the piano (replaced here by a
synth) at the start. The sopranos and altos then tune their third
(E) to the bass root. The tenors then insert the fifth (G). Notice
that the keyboard reference pitch first sounds higher than the
sopranos and altos and then later sound lower than the sopranos
idea was to find out whether the soprano/alto pitch actually moves
higher after the tenors enter or simply appears higher to the
ear. Electronic analysis showed that the pitch actually changedfrom
lower than piano pitch before the fifth entered to higher than
piano pitch after the fifth entered.
That observation seemed to support the idea that the high-third
experience is not simply a psychoacoustic phenomenon, but reflects
some sort of physical/acoustic reality that my novice singers
had sensed. For me, that evidence was welcome, since my own experience
was very comfortable with the notion of a math-based high third.
However, some of the best minds available were not able to discover
what that explanation might be.
While the electronic analysis was proceeding, Paul Erlich (whose
audio clips you listened to at the top of this page) took another
tack. I had suggested that the real high third might
likely be found by searching between the one-cent measurements
usually considered adequate for microtonal work. I made this suggestion
because I had not been able to find my high third
while adjusting pitches in cents on my synthesizer.
Paul prepared a set of triads having various placements of thirds.
I and other participants on the list were invited to select our
preferred items from blind choices. Paul later disclosed the actual
mathematical descriptions. My preferences were fairly consistent,
but they did change somewhat from day to day. I began to think
that either there was no actual high third or that it still did
not appear here because none of these examples actually nailed
it the way one does when tuning pitches in actual performance.
For about a week, I elicited judgments from visitors to my office.
Experienced ears tended to agree somewhat on certain high-third
a very startling thing occurred. Paul posted a series of "high
third" triads. When I heard the first triad, I felt my heart
leap. "Paul has discovered the high third," I thought.
to listen: (Wave,
3.36 mg) or (Mp3,
list member, Joseph Pehrson, also reported that he heard this
triad as having a third higher than tempered-tuned. Others said
they simply heard a just-tuned triad. Paul then revealed that
the third in that triad was in fact an acoustically correct 4:5
ratio to the root. As you might imagine, this evoked some lively
then posted an audio clip in which a just-tuned (acoustically-tuned)
major triad was followed immediately by a tempered-tuned (keyboard)
major triad. Its the one you heard at the top of this discussion.
When I first heard the clip (before Paul revealed its content),
I sensed that the third of chord moved downward in the second
tuning, as did some others. Most reported that they heard the
third move upward in the second tuning. I found that when I focused
on the pitch of the third, it could clearly be heard as ascending.
I then shifted back and forth, first focusing on the chord as
a whole and then focusing on the single pitch. My experience appeared
to be consistent, hearing the high third only when I focused on
the triad as a whole.
That experience clearly favors the idea that the high third is
a psychoacoustic illusion. But what about the actual raising of
the physical third found in my college choir recording? Do some
of us actually physically move the pitch of the third because
we are influenced by an illusion of what is consonant? Are singers
and string/wind players more susceptible to this illusion
than are keyboardists and other instrumentalists?
What do you think? Email
us and well post your ideas on our Sharing
Update: No conclusive trends have emerged so far. Evidently there is more mystery here than a simple survey can solve. Any grad students interested in a research project???
To the top of the page.