The Secret Chord

Now I’ve heard there was a secret chord // That David played, and it pleased the Lord // But you don’t really care for music, do you? – Hallelujah, Leonard Cohen

What if there really were a secret chord; one that sounded somehow better than all of the chords in the history of popular music, from Elvis and The Beatles to Miley Cyrus and Lady Gaga? Guess what. There is.

Below are two major chords (Hallelujah’s “major lift”). One is the standard major chord; the bedrock of pretty much every popular song ever recorded, from Let it Be to The Edge of Glory . The other is the secret chord, which you have almost certainly never heard. Which sounds better?

Scroll down to find the answer


Photo credit: Corey Templeton
Photo credit: Corey Templeton



Most people think the secret chord – Chord A – sounds better, but why? The special property of this chord is that the frequencies (pitches) of the three notes that make it up are perfect ratios. The ratio of the frequency of the highest note to the frequency of the lowest note is exactly 3:2; of the middle note to the lowest note 5:4. This tuning system (known as just intonation) used to be popular, but had all but died out by around 1800, replaced by the modern system of equal temperament. The advantage of the current system is that it allows songs in different keys to be played on the same instrument without sounding horrendously out of tune. The downside is that perfect ratios are eliminated entirely[1].

But this blog (and the accompanying book) is not about music, but psychology. For a psychologist, the interesting question is why perfect ratios sound better to most people (and why others buck the trend).

It is certainly the case that there is something “natural” about perfect ratios. For example, when a string is plucked, it gives off tones of several different frequencies at the same time. The loudest, the fundamental frequency, is what we normally think of as “the pitch” of the note, but the string also gives off quieter overtones whose frequencies are perfect ratios of the fundamental frequency.

So what? – you might be thinking – just because a particular turning system is more “natural”, this doesn’t explain why we should prefer it. Why, in fact, should we prefer certain sounds over others at all? Why should we have a different emotional response to air to air vibrating at one speed as opposed to another?

The answer, at least according to a recent paper by researchers from Duke University in North Carolina, is that it is not only guitars and pianos that give off overtones with perfect-ratio frequencies; another “instrument” with this property is the human vocal tract. This offers a solution to the mystery of the “emotional response”: a preference for human speech and language over other sounds would seem to make sound (sorry) evolutionary sense. So, if these researchers are right, the reason that the “secret chord” sounds so perfect is that its properties more closely mimic that of human speech.

That isn’t quite the end of the story, though. Whilst violinists prefer perfect ratios, pianists – if anything – prefer the modern system of equal temperament. This suggests an effect of learning (i.e., of nurture as well as nature). Because the notes on a piano are fixed to the modern tuning system, pianists perceive other tuning systems as sounding odd (since it has no keys or frets, the pitches on a violin are not fixed). But on the nature side, although listeners with little musical experience often express no explicit preference, even six-month-old infants are better at detecting pitch changes in perfect-ratio than equal temperament chords. This suggests even if we’re not consciously aware of liking it more, we still find perfect-ratio tuning somehow more coherent. Though, as the authors point out, this hardly settles the nature-nurture controversy, as even six-month-olds will have had considerable experience of hearing perfect ratios in human speech.

Whatever the outcome of this nature-nurture debate, the bulk of the evidence suggests, if anything, a preference – or at least a processing advantage – for perfect-ratio music. Which makes it somewhat strange that this system has been all but abandoned. So perhaps it’s time for a radical rethink. While the technological limitations of the day meant that perfect-ratio music was just too much hassle in 1800, today the challenges are far from insurmountable. Modern electronic synthesizers can produce any pitch at all, and some can even detect the key of the piece of music being played and make subtle pitch changes on the fly. Hook one of these up to a MIDI guitar, and there you have it: an instrument that really can play Cohen’s secret, perfect chord.

Find out what your musical taste predicts about your personality and intelligence in Psy-Q by Ben Ambridge, forthcoming from Profile Books (UK) and Penguin (US). 

Gill, K. Z., & Purves, D. (2009). A biological rationale for musical scales. PLoS One4(12), e8144.

Hahn, K. & Vitouch, O. (2002). In C. Stevens, D. Burnham, G. McPherson, E. Schubert, J. Renwick (Eds.). Preference for musical tuning systems: How cognitive anatomy interacts with cultural shaping. Proceedings of the 7th International Conference on Music Perception and Cognition, Sydney.

Schellenberg, E. G., & Trehub, S. E. (1996). Natural musical intervals: Evidence from infant listeners. Psychological Science7(5), 272-277.

Ball, P. (2008). A sound theory? Nature (Muse column): Published online 13 June 2008. doi:10.1038/news.2008.883

Hallelujah. Written by Leonard Cohen, Theresa Christina Calonge de Sa Mattos. Copyright Bad Monk Publishing, Sony/ATV Songs LLC.

[1] Well, not quite entirely. The frequencies of the same note an octave apart are perfect ratios: the higher note is double the frequency of the lower note (which is probably why we consider them to be somehow the “same” note in the first place).


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