The mathematics of music means piano strings can never be in perfect harmony

Unlike with guitars and violins, pianos’ strings can never be perfectly tuned to one another. The solution? As this short animation from MinutePhysics explains, the instrument’s 88 strings across more than seven octaves means tuning a piano using harmonic intervals will inevitably lead to notes being fractionally off-pitch, with the issue compounding across octaves. So instead of using harmonics, piano-tuners generally keep octaves perfect, while leaving every other interval out of tune by just a tiny fraction. This workaround forsakes the appealing mathematical patterns of harmonics, but makes it possible to keep the kind of uniformity that is so valued in an era of mass production and reproduction of music.

Inuit throat singing is half performance, half game, and wholly mesmerising

In traditional katajjaq, also known as Inuit throat singing, two women stand face to face and perform a duet that doubles as something of a musical battle. Chanting in rhythm, they attempt to outlast one another, each waiting for any crack in the pace of her opponent – whether in the form of loss of breath, fatigue or laughter. In this short from the Canada-based First Nations film initiative Wapikoni Mobile, Eva Kaukai and Manon Chamberland, two throat singers from the remote Inuit village of Kangirsuk in northern Québec, face off in a friendly katajjaq duel. With sweeping imagery of the duo’s Arctic home, the short, which screened at the 2019 Sundance Film Festival, is a transfixing melding of music and landscape.

Why Medusa lives on – Mary Beard on the persistent legacy of Ancient Greek misogyny

‘To be men, they have to learn to silence women. I don’t think we’ve entirely got over that.’

From philosophy and politics to literature and art, the Western world has inherited much from Ancient Greece. But one disturbing cultural legacy is the enduring view of women as lesser beings who should shut up and stay out of the public intellectual sphere. Our social media is rife with examples of this persistent misogyny, which casts vocal women as stupid, shrill or some combination of the two. As the classicist Mary Beard of the University of Cambridge argues, nearly every leading female politician has been at some point depicted as Medusa – that beautiful woman of Ancient Greek myth who was transformed into a hideous beast as punishment for her own rape. In this video, commissioned by the Getty Museum on the occasion of Beard receiving their 2019 Getty Medal for contributions to the arts, she elaborates on the telling similarities between Ancient Greek depictions of women and those in our own times.

From sky charts to atomic clocks, time is a mysterious story that humans keep inventing

The standardisation and accuracy of human timekeeping has improved by leaps and bounds over the millennia – from tracing the stars, to the invention of timepieces, to the atomic ‘clocks’ of today. But for all our efforts, the concept of time, including whether it’s little more than an illusion of human psychology, remains deeply puzzling. In this interview with Robert Lawrence Kuhn for the PBS series Closer to Truth, the independent British physicist Julian Barbour endeavours to distinguish between our experience of time and its scientific underpinnings, including what has and hasn’t changed about our conception of time since we first looked to the skies to measure it.

A spy thriller for an era in which the Holocaust risks being forgotten

‘The noose that had hung his friends after the war for what they had done, the noose that he thought he had escaped, had found him.’

In the wake of the Second World War, former SS officials and Nazi collaborators fled Europe, hoping to evade prosecution and knowing that South American governments were sympathetic to the Nazi cause. Adolf Eichmann, the chief ‘architect’ of the Holocaust, was the highest ranking member of the Third Reich to escape to the continent, where he made Buenos Aires his new home and ‘Ricardo Klement’ his new name.

The US artist Randall Christopher’s animation The Driver Is Red follows the Israeli mission that captured Eichmann on 11 May 1960, forcing him to finally stand trial for his crimes. With the pace and tension of a spy thriller, the short documentary frames the fervour for justice as a tribute to those who committed themselves to tracking down Nazi war criminals long after the Second World War’s end. Now that very few people with memories of Nazism’s rise are still alive, Christopher made the film freely available online, warning of the ominous spectre of ‘extreme nationalism, open racism, attacks on the press [and] reckless talk of war’ in our own era.