The Sound of Mathematics - Sarah Hart

00:00 // Introduction 03:04 // One Day Past a Blacksmith's Forge 06:09 // In Which Are These Simple Ratios Involving the Numbers 09:22 // Octave Interval, Then What's the Fifth Note 12:53 // Of Well Let's Just See What We've Had to Do to Go Up 16:21 // But of Course Those Absolute Differences Are Not 19:28 // Be Using Sometimes to Compare Different Tunings 25:35 // Few of These on the Slide 29:52 // Slide Between the Pythagorean Scan and the Ramos Scale 34:27 // If You Want Four of the Same Interval to Equal 38:08 // You a Blown Up Version 41:11 // The Pythagorean Fifth, Obviously the Same Pure Fifth 44:27 // This Is Widely Adopted 47:55 // Rule About This, I Was Vincenzo Galilei 50:59 // Like I Said, the Worst Possible Ratio Would Be One 54:13 // Is That These Two Things 57:36 // Going Up an Octave It has been known since antiquity that there are simple "harmonic" relationships between notes that sound appealing together. This lecture introduces the mathematics of pitch, scales, and just temperament. The pitch of a sound is not its only important property. The same note, played on different instruments, can have a very different quality of sound. We will explore the mathematics governing the relationships between these qualities of sounds, and the shape and dimensions of the instruments used to produce them. This lecture was recorded by Sarah Hart on 17 November 2020. Professor of Geometry (2020 - 2024) Acting Provost of Gresham College (2025) Sarah Hart was the first woman Professor of Geometry at Gresham College, and Acting Provost between March and October 2025. She is also Professor Emerita of Mathematics at Birkbeck, University of London where she served as the Head of Mathematics and Statistics. Professor Hart studied at Oxford and Manchester, gaining her PhD in 2000. Postdoctoral research and teaching followed, including a prestigious Engineering and Physical Sciences Research Council Fellowship, before she was appointed to a lectureship at Birkbeck in 2004. She became Professor of Mathematics there in 2013, and served in various management roles including as Head of Mathematics and Statistics, Assistant Dean, and Programme Director for the MSc Mathematics. Her academic publications have been mainly in the area of pure mathematics known as group theory, which has many applications both inside and outside of mathematics, for example in coding theory and cryptography. She is actively involved in the British Society for the History of Mathematics, and has served a three-year term as President of the Society from 2021-2023. Professor Hart is passionate about communicating mathematics and is a sought-after public speaker. She is particularly interested in the links between mathematics, culture and creativity: many of her public lectures and talks in schools relate to these topics. Her book Once Upon a Prime: the Wondrous Connections between Mathematics and Literature, was published in 2023, and has been positively reviewed in the press, including The Sunday Times, The Observer, The Economist, The New York Times, The Washington Post and the Wall Street Journal. Read more about Sarah Hart in Qanta Magazine The transcript and downloadable versions of the lecture are available from the Gresham College website: https://gres.hm/maths-sound Gresham College has offered free public lectures for over 400 years, thanks to the generosity of our supporters. There are currently over 2,500 lectures free to access. We believe that everyone should have the opportunity to learn from some of the greatest minds. To support Gresham's mission, please consider making a donation: https://gresham.ac.uk/support/ Website: https://gresham.ac.uk Twitter:   / greshamcollege   Facebook:   / greshamcollege   Instagram:   / greshamcollege