What does The Well-Tempered Clavier sound like in actual well temperament?
Ethan Teaches You Music PodcastShow Notes
This episode features Glenn Gould's 1963 recording of Johann Sebastien Bach's Prelude No. 1 in C Major from The Well-Tempered Clavier Book I, BWV 846 (1722). I also tempo-mapped Gould's performances of other WTC preludes and used them for the tempos of the MIDI versions of the various movements. A small correction: I say in the episode that five-limit just intonation is the basis for Western European tuning systems. This is only true from the Renaissance onwards. Medieval Europe used Pythagorean (three-limit) tuning. Also, just intonation was probably more of a theoretical ideal than a practical tuning method. Also, at one point I refer to Bach’s F-sharp major prelude as the F-sharp minor prelude. I did the alternative tunings using MTS-ESP. I used the following tuning ratios for the just intonation parts: * C - 1/1 * C# - 16/15 * D - 9/8 * Eb - 6/5 * E - 5/4 * F - 4/3 * F# - 45/32 * G - 3/2 * Ab - 8/5 * A - 5/3 * Bb - 9/5 * B - 15/8 I also used quarter-comma meantone, Andreas Werckmeister's temperament III from 1681, and Johann Kirnberger's well temperament as described in a letter to Johann Nikolaus Forkel in 1779. In actual practice, Europeans tended to center their tuning around D rather than C. I stick to C for ease of explanation, not historical accuracy. Here are some real humans performing music in historical European tuning systems: * Alice Borciani, Eva Saladin, Brigitte Gasser and Johannes Keller perform a Sabbatini motet in quarter-comma meantone * Daniel Adam Maltz demonstrates Kirnberger * Carl Radford demonstrates Young’s temperament * John Moraitis demonstrates quarter-comma meantone, Rameau and Kirnberger * Alice M. Chuaqui Baldwin demonstrates quarter-comma meantone and Werckmeister III I decided not to talk about Bradley Lehman’s proposed Bach tuning; I like how it sounds, but the controversy around it was too complicated for me to get into. You can hear Dr Charles Tebbs demonstrating Lehman’s tuning, and if you have a longer attention span than I do, you can watch Lehman tune a harpsichord. Wikipedia has a good summary of the various theories about Bach's tuning. John Carlos Baez explains quarter-comma meantone with math and diagrams. Kyle Gann's web site has lots more material on historical tuning with audio examples. For a deeper dive, try the tuning and temperament chapters in The Cambridge History of Western Music Theory.
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Music in this episode: Dolly Parton - “Traveling Man” (1971) Dolly Parton - “Jolene” (1973) Dolly Parton - “9 to 5” (1980) Dolly Parton - “Travelin’ Prayer” (1999) Dolly Parton - “Marry Me” (2001) Dolly Parton - “Stairway to Heaven” (2002) Dolly Parton - “Don’t Think Twice” (2014) Dolly Parton - “Purple Rain” (2023) References: I include excerpts of a couple of interviews with Dolly. There’s this one: and this one: I also include an excerpt of this excellent Paul Thompson video about the bassline in “Traveling Man”:
Music in this episode, not counting my Suno output: Fleetwood Mac - “Dreams” (1977) Thelonious Monk - “Round Midnight” (1968) Cordelia’s Dad - “Montcalm and Wolfe” (1998) The Bee Gees - “Stayin’ Alive” (instrumental) (1977) Catherine Sikora - “The Knowing of Sums” (2016) Ethan Hein - “The Knowing of Sums remix” (2020) The Velvet Sundown - “Dust on the Wind” (2025) Neil Young - “Out on the Weekend” (1972) Koji Kondō - “Super Mario Bros Underworld Theme” (1985) References I refer to Margaret Boden’s 2004 book, The Creative Mind: Myths and Mechanisms. I also refer to a study of a songwriting class that quotes a student talking about the difference between musicians and artists. You can read that study here: Dweck, J. (2023). Children as songwriters: The social-emotional benefits of songwriting in the elementary grades. Research Studies in Music Education, 46(2). Here’s the interview with Mikey Shulman where he says that people don’t enjoy the process of making music. Here’s my summary of the research on the learning impacts of LLM use:
Music in this episode: Mormon Tabernacle Choir - “Old Folks At Home (Way Down Upon the Swanee River)” (1968) Al Jolson - “Swanee River” (1950) Bing Crosby - “Old Folks At Home (Swanee River)” (1945) Pete Seeger - “Swanee River” (1959) Paul Robeson - “Old Folks at Home” (1930) Louis Armstrong & the Mills Brothers - “The Old Folks At Home (Swanee River)” (1937) Ray Charles- “Swanee River Rock (Talkin Bout That River)” (1957) The Honeys - “Surfin’ Down the Swanee River” (1963) Fu-Schnickens - “Sneakin’ Up On Ya” (1994) The Barbershop Singers - “Way Down Upon the Suwannee River” (2011) Hugh Laurie - “Swanee River” (2011) Al Jolson - “Swanee” (1945) Judy Garland - “Swanee” (1954) Aretha Franklin - “Swanee” (1966) Matthew Morrison’s book Blacksound: Making Race and Popular Music in the United States is a must-read. Read more about the history of these songs and the music education challenges they pose. Here’s my 20th century American popular music history syllabus.
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