This Ugly Interval Is the Key to Changing Keys

Two notes, six half steps apart: the tritone, "the devil in music". Out of context it's just rough. Inside a key it's the one interval that tells your ear where home is - and pulls you there. We hear it close inwards to home and open outwards to the key exactly opposite, play a whole blues on nothing but tritones, swap G7 for D-flat 7 the way jazz players do (and "The Girl from Ipanema" does), change key by moving one note, and find the three diminished families with their four doors. The Church never banned it, either. CHAPTERS 0:00 Two notes that want to move 0:50 Half an octave 1:57 The devil in music (never banned) 4:04 Rough alone, restless in a chord 4:47 The only tritone in a key 5:49 The seven chord, and blues in two notes 7:06 Resolving outwards 7:52 The tritone substitution 9:45 Changing keys 10:49 Three diminished families 13:36 Why start here SOURCES AND FURTHER READING 'Mi contra fa' is first documented in Andreas Werckmeister (1702), who read the 'devil' mostly as a minor second - Store norske leksikon, 'tritonus' — https://snl.no/tritonus Jacobus of Liège (c. 1325) on the tritone, rare but 'subtle and beautiful'; Fux (1725) on the 'trite proverb' - quoted in Margo Schulter's survey of medieval tritone practice — https://www.medieval.org/emfaq/harmon... Docta sanctorum patrum (1324/25) permits 'octaves, fifths, fourths and such like' and does not mention the tritone - Rob C. Wegman's translation — https://www.robcwegman.org/materialia... Tony Iommi: 'I didn't know what the term even represented, though I knew I liked the sound of it' (Guitar World, via Rock and Roll Garage) — https://rockandrollgarage.com/tony-io... Heard alone, a half step is rated rougher than a tritone; preference for consonance tracks harmonicity and musical training: McDermott, Lehr & Oxenham (2010), Current Biology 20 — https://www.sciencedirect.com/science... The tritone as one cue among several for finding the key (Browne's rare-interval idea, 1981): Elizabeth West Marvin, Music Theory Online 27.2 (2021) — https://mtosmt.org/issues/mto.21.27.2... Tritone substitution in swing before bebop - Ellington, Tatum, Hawkins and others: Thomas Owens, Bebop: The Music and Its Players (Oxford University Press, 1995) Barry Harris's sixth-diminished approach — https://www.freejazzlessons.com/barry... The other demos' piano (a Kawai grand) and pipe organ (sampled by Simon Dalzell of Ivy Audio): the Versilian Community Sample Library (VCSL), Versilian Studios - CC0 — https://github.com/sgossner/VCSL Thunder: 'Storm thunderbolts', Wikimedia Commons - public domain — https://commons.wikimedia.org/wiki/Fi... The blues and the Ipanema chords are my own playing; the melody over Ipanema's chords is my own sketch, not Jobim's tune. Bach's Toccata in D minor (BWV 565) is played on the organ samples above Left out: that the tritone is behind ALL musical tension (there are other kinds - a sus chord, for one); Coltrane's endings; the tour of famous tritones (Purple Haze, 'Maria', The Simpsons - and sirens, which are a myth); Barry Harris's 'major and minor are one chord', which deserves its own episode All music, playing and voices are my own; the samples and sounds credited above are CC0 or public domain. Made with Blender, Python and a lot of measuring. Corrections are welcome and will be pinned.