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In the key of C, C/E (C major first inversion, with E bass) is written as 1/3; G/B is written as 5/7; Am/G (an inversion of Am7) is written as 6m/5; F/G (F major with G bass) is 4/5. Just as with simple chords, the numbers refer to scale degrees; specifically, the scale degree number used for the bass note is that of the note's position in the ...
The ii–V–I progression is "a staple of virtually every type of [Western] popular music", including jazz, R&B, pop, rock, and country. [1] Examples include " Honeysuckle Rose " (1928), which, "features several bars in which the harmony goes back and forth between the II and V chords before finally resolving on the I chord," [ 1 ] " Satin ...
In 1936, Erdős and Turán made the weaker conjecture that any set of integers with positive natural density contains infinitely many 3 term arithmetic progressions. [1] This was proven by Klaus Roth in 1952, and generalized to arbitrarily long arithmetic progressions by Szemerédi in 1975 in what is now known as Szemerédi's theorem .