Exhibition catalogue grants

The ancient Greeks figured out that if you have a bunch of strings, it sounds really good if you tune them according to the frequency ratios you get from the natural overtone series. In such tuning systems, you get all your notes by picking a starting frequency, and then multiplying or dividing it by whole numbers. The good-sounding (to Western people) note combinations are the ones derived from the lowest harmonics — the ones that have you multiplying or dividing by the smallest prime factors: two, three, and five.

“Thank U, Next”: The sustain of that dreamy electric piano in this chord loop solidifies the G♭ chord as a G♭M13 and the F chord is an F7(#9) secondary dominant (V/vi )! Then we have a regular B♭m before returning to the tonic — but not so fast! We haven’t really returned home, since it’s a D♭7, another secondary dominant (V/IV) that sends us back to G♭M13. These secondary dominants act like coal nuggets to fuel a perpetual motion chord-loop machine. Form-wise, you could also call the chorus extensions “post-choruses,” but I already used up my “P” for the pre-chorus sections, so I’ll just call these extensions “variations” and be done with it.

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