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JIP (just intonation point), or commonly denoted "J", is a point in p-limit tuning space log22 log23 log25 … log2p]. If M is a monzo, then <J|M> is M evaluated in terms of octaves. If we shift to weighted coordinates, so that M = [m2 m3 m5mp is represented by the ket vector [e2log22 e3log23 e5log25 … eplog2p, then J becomes correspondingly the bra vector 1 1 1 … 1].