"Cents" describes an interval by comparing its size to another interval (say the octave at 1200c or the semitone at 100c), and as a ratio, remains a constant measure wherever you may move it around the frequency spectrum. Perceived beat rates measure the distance between pitches of the interval, and are relative to the the location of the pitches. (A 10bps distance is a much bigger interval in the first octave than in the seventh.) <<Are exact cents amounts mainly a tool for those using electronic tuners?>> Yes, but only because that is what their machines use to express the measurement of an interval. Us aural tuners hear a beat rate floating in the air, and we may not have the education to know that the beat rate (at least of the difference tone) is the result of the difference of their frequencies, but it immediately serves the purpose of a measuring tool. Put an A440 fork on a A3 and if you hear 5 bps going between the fork's fundamental and the A3's second partial, you know that the difference between their frequencies (whatever each may be and whichever is higher) is 5 Hz. <<But when someone says a piano is 10 or 12 cents off, I wonder if this is of that great use to me.>> If you feel insecure at parties when the electronic tuners rattle on about the 100ths of a semitone, just know that they had to pay from $150 ( the Sanderson Accu-Fork) to $1500 (the Accu-tuner) to be able to do that. You were issued your measuring tool at birth. Bill Ballard RPT "Never try to teach a pig to sing. It wastes time NH Chapter, PTG and annoys the pig." Sign on the wall of a college voice teacher's studio.
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