[saghm]

> In music, the frequency ratio of a semitone is ideally 2^(1/12), but without some tiny fudging (called tuning), you can't make harmonies as the frequencies almost but don't quite line up right

IIRC correctly, it's not just harmonies; the range of a piano is big enough that if you tune each octave exactly based on that ratio, you'll end up with the first and last octaves sounding off from each other.

[lmm]

If you tune with exact 2^(1/12) semitones then all your octaves will be in tune for obvious reasons. (And pianos are normally tuned this way, equal temperament, so I don't know what the grandparent is talking about; for any tuning system some intervals are just and others are not. Equal temperament gives you just octaves, Pythagorean tuning gives you just fifths, meantone temperaments give you just thirds).

[adrianmonk]

> If you tune with exact 2^(1/12) semitones then all your octaves will be in tune for obvious reasons.

Hypothetically, or on an electronic instrument, you could. But if you did all 2^(1/12) ratios, your octaves wouldn't be in tune. Strings on a piano do not behave like an ideal string. Their overtones are not 2X, 3X, 4X, 5X, etc. times the fundamental frequency. Instead, the actual overtones are higher than the ideal frequencies. This is called inharmonicity (https://en.wikipedia.org/wiki/Inharmonicity).

So when tuning a piano, you have to tailor the way you tune it to each different piano if you want that piano's lower strings to be in tune with its higher strings.

[resters]

> This is called inharmonicity

I think I've been hearing this for a long time but didn't realize it was real so questioned my perceptual system.

Thank you for the info!