4 ms·

> E.g. pianos don't even have perfect octaves. This isn't true (at least in theory). Octaves on piano are (or should be) exact, otherwise the 12-tone equal tem

> E.g. pianos don't even have perfect octaves. This isn't true (at least in theory). Octaves on piano are (or should be) exact, otherwise the 12-tone equal tempering doesn't work out. A4 is 440 Hz, A5 is 880 Hz, and A3 is 220 Hz (using the Acoustical Society of America designations, where middle C = C4). If the octaves weren't pure, the piano would be more in tune in the middle than it would be at either end, which usually isn't the case. > There were experiments with more tones per octave back in the middle ages, but the idea never caught on because the musical benefits aren't obvious. The history of scales and how they came to be in the Western classical system is long and complicated (too long for here, certainly), but I wanted to point out my favorite of these weird old instruments the archicembalo.[1] It was designed by one of the most out there theorists, Nicola Vicentino, in Ferrara, a hotbed of weird music at the time (see Carlo Gesualdo's "Moro lasso" [2], a really chromatic madrigal). 1. http://en.wikipedia.org/wiki/Archicembalo http://en.wikipedia.org/wiki/Archicembalo 2. http://www.youtube.com/watch?v=s_q3EJNUKis http://www.youtube.com/watch?v=s_q3EJNUKis (I'm ABD on a Music Theory PhD, so if anybody has more specific questions I'm happy to help!)

analog31 12y ago
It's been my understanding that the tuning of a piano is "stretched" compared to perfect 2:1 octaves -- at least this is what I heard from one piano tuner. Some details are suggested by all-knowing Wikipedia; http://en.wikipedia.org/wiki/Piano_tuning http://en.wikipedia.org/wiki/Piano_tuning
- TheOtherHobbes 12y ago
  Yes, exactly. Stretch tunings are also standard on some other keyboard instruments, including the Rhodes electric piano. There's some evidence that a preference for stretched octaves is innate: http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/scalestretch.html http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/scal... But stretch tuning is also used as a deliberate musical effect. Some tuners exaggerate it slightly, and some professional pianists ask for it. Simple harmonic theory only really makes sense if you're making music with pure sine waves. The sounds made by non-electronic instruments are very rich and complicated. Describing them with simple math has intuitive appeal, but it doesn't model what really happens. (There should be a name for the bias towards using simple but misleading models, but I'm not sure there is one.)

analog31 12y ago

It's been my understanding that the tuning of a piano is "stretched" compared to perfect 2:1 octaves -- at least this is what I heard from one piano tuner. Some details are suggested by all-knowing Wikipedia; http://en.wikipedia.org/wiki/Piano_tuning http://en.wikipedia.org/wiki/Piano_tuning

TheOtherHobbes 12y ago
Yes, exactly. Stretch tunings are also standard on some other keyboard instruments, including the Rhodes electric piano. There's some evidence that a preference for stretched octaves is innate: http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/scalestretch.html http://www.mmk.e-technik.tu-muenchen.de/persons/ter/top/scal... But stretch tuning is also used as a deliberate musical effect. Some tuners exaggerate it slightly, and some professional pianists ask for it. Simple harmonic theory only really makes sense if you're making music with pure sine waves. The sounds made by non-electronic instruments are very rich and complicated. Describing them with simple math has intuitive appeal, but it doesn't model what really happens. (There should be a name for the bias towards using simple but misleading models, but I'm not sure there is one.)