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The thing that might not be clear from this article is that if you tune with Pythagorean Tuning, you'll run into cases where an Ab reached from one route is dif
by tunesmith 13y ago
The thing that might not be clear from this article is that if you tune with Pythagorean Tuning, you'll run into cases where an Ab reached from one route is different than an Ab reached from another route. Since instruments like the piano need to have only one Ab in a particular octave, that is why they'll be tuned as equal temperament, or some other method that guarantees only one Ab for a particular octave.
Otherwise, you'll run into phenomena where an instrument will sound totally awesome if played in one key, but really awful if they try to play the same tune transposed to a different key.
This is also why those with sensitive ears are frustrated by their inability to make a guitar sound in tune for both G major and E major chords.
- kevincennis 13y agoCan confirm the Gmaj/Emaj frustration. It's usually easy to get a decent compromise. But when a guitar is really consonant in E, it sounds like a train wreck in G.
- fhars 13y agoInstruments don't need to have just one Ab, there has been at least one that had more (as well as a rather uncommon B#): http://en.wikipedia.org/wiki/Archicembalo http://en.wikipedia.org/wiki/Archicembalo
- mrbrowning 13y agoHaving a guitar be in tune across every key is not strictly impossible [1], but it sure isn't easy. [1] http://www.truetemperament.com/site/index.php?go=2&sgo=3 http://www.truetemperament.com/site/index.php?go=2&sgo=3
- osteele 13y agoI heard an interview with a world-class guitarist (forgot who, but not classical) where he said he bends every (presumably fretted) note; I wonder whether this is to play non-even temperaments from an even-tempered fret spacing.
- AaronBBrown 13y agoAll decent musicians adjust every note on every instrument (where possible) in order to be in tune with themselves and the others they are performing with. Musicians that don't do this quickly find themselves out of a job (or making millions as the next big pop act). Mostly, this is not done particularly consciously unless you find yourself performing with a group that is either far more accomplished or far less accomplished than yourself. Of course, there are exceptions, namely open strings and piano. However, even in the case of conventional stringed instruments, it is common to adjust fingerings to avoid open strings in order to maintain tone color and more easily adjust intonation. Basically, while studying temperament is interesting, the reality is it rarely causes practical issues. Most pianos are tuned with equal temperament, which is good enough and almost every other western instrument has enough flexibility to adjust "on the fly."
- baddox 13y agoThat's solving a different problem, which is intonation (having every fret on every string in tune on the entire neck). But it still just provides intonation for a single temperament, like equal temperament. More info here: http://www.truetemperament.com/site/index.php?go=4#A1 http://www.truetemperament.com/site/index.php?go=4#A1
- mrbrowning 13y agoRight, I'm aware. Maybe I misread the last line of the grandparent, but I assumed that was exactly the problem being referred to -- the vagaries of details like string width and action height mean that even an instrument nominally designed with equal temperament in mind requires per-key adjustments to sound in tune by the standards of equal temperament.
- baddox 13y agoThere is no per-key adjustment in equal temperament. Equal temperament assigns an exact pitch (frequency) to each note, regardless of what key, chord, or interval the note is in. These weird frets are intended to make each note on the guitar play the exact pitch that is assigned to it by equal temperament, because normal straight frets cannot do that.
- mrbrowning 13y agoYes, that's a basic fact that I'm well aware of. To hopefully express what I'm saying more clearly: Assume your open strings on a guitar are tuned perfectly in the standard way: the A string is 110 Hz, the low E string is 110 * 2^-5/12 Hz, the D string is 110 * 2^5/12 Hz, and so forth. This will allow you to play an in-tune E minor chord on the open strings, but other chords will not be in tune (again, with reference to the equally-tempered pitch space) to the same degree because of the fact that the strings have different densities and widths. You could imagine accounting for this by tuning the strings such that some other chord was in tune, but then your original E minor chord would no longer be in tune. Thus my point that even though the guitar's design is predicated on equal temperament, it still requires per-key adjustments to be in tune for an arbitrary chord, unless you're using one of the guitars I linked to above.
- snarfy 13y agoIt doesn't make sense to transpose something to a different key on such an instrument since none of the notes repeat. A piano tuned with Pythagorean tuning would only have one key.
- tunesmith 13y agoThat would only work for the simplest tunes. As soon as you get to classical music (which pick certain, different keys for pianistic reasons), or any tune that modulates, you'd be in for some listening pain.
- TylerE 13y agoI have wondered though...you could use a synthesier with an organ-style foot pedalboard, use those to set the active key and just intonate everything to that key, modulation at will.
- snarfy 13y agoAnd that's why equal temperament was invented - so different instruments can play together.
- osteele 13y agoSee also Wolf Interval http://en.m.wikipedia.org/wiki/Wolf_interval http://en.m.wikipedia.org/wiki/Wolf_interval
- tribe 13y agoIn fact, this is fairly common in Hindustani music. Many ragas have different versions of the same note depending on how you approach it and switching between ragas often requires re-tuning
- baddox 13y agoIs that really why G and E chords are that way? I think it's more an issue of fret intonation. Guitars are typically tuned to equal temperament, just like a piano, so such a guitar with perfect intonation should sound just as good on every chord as a perfectly tuned piano.
- acjohnson55 13y agoPianos aren't actually tuned to equal temperament, due to the inharmonicity of their very tense and thick strings. http://en.wikipedia.org/wiki/Stretched_tuning http://en.wikipedia.org/wiki/Stretched_tuning
- baddox 13y agoYes, but that's a technicality. The goal is to have it sound equal tempered.
- acjohnson55 13y agoOf course. I wasn't criticizing, just mentioning, in case anyone found that tidbit interesting.
- tunesmith 13y agoRight, but when tuning by ear and actually turning the tuning knobs, it's easy to "mistakenly" make G major sound better than it would in equal temperament, which would in turn make E major sound worse. Or vice versa.
- thirteenfingers 13y agoPlayers of bowed stringed instruments run into this difficulty too. When playing with piano, cellists often have to tune both their lowest and highest strings to the piano, and then sort of average out the discrepancy in the two strings between.
- analog31 13y agoUse of non-equal temperaments on keyboard instruments is rare but not unheard of. The unique sound of each key can be exploited. As I understand it, there is a school of thought that each piece in Bach's "Well Tempered Klavier" was written for the sound of that key in a keyboard instrument tuned using the well temperament. In addition to being tempered, the entire scale of a piano from bottom to top is "stretched" slightly by a mainstream technician. Also as I understand it, harpsichords tend to use historical tuning methods. One possible reason is that the musician had to tun the instrument quite frequently, as opposed to the much more mechanically stable piano. Students who study string instruments (as I did) are taught that intonation is somewhat malleable for expressive purposes. The strings are tuned in beat-free intervals to maximize resonance when playing in particular keys. And wind instruments are all over the place, with ongoing efforts to improve their intonation.
- dev360 13y agoInteresting - I've had a lot of back and forths with a friend of mine with this.. I'd strum a Gmaj and hed insist its out of tune.