Any musical mathematicians out there? http://mathforum.org/library/drmath/view/52470.html (read the 6th post by "Joel Ellis Rea") This is old news, but I only recently discovered it. To sum up: The "even-tempered" tuning of the piano, guitar & all fretted instruments is wrong. The true musical scale doesn't repeat neatly every 12 notes, like we'd like to believe. Instead there's a 1/4 tone error. Western music compensates by fudging the notes so that it all works out. Example: tune your guitar starting at the low E. Work your way up one string at a time, using only your ears. Now when you get to the high E, compare it with the low E. It will be about 10 Hz off. This is because your ears want to tune to the "natural scale", but the guitar's built for the "even-tempered (fudged) scale". Does this bother anyone, or am I the only one?
I don't think you've quite got the right end of the stick there. It's not Equal Temperament that's flawed - it's Pythagorean Tuning. Equal Temperament IS the fudge that fixes the flaw in Pythagorean Tuning.
It "fixes" it only in the sense that it makes it possible for us to conveniently change key signatures. But it does so by botching the perfect 5th. To me, that's not a fix; it's a compromise. Orsino, have you tried the Buzz Feiten mod? I've heard of it before but never heard it in action. Also, it doesn't help pianos & wind instruments much.
Yes, it is a compromise. That's why it's called EQUAL temperament. It compromises the tuning of all the different keys so that they all sound reasonably acceptable. Otherwise you could have an instrument perfectly in tune in one key but it would mean that all the other keys would be horribly out of tune (well, some more than others). Unless of course you had 3 versions of each note, one for each enharmonic (except for G#/Ab where there are only two), in which case you could allow for all possibilities.
Well, it's one thing to hear it, but you'd probably have to do a string change and tune it up, try it out, etc. It works as far as I can tell, but I don't have it on any of mine. I'd like to, but I don't have a dealer near me that can do the mod, though I'm moving, so I'll find out...
From what I've read, Bach used the WELL-tempered scale which is something like what you described: most keys gel fine, but there's an occasional "wolf tone" (I think it's also called a "ditonic comma") that makes up for it. Most of the old church organs are tuned this way, which is why they have a powerful 5th but occasionally they hit an out-of-tune note. I haven't made up my mind which is better. To be honest, with today's MIDI capabilities & studio magic, I think it's possible to record in a series of "natural (Pythagorean) scales", maintaining perfect integrity all the time. Live performances are hopeless, of course. Orsino: btw, I found a website where some guy says the Buzz Feiten method is a waste of money (http://home.midsouth.rr.com/ssd/Stretch_Tuning_DW.html). He says you can accomplish the same thing by tuning your strings to the following offsets: I'm not a guitar player, so I wouldn't know. But it sounds worth a shot before you shell out the big bux for the retrofit kit.
Well, I used to do my best to tune to the offsets and I still try to, but it just becomes a big pain in the ass to keep exactly in tune, which is kind of the point with Buzz Feiten. When I tried it, it was great, but I can manage without it for now, and it would be easier just to not worry, so I'd have more control over it and learn little techniques and things. Maybe someday... What I really want is one of these... http://www.transperformance.com/
that's why b sharp is actually c, you could tweak the equation and mod out the scale, but why? this one works this is why every other key on a piano isn't black, and I like having the variable pattern myself......
\bach wrote for his 48 preludes and fugues for what he called the well-tempered clavier which does not mean equal tempered exactly, but nor is does it follow pythagorean tuning in any one key. I don't know much about how harpsichords or organs even were tuned in Bach's time but it probably wasn't the equal temperament that we know today. Of course singers and stringed instruments don't use equal temperament because they have a continuous range of frequencies that they can play - on the other hand string players tend to learn just one fingering for all the enharmonics of a single note so it's only the really good ones who can use their ear to adjust it slightly rather than thinking of three different versions of each note. As far as MIDI goes - well why couldn't you use it to play live? All you'd have to do would be to run a pre-built midi setup file that contained all the appropriate tuning commands to get pythagorean tuning for the key you were playing in for each piece. In fact in a lot of gigs you'd be running MIDI files for some of your instrument parts anyway whilst playing others live so you could have all the events you need timed for exactly when you need them, which would therefore mean you could modulate to other keys as well.
yes it works, if you're prepared to learn three ever so slightly different finger positions for each note!
yeah, but you never have to worry your head about this again either take the system, build a new guitar with a different system (or just swap out your fretboard), or go fretless.......
Just knowing the difference between equal-temperament & Pythagorean-tuning can give the composer/performer a heap of power. Yah, I agree, it's probably best to stay in equal most of the time, but for those powerful moments, imagine having the ability to shift to the pure interval. Bach knew this, and many (all?) of his compositions were written with that in mind. Man, just once I'd love to hear his "Well Tempered" preludes on a well-tempered keyboard, the way it was intended. Re: voices... Most vocal instruction these days is accompanied by the piano. Someone recently told me "today's vocalists wouldn't know a perfect 5th if it hit them over the head". I wonder how much of that is true. Maybe that's why sopranos love vibrato--they don't have to learn all the notes. Yuk yuk.
Btw... doesn't the sitar have variable frets that can be changed on the fly ...or something like that?
It has sympathetic strings designed to respond to the vibrations of the primary strings. So in theory you could tune the sympathetic strings differently to create rather cool beating effects - or possibly have the main strings on equal temperament but use just intonation, maybe pythagorean tuning on the sympathetic strings so there's always a hint of the right note being played. Of course in indian music it's not the diatonic scale that's used most of the time so it's a whole different set of rules. Pythagorean tuning would be great if you're certain you're going to stay in the home key all of the time. Would be fine for Mozart for example (all tonic and dominant scales and arpeggios), and I suppose equally good for a lot of rock music, particularly modern metal and punk, which rarely uses more than two different chords.
