You know , my quest for musical knowledge ended way before I got online. And from what I see , the online information remains untouched by big business ( unlike other topics that I need info and now have to pay money for like some hvac engineering info that used to be free ).
I have always thought in my mind that " tuning " has to be relative to the piece your playing. I knew a guy who smashed alot of electronic tuners ( one being a Conn Strobe ) and had a different guitar every time I saw him it seemed ...and tonight I read this.
So now I know why I tuned onstage ( often during a song ). My Fender Precision didn't come with this " Harvard Dictionary " ...but damn it should have.
Again, quoting from the Harvard Dictionary of Music, "The exact measurement of a semitone (halfstep) varies slightly according to the system of tuning. In equal temperament, each semitone equals exactly 100 cents." --- Eeeek!! What are some of these words???
"Cents" is the measurement unit devised to measure musical intervals.
"Equal temperament" is the way a piano is tuned. Every half step is 100 cents, no more, no less.
"Mean temperament" and the "Pythagorean system of tuning" both have unequal intervals. Some semitones are as small as 90 cents and others as large as 114 cents.
Our ears do not hear in Equal Temperament; our ears want to hear the relationships between the notes to be different depending on how the note fits into the scale. Example 1: when a wind player or string player plays a melody, the note fingered as a D# or and Eb will actually be slightly different depending on whether it is a D# in the scale, or an Eb. Example 2: an F will be tuned slightly differently depending on whether it is the 3rd of the scale or the 5th of the scale. In an advanced player, the ear takes care of this discrepancy and the player doesn't really have to think about it.
So why have equal temperament?? Early in the history of keyboard instruments the player had to retune the harpsichord for each key -- in the key of C, an E was the third, but if we switched to the key of D, the E is now the second and needed to be tuned differently. Equal temperament was invented as a means of averaging out the difference and making everything just a little out of tune and a little in tune. Our ear gets used to this tuning and it works fine.
I started looking into these details after I tried out my first fretless guitar about a month ago (which, by the way, are awesome), and it made me think twice every time I played a normal guitar again. It's also been coming up when I look into information about Indian Classical music. Since normal guitars are bound to equal temperament (unless you use virtuosic bending?), I haven't really thought about it much, but seeing as I'm planning on defretting an old strat copy I have, it might come into play more in the future. The detail about the ear sorting out the difference by itself makes it seem really trivial, though.
Interesting stuff. First time I've about any of this.