Kite Guitar explanation for non-microtonalists: Difference between revisions

== Introduction ==

There are two main reasons for going microtonal. One is to get new sounds, such as barbershop 7ths or Middle Eastern quartertones. Another is to improve the sounds we already have by tuning them better. The Kite guitar does both.

Getting new sounds is easy -- just add new frets anywhere, and you get something new! But getting everything in tune is far harder. So most of this page is about that. But it turns out that by getting enough notes to tune everything accurately, we also get many exciting new sounds "for free".

Our standard tuning divides the octave into 12 equal steps, which is called 12-equal or 12-EDO. Each step is a semitone. Microtonalists measure intervals using cents. One hundred cents equals a semitone. For example, a minor 3rd is 3 semitones, or 300¢.

Here's something many musicians don't know: Choose any two numbers from 1 to 10, and you've made a recognizable musical interval. For example, choose 4 and 5, and you get 5/4, a just major 3rd. Choose 5 and 6, and you get a minor 3rd. More examples:

2/1 and 3/2 have very small numbers, and as a result are easily tuned by ear. One can hear the harmonics coinciding or not, causing interference beats if they don't. (Interference beats are that rapid wah-wah-wah you hear when your guitar is a little out of tune.) More complex ratios like 8/5 or 16/9 are harder to tune by ear. The idea behind just intonation is to use only simple ratios in all one's chords, and avoid all interference beats. This makes harmonies much smoother.

Ratios add up not only within a chord, but also when two chords have common notes. Consider a I - V progression in C. The G note is 3/2 from C, and the B in the G chord is 5/4 above this. 3/2 x 5/4 = 15/8, so the interval from C to B is 15/8. Thus two simple chords can produce a complex ratio.

Thus large numbers that factor into smaller numbers are not as complex as they appear. So rather than limiting the size of the numbers, one might limit the size of the factors. It just so happens that every number can be factored into prime numbers (2, 3, 5, 7, 11...) in only one way. So it makes sense to limit the size of the primes used. This is called the prime limit, or limit for short.

Since the Renaissance, Western music is 5-limit. All our example ratios so far have been 5-limit. Historically, the prime limit of Western music has steadily increased. In the Middle Ages, ratios only used primes 2 and 3. In the Renaissance, prime 5 was added. Many modern theorists argue that the complex harmonies of jazz, blues and other forms of 20th century music imply prime 7.

7-limit JI, or "jazzy JI", has ratios such as 7/6 and 7/4. They do sound different. To ears accustomed to 12-edo, they sound flat. But paradoxically, even though the individual notes sound off, often they make a chord sound better. For example, the dom7 chord is noticeably smoother when the minor 7th is heavily flattened. You can hear this for yourself by detuning your guitar. Tune the B string 14¢ flat and the high E string 31¢ flat, and play a G7 chord as x-x-0-0-0-1. Listen to the sound of the chord, not the individual notes. Now play the exact same chord as 10-10-9-10-x-x. Hear the difference?

I personally find 7-limit JI new and exciting, and barbershoppers love it! Admittedly it's strange, and you may or may not like it at first. But it comes "for free" as a result of getting all the 5-limit intervals more in tune. You can also get an 11-limit middle eastern sound. For example, the minor scale can have a 2nd midway between major and minor. It's only 1 fret away from the usual major 2nd, so you can even hammer on and slide off. There's also a half-augmented 4th right next to the usual 4th that lines up with the 11th harmonic. Again, you may or may not like these sounds. But many people do, and it's there along with everything else.

The other way is to detune the strings. A guitar has a built in redundancy, because a note appears in more than 1 place. The open 1st string note (middle-E) also appears on the 2nd string at fret 5, the 3rd string at fret 9, 4th at fret 14, etc. If you tune every other string half a fret sharp, every other middle-E becomes a new note. Same for every note, and you now have twice as many notes (24-EDO). The downside is that E appears in fewer places and it's sometimes harder to reach. Before, a major 3rd was one string over, one fret back. Now, there's a half-augmented 3rd there, and all your major chords sound awful! The major 3rd is still on the guitar, but 4 frets away where it's hard to reach. The perfect 4th and 5th are also inaccessible, because the nearby ones have been replaced with half-augmented 4ths and 5ths. So tuning your guitar this way gives you something new, but you lose a lot of what you had before.

Unfortunately, the standard EADGBE tuning simply won't work. Because then those slightly sharp/flat octaves and 5ths become all too accessible, and show up in the familiar A and E barre chord shapes. Instead, the guitar is tuned in major 3rds. (There are also some open tunings, but those limit your ability to modulate.)