Kite Guitar explanation for non-microtonalists: Difference between revisions
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* 1/1 = unison | * 1/1 = unison | ||
* 2/1 = octave | * 2/1 = octave | ||
* 3/2 = perfect 5th | * 3/2 = perfect 5th | ||
* 3/1 = perfect 12th | * 3/1 = perfect 12th | ||
* 4/3 = perfect 4th | * 4/3 = perfect 4th | ||
* 4/2 = same as 2/1 | * 4/2 = same as 2/1 | ||
* 4/1 = double octave | * 4/1 = double octave | ||
* 5/4 = major 3rd | * 5/4 = major 3rd | ||
* 5/3 = major 6th | * 5/3 = major 6th | ||
* 5/2 = major 10th | * 5/2 = major 10th | ||
* 5/1 = major 10th plus an octave | * 5/1 = major 10th plus an octave | ||
* 6/5 = minor 3rd | * 6/5 = minor 3rd | ||
* 6/4 = same as 3/2 | * 6/4 = same as 3/2 | ||
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* 6/1 = perfect 12th plus an octave | * 6/1 = perfect 12th plus an octave | ||
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 | 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 9/4 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. | ||
For example, the 12-EDO major 3rd is 14¢ sharp of the 5/4 ratio. That's close enough that it still sounds like 5/4 and not some other ratio. But it's off far enough that flattening it down to 5/4 does indeed make it sound calmer and more relaxed. And a major chord sounds smoother with the 3rd slightly flattened. There are subtle interference beats in a 12-EDO chord that go away in JI. This is why it's so hard to tune a guitar by ear, because 12-EDO makes it impossible to get rid of all the beating. | For example, the 12-EDO major 3rd is 14¢ sharp of the 5/4 ratio. That's close enough that it still sounds like 5/4 and not some other ratio. But it's off far enough that flattening it down to 5/4 does indeed make it sound calmer and more relaxed. And a major chord sounds smoother with the 3rd slightly flattened. There are subtle interference beats in a 12-EDO chord that go away in JI. This is why it's so hard to tune a guitar by ear, because 12-EDO makes it impossible to get rid of all the beating. | ||
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We've seen that pure JI is impractical on a guitar, and we want the simplicity and transpose-ability of an EDO. But it's simply not possible to fit enough frets on the guitar to get everything really in tune. | We've seen that pure JI is impractical on a guitar, and we want the simplicity and transpose-ability of an EDO. But it's simply not possible to fit enough frets on the guitar to get everything really in tune. | ||
Fortunately, there's another way to get more notes besides adding frets: detune the strings. A guitar has a built in redundancy, because a note appears in more than one place on the fretboard. 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 | Fortunately, there's another way to get more notes besides adding frets: detune the strings. A guitar has a built in redundancy, because a note appears in more than one place on the fretboard. 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 very weird! 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 strange half-augmented or half-diminished 4ths and 5ths. So tuning your guitar this way gives you something new, but you lose a lot of what you had before. | ||
The Kite guitar adds notes <u>both</u> ways. There are almost twice as many frets, <u>and</u> every other string is detuned by a half-fret. The Kite guitar uses 41-EDO, a very accurate EDO. Omitting half the frets makes such a large EDO quite playable. It feels like and plays like an EDO half the size. The downside is that half the notes are hard to reach. But by an amazing coincidence, in 41-EDO, and <u>only</u> in 41-EDO, these are all dissonant intervals! For example, 41-EDO has good octaves and 5ths, but it also has octaves and 5ths that are ~30¢ sharp or flat of the good ones, that sound awful! Those intervals are moved safely out of the way. | The Kite guitar adds notes <u>both</u> ways. There are almost twice as many frets, <u>and</u> every other string is detuned by a half-fret. The Kite guitar uses 41-EDO, a very accurate EDO. Omitting half the frets makes such a large EDO quite playable. It feels like and plays like an EDO half the size. The downside is that half the notes are hard to reach. But by an amazing coincidence, in 41-EDO, and <u>only</u> in 41-EDO, these are all dissonant intervals! For example, 41-EDO has good octaves and 5ths, but it also has octaves and 5ths that are ~30¢ sharp or flat of the good ones, that sound awful! Those intervals are moved safely out of the way. Those faraway notes in another context will be exactly the notes you want. It works out that in those contexts, your hand will naturally move to that part of the fretboard, and those notes will become the easily accessible ones. in other words, the layout of the Kite guitar automatically filters out the "wrong" notes, without you even having to think about it! | ||
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 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.) | 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 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.) | ||
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There's a few other drawbacks. Obviously the closer fret spacing is somewhat more difficult. Omitting half the frets makes finding notes a little harder. Also the major-3rds tuning reduces the overall range of the guitar. Unless you're using an open tuning, 6 strings isn't quite enough, and 7 or 8 is best. And of course, there's a learning curve in training your ears to hear all these new sounds. But that's the fun part! | There's a few other drawbacks. Obviously the closer fret spacing is somewhat more difficult. Omitting half the frets makes finding notes a little harder. Also the major-3rds tuning reduces the overall range of the guitar. Unless you're using an open tuning, 6 strings isn't quite enough, and 7 or 8 is best. And of course, there's a learning curve in training your ears to hear all these new sounds. But that's the fun part! | ||
Finally, there's subtle pitch shifts of a comma sometimes. These are the inevitable result of getting everything more in tune. When you really study harmony, you find that there are more than 7 notes in a major scale. Weird, but true! The good news is that like watching a magician's trick, | Finally, there's subtle pitch shifts of a comma sometimes. These are the inevitable result of getting everything more in tune. When you really study harmony, you find that there are more than 7 notes in a major scale. Weird, but true! The good news is that like watching a magician's trick, casual listeners are completely fooled and don't notice the pitch shifts. | ||
So there are disadvantages, but the advantages are enormous. Chords are only a few cents away from JI, and sound great! And there are so many harmonic options. There are four main kinds of 3rds: large major, small major, large minor and small minor. There are likewise four 6ths and four 7ths. There's more of everything: two major chords, two minor chords, two dim7 chords, three augmented chords, four dom7 chords, etc. | So there are disadvantages, but the advantages are enormous. Chords are only a few cents away from JI, and sound great! And there are so many harmonic options. There are four main kinds of 3rds: large major, small major, large minor and small minor. There are likewise four 6ths and four 7ths. There's more of everything: two major chords, two minor chords, two dim7 chords, three augmented chords, four dom7 chords, etc. | ||