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Kite Guitar explanation for non-microtonalists: Difference between revisions

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Getting new sounds is easy -- just add new frets anywhere, and you get something new! But getting everything in tune is much harder. So most of this article 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".
Getting new sounds is easy -- just add new frets anywhere, and you get something new! But getting everything in tune is much harder. So most of this article 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".


First, some terminology: Our standard tuning divides the octave into 12 equal steps, which is called 12-ET ('''E'''qual '''T'''emperament) or 12-EDO ('''E'''qual '''D'''ivision of the '''O'''ctave). Microtonal music is anything that deviates significantly from that. Intervals are measured in cents. One hundred cents equals a semitone. For example, a 12-EDO minor 3rd is 3 semitones, or 300¢.
First, some terminology: Our standard tuning divides the octave into 12 equal steps, which is called 12-equal or 12-ET ('''E'''qual '''T'''emperament) or 12-EDO ('''E'''qual '''D'''ivision of the '''O'''ctave). Microtonal music is anything that deviates significantly from that. Intervals are measured in cents. One hundred cents equals a semitone. For example, a 12-EDO minor 3rd is 3 semitones, or 300¢.


A musical pitch is actually a frequency. In fact, it's multiple frequencies at once. For example, A below middle-C is 220hz, but it's also 440 hz, 660 hz, 880 hz, etc. These higher frequencies are called harmonics, and they make a harmonic series. Every string and wind instrument including the voice has these harmonics present in every note. Understanding the harmonic series is <u>essential</u> for understanding microtonal music theory. For more on this, see the [[wikipedia:Harmonic_series_(music)|wikipedia article]], or  these excellent youtube videos by [https://youtu.be/Wx_kugSemfY Andrew Huang] and [https://youtu.be/i_0DXxNeaQ0 Vi Hart].
A musical pitch is actually a frequency. In fact, it's multiple frequencies at once. For example, A below middle-C is 220hz, but it's also 440 hz, 660 hz, 880 hz, etc. These higher frequencies are called harmonics, and they make a harmonic series. Every string and wind instrument including the voice has these harmonics present in every note. Understanding the harmonic series is <u>essential</u> for understanding microtonal music theory. For more on this, see the [[wikipedia:Harmonic_series_(music)|wikipedia article]], or  these excellent youtube videos by [https://youtu.be/Wx_kugSemfY Andrew Huang] and [https://youtu.be/i_0DXxNeaQ0 Vi Hart].


== Just Intonation (JI) part 1 ==
== Just Intonation part 1 ==


Just intonation is based on the idea that musical intervals are in essence frequency ratios. Any two frequencies in a 2-to-1 ratio are an octave apart, e.g. A-220 and A-440. Thus an octave is in essence the ratio 1:2 or 2/1. Any two frequencies in a 3-to-2 ratio are a fifth apart, e.g. A-220 and E-330. The ratio needn't be exact. A-220 and E-331 will still sound like a fifth, but ever so slightly sharp.  
Just intonation (often abbreviated as JI) is based on the idea that musical intervals are in essence frequency ratios. Any two frequencies in a 2-to-1 ratio are an octave apart, e.g. A-220 and A-440. Thus an octave is in essence the ratio 1:2 or 2/1. Any two frequencies in a 3-to-2 ratio are a fifth apart, e.g. A-220 and E-330. The ratio needn't be exact. A-220 and E-331 make a 331/220 ratio. But the ear "rounds it off" to 3/2, and hears it as an ever so slightly sharp fifth.  


In theory, every interval is (or is close to) some sort of ratio, but that ratio might be very complex, like say 37/23. In practice, ratios are only musically meaningful when the two numbers are reasonably sized. The upper limit on the size of the numbers is hotly debated, but it's certainly at least 10.  
In theory, every interval is (or is close to) some sort of ratio, but that ratio might be very complex, like say 37/23. In practice, ratios are only musically meaningful when the two numbers are reasonably sized. The upper limit on the size of the numbers is hotly debated, but it's certainly at least 10.  
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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.
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?
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?


Unfortunately, detuning the guitar like this improves only the G7 chord, and ruins most other chords. To get this sweet chord in all the keys, you need <u>way</u> more than 12 notes per octave.  
Unfortunately, detuning the guitar like this improves only the G7 chord, and ruins most other chords. To get this sweet chord in all the keys, you need <u>way</u> more than 12 notes per octave.  
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The next prime after 7 is 11. Ratios like 11/6, 11/9 and 12/11 make neutral intervals midway between major and minor. They give melodies a middle eastern sound. For example, [https://www.maqamworld.com/en/maqam/f_bayati.php Maqam Bayati]is a minor scale with a neutral 2nd and a neutral 6th. There's also 11/8, a 551¢ 4th. Hearing it for the first time is disorienting, because we're used to classifying a 4th as either perfect or augmented. But 11/8 is midway between, making it both and neither. It also falls midway between the major 3rd and the 5th, making for interesting melodies that sound like a cross between major and lydian. Again, you may or may not like these sounds. But many people do, and it's there along with everything else.
The next prime after 7 is 11. Ratios like 11/6, 11/9 and 12/11 make neutral intervals midway between major and minor. They give melodies a middle eastern sound. For example, [https://www.maqamworld.com/en/maqam/f_bayati.php Maqam Bayati]is a minor scale with a neutral 2nd and a neutral 6th. There's also 11/8, a 551¢ 4th. Hearing it for the first time is disorienting, because we're used to classifying a 4th as either perfect or augmented. But 11/8 is midway between, making it both and neither. It also falls midway between the major 3rd and the 5th, making for interesting melodies that sound like a cross between major and lydian. Again, you may or may not like these sounds. But many people do, and it's there along with everything else.


== EDOs ==
== EDOs (Equal Divisions of an Octave) ==


JI ratios are one way to approach tuning. Another way is to take the octave and divide it up into equal-sized steps, making an EDO. Our standard tuning is 12-EDO. Instead of 12, one could have any number of steps. Guitars have been made in many EDOs. Above about 24-EDO, the frets become too close to play comfortably.
JI ratios are one way to approach tuning. Another way is to take the octave and divide it up into equal-sized steps, making an EDO. Our standard tuning is 12-EDO. Instead of 12, one could have any number of steps. Guitars have been made in many EDOs. Above about 24-EDO, the frets become too close to play comfortably.
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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, casual listeners are completely fooled and don't notice the pitch shifts.  
Finally, there's subtle pitch shifts of a half-fret 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.  


The Kite guitar also gives you lots of melodic options. Going up one fret takes you up about 60¢. This is the perfect size -- barely large enough to feel like a small minor 2nd and not a quartertone. In other words, in the right context, two notes a fret apart can feel like two distinct notes of a scale, and not two microtonal versions of the same note. But 60¢ is also small enough that two frets (120¢) still feels like a minor 2nd, although a large one. Three frets is a small major 2nd and four frets is a large one. Many melodic pathways from note A to note B. And there's more! The next string up has other 2nds in between these. There's a mid-sized minor 2nd of 1.5 frets and a mid-sized major 2nd of 3.5 frets. Right between them is the middle-eastern-sounding 11-limit neutral 2nd of 2.5 frets. All these 2nds are available for heptatonic scales. Or you can use the large major 2nd and the small minor 3rd to make an African-sounding near-equipentatonic scale. Or you can play exotic octotonic, nonotonic and decatonic scales.  
The Kite guitar also gives you lots of melodic options. Going up one fret takes you up about 60¢. This is the perfect size -- barely large enough to feel like a small minor 2nd and not a quartertone. In other words, in the right context, two notes a fret apart can feel like two distinct notes of a scale, and not two microtonal versions of the same note. And yet 60¢ is barely ''small'' enough so that the ear can be fooled by pitch shifts of half a fret (30¢).
 
60¢ is also small enough that two frets (120¢) still feels like a minor 2nd, although a large one. Three frets is a small major 2nd and four frets is a large one. Many melodic pathways from note A to note B. And there's more! The next string up has other 2nds in between these. There's a mid-sized minor 2nd of 1.5 frets and a mid-sized major 2nd of 3.5 frets. Right between them is the middle-eastern-sounding 11-limit neutral 2nd of 2.5 frets. All these 2nds are available for heptatonic scales. Or you can use the large major 2nd and the small minor 3rd to make an African-sounding near-equipentatonic scale. Or you can play exotic octotonic, nonotonic and decatonic scales.  


Naming all 41 notes in all 41 keys, and all the intervals, scales and chords they make, is no small feat. Kite's [[Ups and Downs Notation|ups and downs]] notation manages it by adding only two symbols to the standard notation. Notes are named ^C and vD (up-C and down-D), intervals are named ^4 and vM3 (up-fourth and down-major 3rd), chords are named E^m  and vF#v7 (E upminor and down-F# down-7), and so forth.  
Naming all 41 notes in all 41 keys, and all the intervals, scales and chords they make, is no small feat. Kite's [[Ups and Downs Notation|ups and downs]] notation manages it by adding only two symbols to the standard notation. Notes are named ^C and vD (up-C and down-D), intervals are named ^4 and vM3 (up-fourth and down-major 3rd), chords are named E^m  and vF#v7 (E upminor and down-F# down-7), and so forth.  
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