Kite Guitar explanation for non-microtonalists: Difference between revisions
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A musical pitch is actually a frequency, e.g. A below middle-C is 220hz. In fact it's multiple frequencies at once, e.g. A-220 is also A-440, A-660, A-880, etc. These higher frequencies are called harmonics, and they make a harmonic series. Every string and wind instrument has these harmonics, including the voice. Understanding the harmonic series is <u>essential</u> for understanding microtonal music theory. See Andrew Huang's excellent video on the subject: [https://www.youtube.com/watch?v=Wx_kugSemfY www.youtube.com/watch?v=Wx_kugSemfY]. | A musical pitch is actually a frequency, e.g. A below middle-C is 220hz. In fact it's multiple frequencies at once, e.g. A-220 is also A-440, A-660, A-880, etc. These higher frequencies are called harmonics, and they make a harmonic series. Every string and wind instrument has these harmonics, including the voice. Understanding the harmonic series is <u>essential</u> for understanding microtonal music theory. See Andrew Huang's excellent video on the subject: [https://www.youtube.com/watch?v=Wx_kugSemfY www.youtube.com/watch?v=Wx_kugSemfY]. | ||
== Just Intonation part 1 == | == Just Intonation (JI) part 1 == | ||
Just intonation | 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. | ||
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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So you need both major 2nds available. And to stay in tune, your melody often has to use both, making small pitch shifts of a comma. Thus 12 notes per octave isn't enough to do JI justice. You really need 20 or so. That's not a problem for choirs and string quartets, and the better ones do indeed sing/play in just intonation. But on a guitar, you need two frets only 20¢ apart. That's so close together that it's hard to physically fit your finger between them. Also, JI guitars often have partial frets that don't span the full fretboard. The problem with those is that when you bend a string, you can go past the end of the fret. So JI guitars tend to be hard to play. | So you need both major 2nds available. And to stay in tune, your melody often has to use both, making small pitch shifts of a comma. Thus 12 notes per octave isn't enough to do JI justice. You really need 20 or so. That's not a problem for choirs and string quartets, and the better ones do indeed sing/play in just intonation. But on a guitar, you need two frets only 20¢ apart. That's so close together that it's hard to physically fit your finger between them. Also, JI guitars often have partial frets that don't span the full fretboard. The problem with those is that when you bend a string, you can go past the end of the fret. So JI guitars tend to be hard to play. | ||
Another drawback is the lack of symmetry. In 12-EDO, every note of the 12 can be the root of any chord. Thus there's 12 major chords, 12 minor chords, 12 dom7 chords, etc. And every note can be the tonic of any scale. There's 12 major scales, 12 minor scales, etc. Anything you can do in one key, you can do in any key. But even with 20 notes, a JI guitar can't play in all 12 keys. Often it can only play in a few. And if a song modulates between several keys, it may be impossible to play. | Another drawback is the lack of symmetry. In 12-EDO, every note of the 12 can be the root of any chord. Thus there's 12 major chords, 12 minor chords, 12 dom7 chords, etc. And every note can be the tonic of any scale. There's 12 major scales, 12 minor scales, etc. Anything you can do in one key, you can do in any key. Very handy when transposing a song to suit the vocalist's range. But even with 20 notes, a JI guitar can't play in all 12 keys. Often it can only play in a few. And if a song modulates between several keys, it may be impossible to play. | ||
But even with its drawbacks, there's no question that just intonation sounds pleasant, and getting one's harmonies better in tune is a powerful motivation for going beyond 12-EDO. For more about just intonation, see [https://www.kylegann.com/tuning.html www.kylegann.com/tuning.html]. | But even with its drawbacks, there's no question that just intonation sounds pleasant, and getting one's harmonies better in tune is a powerful motivation for going beyond 12-EDO. For more about just intonation, see [https://www.kylegann.com/tuning.html www.kylegann.com/tuning.html]. | ||
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Unfortunately, detuning the guitar like this only improves 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 only improves 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. | ||
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 on the Kite guitar, | 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 on the Kite guitar, 7-limit comes "for free" as a result of getting all the 5-limit intervals more in tune. | ||
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 like meeting an androgynous person that could be either gender. is it perfect or is it augmented? Both and neither. It 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 like meeting an androgynous person that could be either gender. is it perfect or is it augmented? Both and neither. It 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. | ||