Guitar that gives the best harmonics
I'm trying to learn just intonation and was recommended by my harmony/theory teacher to use a guitar's harmonics for doing so since 1. it's easy to tune the strings and 2. produce the harmonics.
Can anyone recommend a guitar that has the "best" harmonics, i.e. 1. easiest to produce 2. longest sustain 3. cleanest sound?
Since it's for learning theory/harmony, budget instruments are preferable.
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How to get the loudest, most sustained harmonics
I've found that the volume and sustain of the harmonics correlates pretty directly with the volume and sustain of the instrument in general. Therefore, if you are looking only to play loud, distinct harmonics, I would recommend an electric guitar. Mix the neck and bridge pickups, with the volume and tone on the guitar nearly maxed out, and perhaps look for a guitar with humbuckers instead of single-coil pickups.
Position the amp so it faces at the guitar to generate a bit of feedback, and perhaps use moderate to heavy distortion if you are still dissatisfied with the level of sustain.
This produce fairly strong harmonics, not just at the 5th, 7th, and 12th frets, but also the subtler M3 harmonics near the 4th fret. But it isn't necessarily a very good tone, and having a lot of distortion won't enable you to hear the character of a perfect open chord tuned to its root's harmonics.
What I actually recommend
Your goal is to experiment with just intonation, so you don't necessarily need the loudest or even "best" harmonics. You just need harmonics that are audible enough to let you tune e.g. your B string to the Pythagorean major 3rd of a G, then play open G chords to hear the difference with equal temperament.
So, rather than getting a(nother?) new instrument, I would focus on improving your ears and fingers. Listen closely to the harmonics you are currently and try to identify what's wrong with them. If they sound muted, you are applying too much pressure with your fingers. If they sound indistinct (in pitch), it's an issue of horizontal placement. Bear in mind that the true location of the M3 harmonic is not over the 4th fret, but slightly below it, since the M3 interval in equal temperament runs sharp.
After getting your harmonic technique down, if you are tuning the B string to the M3 harmonic of the G and still find that the M3 harmonic is too quiet, I'd recommend just playing the open B string quieter too, instead of trying to amplify the harmonic itself. You don't have to play loud to tell whether two notes are in tune.
The closer to the bridge you pluck, the better defined will be any harmonic. The smaller the fingerprint on the node, the better defined will be the harmonic.
You don't even need to take your finger off immediately after you play the harmonic - which someone will probably tell you. In fact, you can put that finger back touching the string - at the node - and it won't make a scrap of difference. Why should it? The string isn't even vibrating at the node!
Don't spend money on a guitar just for its propensity to play harmonics. That's crazy.
First of all the "harmonics" you generate by attacking the strings properly are a property of the string. In my opinion they are not necessarily "easy" to produce. Also, if you use "harmonics" alone then your equal tempered notes will fall out of alignment so there is a bit of a compromise to make.
You excite the harmonic by touching the string at a node and then plucking it, preferably at an anti node. You can also excite them by hammering the string correctly. Once excited you want to know which guitar brand produce the "best" harmonics and provide some criterion for "best". The ease of excitement would be more related to the set up and quality of string, and well as your training, than anything else. It should be just as "easy" to excite a harmonic on a cheap guitar as on a ,000 hand made arch top or Remirez. Which brings me to the next point, sustain. Acoustic guitars will differ with respect to sustain and this may correlate with quality. But if you're playing electric then you can get whatever sustain you want with a good amp+effects set up. In the world of electric guitars one could argue that the guitar is no longer the instrument. Regardless, a good set up will produce good, long lasting harmonics. If you are having trouble getting a good sound for the harmonics then it could be technique. If you don't touch the string (and release that touch) just right you get nothing. On the other hand once you figure out the right touch and timing you can make it ring every time.
Among guitars, I'd say any cheap acoustic guitar with heavy roundwound strings will produce comparatively loud harmonics.
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