Brace yourself, this is a LONG post.
If you have an idea of 'hiyaw', probably you have seen firemodel's early ramblings in this forum.
(NOTE: This thread is meant to focus on HIYAW, and its role in our quest for the ultimate guitar. The science and the myths need to be unveiled. NO FIGHTING, PLEASE!)
First off, in my own limited understanding, I can deduce what I think HIYAW is most mistaken as...
1) HIYAW is NOT sustain. A good guitar WITH hiyaw would most likely have good sustain. But the converse is not true. A guitar with good sustain is simply, a guitar that has good energy transfer from the strings to the whole guitar, that yields favorable ADSR (attack -decay - sustain -release) traits but not necessarily what 'hiyaw' is.
2. HIYAW is NOT compression. When a guitar 'compresses' well, I think this is best described as a guitar that makes your softer attacks louder, and makes your louder attacks less harsh. IMO, a good guitar that exhibits 'compression' is a guitar that has inherently good response, coupled with good electronics.
3. HIYAW is NOT resonance. Any guitar, has a resonant frequency, meaning, it will exhibit its loudest perceivable 'volume' when it puts out its resonant frequency. Pickups have a resonant peak, and the interplay of frequencies and harmonics of the guitar itself yield a resonant frequency for the guitar. Once you strike that note, the guitar would appear to have great sustain...
Now what is HIYAW to me...
'Hiyaw' in my understanding, is a trait of a guitar that exhibits GREAT SUSTAIN, that highlights the DYNAMICS of your playing, that seems to have the ability to RING OUT (or resonate) MAJORITY OR ALL THE NOTES on the guitar. When you do a bend on one fret, the same characteristic should be exhibited on all other frets. And what does that mean? IT RESONATES ALL ACROSS THE FRETBOARD. And because of that, you can hear that undeniable 'swirl' that most people call it. THAT swirl, IS 'hiyaw'.
I guess you remember this experiment back in grade school: Get two tuning forks of the same pitch, and hit one of them and place them a foot apart from each other; the result is, the other one will vibrate in resonance with the other! If you line up all tuning forks with the same harmonic traits (usually even-ordered), you can actually make a single note sustain in the whole room with an unspeakable richness to it when all the tuning forks resonate with each other. This is also similar to George Martin's approach to recording piano, where he stuffs 3 grand pianos in the studio and slams a single chord, so the 2 other pianos would resonate with the one being played.
Now what does this have to do with guitars? IMO, a guitar with 'hiyaw' is a guitar that can exhibit overtones in a way that creates very rich tones. And this has nothing to do with humbuckers or single coils... It is a trait from the PHYSICAL build of the guitar.
Hiyaw is a trait exhibited by VERY FEW guitars. IMO, it is not endemic to boutique or topodollar custom guitars. And also, take note that they can also NOT be inherent in expensive guitars. The science to hiyaw is not very much known to man. All I know is that, I can hear it when it's there. But it is hard to find. In my experience as a recording dude, I would say out of 100 guitars I've heard, maybe 1 or 2 had it. And they ain't necessarily the most expensive ones.
Hiyaw is best heard in an A/B test. Recording it is NOT simply possible. Why? Because even recording equipment cannot capture all the overtones; you may be able to record the timbre or voice of the guitar rig, but you cannot simply capture the swirly effect.
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And the question: Would you spend the extra thousands of $$$ with recommendation from tone gurus, to get hiyaw? Hey, maybe you can try 100 cheap guitars in a store and maybe be able to get one with hiyaw.