Putting aside the emotional value of listening to a great guitar solo, what are some of the criteria that can be applied to make an educated judgement as to the quality of a solo within the context of the song it's nestled in?
I have always viewed the rock/pop type guitar solo as being all about tension and release.
You want to build to a climax, with any combination of speed and phrasing and note choices that fall slightly outside the chord structure, and then release that tension by resolving to something that is central to the song's melody or at least the chord changes that you're playing over.
I know a lot of people harp on Phish for being somewhat indulgent in their solo breaks, but there's a lot be learned from listening to one of their better jams when it comes to crafting a great build followed by a release that puts the listener back on melody and grounds them back in the original song again.
Trey's solos tend to start with some fairly in-the-pocket melody lines, usually repeating a common vocal melody. Nothing challenging on the ears, all the notes fairly consonant. And then he introduces bends and quick notes that go "outside" the key -- stuff that hangs, dissonant, in the air for a short time, before returning to things that are in key, on melody. He'll keep building on this approach throughout a solo, going "outside" more and more for longer periods of notes, and then bringing it back to something in key. Working his way up to neck to the higher register, adding more notes to the phrases being played. And when the solo is going to resolve the whole band will come back to something that's on theme, everything in key, and it'll just feel good on your ears.
This is impossible to answer because music is an aesthetic and you can find solos all over the place that will break any rules you setup. You can take some general principles but again they will fail in many cases too. You can generally get an idea of how certain people "solo" and attempt to copy them.
In any case the guidelines tend to be:
You really need to have a good understand when you are creating a solo as to where it is taking your listener and where you actually want to take it. Is this dive bomb going to really add anything or is it just a waste of time? If you let your emotions take the reins and you have anything useful to say then it will automatically figure out all that stuff for you. If your just mechanically going about it then chances are you won't have anything important to say and it won't be any good. If you have sex just to have it(just because you do it every day at 9pm you gotta do it today at 9pm) your not going to feel it like you did it for the "first time" are you? Well, you gotta solo like it's your "first time" every time.
Many years ago, when Duane Allman was alive, the Allman Brother's "At the Fillmore East (Live)" album was referred to as one of the very best examples of developing solos ever.
At the time I was taking music theory and playing jazz in stage band, so it was of particular interest to me to learn what it was that Allman and Dickie Betts did that made reviewers say such things.
In music theory, they talk about creating and releasing tension. The lack of tension in music leads to music that bores the listener, such as the most boring elevator music you've ever heard. Music that is totally tension - something that makes the listener's skin itch and makes them want to run away from the bad sound - is equally bad because the listener will lose interest - or kill themselves.
So, interesting music walks a line from being relaxed to tense; How it achieves tension varies. In general, tension is caused by changing between the opposite ends of volume, frequency, speed, in-harmony vs. dissonance, repetition vs. never repeating, etc.
A song/solo that is relaxed and quiet that suddenly speeds up and gets loud will generate tension. A song/solo that has been following simple enharmonic tones, ones that belong in the key (root/octave, 3rds, 4ths/11ths, 5ths, 6ths), then begins to move into more complex harmonies (2nds/9ths, 7ths, 13ths) will be more tense.
A song/solo that has a nice line, then repeats it, repeats it again, then again, can cause tension, a relaxing, then more tension as the listener is first intrigued by the phrase, then bored because they've heard it several times, then intrigued again because "it's gotta change sometime!". The listener likes being challenged; total repetition, like a "round" like "Row, Row, Row Your Boat" becomes boring. Change the melody, and the listener perks up. Repeat it, change it, repeat the new change, repeat the original line, then branch out further ends up teasing the listener; You're flirting with them, playing with their musical memory. Create a nice line, repeat it, play some variations, wander a-field, then return to it later, takes the listener on a trip and brings them back home.
So, back to Duane Allman and Dickie Betts. On that album, they played for hours. The solos are improvised, and pull out all the theory tension/release tricks. They develop themes, spin off, return to them, then the other takes over, develops it further, then they finish together. There are spots where the entire band backs down to very quiet volumes and the guitar quietly follows, then leads the band back to full volume.
There are plenty of other great solos, and soloists, but there have not been very many bands made up of musicians who understood improvisation like The Allman Brothers, and who could pull it off live as well.
Derek Trucks and Warren Hayes, who incidentally play often with the Allman Brothers these days, are also great soloists. I've heard Jimmy Herron, who also hangs with the same people, can work over a song very nicely too.
So, writing a good melody/song/solo is an awareness of the creation and release of tension, not only when writing it, but when performing it. When improvising, there's an immediate awareness of where you want the song to go, how you'll control the tension and what you'll do to release it.
Most guitar solos I can think of that I think are the closest thing to "objectively good" fit the song somehow. It's hard to really qualify it better than that. For example, consider the following:
These are just 2 examples of solos I think are "good" that aren't the most typical type. What do they have in common? They seem to "fit" the song. It almost seems like the "I know it when I see it" kind of thing.
I agree with the answers here. Tension, release, sure.
Here's what I tell myself: A solo is like a story. It needs to have acts and components. We can draw direct lines between literary mechanisms like repeating motifs and themes. We see this same kind of thing in good stand up comedy acts. The best aren't formulaic, but have a discerning structure and sense. As players we can also have humor, reference to other tunes, reference to pop culture. Again, just like a short story. It's mindful, strategic improvisation. It is cultivated.
So to me plugging a formula into making a good solo is like plugging a formula into making good literature. It can never work - they are more sophisticated than that.
The second thing I haven't seen here is any mention of heart or intent. We may claim it's not an 'objective' element, but I maintain much on this topic isn't. Some of the most theory-driven players I know have no character or passion in their playing. No fire. No personality. That's because it can't be taught in this literal kind of sense. You need to let go and look at is a kind of fugue meditation. I'm personally an eye-closer when I solo (ok, not true on super hard tunes). It's part of the whole process. Performing is a communion; a solo is a sacred story - you want to show people something unique and (for me anyway) passionate. When I play a show, I'm always complimented for my soloing. Usually a particular solo. They may say: "Man, that was amazing. That was really sad!" And that's just so. If I'm playing Claire De Lune, I do sad. If just one person gets that, we're communicating and I'm doing my job. Play with heart. Play it like you mean it. That is a good solo.
A good guitar solo should do exactly what the vocalist does i.e. express the emotions of the song!! Once a solo can do that, it's a great solo!
A couple of things I would like to point out.
Coming back to where I started. A solo should convey emotion!! Listen to Joe Satriani's or Steve Vai's or Marty Friedman's solos and I'M A 100% SURE you will understand what I'm trying to say.
Hope this helps!!
A memorable guitar solo tells a story. Roy Buchanan once played an amazing guitar solo where he only played one note many different ways.
See Guitar solo techniques, particularly my answer about solo stories and narrative arcs.