I think he was the founder and commissioner of that league.
Absolutely, yes, a master producer can be critical to a band’s success, especially in an environment that was evolving as fast as pop/rock in the 60s. Martin was integral to the Beatles sound in so many ways.
Let the orchestra rise in an unscored crescendo and close on a crashing chord to send him off…
Fresh Air on NPR had a tribute to him today. They played a clip from when Terry Gross interviewed him in 1980. George is interesting - he discusses how he had his engineers create the tape loop playing through Being for the Benefit of Mr. Kite.
What was really funny was Terry Gross’s voice - she sounded very young and almost like Diane Keaton from Manhattan. “We’ll I’m from Philadelphia…” 
Good question. As others have said, in this case the answer is “yes.” John Lennon has an idea – a sound in his head – “I want to smell the sawdust.” George Martin could then help achieve the effect John was after – get that smell on vinyl, as it were.
Or, Paul could come in, sing a melody he’d invented, maybe strum a few chords. George would say, “You know, Paul, that’s so lovely – let’s try something different. Just your voice and a string quartet.”
ETA: Ha! I just read the tribute by Paul, and he quoted me, almost word for word. But you heard it from me first! 
He worked a lot with John, Paul and George on vocal harmonies. And I think his genius was recognizing some of the non-standard approaches that the Beatles would bring to him were even better than the “textbook” approach.
For example, John and Paul often harmonized in “Fifths”. I’m sure that 100 percent of classical trained musicians would say “No, no, no. You can’t do that”.
How many people can turn the opening chord of a song and into a 50 year mystery.
Are you not familiar with the circle of fifths? It’s an absolutely classic harmony. I suppose one could say that the Beatles popularized it in rock-n-roll, but they certainly didn’t invent it or make it acceptable to classical musicians. They had been there for hundreds of years.
I aways love this deconstruction from Randy Bachman’s Guitarology:
Yeah, fifths is the default harmony for everything I think.
Facts:
When the Beatles sang george the ending vocal chord in “She Loves You,” (The fourth Yeah) he said: You can’t do it; It’s too corny; It’s an anachronism. But they had to have it. And they were right. George had the historical perspective but the fabs were talking to a new audience. the rest is history.
The song Sir George would have left off of Pepper was Lovely Rita.
No, he’s talking about arranging chord voicings, and he’s right. One of the rules that was drummed into us in Music Theory class was that in baroque and classical, as one chord moves into the next, voicings containing parallel 5ths and octaves are absolutely not allowed, under penalty of, um, something about Beethoven’s britches.
The interval of the fifth, not the relationship of chords. I should have said parallel fifths to be more specific. Done in the medieval era and certain folk music, but forbidden in “Classical” voice leading.
But the Beatles being vernacular musicians would be singing in fifths naturally, and George martin would know this, as well as be able to play it himself, no?. He wouldn’t have produced a classical disc on them.
What does “in fifths” mean please? Explain it like I know nothing, because I don’t.
A fifth is a note 7 keys, or frets above the tonic note, being the fifth note in the scale. It is the most consonant sound in western harmony that is not the actual note repeated at another register. I think it exists in other musical systems independently arrived at. The fifth of G is D. It’s basically a method of singing in harmony with someone else and using that as your basis. It occurs all the time in folk and country. That’s as far as I can go with that at my pay grade.
Under penalty of sounding like crap.
On this page you can here what different intervals sound like. Go to the blue box with the piano keyboard and click “perfect 5th”.
Right. The reason it sounds good is that it’s half an octave, pitch-wise. Pluck a string on a guitar, for example. If you press it at the twelfth fret, effectively halving its length, you get the same note, an octave higher. If you press the string a QUARTER of the way along – that is, half of that half (the seventh fret) – you hear its “fifth,” when plucked. A pleasant interval.
This topic is getting beaten. Bottom line is that J&P sang a variety of fun, complex harmonies* and George Martin, because of his classical training and his open mind, both rolled with what they were doing and helped them use it to increase the appeal of their songs.
Can we move past this now?
Different question: I haven’t heard what folks like Geoff Emerick and others who worked as engineers under Martin are saying. I would hope and assume high praise. Emerick kind of portrayed Martin has a person an arm’s-length away when the boys started doing more drugs and things got more tense.
ETA: found this on Billboard. Nothing but praise: Beatles Engineer Geoff Emerick Remembers the Late George Martin – Billboard
*I believe this has been posted on the SDMB before, but here is an Italian YouTube guy who does an excellent job breaking down the harmonies for one of their earlier, simpler songs, I Saw Her Standing There: How to Sing I Saw Her Standing There Beatles Vocal Harmony - Galeazzo Frudua - YouTube
Some “bands” are entirely their producer.
You’ve heard of the “Phil Spector” sound? Spector was the producer. He produced many important hits in the early-mid Rock era, and tends to have more recognizable credit than the groups who actually performed the music.
FWIW, I think the creative balance between the four lads and Martin was just perfect. He really did complement their strengths with his own experience and skills.
The link in post 5 about the Hard Days night chord is superb.
Somehow Randy Bachman heard Lennons chord differently. Don’t think he accounted for Martins piano.
I just read the Peter Guralnick book about Sam Phillips, and he says in that book that Elvis was his own producer after the first batch of chet atkins produced sides. I find this surprising and hard to feature. He could’ve used a Sir George himself I think.