Wait!
It isn’t a C5 dominant seventh. [slapping forehead…] It’s C augmented dominant seventh, no first, no fifth, with a B flat bass. Man, you have to twist up C like a pretzel to make it fit!
Why not just call it a B flat diminished fifth?
Here is the source, sixseatport, (say that three times fast) with more detail.
http://ocelot.cc.purdue.edu/~raybro/solmization.html
Works for me, though I doubt you will see it written that way on chord charts for the song. I like any chord that is able to pull off having two notes that are only a 1/2 step apart. My favorite example is minor 9ths.
As to the debate on the assignment of context to melody, the answer is … splunge!
Music theorists look at an entire melody to determine its key, not just the first or last notes. Now in most Western music, the last note almost always identifies the key, so it’s a good quick indicator. I am sure there are similar things in math, where an easy algorithm gives you the right answer most of the time, but not every time. I suppose it’s possible for two theorists to analyze a melody that is vague in terms of tonality, and disagree on its key, but I never heard one say “See, this is in C, because C is the first note.” That theorist should be forced to listen to Terry Riley’s “In C.” (Or maybe not, that would be coercion.)
Time to go home and diminish a fifth.
But seriously, Gilligan, if it’s diatonic, why can’t you call it any arbitrary key? I mean, isn’t key simply a “convenience” like HardCore said? Now, you might could ask, what key sig would render the fewest accidentals, but then what key do you say I’ve Seen the Saucers (EJ/BT) is in? Or for that matter, Here, There, and Everywhere (Beatles, McCartney)? It’s called the key of G, but it goes G, Em, Gm, Bb (tonic, parallel minor, relative minor, relative major).
Actually, assuming the song referenced in the thread title is in fact intended to be “Happy Birthday To You,” the proper sequence is do do re do fa mi, or, alternatively, sol sol la sol do ti.
My vote goes to sol sol la sol do ti because that way, when I sing it by its “do re mi” words, I can get to the last line and just sing “fa fa mi do re do.”
See, if you have it start at “do,” the last line has to be “si si la fa sol fa,” “si” being the solfege equivalent of a flatted “ti.”
BTW, Lib, what note exactly are you referring to when you say a song ends on the note B5?
B5…BINGO!
Well, yes, it’s just a convenience, and as hardcore said: “(but what a convenience!)” You could be use the key signature with the fewest accidentals, but if you expect to play with other musicians, or have them play your music, you’re best off to follow the conventions. This is especially true if you are playing with musicians with transposing instruments, such as pretty much all the wind instruments.
This reminds me of when I was a kid in church, and the hymn “O God, Our Help in Ages Past.” (aka Old 100th) This was in our hymnals in the key of F major, with the B flat right there on every staff. (melody only in our copies) But there is only one “B” in the tune, and it’s natural! This used to bug me, I mean, why tell me on every line that B’s are flat, but then when you finally get to the B, they make it natural?
Gilligan, I don’t know the song, but I would bet it is because of the chords, not the melody.
B5 … two million, five hindred thousand tons of spinning metal, all alone in the night.
– tracer, applying for the job of Vorlon Ambassador
The key that a string of music “belongs” to seems so transparent that it is sometimes hard to retro-analyze the process by which this assignment takes place. It’s almost like asking “How do you decide that a given object that you see is red?”
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I think it is more akin to choosing a Base numbering system to do specific math functions. If you are balancing your checkbook, you probably use Base-10. If you are a programmer, you are familiar with Base-16 because your computer likes Base-2.
Theoretically, you could do your banking transactions in Base-13, but why would you want to?
KaylasDad99
Actually, I’m referring to a chord, consisting of a B and a G sharp only — in other words, a B major chord with no third.
Gilligan
[qutoe]This was in our hymnals in the key of F major, with the B flat right there on every staff. (melody only in our copies) But there is only one “B” in the tune, and it’s natural!
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You mean there is a hymn that never uses the subdominant chord (or note)? That’s amazing. That would be like stumbling on a piece of dinner music that used no major sevenths!
Hardcore
Maybe. But what do you do about a heavily chromatic song, like the two I mentioned above? Didn’t Chick Corea once say, “Everything I write is in C.” (I think the mystical inference is that his music is so chromatic, it almost doesn’t matter.)
Hardcore, you are right, it was because of the chords, or harmony, that the song was F major, and needed the B flat. I didn’t understand that until I began studying music. I can’t recall if there was a B flat chord or not; I’ll have to check. I’m sure there were some B flats in the harmony somewhere, though.
In chromatic or atonal music I’ve played, the key signature usually has been that of C major, but I guess I never thought about it as being in C, but as being in no key at all, and thus using the no sharps or flats key signature by default.
Aw… Lib, you are just trying to get on my good side by mentioning Chick Corea and the Beatles in the same thread! 
I don’t know the song I’ve Seen the Saucers, but Here, There, and Everywhere is not very chromatic, IMO. It fits very nicely in the key of G if you look at the chord progressions. I’m not sure what section your posted progression comes from, but AFAIK, the intro goes G Bm Bb Am7 D7. The main repeating progression throughout the song is G Am7 Bm C. Interestingly enough, the bridge really changes key to Bb, but I see it written where they stay in G and use accidentals.
As to the more general question about what to do with heavily chromatic songs, I think the original creator of the tune would probably write it in whatever key they are most comfortable. I use to have a Chick Corea songbook, but it was so complicated it was like reading sanskrit.
Gilligan, if there was a Bb in the harmony, there would almost have to be a chord in the song with Bb in it. But it wouldn’t have to be a Bb chord. Gm, C7 or F11 works nicely.
HardCore
You’re right about Here, There, and Everywhere. Chromatic was a really bad label to put on it.
Phil sent me a link, which he described this way:
You can check it out here, if you like.
As I think of it, I’ve Seen the Saucers isn’t really chromatic either. It just changes keys back and forth a lot. But each key phrase is basically a tonic, dominant, subdominant, and minor third sequence.
Oh, dammit.
Gaudere, could you be a dear? A female dear? A drop of golden sun?
According to my mother, who was a professional music teacher and has a master’s degree in music education, ‘do’ always refers to the tonic note of the key.
He’s the sort to stand on a hilltop in a thunderstorm wearing wet copper armor, shouting ‘All Gods are Bastards!’
Well, yes, of course it is. By definition. But that doesn’t mean it is either the first or the last note.
True. There is no musical requirement that the tonic be either the first or last note of a melody. However, in whichever key you write “Happy Birthday,” its initial note is not on the tonic of that key, therefore it is never accurate to represent that note as ‘do’.
But that assumes the consequent.
As has been pointed out, you can write Happy Birthday in any arbitrary key, using accidentals where necessary. You can begin by singing do do re do fa mi, so long as you end with si si la fa sol fa.
The si is a flatted ti.
What is your argument against this, other than it’s unusual?