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I have what I'm sure is a simple theory question:

If I play a conventional version of Amazing Grace and begin with a C on my alto (playing C-F-A-...), I will finish with an F. The only sharp or flat that seems to makes sense along the way is a Bb and a B sounds off. Does this mean I played it in the key of F or did I begin in the key of C and finish in F, with a change along the way? And, if it's in the key of F on my alto, does that mean someone on guitar or piano would consider it to be in D? Finally, if a band is going to play it and someone calls out the key before they start, would the person say D no matter whether the person plays piano or alto?
 

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It's not really a theory question. It's more a question of convention. What do people actually do in this circumstance?
Typically, songs are called in a "concert" key, meaning the key with no transpositions. Piano is a non-transposing instrument; same for guitar. So, F "concert" is the key of F for them.
But your alto IS a transposing instrument. It is an "Eb" instrument, meaning when you "play" a C on your horn, it sounds as a concert Eb.

So, F "concert" is your "D". Knowing your transpositions is important, obviously.

For Eb instruments like yours, think DOWN a minor 3rd ( 3 half steps). Concert F is your D, which is 3 half steps below F.

Now, about Amazing Grace. The first note does not designate the key of the music. In this case, the song begins with the 5th of F, which is C. Your ears are correct to have identified F as the tonal center.
 

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And, if it's in the key of F on my alto, does that mean someone on guitar or piano would consider it to be in D? Finally, if a band is going to play it and someone calls out the key before they start, would the person say D no matter whether the person plays piano or alto?
If you play in your (alto) F the band would be in Ab.

They would call it in Ab as that is the actual concert pitch.
 

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You are playing in the key of F on the alto. That first C is just a single note, not what key you are in nor what the chord is right there.

When you play in F on the alto, you are playing in the Concert Pitch key of Ab.
The chords change during the song, but the whole song is in your key of F, Concert Ab.
As a horn player I ALWAYS say Concert pitches and keys. To anybody. It keeps things simple.


Somebody would say the song is "in the key of Ab." It is proper to say "Concert Ab", but folks that play C instruments like piano and guitar usually do not say all that.

In fact, many piano and guitar players do not even know about the transposing business.
 

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I think every part of your question was answered except how to tell what key the song is in. If it's written, then just look at the key signature. You'll have to memorize your circle of 5ths to know how the key signature tells you the key. To tell the key signature solely by ear is trickier, but your method of finding the notes that sound right, and sometimes the last note of the tune is a good way to do it.

If you have music written for guitar/piano/voice, it will be in concert key, as others have said, and you have to transpose down 1-1/2 steps for alto sax key. Go up for concert (piano) key.

You can go clockwise 3 notes on the circle to transpose concert to alto or counterclockwise 3 notes to transpose alto to concert. Maybe print it out and keep it handy until you memorize it. I use a few tricks to make it easier. It has the word BEAD on it twice, plus the sequence GCF or FCG depending on which way you go. If you go 1/2 step up from the last sharp, that's the key. For example, if the last sharp is G#, that means the key is a half step up, which is A. If you remove the last flat, the remaining flat is the key. For example, if the last flat is Ab, and you hide it, the next one is Eb. So the key is Eb. The only exception is the key of F. It has one flat, something you just have to memorize.

Circle of 5ths:
Rectangle Line Font Slope Circle
 

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As a horn player I ALWAYS say Concert pitches and keys. To anybody. It keeps things simple.
+1. This should be up in lights somewhere. Especially on the bandstand when communicating with other musicians, always, always, always, speak in concert key.

The only exception I would make to this 'rule' is when discussing something SPECIFIC to the sax, such as fingerings. And even then, make it clear you are speaking in the sax key.
 
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