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I'm struggling to understand how the key signature effects a composition.

If you took an average person and played them the national anthem in any key (as long as you stay major of course) they would recognize it right away as the same song - this to me alone gravitates me think the key is a rather trivial choice when composing...

Overall question: What is a tonal composer considering when choosing a key and what does it change about the piece?

I understand that a piece is modulated to accommodate for a vocal/instrument range, but do different keys evoke different emotion than others even when the piece is the same?

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Whooooo, this is a doozie of a question! There are several approaches to this answer, some given in topo morto's comments, but I'll focus on two others:

Historical Reasons

Most modern instruments today use what is called 12-tone equal temperament. (Even wind instruments, tympani, etc. tune based on this system.) This means that that each tone is precisely 100 cents apart from the next one. C is 100 cents away from C♯, which is 100 cents away from D, etc. This wasn't always the case; throughout history there were various tuning systems. We call these "temperaments" because the pitches are "tempered" to fit into a particular system. In the Pythagorean system, perfect fifths were emphasized, which meant that major thirds were out of whack. In "concentric" systems, the system emphasized the most-used keys, meaning that keys like F♯ were basically unusable.

Thus, when past composers were using particular tuning systems, different keys could actually sound different. The "quality" of C major was different than the quality of E♭ major, and so the choice of key could have been a deliberate choice. Or if a composer knew he wanted the second section of the piece to modulate down a major third, he'd have a limited number of original tonics where both keys would be successful in a given tuning system.

But as I said, today we have 12-tone equal temperament. However, some instruments just work better in some keys. Orchestra brass will sound fuller and richer in a key like D♭ major than they will in B major, and (good) composers will use this to their advantage.

Some Remarks on Cognition

You're right that we'd all recognize the national anthem no matter what key it's in. We call it "absolute pitch" (some erroneously call it "perfect pitch") when someone can instantly recognize a pitch, a tonal level, etc. But here's something interesting! A study took several famous songs---for example, the Jeopardy! theme---and played it at two different pitch levels for a group of listeners (musicians and non-musicians alike). The majority of listeners could discern which recording was at the "actual" pitch level. (I'll try to find the source for this.) Long story short, there is good reason to believe that absolute pitch is really just long-term pitch memory, and not some innate ability to just grab pitches and keys out of thin air.

In other words, there could be cognitive reasons for using particular keys, but I would say we're still a little too early in our understanding to say for sure.

  • Ahem. Some modern instruments use 12-edo temperament, namely those that can only produce a discrete set of different pitches. For the majority of instruments, not that much changed tuning-wise – they are and were always able to play the correct just intonation, but it would always be more difficult in some keys than others. – leftaroundabout Aug 12 '16 at 21:42
  • When people tell me perfect pitch is innate I never really believed it. It sounds like you found evidence that it may not be. For example, If you knew a song was in C like "Let it be", you could just think of that root note and build every other pitch from your memory of the song. – Kolob Canyon Aug 12 '16 at 21:42
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    @KolobCanyon I reckon the problem is that most people can only notice if an entire recording is in a different key; it doesn't mean they can also “imagine” the pitch of individual notes therein without actually having that recording as a context. However, I think quite a lot of people get it more or less right if they actually sing a piece. – leftaroundabout Aug 12 '16 at 21:46
  • In the last bold part, Richard is referring to the Levitin effect. – Dekkadeci May 17 '17 at 12:08
  • @Dekkadeci Did Daniel Levatin really name that after himself? – Kolob Canyon Jan 7 at 22:35
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Sometimes the range of the instruments dictate particular keys, sometimes it is better, for playing and the sound, that certain instruments play songs in certain keys. And, yes, the vocal tessitura has a big influence on a song's key.

I guess that when a composer is writing something new, he is messing about in one key initially, probably well aware of the physical constrictions it has on the instruments he has in mind.

But as far as a song sounding very different in one key as opposed to another, probably not. Having said that, some guitar-based songs will use the guitar friendly keys of E or A, emphasising the open strings, so changing their keys will lose some authenticity. I remember having to play the intro to the Big O's 'Pretty Woman', which had been transposed to Ab, from the original A. Starting that intro almost an octave too high on guitar spoiled it somewhat, but the horns seemed happier to play in Ab rather than A.

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"I'm struggling to understand how the key signature effects a composition".

I think Richard answered the muaical questions. One thing else to consider.

It is the singer that sets the key. If a singer can't sing a song in the key of G, but but his/her voice sounds best in B, then that will be the key played. I think it is singer preference what key signature is used. Also, you should strive to play a song in any key requested.

  • Every key has it is own fingering pattern on piano and strings. Many virtuoso pros prefered black keys for fast fluent music (Chopin, Liszt, for example). You should play in all keys fluently on any chosen instrument. Some orchestra instruments are in one key (B or B flat or E flat) only. Every history period had it`s popular pitch. The majority of guitar and lute music are in the keys of open strings (or half step down). Keys of D minor and C minor seem more sad and dark to me, D major and G major are much more brighter and alive.... – VassiaAlk Aug 14 '16 at 18:29

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