Why can I play a melody starting with any key, or even change the key in the middle of the melody?

Question

I just realized that I can play any melody starting with any key on a piano, and it sounds weird only for the first key I press, and afterwards I have trouble remembering what the original sounded like.

For example, mary had a little lamb melody can be played with

1. c, bb, ab or b# a# g#
2. c#, b, a
3. d, c, a#
4. d#, c#, b
5. e, d, c
6. f, d#, c#
7. f#, e, d
8. g, f, d#
9. g#, f#, e
10. a, g, f
11. a#, g#, f#
12. b, a, g

This phenomenon really screws with my head when I'm trying to pick correct keys from memory, since any single sound i think of out of context can be satisfied by any key, in some context, and in most cases I can't quite remember the context correctly.

Can somebody explain what is going on here? Why do I remember all of these variants as equivelent, even though they're clearly distinct key sequences with quite varying key gaps in some of them? I am extremely confused, since even the basic do, re, me, fa, so, la, si, do(cdefgab) melody can be played with any key as "do", but they won't all be white consecutive keys anymore, for example, I can do so with b,c#,d#,e,f#,g#,a#,b and no longer be able to recall what the cdefgab even sounded like afterwards, and unlike original it hits every black note in one sequence.

Another consequence of this is that it's possible to, if I mess up a note, to keep playing as if I didn't mess up, pretending that that key was the key I wanted to hit, and it'll only sound weird for the instant I hit the wrong note, but not afterwards(although at the moment of the wrong note, it's tricky to realize how much to alter the original melody for it to work out). For example, I can play mary had a little lamb as follows:

a,g,f,b,c#,c#,d,d,d,e,e,e, g,f,d#,c,d,d,d, a#,g#,g#,a#,g#,f#,f#

and get really confused about what just happened - I know it sounded weird, but I can't remember what I just heard, in my memory all I remember is the original tune as if there was nothing wrong.

Answer 1

You realized two phenomena:

• Melodies are identified by the notes' pitch positions relative to a tonal center, not by their absolute pitches.
• If you move a melody line up or down, you move the tonal center as well. When that happens, your ear cannot make sense of the notes in the old key, and so it begins to re-identify what the tonal center is. After a few notes you get used to it, and it feels like the same melody again - until the next change. Deliberate relocation of the tonal center is called a modulation.

I thought your "a,g,f,b,c#,c#,d,d,d,e,e,e, g,f,d#,c,d,d,d, a#,g#,g#,a#,g#,f#,f#" idea was funny, so I made an arrangement for it:

I split the melody to segments, and every modulation spot is preceded by one or two chords that have a "dominant" function in the next key. The chords establish the new tonal center (key), preparing the ear to understand the following melody notes in their context. You could do modulations even like an abrupt "cold start" without any warning or warming up.

(Apologies for the incorrect enharmonic spelling of Cb as "B")

Answer 2

You've realised that you can play any tune in any of the twelve keys. You also may have realised that the spacing - in tones and semitones - doesn't change at all. Yes, the physical spacing does, due to the set up of black and white keys on a piano. It would be folly to have qa piano with only white keys - it would be too wide! But if you did, the spacing for the tune would be the same wherever you started.

If you played the tune on one string of a guitar, the spacing would be like that, except as you went higher, the frets would get smaller.

The making mistakes is explained by your inner music staying in the same key as you started - the wrong notes will sound wrong, but once you're back on track, they get forgotten in the pleasure of hearing the song literally back on track.

The do, re, me is interesting. Some countries use fixed do, which is always C, whereas others use moveable do, where do is the root (key) note in a key.

Also be aware that the first note of a lot of tunes is not the actual key note. That's the case with 'Mary Had a Little Lamb'. Start on your no. 12, B A G, it's actually in key G, not B. And your first example can't be right.

Answer 3

If every key was white, the pattern would be the same in each variant

Yes - and that would mean you were using an example of an isomorphic keyboard, which is a keyboard deliberately designed so that the same interval pattern relates to the same shape on the keyboard. This type of keyboard has seen an uptick in popularity recently, helped by the fact that if you don't mind playing on a touchscreen, an isomorphic layout is easy to create in software.

So although you've worked out that the various keys in which you were playing your tune needed the same interval pattern, the reason that the physical 'shape' of what you play is not the same in each case is because the traditional piano keyboard is not isomorphic.