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I watched Adam Neely's video on polytonality and came across a special case of polytonality. He was playing and singing Mary Had a Little Lamb in 2 different keys.

The keys were a minor third apart and both were major keys.

Here are the pitch classes of the keys used:

C major:

C D E F G A B C

Eb major:

Eb F G Ab Bb C D Eb

The result registers in my ears as being in a single key, C minor.

Why is it that these 2 unrelated keys sound like a single key related to both of them? Does it have to do with both keys being major and them being a minor third apart?

leftaroundabout
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Caters
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2 Answers2

6

Eb major is the relative major of C minor. The C major tonality centers your ear on the C root, and throwing Eb major on top of it also points your ear to C minor because of the common tones between the two keys, namely C, F, and G - the roots of the I/i, IV/iv and V/v chords of both C major and C minor respectively, the 3 most important chords in "tonal" harmony. It also is important that the Eb tonality was placed in a higher register, as (for various reasons) your ear will gravitate toward C as being the bass against which Eb is contrasted (as opposed to your ear hearing the Eb tonality as the "bass" tonality). It's a bit of a musical "optical illusion," and not so an extreme version of polytonality, where completely unrelated keys might be put together (e.g., C major and F# major, as in Stravinsky's Petrushka, etc).

LSM07
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Here's the exact part he's playing:

X:1
L:1/8
M:C
K:C
%%score T B
V:T            clef=treble
V:B            clef=bass
% 1
[V:T] GF       _EF      GG       G2       | FF       F2        G_B      B2
[V:B] C,[E,G,] C,[E,G,] C,[E,G,] C,[E,G,] | D,[G,B,] D,[G,B,]  C,[E,G,] C,[E,G,]
[V:T] GF       _EF      GG       GG       | FF       GF        _E4
[V:B] C,[E,G,] C,[E,G,] C,[E,G,] C,[E,G,] | D,[G,B,] D,[G,B,]  C,4

I've use the signature of C for both parts, which highlights what you're hearing: most of the notes in the melody actually fit perfectly well in the accompaniment's C-major, only a couple of ♭ accidentals are out. As LSM07 said, those ♭ notes are perceived as borrowed from the isotonic minor mode, i.e. C-minor. You might see them as blue notes: in blues, the accompaniment is usually in major but the melody often deviates from the major thirds downwards to make it, well, “blue” (usually with some microtonal bending though).

If you list the resultant harmonies, it's basically this:

X:1
L:1/8
M:C
K:C
%%score T B
V:B            clef=bass
% 1
[V:B] "C"[C,E,G,]2 "cm"[C,_E,G,] "C"[C,=E,G,]3 [C,E,G,]2 | "G7"[D,G,B,F,]2 [D,F,G,B,]2  "C"[C,E,G,] "C7"[C,E,G,_B,] [C,E,G,B,]2
[V:B] "C"[C,E,G,]2 "cm"[C,_E,G,] "C"[C,=E,G,]3 [C,E,G,]2 | "G7"[D,G,B,F,]4   "cm"[C,_E,G,]4

The only thing that's really jarring here is that it actually ends on minor, giving a kind of inverse Picardy Third effect.

leftaroundabout
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  • How do you get notes and staves to show up in the post without using images? I have always used images to show the notes and staves in my posts. I am thinking of posting a question about how to have my trio end, specifically whether or not to have the violin do a double stop and am thinking of doing the notes in the gray boxes. But I have no idea how to do that. – Caters Mar 15 '19 at 16:29
  • https://music.meta.stackexchange.com/questions/2782/documentation-for-abcjs?cb=1 – leftaroundabout Mar 16 '19 at 08:06