Often when I have been composing, I have noticed a peculiar phenomenon. Sometimes I can't think of a new way to tweak my song and it helps to change the key. I get new ideas and can then switch back to my original key. But it matters a lot which key I switch to. There is usually one or two other keys that have a similar feel to the current one I am in.
Are there any scientifically substantiated theories about the differences between keys? Why might only a few keys preserve the original feel of my song?
For example, I have found Ludivico Eindaudi's song Nuvole Bianche (originally in A flat major) sounds very similar in A major but sounds terrible in G major and acceptable in C major.
I also find that it is necessary to listen to several stanzas. If you listen to just a few bars, the keys all sound pretty similar and pleasant. It is only over the course of the song it becomes clear the song is in the wrong keys.
Discussion of the probe tone method:
The subsequent Krumhansl and Kessler (1982) study used this method with a variety of musical contexts at the beginning of the trials. They were chosen because they are clear indicators of the key. They included the scale, the tonic triad chord, and chord cadences in both major and minor keys. These were followed by all possible probe tones in the chromatic scale, which the listeners were instructed to judge in terms of how well they fit with the preceding context in a musical sense. Different major keys were used, as were different minor keys, but the results were similar when transposed to a common tonic. Also, the results were similar independent of which particular context was used. Consequently, the data were averaged over these factors. We call the resulting values the K-K profiles, which can be expressed as vectors. The vector for major keys is: K-K major = <6.35, 2.23, 3.48, 2.33, 4.38, 4.09, 2.52, 5.19, 2.39, 3.66, 2.29, 2.88>. The vector for minor keys is: K-K minor = <6.33, 2.68, 3.52, 5.38, 2.60, 3.53, 2.54, 4.75, 3.98, 2.69, 3.34, 3.17>.
We can generate K-K profiles for 12 major keys and 12 minor keys from these. If we adopt the convention that the first entry in the vector corresponds to the tone C, the second to C#/Db, the third to D, and so on, then the vector for C major is: <6.35, 2.23, 3.48, 2.33, 4.38, 4.09, 2.52, 5.19, 2.39, 3.66, 2.29, 2.88>, the vector for C# major is: : <2.88, 6.35, 2.23, 3.48, 2.33, 4.38, 4.09, 2.52, 5.19, 2.39, 3.66, 2.29>, and so on. The vectors for the different keys result from shifting the entries to appropriate number of places to the tonic of the key.
Krumhansl and Kessler (1982) then used these data to study how the sense of key develops and changes over time. They used ten nine-chord sequences, some of which contained modulations between keys. Listeners did the probe tone task after the first chord, then after the first two chords, then after the first three chords, and continued until the full sequence was heard. This meant that 12 (probe tones) x 9 (chord positions) x 10 (sequences) = 1080 judgments were made by each listener. Each of the 90 probe tone ratings were compared with the ratings made for the unambiguous key-defining contexts. That is, each set of probe tone ratings was correlated with the K-K profiles for the 24 major and minor keys. For some of the sets of probe tone ratings (some probe positions in some of the chord sequences), a high correlation was found indicating a strong sense of key. For other sets of probe tone ratings, no key was highly correlated which was interpreted as an ambiguous sense of key.