In difficult keys, is it really best to think in terms of accidentals?
I know that every major and minor scale can be thought of as the notes of a C diatonic with specific sharp and flat modifications. This way of thinking works well for simple keys like G, D, A, F, etc. but for me it kind of falls apart with keys that really far from C on the circle of fourths, like Db, Gb, etc. For those I just end up memorizing which notes are in the scales and thinking of the chromatic scale relative to the key sort of as a group of 12 equally important notes. This also makes it easier because it avoids the whole switch at like C# major to Gb major and having to change back and forth from sharps to flats.
Is there any reason not to think like this? Do the notes of C diatonic always have to have special preference in our playing? I'm specifically asking from a jazz perspective, but all thoughts are welcome.
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Our system of naming notes forces the sort of thinking you describe to a certain extent. But try to develop away from it - let every key and scale have its own identity. Quite soon you won't be spelling out the note names consciously, any more than you spell out the individual letters while reading this.
It seems completely useless to me to think in terms of "C diatonic with specific sharp and flat modifications" with regard to any modes not using C as a tonic. That sounds like approaching music from the angle of the keys of a particular instrument rather than notes. Our notation system is based on the C major scale, sure. That's like a computer keyboard being based on the "qwerty" arrangement minimizing type levers of mechanical typewriters sticking together.
It's still not a basis for understanding poetry, even though poetry is written on such keyboards.
I play various instruments, like violin and chromatic button accordion, and you work in the relative scales musically in either. While I have little experience with a piano keyboard, I would consider it awfully strange to think of musical material in terms of "C major with modifications" rather than a particular tonic and scale/mode.
The execution might be viewed through the lens of the exercised mechanics (and the various levers will be subjected to according amounts of wear) but I would consider it surprising if a typical player would have much to gain from this view.
Everyone processes information differently, so you have to do what works for you. When I play trumpet, every note to me is a fingering, whether 2 & 3 is Eb or D# doesn't even cross my mind. I've practiced every scale so much that the muscle memory is far more important than the mental memory of how the scale is constructed.
That being said, a decent jazz musician ought to be able to transpose in his head. For example, you may need to be able to play a saxophone part when only a piano score is available. Also, you need to know your scales and how they function in order to improvise well. In those cases, I'm not sure whether your approach will hinder or help.
You can certainly try your method, but if you have trouble transposing or improvising, consider trying to work it out the traditional way.
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