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for example the tones C and Eb appear in Db(-5 flats), Ab(-4 flats) Eb(-3 flats) and Bb(-2 flats)(relative to the key of C).

in each key they appear in, those two tones have diffrent functions(regardless of spelling the whole chord)

considering that I'm mostly self-taught in music I would like to know how this type of analysis is called in formal music education so I could learn more about it.

also - why is it the case that its mostly flatter keys two tones share in common rather then sharper keys?

I think I read something about it how progressions tend to go into flatter keys and it seems there some fundamental reason for it?

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I would like to know how this type of analysis

I'm not sure there's really a name for it; in fact, I'm not sure "analysis" is even the right word. Rather, you're just thinking through the logistics of major keys and how two pitches fit into those major keys. It would fall under the umbrella of "music theory," but I think that's about it.

why is it the case that its mostly flatter keys two tones share in common rather then sharper keys?

This is just a byproduct of the two tones you chose, C and E♭. Since one of the two pitches has a ♭, it's understandable that the keys will be flat keys.

If we were to find the keys that have C♯ and F♯, for instance, we'd be left with C♯ (7 sharps), F♯ (6 sharps), B (5 sharps), E (4 sharps), A (3 sharps), and D (2 sharps).

I think I read something about it how progressions tend to go into flatter keys and it seems there some fundamental reason for it?

I'm not sure of this source, but if that claim is true, it might be because of the descending circle of fifths, which moves towards more flat keys (or, put another way, it subtracts sharps/adds flats to the key area).

  • perhaps "flatter" was not the right word rather both my example and your example goes counter-clockwise on the circle of fifths , that is what I observed. – Silenus Dec 12 '18 at 23:04
  • To add some thoughts, the flat keys are more used than the sharp keys, because in general they have less accidentals then their sharp twins. This can have something to do with progressions "tending to go into flatter keys". – coconochao Dec 13 '18 at 12:53
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I think the idea your question relates to is the circle of fifths.

Any key signature will have 7 pitches.

When comparing keys there will be a varying amount of pitches shared from none to 6 out of 7.

To keep things simple lets compare only major to major and minor to minor.

If you compare C major to C# major, there are no shared pitches. All 7 are different.

The greatest possible amount of shared pitches must be 1 less than 7. Obviously if all 7 pitches are shared you would be comparing the same keys.

Key whose tonics are either a descending or ascending fifth apart will differ by only one pitch. In terms of key signatures descending a fifth will add a flat (or remove a sharp) and ascending a fifth will add a sharp (or remove a flat.)

That relationship of keys by fifths is of course the circle of fifths.

also - why is it the case that its mostly flatter keys two tones share in common rather then sharper keys?

This simply isn't true, but it's easy to understand why that doesn't make sense. Music works on relative relationships. Ex. chord V7-I shows relative relationships rather than concrete labels like G7-C. These relative relationships are transposable. If two tones are shared by two keys - F & C are shared by F major and D flat major, then the same is true of any two keys 4 steps apart on the circle of fifths. B & E are shared by C major and B major.

I think I read something about it how progressions tend to go into flatter keys and it seems there some fundamental reason for it?

This sounds like a mix up of the circle of fifths and chord root progressions by descending fifths. They aren't the same thing. There is a circle of fifths arrangement of key signatures and there is the separate circle of fifths harmonic sequence. Root progression by descending fifth - ex C to F - is considered the "strongest" progression. If you casually look at the circle of fifths C major to F major looks like that chord progression and it does seem to move into keys with flats. But the complete circle of fifths harmonic sequence does not match the key signature circle of fifths.

The full circle of fifth harmonic sequence is diatonic. Notice how all the roots stay in the key of C major and the move F to b is diminished fifth...

C F bdim em am dm G C

The key signature circle of fifths is chromatic. Notice that the roots leave the key of C major by the 3rd step and all the moves are perfect fifths...

C F Bb Eb Ab Db Gb B

The point is to not mix up harmonic root progress by descending fifth with steps along the key signature circle of fifths.

  • I think this is the right answer.+1. But someone will pick up on Gb>B not being a P5P4..! – Tim Dec 14 '18 at 15:54
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for example the tones C and Eb appear in Db(-5 flats), Ab(-4 flats) Eb(-3 flats) and Bb(-2 flats)(relative to the key of C).

...snipped...

also - why is it the case that its mostly flatter keys two tones share in common rather then sharper keys?

I don't think there is a difference. That wouldn't make sense. An example similar to your example:

The tones C sharp and E appear in B (5 sharps), E (4 sharps), A (3 sharps) and D (2 sharps)

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There is a finite number of keys, and a finite number of notes. With major keys there are probably 15 (based on maximum 7 # , 7 b, and neither (C). With all the naturals, sharps and flats, there are 21 note names.But it's unusual to find keys such as B# maj, or Fb maj. Not considering bb and x, as they don't constitute keys' names. Mathematically, there are going to be common notes in certain keys. Some will have 6, some 5, right down to NO common notes. As in C maj. and C# maj. It could be argued (and probably will be...) that C#'s leading note is common , although C doesn't equal B#, only sounding the same in 12tet.

True, a C note in C doesn't function the same as it does in Ab maj. I don't think there's a name for this kind of analysis, or indeed if there's a lot of mileage in pursuing it - possibly a reason for not being named!

'Progressions going into flatter keys' - I'm sceptical on that. There's probably a 50/50.

  • There are 21 note names (excluding double sharps and double flats), not 17. They are as follows: A B C D E F G, A# B# C# D# E# F# G# and Ab Bb Cb Db Eb Fb Gb. – Lars Peter Schultz Dec 14 '18 at 13:39
  • @LarsPeterSchultz - thanks. I omitted the E#, B# and Cb, Fb, which all crop up as notes in certain keys. Corrected. – Tim Dec 14 '18 at 15:44
  • Now I love to play Chopin which means I am used to see these "odd" notes like E#, B# and Cb, Fb. I don't find them odd at all. Often they are much easier to read than the similar natural keys. An example: Say Chopin wrote a C# major chord, so I see the notes C#, E# and G#, I can see right away it is a C# chord, just like reading a word you see the whole word and doesn't spell each letter. But if Chopin instead had written the notes C#, F and G# it would be confusing and difficult to see right away that it is just a C# chord. Thus the notation with the E# is faster and easier to read. – Lars Peter Schultz Dec 15 '18 at 20:25
  • @LarsPeterSchultz - assuming the notes are in close triad form, then, yes, it's easier to read when it looks like a pattern. Chopin knew better than to use an F in key C#, though, as it would be F# in the key sig, and have to have a natural! – Tim Dec 16 '18 at 7:47
  • I don't understand what you mean by "have to have a natural". Anyway, it is not just chords but also in scale type of patterns where it makes sense to see notes like Cb. A sequence of notes like Bb-B-Bb-B compared with Bb-Cb-Bb-Cb where the latter makes sense. – Lars Peter Schultz Dec 16 '18 at 12:26

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