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Question
i just noticed, when writing out the Cmajor scale, then the d, and e etc.
that the notes are related. eg. between
c and d, is M2
e to f is m2
g to a is M2
every interesting as well that there
are only two chords with related
minor seconds between iii and IV
and viii and I.

what is this all about?

Answer
The relationships shared among the different scales that you mentioned address the use of modes.

Using all natural pitches:

C to C is the C Ionian mode
D to D is the D Dorian mode
E to E is the E Phrygian mode
F to F is the F Lydian mode
G to G is the G Mixolydian mode
A to A is the A Aeolian mode
B to B is the B Locrian mode

Ionian mode is synonymous with the major scale. Aeolian is synonymous with the natural or pure minor scale. The other also modes have alternate names, like the Mixolydian mode, which is also known as the dominant scale. The modes listed above also have a number of other names, as exotic scales, that are used within the contexts of different styles of music.

You pointed out the second scale degree relationship between any two successive note names. Those notes do not always consist of a major second or minor second interval. They could also be labeled as a diminished second, augmented second, or if you want to go to the extreme then doubly diminished and doubly augmented intervals (the term "doubly" is interchangeable with "double"). Although it is rare, you could keep going: triple, quadruple, and so on.

Below are some examples.

Diminishing the intervals:

C to D is a major 2nd
C to Db is a minor 2nd
C to Dbb is a diminished 2nd ("bb" is read as "double flat")
C to Dbbb is a double diminished 2nd ("bbb" is read as "triple flat")

Augmenting the intervals:

C to D is a major 2nd
C to D# is an augmented 2nd
C to Dx is a double augmented 2nd ("x" is read as "double sharp")
C to D#x is a triple augmented 2nd ("#x" is read as "triple sharp")

You mentioned the minor second interval between the 3rd and 4th, and the 7th and 1st scale degrees of the major scale. You also mentioned chords, though the topic that you are addressing revolves primarily around intervals as they pertain to scales. While there is an intrinsic relationship between scales and chords, they should not be confused.

Using the C Major scale as an example, here is the interval between each successive note:

C to D is a major 2nd (whole step)
D to E is a major 2nd (whole step)
E to F is a minor 2nd (half step)
F to G is a major 2nd (whole step)
G to A is a major 2nd (whole step)
A to B is a major 2nd (whole step)
B to C is a minor 2nd (half step)

Whole step (abbreviated "W") and half step (abbreviated "H") refer to the distance between two notes.

As long as the pitches in the scale consist of the following intervals, when arranged in order of seconds, and within this specific order, they will form a major scale:

WWHWWWH

The common modes consist of the similar arrangements, only with a different pitch functioning as the primary note or tonic in the scale:

WWHWWWH is Ionian
WHWWWHW is Dorian
HWWWHWW is Phrygian
WWWHWWH is Lydian
WWHWWHW is Mixolydian
WHWWHWW is Aeolian
HWWHWWW is Locrian

To further expand on the relationships and terminology of pitches within scales, the notes in the C Major scale also have scale degree names:

C is tonic
D is supertonic
E is mediant
F is subdominant
G is dominant
A is submediant
B is leading tone

The same names apply to any major scale. If the interval is altered, thus altering the actual scale, then the scale degree name is also altered. For example, when changing B in the C Major scale to Bb, the Bb is classified as a subtonic, and the scale becomes a Mixolydian or Dominant scale. This concept applies to any of the pitches, with singular or multiple changes.

If you would like to learn more about these topics and music theory in general, check out the "Elements of Music" books by Ralph Turek.

Best of luck!

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