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This is among the first things we learn in a collage level study of Harmony:  This is the result of stacking the 'C' Major Scale in 3rd intervals (up to the Triad). Every Major Scale creates this unique (and identical) group of chords (by formula). The 'sound' of this grouping of chords must be absorbed into our ear's memory. We learn to identify the sounds (at first) by giving each chord a number (a 'Roman Numeral' that represents a 'sound' within a key - by formula). We call each numeral: a "Chord Function" (to connect the ear with the memory of the brain).  There are two points to be made here that are not necessarily explicit in the textbooks: The first is about easy memorization of formula: I, IV, & V are always Major Triads --- and --- II, III, & VI are always Minor Triads -- and -- VII is always a Diminished Triad. The second point is about the ear: Any Major triad that we ever hear in our lives - will "most naturally" be heard as either: Ima, IVma, or Vma (in a Major key). --- and --- Any Minor Triad that we ever hear in our lives - will "most naturally" be heard as either: VImi, IImi, or IIImi (in a Major Key). a Cma Chord (for instance) will be heard as either: Ima in the key of 'C' Major ('C' Ionian); IVma in the key of 'G' Major ('C' Lydian); or Vma in the key of 'F' Major ('C' Mixolydian). a Dmi Chord (for instance) will be heard as either: VImi in the key of 'F' Major ('D' Aeolion); IImi in the key of 'C' Major ('D' Dorian); or IIImi in the key of 'Bb' Major ('D' Phrygian). As for the VII(dim.) triad -- though it is rarely heard in popular music (by itself) - it is the only chord type of its kind within this group of 'Diatonic Triads.' It's uniqueness allows the ear the luxury of certain orientation (certain function within a key). Because it is unique -- the ear uses it to identify (without a shred of ambiguity) the key of its 'function.' It is the reason we see (for example) the '7' in a 'G7.' --- When we see a G7 in a chord chart -- that '7' is an indication of a Vma chord function. Whether we actually 'play' the '7th' tone (beyond the triad) depends on whether we want to hear the tone of 'Fa' (an active melodic tone) in the harmony as it progresses. [Take care not to confuse the '7' (a singe extension tone) and the VII(dim.) (a 3-note triad). For the purpose of this discussion - the VII(dim.) triad is thought of as being combined with the Vma triad. --- In the key of 'C' Major - this would be G,B,D (Vma) combined with B,D,F (VII(dim.)). The tones of the G7 chord are: G,B,D,F -- the 'F' note is the extension tone we call '7' -- and is the tone 'Fa' within the key]. This is keeping it simple -- focusing on the ear's response (and early training) to 'Diatonic Harmony' (harmony of the Major Scale). "Diatonic Harmony" is often referred to as "Modal Harmony" (the two terms are [virtually] interchangeable.
We begin with the Diatonic Triads of 'C' Major (Ionian)  'Aeolian' is the mode that uses the 'Root' (the 'Tonic') of the 6th 'degree.' This means that the VI Chord becomes a I Chord. But before we change the Chord Function(s) - let's look at the Diatonic Triads of Aeolian in their native habitat... their Relative Major Scale.  Now let's begin the work of understanding the Aeolian Mode as its own Key Center from the Tonic of 'A': By Formula - the 'A' Major Scale is constructed:  When we remove the sharps (to get back to the notes of 'C' Major) -- we get the following formula:  This is the Formula for the Aeolian Mode: 1,2,b3,4,5,b6,b7 --or -- Major Scale (b3)(b6)(b7)... it's ok to memorize this because it will never change. Now, let's take a look at how the Diatonic Chord Functions of Aeolian have changed -- when it is considered to be its own Key Center [with 'Ami' functioning as the Tonic (the I Chord)]:  We might ask: Why bother learning two different chord functions for the same diatonic chords? The answer: because it changes the way they are heard (remember - this is all about training the ear). Even though the bVIma Chord of the Relative Minor Key Center is really just a IVma Chord in the 'Mother Scale' -- the root movement (in the bass) of a bVIma returning to its Tonic (Imi chord) sounds very different than the root movement of a IVma returning to its Tonic (Ima). There is also something else to be mindful of at this point: any Minor Triad that we ever hear in our lives - will (most naturally) be heard as a VImi - IImi - or IIImi - in a Major Key Center - or - as a Imi - IVmi - or Vmi in a Minor Key Center. Likewise - any Major Triad that we ever hear in our lives - will (most naturally) be heard as a Ima - IVma - or Vma in a Major Key Center - or - as a bIIIma - bVIma - or bVIIma in a Minor Key Center. This discussion has been about 'Relative Minor' (often referred to as 'Natural Minor'). Because the chord types have not changed within the diatonic sequence - it can be said that this discussion has been limited to 'Aeolian' - and could also be referred to as a discussion of Modal Minor or Diatonic Minor. In Part II of this series - we will explore 'Parallel Minor' in a way that is also 'restrictive' to diatonic ideas -- this restriction is for the purpose of training the ear for things to come.
When I hear a melody in my head - the first thing I want to know is: Where's 'Do' (the Tonic)? This tells me whether I'm hearing a Major or a Minor Key Center [this is determined by whether I'm hearing 'me' (b3) or 'mi' (natural 3rd)] - with/against the Tonic. When I first started doing this - I would reference (in my head) any Major sounds to 'C' Major -- and any Minor sounds to 'A' Minor. The reason I chose this reference was because it was comfortable. I used this method - even at times when I was hearing both - Major and Minor sounds (in relation to the same Tonic). I would spare anyone the confusion this caused by suggesting that we become comfortable with the Key Center of 'C' Minor (to get to know the sounds of the direct contrast between a Minor Key Center and a Major Key Center -- that share the same Tonic... the same perspective. Realize that what we're doing here is combining the harmony of Two Major Scales ['C' Major and 'Eb' Major] into a single palette (with a single Tonic) to train the ear. We begin by asking the question: In which Major Scale does the 'C' note reside as the sixth degree? The answer (in the case of Aeolian) is always one whole step + one half step up from the note in question -- this translates to the Eb Major Scale:  From the 'Relative Minor Tonic of 'C' - we see: 'C' Minor  Now we compare the 'C' Minor Key Center to the 'C' Major Key Center:  Here - we begin to move the chords (from 'C' Minor) that offer unique root movement (in relation to 'C' Major) 'up' into a new palette to explore:  I find it interesting that the chords in 'C' Minor (Aeolian) that offer 'unique' root movement (in relation to the key of 'C' Major) happen to be the I,IV, and V chords of its Relative Major (Eb Major). As outlined in a previous post - the diminished triad can be heard as an extension of a Vma triad function - as a V7 (Dominant Chord). We can eliminate the diminished triads in our palette by adding the 7th (extension tone) to the V Chords of the two Major Keys we are combining: 'Eb' Major (Bb7) and 'C' Major (G7):  So that finally we end up with a palette (of likely chord types - and new possibilities for root movement) that looks like this:  Diatonic Triads: Using The Root Movement Of The VII Diminished Triad Without The Diminished Sound11/15/2015
We've established that the VII(dim) can be thought of as the result of combining two triads -- Vma + VII(dim) = V7 (the V7 is just a Vma Triad with one extension tone (7) -- which happens to be 'Fa' of the 'Mother Major Scale.') Because this knowledge becomes useful when we begin to study 4-part harmony -- we've made an attempt to include the VII(dim) Triad Function (in the theory). But, while the sound of the VII(dim) is excellent for ear training -- the 'angular' sound of the Diminished Triad is not commonly heard in the context of modern modal harmony. However, the functional root movement (VII in the bass) is absolutely essential in modern modal harmony. Here's how we exclude the VII(dim) triad sound while utilizing the 'VII' Function's root movement: The Key Center of 'C' Major ('C' Ionian) would look like this:  The G/B is called a 'Slash Chord' -- it is a G Major Triad with the B-note in the bass (it is an 'inversion' of the G triad). [For guitar players - it may help to know that this can be as simple as a two-note chord (G-note with a B-note in the bass -- a minor 6th interval that we all get to know well when we are learning tunes)]. The Key Center of 'A' Minor ('A' Aeolian) would look like this:  The Key Center of 'Eb' Major ('Eb' Ionian) would look like this:  The Key Center of 'C' Minor ('C' Aeolian) would look like this:  The combination of the 'C' Major and 'C' Minor Key Centers looks like this:  |