The tonal system is supposed to be a simplification of the older modal system since it only consists of two modes namely the Major and minor modes. That is a kind of « swindle » since actually the so called minor mode consists of three derivative versions from old minor church modes.It would be more « honest » to state that key center has two possible tonics a major sixth apart. (CM-am)
It is not easy to define the tonal system which is a slow process so let’s assume few things
- Tonal system is made of 12 major scales and 12 minor scales (6 flat and six Sharps). In theory there are 15 scales from 0 to 7 alterations (sharps or flats)but 3 scales sound similar with flats and sharps by enharmony thanks to the equal temperament system.
- Tonality consists of 7 fifths according to the Pythagorean Principe of string length division: A string 1.5 shorter sounds a fifth higher.However the fifths series doesn’t yield directly a scale; Some division of length and new order are necessary to keep the seven tones within an octave. Example CM
- The tonal model is the major scale made of two tetrachords that yield a symmetric distribution of tone -semitone C-D-EF and G-A-BC
- Each scale degree supports a triad made of stack of diatonic (that belongs to the scale) thirds. The triads are –
- -Minor on II,III and VI
- diminished(the fifth) on VIIth degree
- The fifths circle is therefore IV-I-V-ii-vi-iii-vii Notice IV -VII form a tritone: the tonality limits
- The primary chords which supply all scale tones are grouped on the left.Their roots are the tonal notes whereas their modal notes (thirds) are grouped on the right.On the middle stands the fifth of the dominante.
(all those chords are called perfect because the bottom – top notes form a perfect fifth ) –
- the direction of the scale is opposite to the circle of fifths direction.
We can represent the tonal system as a sliding rule with a long series of fifths from Cb(7 flats) to C#(7 sharps) on the fixed part of the rule and our seven fifths ( from IV to vii) on the sliding part of the rule. The tonality is I on the sliding part and the key signature is on the fixed part facing I
Notice that numbered 5-6-7 tones on the right sound like the 7-6-5 ones on the left thanks to enharmony So the chain is closed forming a circle.
Thank to the sliding,we can see how a chord can easily be reinterpreted for modulation.
Unfortunately minor mode obscures this very simple system.
If we want to write a mirror scale (opposite) to the major scale with respect to the key signature and Tone -semitone distribution we must start with the third degree of the scale which produces a minor descending scale .
No ascending minor scale fits to these two conditions; none respects the tone -semi tone distribution.
we must start the scale on II, III or VI to have a minor third but none would produce a leading tone which require a Major third . Therefore the second tetrachord can’t be symmetric to the first one and we must add some alterations.
Notice the symmetric D mode (Dorian) which was the most frequent minor mode used during the baroque era.
With our CM scale
II (D) needs C#, III(E)requires D#, and VI(A) G# which are not the direct continuation of the fifths circle.
Mind you, that is an explanation of the problem but not the reality:Both D and E modes are to be transposed on A so only G# and F# (coming from the B of the D mode) appear.
Adding a leading tone to the a minor scale creates an unmelodic augmented second interval so the VIth degree is altered (the borrowed B from D mode) to enhance the melody
So, the minor scale has three aspects
1-Natural or descending melodic or Aeolian mode A-BC-D-EF-G-A which does not have a leading tone.
2-Harmonic: A- BC- D -EF—G#A which provides a leading tone and a bad augmented second.
3- Ascending melodic A-BC-D-E-F#-G#A. with a leading tone and an altered VI th degree to correct the unmelodic augmented second
The complete minor scale (natural plus the two ascending scales)produces 13 triads
Why A rather than D or E?
From the natural minor scale the A scale need F# and G# to complete the ascending scale.
The D (Dorian)scale would request Bb and C# and the E (Phrygian) scale would need F# ,C# and D#
So A is the nearest from the Fifths circle.
Since the A minor scale has no alteration it’s associated to the C major and our sliding rule can be expanded like this
So, to find the key signature of a minor scale one must refer to the relative major scale or the third degree of the minor scale.
It must be pointed out the reverse image of the major mode
The major numeration is In yellow
Rationale in tonal music is to consider a scale as a Pentachord and a tetrachord (with a common tone)
For a given tonic, all notes of the pentachord but the Third are common to all tonal kind of scales
Tetrachord has two movable notes (The sixth and seventh degrees)