Second lesson - intervals

"In the first lesson we defined the Major scale as a sequence of 8 notes, each separated by these distances:
TTSTTTS (Tone and Semitone).

Starting from the tone building of the Major scale,
let's distinguish now the possibility to introduce a tone at the same time as C,
from that of having a tone follow C.

This allows us to define the double nature of the intervals:
harmonic if the two notes are played at the same time, or melodic if a tone follows the other,
that is, when a voice ascends or descends.

Now, in order to build a Theoretic system of notes
it will be useful to assign a name to all the (harmonic or melodic) intervals generated by a sound
in relation to the other 11 in a chromatic octave.

This is more pertinent to "musical grammar" than it is to harmonic theory, but it'll be best to define this topic before beginning its discussion. And to do just that we will begin from C, naming all the intervals that this sound can form meeting the other 11 of the chromatic scale, ascending or descending.

These are all the intervals that a C can determine
with the other 11 notes of the chromatic scale.
It is evident that some notes are equivalent
(C# e D flat, for example, or F# and G flat.
The two notes presenting this equivalence are called enharmonic;
the name of the interval forming initial C changes to signal
the change in the harmonic function of the interval.

C C Unisono Root
C C# Semitono cromatico
C Db 2 min 2
C D 2 Maj
C D# 2 aug
C Ebb 3 dim 3
C Eb 3 min
C E 3 Maj
C E# 3 aug
C Fb

4 dim

C F 4 giusta
C F# 4aug
C Gb 5 dim 5
C G 5 giusta
C G# 5 aug
C Abb 6 dim 6
C Ab 6 min
C A 6 maj
C A# 6 aug
C Bbb 7 dim 7
C Bb 7 min
C B 7 Maj
C Cb 8 dim 8
C C 8 giusta
C C# 8 aug

C la tonica, da il nome alla scala
D è la 2 Maj (maggiore) di C
E è la 3 Maj di C
F è la 4 giusta di C
G è la 5 giusta di C
A 6 Maj di C
B 7 Maj di C

At this point, musical theory distinguishes the intervals in consonant and dissonant.
I would like to clarify that a consonant interval is no more pleasant or more right than a dissonant one; more precisely a consonant interval is a stable interval, therefore it is said that it implies a sense of rest On the contrary, a dissonant interval is recognized as unstable and moving, since it must resolve itself on a consonant interval.

The unison, the octave, perfect 5, 3rd and 6th. (both Major and Minor), are defined consonant intervals.
The 2nd., 7th. and 9th. (both Major and Minor), and all diminished or augmented chords are classified as dissonant.
Finally, the interval of the perfect 4th. (C – F) is considered consonant if a 3rd. or a 5th. is added to its lowest tone.

To exhaust this parenthesis - purely grammatical but necessary – it is important to note what happens when these intervals are reversed, that is to say when the one below goes above and vice versa.
I am referring here (below) to the harmonic intervals, but the same holds true also for melodic intervals.

The second interval is the reverse of the first

This brings us to note that in reverse, unison becomes the octave, the perfect intervals (4th. and 5th.) remain perfect, Major chords become Minor and vice versa, the reverse of the diminished chords become extended and viceversa.

So, in summary, how do we determine that the harmonic interval E – C (for example) is a Minor 6th.?

We have to build the Major scale from the lowest tone, that is E (E – F# - G# - A – B – C# - D#); since we have defined the 6th. tone of the Major scale of E (C#) as the interval of 6 Major (see above), the bichord E – C will be a Minor 6th. (taking C as the tonic, the equivalent interval is Ab, the consonant interval)."

And to end this"grammatical" and rather boring lesson, the Maestro assigned me about fifty intervals to be correctly denominated.

"Obviously I do not intend to verify that you have understood the procedure, because I am certain of that." he reassured me, "but I want to help you make this reasoning automatic. Music is made out of this material and we must know it well in order to handle it securely. We must start from here if we want to try and express its charm, its magic, which we haven't yet managed to divide or measure, and to which we haven't even been able to give a name."

And going from grammar to philosophy, we departed from each other, deciding that the next lesson will take place in three weeks.
Obviously I champ at the bit, but I have faith in the Maestro.

He decided to show me the System; we have agreed on the fact that its discussion won't overlook topics that I need to know, but will rather exhaust the theory of musical artistic creation in all of its parts. That is why I shall follow his method and his planning, which, according to his promise, will guarantee me a sure, correct and coherent musical writing, which is what I need in order to travel the diverse musical landscapes that I wish to visit.