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[TITLE]CHORDS AND TRIADS
A chord is a whole of notes that played together produces an harmonic overlap. Chords are composed by a minimum of 3 notes taken from the scale to which it refers. These 3 main notes are identified as the 1th, 3rd and 5th scale degrees: i.e. a major triad for major C chord is found considering the 1th, 3rd and 5th notes of the C SDM:
C, d, E, f, G, a, b -> C, E, G
Playing only 1th and 3th degree, we'll produce a bichord, much used in Rock.

These 3 notes (degrees 1, 3, 5) are considered  CONSONANTS; adding one more third interval to the chord means that we'll consider also the 7th scale degree, called DISSONANT. Playing the degrees 1, 3, 5 and 7 will produce a more rich chord.
 
[TXT]Let's create a D major 7th:
>considering degrees 1, 3, 5 of the D SDM we'll find:
D (I),
F# (III),
A (V)
>now add the 7th degree (dissonant):
C# (VII)
 
We can find any triads of every mode of a tonality using the same method, considering the degrees 1, 3, 5 of any scale.
Look at the C Ionian structure (C,D,E,F,G,A,B) and extract the related triad (C,E,G), or move to the 2th mode (D Dorian: D,E,F,G,A,B,C) to find a minor D: D,F,A. Now add a 7th to find the chord D minor 7th: D,F,A,C.
 
We can find any chord starting from the C SDM, choosing any degree as a tonic, considering degrees 1,3,5,7 from the result scale, and comparing the distance of the notes/degrees of both the scales. We'll find some degrees moved by 1 semitone up or down, which will suggest us the name of the scale and the possible modifications.
 
[TXTE]I.e. if we wanna find a E major 7:
>E is the 3th degree (Phrygian) of the C SDM
>so we have E,F,G,A,B,C,D
>now we get degrees 1,3,5,7: E,G,B,D
>and compare the intervals of the 2 scales (C SDM and C Phrygian):
[IMG]DO_ionico.png
[IMG]DO_frigio.png
 
We'll discover that the 2th C SDM degree (D) is 1 tone far from the tonic (C), but observing the scale we've found, its 2th (F) degree is only 1 semitone far from the tonic (E): then we have a MINOR SECOND. Third degree is far 2 tones from the first in the C SDM, but there are 1.5 tones (3 semitones) between the 1st and the 3rd degree in our scale: we have a MINOR THIRD. In the end, degrees 6 and 7 are also 1 semitone low.
>play degrees 1,3,5,7 of our scale (C Phrygian) to produce an E minor [E,G,B,D]
>set 3rd degree a semitone up to produce an E major (a triad in E tonality with the same intervals of the C major scale - C SDM) [G -> G#]
>also set the 7th degree a semitone up to add a dissonant note to our triad which name now is E major 7th [D -> D#]
> set degrees 2 and 6 up to a semitone to obtain the whole E major scale (FA, DO -> F#, DO#)
[IMG]MI_ionico.png
  
We've just found our E major 7th, working around degrees 1,3,5,7 of the C SDM played starting from E (E Phrygian), comparing it with the same C Ionian (SDM) scale degrees and adjusting it as needed to have the same intervals.
 
We can produce any triad this way; playing the C SDM in the 7 possible way (using every note as tonic) we'll find some characteristic variants, described by the following main triads:
>major (3rd major and 5th perfect)
>minor (3th minor and 5th perfect)
>fifth augmented (3rd major and 5th augmented)
> quinta diminuita (3th and 5th)
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