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Why the chords coming from an scale (harmonized chords) are made by using the first, third and fifth notes? Is that a convention? It's true that, for instance, in the natural major scale, these degrees have "stable" sound, but it's something beyond that?

Lucas Paiva
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    The chords derived from a major scale are not just the chord made from the first third and fifth scale degrees, there's also the second, fourth, and sixth degrees making up the minor ii chord, the third, fifth, and seventh degrees making the minor iii chord, the fourth, sixth, and octave making the major IV chord, etc. (major V, minor vi, and diminished vii). – Todd Wilcox Dec 13 '16 at 03:37
  • Adding to Todd's comment - it goes beyond, to 7ths, 9ths, 11ths, 13ths. Those notes sound good together, (consonant), or are you asking if there's a more scientific reason why they work? – Tim Dec 13 '16 at 07:52
  • The question was not clear, I'm sorry. I know that all notes are used to composite the harmony, that arrives from a scale. I meant why these chords, for instance, the first chord of the major scale has 1 3 5 notes as triad and 1 3 5 7 notes as Tetrad. The second chord has 2 4 6, etc. I meant, based on what logic these notes were selected? Why the first chord are not made by any other note from the scale? PS: For sure, C6 or C7M have other notes, but these are not the standard harmony in C major key. That was the real question, I think. – Lucas Paiva Dec 13 '16 at 23:04

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To generalize your question: why do some chords sound more stable than others? This is a difficult to answer, as harmony is largely subjective.

However, there is at least a scientific reason for the stability of specific intervals: the harmonic series. The most stable ratio is 1:1, or a unison. Then comes 2:1, which is an octave. After that is 3:1 (or octave reduced, 3:2) which is close to a perfect fifth in equal temperament. (More about temperaments below.) After that is 4:1, another octave. Then 5:4, close to a major third in equal temperament. And so on.

These intervals occur in nature. For example when you strike a single note on a piano, you can hear not only the fundamental note, but also its harmonics emanating from the actual string. In most cases, harmonics decrease sharply in volume as they go higher, so it is easier to hear the lower harmonics. Thus if you play a perfect fifth, it will sound more "stable" than if you play, for example, a tritone, because many of the harmonics match each other's frequency. A triad built with root, fifth, and major third will sound very "stable."

Older tuning systems in Western music were actually based on these ratios. However, the problem is that if you base a tuning system on ratios, that tuning system will be based on a single note, and will sound out of tune when you play in other keys. A "temperament" is a compromise of tuning that allows modulation to other keys. Equal temperament, most widely used today, has the exact same distance between each note, so intervals in all keys sound the same. The catch is that a major third is not exactly the same "perfect" interval as the 5:4 one can hear in nature. Personally I think it's close enough that it still sounds pretty "stable".

Agargara
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