Have you ever wondered if you could just sit down with your instrument and figure out how it all works. Creating a couple of simple rules, we will find that scales, triads, and so on, are fairly accessible, discoverable and fun to figure out. Find an octave on your instrument and try out these simple rules.
The first rule is to keep notes as far away from each other as possible. This is important. Imagine notes as you might a group of strangers in a doctor’s office waiting room. These people have no interest in meeting one another and have only twelve chairs available to sit. They will find seats as far from one another as possible. In this way, no matter how many notes you are including as you divide the octave, place each note as far away from the next as possible.
The second rule involves a choice. If the desired sound is consonant, avoid symmetry or equal division of the octave or any interval within that octave. Conversely, if we are looking for a dissonant sound, we will use symmetry. Additionally, imagine that because of first rule, notes or people have a strong desire not to sit right next to each other and will choose symmetry to avoid such a situation.
Putting these two rules together let us imagine our group of strangers again. The chairs arranged in the circle and faced in toward the center of this circle. Now consider there are two people in the waiting room. According to the first rule these two people will prefer to have the greatest amount empty seats separating them.
The largest amount empty seats is five on the left and right. Now if they choose to sit with the greatest number of seats on their left and right, these two people will be sitting directly across from each other. They may prefer not to sit face to face. This is equal to dissonance with our notes. For a more comfortable situation the strangers might choose to sit slightly off-center. Four chairs on one side and six chairs on the other. This is a consonant situation for notes too. An interval of a fourth on one side and a fifth on the other.
Try exploring this deeper, creating further divisions. Triads, seventh chords, pentatonic scales, whole and augmented scales, major and minor scales, followed by diminished or octatonic scales will emerge. Notice that pentatonic and major/minor scales are mostly forced into a relatively consonant grouping because twelve cannot be divided evenly by those numbers. Additionally, once the group of notes has exceeded eight, then some notes will need to have two neighbors. Perhaps our imaginary waiting room participants would start getting impatient at such a point.