Perhaps more a topic of chords / harmony, the importance of the structural triad as a melodic resource should not be overlooked. Thinking from the root, we stack a minor third then a major third interval to create the minor triad. Here is a handy picture of the building process of the proper two intervals between the three pitches of the minor triad. Example 1.

Thinking in the tonal center of C minor, the tonic or C minor triad is created by the 1st, b3rd and 5th scale degrees of the C minor scale. Here is a chart combining the pitches of the C natural minor scale with their theoretical numerical scale degrees. Example 1a.
| pitches | C | D | Eb | F | G | Ab | Bb | C |
| scale degree | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Here is a piano illustration of C, Eb, and G, (1, b3, 5). At the piano, a root position C minor triad is struck thus, illustrated by the gray keys. Example 2.

Here is the sound of the above triad in various registers and inversions. Example 2a.
Cool with this? So why is thinking in terms of the triad important as a melodic resource? By creating melodies based on the triad, we continue an ancient artistic tradition of exploring the process of how these three pitches can define and create a complete tonality, providing the basis for our story or song. And as simple as triadic melodies can be, the energy created between these three pitches can be very powerful. With the recent addition of harmony as we know it today, (added roughly 300 years ago), this ancient search is fortified and expanded by the possible combinations provided by the harmony. For the creative artist can superimpose diverse elements, using the strength of the triad to "glue things together."
For example, we commonly place a minor triadic melody over harmony of the same pitches, i.e., a minor chord. Rock and blues music is often based at this level. Example 3.
We can also place a minor triadic melody over a minor chord with a different root, common for jazz players. This gets the sound into the upper structure part of the chord. The following idea uses an A minor triad over a D minor 7 chord. Example 4.
Why not try a minor triadic melody over major chords? Again, moving into the color tones of a chord and tending towards chord substitution. Example 4.
It is partly in the magical strength of the triad that helps players to venture forth to the edges of tonality as we know it, possibly searching for the energies that exist there. Musical artists channel this energy for their listeners, who absorb it and respond in their own unique way. Thus, part of the "power of music." The following idea attempts to use a minor triadic melodic figure on the edge of tonality. Thus, a C# minor triad ( bars 19 and 20 ) over the extended chord C major 9 #11. C# minor over C major? Yep, welcome to an entry into polytonality. Example 5.
Is this extended arpeggio also a part of that "tonality without a tritone" thing? Yepper.
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