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Here, for example, I see the following rule:

Consecutive leaps should outline a triad

What does it exactly mean?

My assumption was that, if we have a sequence of tones that leaps-wise go in one direction, then the first note of the sequence and the last note of the sequence should span a chord (triad). In other word, the interval between the first and the last note of the sequence should be 5th (interval between the first and last note of a chord consisting of 3 tones).

However, it is clear that my interpretation does not make sense, since my restriction can be fulfilled only by two leaps of 3d interval (3d + 3d = 5th).

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The idea is that two or more consecutive leaps can be difficult to sing; if these leaps outline a chord, it's a really short arpeggio and easy to sing.

For example, C-E-G (upward) is a C major chord with the notes played consecutively. (Lots of pieces start with this; Blue Danube, Marines Hymn, etc.) Other possibilities are things like E-G-C outlining a first inversion C major chord. Even larger leaps may work, the song Siboney starts with E-G-E (outlines a C chord because the harmony continuers with C-oriented melody avoiding an early B); the introduction uses Eb-G-Eb outining a C minor chord (avoiding an early Bb); the contrast is reflected in the lyrics.

Most any chords may be outlined in a melody without introducing difficulties. Even things like D-F-G-Ab-B can work (a G9 chord) in C minor as outlining the chord compensates for the Ab-B augmented second.

A good if (Very) dated book is "Exercises in Melody-Writing" by Percy Goetschius. His "rules" are suggestions on how to compose good melodies. (I put "rules" in parenthesis as Goetschius does relax restrictions as more ideas are introduced; this applies to most "rules" in music writing.)

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The background:

A triad, as commonly understood[^1], may be voiced in any position or inversion, with any of the three members in the lowest register: G-C-E spans a sixth, for example, so it's possible to "outline a triad" without limiting the intervals to consecutive thirds.

A triad can also be "spread out" or voiced across more than one octave: reading up from the bass, C-G-E would span a tenth, but it's also a triad. This spread-out voicing is called open position. But because large leaps are highly restricted in most melody/counterpoint practices, it is implied that "outline a triad" assumes a triad in close position, with no gaps.

The answer:

If we wish to "outline" a C-Major triad in this practice, there are three possible upward permutations (C-E-G, E-G-C, and G-C-E) and three possible downward (G-E-C, E-C-G, and C-G-E). In four of these six permutations, the overall or "spanning" interval is a sixth—not a fifth.


The footnote:

[^1]: Since "triad" just means "having three parts/components," there's an added implicit condition that the three members may be "stacked" in thirds. So G-C-E is a "triad" because we may arrange it in close position as C-E-G (stacked thirds); F-D-G is not, because it can't be arranged in stacked thirds.

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