Auxiliary tetrachords structured in the second, third, and fourth degrees of the main tetrachords by intermediate tones, are also of great importance in the formation of scales.
Here are examples based on the auxiliary tetrachords:

Out of the above tetrachords:

Tetrachord a is perfect one; its structure is represented by the formula: 1-¹/₂ -1.

Tetrachord b is perfect, too; formula of its structure is ¹/₂ -1-1.

Tetrachord с is an increased tetrachord; formula of its structure is 1 - 1 - 1 (a tritone).

Each tetrachord degree structured by formula 1 - 1 - ¹/₂ (main) and built by formula 1-¹/₂ -1 (auxiliary) is also good for a satisfactory resolution of musical phrases and cadences.

Within frameworks of the main tetrachord:

An example based on the perfect auxiliary tetrachord from the second step:

This is also good for a satisfactory resolution of all degrees of auxiliary tetrachords constructed by formula ¹/₂ -1-1 with exception of the fourth degree due to its strong inclination to conclusion in the third degree:

As to the tetrachord constructed by formula I -1-1 (tritone), none of this tetrachord degrees can be good for satisfactory resolution of musical phrases or cadences. It is due to the functional interrelation of these tetrachords degrees. They are not distinctly expressed due to lack of semitones. Therefore, we observe complete lack of tritones in Azerbaijani modes, which scales are combined with equal tetrachords.

However, tritone is an unavoidable phenomenon when the 2-nd way of tetrachords combination (mixed combination) is applied. We get a new scale consisted of gradual number of perfect quintes by this way of combination. Then we face a dilemma: whether avoid the tritone as ineligible scale for the formation of meaningful musical phrases, or avoid the quinte structure though the latter, compared to the quarte structure, is a further step in the musical art's development history.

But there is the 3-rd way: to violate the gradual succession of three complete tones of tritone by semitone inclusion. Tritone is unfit because of succession of three complete tones, not because its first and last degrees form the interval of increased quarte. Hence, raising and lowering one of the medial tones, we can achieve the violation of three complete tones succession:

Middle sounds of tritone in the above scale are sol and la . In the quinte circle the most suitable alternation for sol is sol-sharp, for la is la flat.
If we change sol for sol sharp, then the scale in example 20 can be presented as follows:

Succession of three complete tones violates the quinte consequence of the scale, as well. To restore the violated perfect quinte, it is necessary to raise the first degree of the scale (do sharp), and then one can receive a correctly arranged scale consisted of gradual succession of perfect quintes:

2-nd way to violate succession of three complete tones is to transform la into la flat, and then the scale in example 20 will be presented as follows:

Succession of three complete tones violates the quinte consequence of the scale, as well. To restore the violated perfect quinte, it is necessary to lower the second degree of the scale (re flat). Then one could achieve the following correctly arranged scale consisted of gradual succession of perfect quintes, like this:

The scale in example 24 consists of two tetrachords structured by formula ¹/₂- 1¹/₂ - ¹/₂, i.e. the 2-nd way of combination (separate) is involved. In the tetrachord structured by formula ¹/₂ - 1¹/₂ - ¹/₂, the 1-st and 4-th degrees can function as the main tones of the scale.

New interval of the increased second appears in examples 21 and 23. All the above shows the increased second to become the result of the violation of three complete tones' gradual succession. It is achieved by alternation of triton's middle tones.