## Part one

*MAIN PRINCIPLES*

III. RULES TO CONSTRUCT SCALES OF AZERBAIJAN MODES

The structure of major sixths

If major sixths are constructed from each grade of the
auxiliary tetrachord, we receive a scale, consisting of successive major
sixths:

This scale could not be the basis for Azerbaijan mode, due to two tritones
are available.

Scales formed by the combination of equal diminished tetrachords
1/2 - 1 - 1/2

**The structure of perfect quarts**

If perfect quarts are constructed from each grade of the
diminished tetrachord (1/2 - 1 - 1/2), we receive a scale consisting
of successive perfect quarts, for instance:

This scale is ineligible, due to availability of chromatic run fa -
fa sharp.

**The structure of perfect quints**

If perfect quints are constructed from each grade of the
diminished tetrachord 1/2 - 1 - 1/2, we receive a scale consisting of
successive perfect quints:

This scale consists of two equal diminished tetrachords
built on the formula 1/2 - 1 - 1/2, combined by the second way of combination
(mixed one). This scale is the basis for Azerbaijan mode "Seygakh".

**The structure of minor sixths**

If minor sixths are constructed from each grade of the
diminished tetrachord, we receive a scale consisting of successive minor
sixths:

This scale may be the modulation formula for transition
from one mode to another.

The structure of major sixths

If major sixths are constructed from each grade of the
diminished tetrachord, we receive a scale, consisting of successive
major sixths:

This scale may be the modulation formula for transition
from one mode to another.

Scales formed by the combination of equal tetrachords
1/2- 11/2- 1/2

The structure of perfect quarts

If perfect quarts are constructed from each grade of the
tetrachord (1/2- 11/2- 1/), we receive a scale consisting of successive
perfect quarts, for instance:

This scale consists of two equal tetrachords 1/2- 11/2- 1/2, combined
by the first way of combination (conjoint one). This scale is the basis
for Azerbaijan mode "Chargakh".

The structure of perfect quints

If perfect quints are constructed from each grade of the
tetrachord (1/2- 11/2 - 1/2) we receive a scale consisting of successive
perfect quints, for instance:

This scale consists of two equal tetrachords 1/2- 11/2 - 1/2, combined
by the second way of combination (mixed one). This scale is the basis
for Azerbaijan mode "Chargakh" as well.

The structure of minor sixths

If minor sixths are constructed from each grade of the
tetrachord (1/2 - 11/2 - 1/), we receive a scale consisting of successive
minor sixths:

This scale may be the modulation formula for transition
from one mode to another.

The structure of major sixths

If major sixths are constructed from each grade of the
tetrachord (1/2- 11/2 - 1/2), we receive a scale, consisting of successive
major sixths:

This scale is the basis for Azerbaijan mode "Khumayun"

*B. The scale of the auxiliary mode*

1. The scales of the auxiliary Azerbaijan modes are formed by the combination
of unequal tetrachords.

2. Combination of unequal tetrachords may be expressed
by the following formulas:

1) 1 - 1 - 1/2 + 1 - 1/2 -1

2) 1 - 1 - 1/2 + 1/2 - 1 - 1

3) 1 - 1 - 1/2 + 1/2 - 1 - 1/2

4) 1 - 1 - 1/2 + 1/2 - 1 - 1

5) 1 - 1/2- 1 + 1 - 1 - 1/2

6) 1 - 1/2- 1/2 + 1/2 - 1 - 1

7) 1 - 1/2 - 1 + 1/2 - 1 - 1/2

8) 1 - 1/2 - 1 + 1/2 - 1^{1}/_{2}- 1/2

9) 1/2 - 1 - 1 + 1 - 1 - 1/2

10) 1/2 - 1 - 1 + 1 - 1/2 - 1

11) 1/2 - 1 - 1 + 1/2 - 1 - 1/2

12) 1/2 - 1 - 1 + 1/2 - 1^{1}/_{2} - 1/2

13) 1/2- 1 - 1/2+ 1 - 1 - 1/2

14) 1/2 - 1 - 1/2 + 1 - 1/2 - 1

15) 1/2 - 1 - 1/2 + 1 - 1/2 - 1

16) 1/2 - 1 - 1/2 + 1/2- 1^{1}/_{2} - 1/2

17) 1/2 - 1^{1}/_{2} - 1/2 + 1 - 1 - 1/2

18) 1/2 - 1^{1}/_{2} - 1/2 + 1 - 1/2 - 1

19) 1/2 - 1^{1}/_{2} - 1/2 + 1/2 - 1 - 1/2

20) 1/2 - 1^{1}/_{2}- 1/2 + 1/2 - 1 - 1/2

If these formulas are applied to four ways of tetrachords'
combination, then 80 various scale would be achieved. But of all these,
only formulas 4 and 17 could be applied to Azerbaijan modes. In this
case, tetrachords are combined by the second way of combination (mixed
one), as well.

The scale formed by the mixed combination of tetrachords
following the formula

1 - 1 - 1/2 with tetrachords following the formula 1 - 1 - 1/2, forms
the scale of the auxiliary Azerbaijan mode "Shakhnaz":

The scale formed by the mixed combination of tetrachords on the formula
1/2 - 1^{1}/_{2}- 1/2 with tetrachords on the formula
1 - 1 - 1/2 forms the scale of the auxiliary Azerbaijan mode "Chargah":

The scale formed by the mixed combination of tetrachords on the formula
1/2 - 1^{1}/_{2} - 1/2 with tetrachords on the formula
1 - 1 - 1/2 forms the scale of Azerbaijan mode "Saranj". Unlike
the previous scale of the auxiliary mode "Chargah" where mixed
combination is performed by a complete tone. However, in this scale
the same tetrachords are combined mixed by a semitone:

[ MAIN PRINCIPLES: page 1 2
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