Armodue harmony: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:~~tetraF~~|~~tetraF~~]] and made on <tt>2010-09-~~14 17~~:26:00 UTC</tt>.

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-09-15 10:59:11 UTC</tt>.

: The original revision id was <tt>~~162645347~~</tt>.

: The original revision id was <tt>162831079</tt>.

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Line 303:

="Geometric" harmonic constructions with Armodue=

The composer Scriabin has based much of his compositions on nucleopolar accordances.

The composer Scriabin has based much of his compositions on "nucleopolar accordances" or "chord centers" (Klangzentrum).

To understand the nature of such accordances we should refer to specular reflections of light in a crystal, according to a ~~tidy~~ symmetry.

To understand the nature of such accordances we should refer to specular reflections of light in a crystal, according to a strict central symmetry.

~~{ ! -- rough translation begins here --}~~

An image that comes in mind about is the eight pointed 'star' that sometimes appears in a photo area when the lens faces a rather intense light source.

Scriabin's idea is to render {paint?} this optical phenomena through the sounds.

Hence the formation of a center-note (central light source) from which depart upper interval-rays and relative higher notes and, by symmetry or reflection law, lower reflected rays-intervals with equal amplitude but with reversed direction and the corresponding notes lower than the central note.

The central note is thus more properly called nucleopolar note, a real mirror where the lower intervals and low notes are reflected in the higher intervals and high notes.

The resulting chord - built in perfect central symmetry or nucleopolarity - constitutes the fundamental sound system to which we will refer in the texture of the melodies and architecture of the chords.

The modulation principle, in this environment, is to be be meant as minimal andgradual variation of the size of one or several intervals that are pivoted on the chord's nucleopolar note, or - more drastically - to be interpreted as a radical and brusque transformation of the same intervals.

In Armodue, nucleopolar harmony cans find a wider and more perfect application , compared to the twelve notes system. In fact, a sixteen notes scale seems already to contain implicitly the central symmetry principle (sixteen is the perfect square of a perfect square -4- and corresponds to the mandala archetype as conceived in almost all cultures and traditions of the world: a wheel with eight or sixteen spokes).

Let's assume, for example, the note 5 as nucleopolar. The note 5 will work as a mirror in which lower and higher intervals and notes will reflect.

If we elect the three intevals of 6, 8 and 13 eka, it will generate the following sound structure (read the notes from left to right in an orderly proceeding from low to high):

~~An image that comes in mind about is the eight pointed 'star' sometimes appear in a photo area when the lens is stroke by a rather intense light source.~~

~~The Scriabin idea, so, is to render {paint?} this optical phenomena through the sounds.~~

From here the formation of a center-note (luminous central source) from which departs upper interval-rays and relative higher notes and, for simmetry or specularity law, lower reflected rays-intervals with equal amplitude but with upside-down direction and with relative notes lower than central note.

~~The central note so is called much properly nucleopolar note, out-and-out mirror where lower intervals and low notes reflects themselves in the higher intevals and the high notes.~~

~~The resulting chord - builded in perfect central simmetry or nucleopolarity - be the main sound plant at whom referring in the melody texture and int hte chord's architecture.~~

~~The modulation principle, in this sphere, must be meant as the least and~~

gradual variation of wideness of one or several intervals that are pivoted on the chord's nucleopolar note, or - more drastically - must be read as a radical and brusque transformation of the same intervals.

In Armodue, the nucleopolar harmony cans find a wider and more perfect enforcement, compared to twelve notes system. IN fact, a sixteen notes scale seems already to contain implicitly the central simmetry principle (sixteen is the perfect square of a perfect square -4- and corresponds to the mandala archetype as conceived in the almost entirety of world's cultures and traditions: an eight or sixteens rays wheel).

~~Let's assume, if example, the note 5 as nucleopolar. The note 5 will work as a mirror in which lower and higher intervals and notes will reflects.~~

~~If we elect the three intevals of six, eight and thirteen eka it will generate the sound structure (readed notes from left to right proceed neatly from low to high):~~

7 - 9 - 1# - 5 - 8 - 9 - 3

As we can verify, from the note 5 ~~it spreads~~ the two mirrored ~~six~~ eka intervals (defined by notes 1# - 5 and 5 - 8), the two intervals of ~~eight~~ eka (defined by notes 9 - 5 and 5 - 9) and the two intevals of ~~thirteen~~ eka (defined by notes 7 - 5 and 5 - 3).

We have so obtained three notes lower than nucleopolar 5 (the 7, 9 and 1#) and three higher than the same note 5 (~~the~~ 8, 9, 3 ~~notes~~)

As we can verify, from the note 5 the two mirrored 6 eka intervals spread (defined by notes 1# - 5 and 5 - 8), the two intervals of 8 eka (defined by notes 9 - 5 and 5 - 9) and the two intevals of 13 eka (defined by notes 7 - 5 and 5 - 3).

The sound structure so obtained can be used as is in the construction of ~~melody~~ and chords, or it can be liable to undergo microvariations and be modulated.

If example, we can just bring a slight variation - so an ~~asimmetry~~ - that momentarily ~~destabilize~~ but in a significant way the strict "crystallinity" of sound ~~altering~~ the note 1# for bend one eka (~~substituting with~~ note 2):

We have thus obtained three notes lower than the nucleopolar note 5 (the notes 7, 9 and 1#) and three higher than the same note 5 (thenotes 8, 9, 3)

The sound structure obtained this way can be used as is in the construction of melodies and chords, or it can be liable to undergo microvariations and be modulated.

For example, we can just bring a slight variation - hence an asymmetry - that momentarily but in a significant way destabilizes the strict "crystallinity" of the sound raising the note 1# for bend one eka (replace it by note 2):

7 - 9 - 2 - 5 - 8 - 9 - 3

Later, we can restore the perfect equilibrium and ~~simmetry~~ of ~~sonor~~ structure altering in equal sense and contrary the note 8 that balances the note 2 (the 8 so goes down - in diametrally opposite way - of one eka and so ~~substituted with~~ note 7#):

Later, we can restore the perfect equilibrium and symmetry of the sound structure altering in equal sense and contrary motion the note 8 that balances the note 2 (the 8 so goes down - in diametrally opposite way - of one eka and so is replaced by note 7#):

7 - 9 - 2 - 5 - 7# - 9 - 3

~~The shown microvariation principle can be obviously applied also to more than a single note simultaneously.~~

~~In other circumstances, we can integrate the original structure with the addition of new intervals and notes or changing radically the structure by employing different generator intervals.~~

The shown microvariation principle can obviously be applied also to more than a single note simultaneously.

In other circumstances, we can integrate the original structure with the addition of new intervals and notes or change the structure radically by employing different generator intervals.

~~{ ! -- end of rough translation --}~~

----

Chapter 5:

Line 652:

Line 664:

<h1 id="toc21"><a name="x&quot;Geometric&quot; harmonic constructions with Armodue"></a>&quot;Geometric&quot; harmonic constructions with Armodue</h1>

The composer Scriabin has based much of his compositions on nucleopolar accordances.

The composer Scriabin has based much of his compositions on &quot;nucleopolar accordances&quot; or &quot;chord centers&quot; (Klangzentrum).

To understand the nature of such accordances we should refer to specular reflections of light in a crystal, according to a strict central symmetry.

An image that comes in mind about is the eight pointed 'star' that sometimes appears in a photo area when the lens faces a rather intense light source.

Scriabin's idea is to render {paint?} this optical phenomena through the sounds.

Hence the formation of a center-note (central light source) from which depart upper interval-rays and relative higher notes and, by symmetry or reflection law, lower reflected rays-intervals with equal amplitude but with reversed direction and the corresponding notes lower than the central note.

The central note is thus more properly called nucleopolar note, a real mirror where the lower intervals and low notes are reflected in the higher intervals and high notes.

The resulting chord - built in perfect central symmetry or nucleopolarity - constitutes the fundamental sound system to which we will refer in the texture of the melodies and architecture of the chords.

The modulation principle, in this environment, is to be be meant as minimal andgradual variation of the size of one or several intervals that are pivoted on the chord's nucleopolar note, or - more drastically - to be interpreted as a radical and brusque transformation of the same intervals.

~~To understand~~ the ~~nature of such accordances we should refer~~ to ~~specular reflections~~ of ~~light in~~ a ~~crystal, according~~ to a ~~tidy symmetry~~.

In Armodue, nucleopolar harmony cans find a wider and more perfect application , compared to the twelve notes system. In fact, a sixteen notes scale seems already to contain implicitly the central symmetry principle (sixteen is the perfect square of a perfect square -4- and corresponds to the mandala archetype as conceived in almost all cultures and traditions of the world: a wheel with eight or sixteen spokes).

~~{ ! -- rough translation begins here --}~~

Let's assume, for example, the note 5 as nucleopolar. The note 5 will work as a mirror in which lower and higher intervals and notes will reflect.

If we elect the three intevals of 6, 8 and 13 eka, it will generate the following sound structure (read the notes from left to right in an orderly proceeding from low to high):

~~An image that comes in mind about is the eight pointed 'star' sometimes appear in a photo area when the lens is stroke by a rather intense light source. ~~

~~The Scriabin idea, so, is to render {paint?} this optical phenomena through the sounds. ~~

From here the formation of a center-note (luminous central source) from which departs upper interval-rays and relative higher notes and, for simmetry or specularity law, lower reflected rays-intervals with equal amplitude but with upside-down direction and with relative notes lower than central note.

~~The central note so is called much properly nucleopolar note, out-and-out mirror where lower intervals and low notes reflects themselves in the higher intevals and the high notes. ~~

~~The resulting chord - builded in perfect central simmetry or nucleopolarity - be the main sound plant at whom referring in the melody texture and int hte chord's architecture. ~~

~~The modulation principle, in this sphere, must be meant as the least and ~~

gradual variation of wideness of one or several intervals that are pivoted on the chord's nucleopolar note, or - more drastically - must be read as a radical and brusque transformation of the same intervals.

In Armodue, the nucleopolar harmony cans find a wider and more perfect enforcement, compared to twelve notes system. IN fact, a sixteen notes scale seems already to contain implicitly the central simmetry principle (sixteen is the perfect square of a perfect square -4- and corresponds to the mandala archetype as conceived in the almost entirety of world's cultures and traditions: an eight or sixteens rays wheel).

~~Let's assume, if example, the note 5 as nucleopolar. The note 5 will work as a mirror in which lower and higher intervals and notes will reflects. ~~

~~If we elect the three intevals of six, eight and thirteen eka it will generate the sound structure (readed notes from left to right proceed neatly from low to high): ~~

7 - 9 - 1# - 5 - 8 - 9 - 3

As we can verify, from the note 5 ~~it spreads~~ the two mirrored ~~six~~ eka intervals (defined by notes 1# - 5 and 5 - 8), the two intervals of ~~eight~~ eka (defined by notes 9 - 5 and 5 - 9) and the two intevals of ~~thirteen~~ eka (defined by notes 7 - 5 and 5 - 3).

We have so obtained three notes lower than nucleopolar 5 (the 7, 9 and 1#) and three higher than the same note 5 (~~the~~ 8, 9, 3 ~~notes~~)

As we can verify, from the note 5 the two mirrored 6 eka intervals spread (defined by notes 1# - 5 and 5 - 8), the two intervals of 8 eka (defined by notes 9 - 5 and 5 - 9) and the two intevals of 13 eka (defined by notes 7 - 5 and 5 - 3).

The sound structure so obtained can be used as is in the construction of ~~melody~~ and chords, or it can be liable to undergo microvariations and be modulated.

If example, we can just bring a slight variation - so an ~~asimmetry~~ - that momentarily ~~destabilize~~ but in a significant way the strict &quot;crystallinity&quot; of sound ~~altering~~ the note 1# for bend one eka (~~substituting with~~ note 2):

We have thus obtained three notes lower than the nucleopolar note 5 (the notes 7, 9 and 1#) and three higher than the same note 5 (thenotes 8, 9, 3)

The sound structure obtained this way can be used as is in the construction of melodies and chords, or it can be liable to undergo microvariations and be modulated.

For example, we can just bring a slight variation - hence an asymmetry - that momentarily but in a significant way destabilizes the strict &quot;crystallinity&quot; of the sound raising the note 1# for bend one eka (replace it by note 2):

7 - 9 - 2 - 5 - 8 - 9 - 3

Later, we can restore the perfect equilibrium and ~~simmetry~~ of ~~sonor~~ structure altering in equal sense and contrary the note 8 that balances the note 2 (the 8 so goes down - in diametrally opposite way - of one eka and so ~~substituted with~~ note 7#):

Later, we can restore the perfect equilibrium and symmetry of the sound structure altering in equal sense and contrary motion the note 8 that balances the note 2 (the 8 so goes down - in diametrally opposite way - of one eka and so is replaced by note 7#):

7 - 9 - 2 - 5 - 7# - 9 - 3

~~The shown microvariation principle can be obviously applied also to more than a single note simultaneously. ~~

~~In other circumstances, we can integrate the original structure with the addition of new intervals and notes or changing radically the structure by employing different generator intervals. ~~

The shown microvariation principle can obviously be applied also to more than a single note simultaneously.

In other circumstances, we can integrate the original structure with the addition of new intervals and notes or change the structure radically by employing different generator intervals.

~~{ ! -- end of rough translation --} ~~

<hr />

Chapter 5:

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:tetraF|tetraF]] and made on <tt>2010-09-14 17:26:00 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2010-09-15 10:59:11 UTC</tt>.<br>
-: The original revision id was <tt>162645347</tt>.<br>
+: The original revision id was <tt>162831079</tt>.<br>
 : The revision comment was: <tt></tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
@@ Line 303: / Line 303: @@
 ="Geometric" harmonic constructions with Armodue=
-The composer Scriabin has based much of his compositions on nucleopolar accordances.
+The composer Scriabin has based much of his compositions on "nucleopolar accordances" or "chord centers" (Klangzentrum).
-To understand the nature of such accordances we should refer to specular reflections of light in a crystal, according to a tidy symmetry.
+To understand the nature of such accordances we should refer to specular reflections of light in a crystal, according to a strict central symmetry.
-{ ! -- rough translation begins here --}
+An image that comes in mind about is the eight pointed 'star' that sometimes appears in a photo area when the lens faces a rather intense light source.
+Scriabin's idea is to render {paint?} this optical phenomena through the sounds.
+Hence the formation of a center-note (central light source) from which depart upper interval-rays and relative higher notes and, by symmetry or reflection law, lower reflected rays-intervals with equal amplitude but with reversed direction and the corresponding notes lower than the central note.
+The central note is thus more properly called nucleopolar note, a real mirror where the lower intervals and low notes are reflected in the higher intervals and high notes.
+The resulting chord - built in perfect central symmetry or nucleopolarity - constitutes the fundamental sound system to which we will refer in the texture of the melodies and architecture of the chords.
+The modulation principle, in this environment, is to be be meant as minimal andgradual variation of the size of one or several intervals that are pivoted on the chord's nucleopolar note, or - more drastically - to be interpreted as a radical and brusque transformation of the same intervals.
+In Armodue, nucleopolar harmony cans find a wider and more perfect application , compared to the twelve notes system. In fact, a sixteen notes scale seems already to contain implicitly the central symmetry principle (sixteen is the perfect square of a perfect square -4- and corresponds to the mandala archetype as conceived in almost all cultures and traditions of the world: a wheel with eight or sixteen spokes).
+Let's assume, for example, the note 5 as nucleopolar. The note 5 will work as a mirror in which lower and higher intervals and notes will reflect.
+If we elect the three intevals of 6, 8 and 13 eka, it will generate the following sound structure (read the notes from left to right in an orderly proceeding from low to high):
-An image that comes in mind about is the eight pointed 'star' sometimes appear in a photo area when the lens is stroke by a rather intense light source.
-The Scriabin idea, so, is to render {paint?} this optical phenomena through the sounds.
-From here the formation of a center-note (luminous central source) from which departs upper interval-rays and relative higher notes and, for simmetry or specularity law, lower reflected rays-intervals with equal amplitude but with upside-down direction and with relative notes lower than central note.
-The central note so is called much properly nucleopolar note, out-and-out mirror where lower intervals and low notes reflects themselves in the higher intevals and the high notes.
-The resulting chord - builded in perfect central simmetry or nucleopolarity - be the main sound plant at whom referring in the melody texture and int hte chord's architecture.
-The modulation principle, in this sphere, must be meant as the least and
-gradual variation of wideness of one or several intervals that are pivoted on the chord's nucleopolar note, or - more drastically - must be read as a radical and brusque transformation of the same intervals.
-In Armodue, the nucleopolar harmony cans find a wider and more perfect enforcement, compared to twelve notes system. IN fact, a sixteen notes scale seems already to contain implicitly the central simmetry principle (sixteen is the perfect square of a perfect square -4- and corresponds to the mandala archetype as conceived in the almost entirety of world's cultures and traditions: an eight or sixteens rays wheel).
-Let's assume, if example, the note 5 as nucleopolar. The note 5 will work as a mirror in which lower and higher intervals and notes will reflects.
-If we elect the three intevals of six, eight and thirteen eka it will generate the sound structure (readed notes from left to right proceed neatly from low to high):
 - 9 - 1# - 5 - 8 - 9 - 3
-As we can verify, from the note 5 it spreads the two mirrored six eka intervals (defined by notes 1# - 5 and 5 - 8), the two intervals of eight eka (defined by notes 9 - 5 and 5 - 9) and the two intevals of thirteen eka (defined by notes 7 - 5 and 5 - 3).
-We have so obtained three notes lower than nucleopolar 5 (the 7, 9 and 1#) and three higher than the same note 5 (the 8, 9, 3 notes)
+As we can verify, from the note 5 the two mirrored 6 eka intervals spread (defined by notes 1# - 5 and 5 - 8), the two intervals of 8 eka (defined by notes 9 - 5 and 5 - 9) and the two intevals of 13 eka (defined by notes 7 - 5 and 5 - 3).
-The sound structure so obtained can be used as is in the construction of melody and chords, or it can be liable to undergo microvariations and be modulated.
-If example, we can just bring a slight variation - so an asimmetry - that momentarily destabilize but in a significant way the strict "crystallinity" of sound altering the note 1# for bend one eka (substituting with note 2):
+We have thus obtained three notes lower than the nucleopolar note 5 (the notes 7, 9 and 1#) and three higher than the same note 5 (thenotes 8, 9, 3)
+The sound structure obtained this way can be used as is in the construction of melodies and chords, or it can be liable to undergo microvariations and be modulated.
+For example, we can just bring a slight variation - hence an asymmetry - that momentarily but in a significant way destabilizes the strict "crystallinity" of the sound raising the note 1# for bend one eka (replace it by note 2):
 - 9 - 2 - 5 - 8 - 9 - 3
-Later, we can restore the perfect equilibrium and simmetry of sonor structure altering in equal sense and contrary the note 8 that balances the note 2 (the 8 so goes down - in diametrally opposite way - of one eka and so substituted with note 7#):
+Later, we can restore the perfect equilibrium and symmetry of the sound structure altering in equal sense and contrary motion the note 8 that balances the note 2 (the 8 so goes down - in diametrally opposite way - of one eka and so is replaced by note 7#):
 - 9 - 2 - 5 - 7# - 9 - 3
-The shown microvariation principle can be obviously applied also to more than a single note simultaneously.
-In other circumstances, we can integrate the original structure with the addition of new intervals and notes or changing radically the structure by employing different generator intervals.
+The shown microvariation principle can obviously be applied also to more than a single note simultaneously.
+In other circumstances, we can integrate the original structure with the addition of new intervals and notes or change the structure radically by employing different generator intervals.
-{ ! -- end of rough translation --}
 ----
 Chapter 5:
@@ Line 652: / Line 664: @@
 &lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="x&amp;quot;Geometric&amp;quot; harmonic constructions with Armodue"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;&amp;quot;Geometric&amp;quot; harmonic constructions with Armodue&lt;/h1&gt;
   &lt;br /&gt;
-The composer Scriabin has based much of his compositions on nucleopolar accordances.&lt;br /&gt;
+The composer Scriabin has based much of his compositions on &amp;quot;nucleopolar accordances&amp;quot; or &amp;quot;chord centers&amp;quot; (Klangzentrum).&lt;br /&gt;
+&lt;br /&gt;
+To understand the nature of such accordances we should refer to specular reflections of light in a crystal, according to a strict central symmetry.&lt;br /&gt;
+&lt;br /&gt;
+An image that comes in mind about is the eight pointed 'star' that sometimes appears in a photo area when the lens faces a rather intense light source.&lt;br /&gt;
+&lt;br /&gt;
+Scriabin's idea is to render {paint?} this optical phenomena through the sounds.&lt;br /&gt;
+&lt;br /&gt;
+Hence the formation of a center-note (central light source) from which depart upper interval-rays and relative higher notes and, by symmetry or reflection law, lower reflected rays-intervals with equal amplitude but with reversed direction and the corresponding notes lower than the central note.&lt;br /&gt;
+&lt;br /&gt;
+The central note is thus more properly called nucleopolar note, a real mirror where the lower intervals and low notes are reflected in the higher intervals and high notes.&lt;br /&gt;
+&lt;br /&gt;
+The resulting chord - built in perfect central symmetry or nucleopolarity - constitutes the fundamental sound system to which we will refer in the texture of the melodies and architecture of the chords.&lt;br /&gt;
+&lt;br /&gt;
+The modulation principle, in this environment, is to be be meant as minimal andgradual variation of the size of one or several intervals that are pivoted on the chord's nucleopolar note, or - more drastically - to be interpreted as a radical and brusque transformation of the same intervals.&lt;br /&gt;
 &lt;br /&gt;
-To understand the nature of such accordances we should refer to specular reflections of light in a crystal, according to a tidy symmetry.&lt;br /&gt;
+In Armodue, nucleopolar harmony cans find a wider and more perfect application , compared to the twelve notes system. In fact, a sixteen notes scale seems already to contain implicitly the central symmetry principle (sixteen is the perfect square of a perfect square -4- and corresponds to the mandala archetype as conceived in almost all cultures and traditions of the world: a wheel with eight or sixteen spokes).&lt;br /&gt;
 &lt;br /&gt;
-{ ! -- rough translation begins here --}&lt;br /&gt;
+Let's assume, for example, the note 5 as nucleopolar. The note 5 will work as a mirror in which lower and higher intervals and notes will reflect.&lt;br /&gt;
 &lt;br /&gt;
+If we elect the three intevals of 6, 8 and 13 eka, it will generate the following sound structure (read the notes from left to right in an orderly proceeding from low to high):&lt;br /&gt;
 &lt;br /&gt;
-An image that comes in mind about is the eight pointed 'star' sometimes appear in a photo area when the lens is stroke by a rather intense light source.&lt;br /&gt;
-The Scriabin idea, so, is to render {paint?} this optical phenomena through the sounds.&lt;br /&gt;
-From here the formation of a center-note (luminous central source) from which departs upper interval-rays and relative higher notes and, for simmetry or specularity law, lower reflected rays-intervals with equal amplitude but with upside-down direction and with relative notes lower than central note.&lt;br /&gt;
-The central note so is called much properly nucleopolar note, out-and-out mirror where lower intervals and low notes reflects themselves in the higher intevals and the high notes.&lt;br /&gt;
-The resulting chord - builded in perfect central simmetry or nucleopolarity - be the main sound plant at whom referring in the melody texture and int hte chord's architecture.&lt;br /&gt;
-The modulation principle, in this sphere, must be meant as the least and &lt;br /&gt;
-gradual variation of wideness of one or several intervals that are pivoted on the chord's nucleopolar note, or - more drastically - must be read as a radical and brusque transformation of the same intervals.&lt;br /&gt;
-In Armodue, the nucleopolar harmony cans find a wider and more perfect enforcement, compared to twelve notes system. IN fact, a sixteen notes scale seems already to contain implicitly the central simmetry principle (sixteen is the perfect square of a perfect square -4- and corresponds to the mandala archetype as conceived in the almost entirety of world's cultures and traditions: an eight or sixteens rays wheel).&lt;br /&gt;
-Let's assume, if example, the note 5 as nucleopolar. The note 5 will work as a mirror in which lower and higher intervals and notes will reflects.&lt;br /&gt;
-If we elect the three intevals of six, eight and thirteen eka it will generate the sound structure (readed notes from left to right proceed neatly from low to high):&lt;br /&gt;
 - 9 - 1# - 5 - 8 - 9 - 3&lt;br /&gt;
-As we can verify, from the note 5 it spreads the two mirrored six eka intervals (defined by notes 1# - 5 and 5 - 8), the two intervals of eight eka (defined by notes 9 - 5 and 5 - 9) and the two intevals of thirteen eka (defined by notes 7 - 5 and 5 - 3).&lt;br /&gt;
+&lt;br /&gt;
-We have so obtained three notes lower than nucleopolar 5 (the 7, 9 and 1#) and three higher than the same note 5 (the 8, 9, 3 notes)&lt;br /&gt;
+As we can verify, from the note 5 the two mirrored 6 eka intervals spread (defined by notes 1# - 5 and 5 - 8), the two intervals of 8 eka (defined by notes 9 - 5 and 5 - 9) and the two intevals of 13 eka (defined by notes 7 - 5 and 5 - 3).&lt;br /&gt;
-The sound structure so obtained can be used as is in the construction of melody and chords, or it can be liable to undergo microvariations and be modulated.&lt;br /&gt;
+&lt;br /&gt;
-If example, we can just bring a slight variation - so an asimmetry - that momentarily destabilize but in a significant way the strict &amp;quot;crystallinity&amp;quot; of sound altering the note 1# for bend one eka (substituting with note 2):&lt;br /&gt;
+We have thus obtained three notes lower than the nucleopolar note 5 (the notes 7, 9 and 1#) and three higher than the same note 5 (thenotes 8, 9, 3)&lt;br /&gt;
+&lt;br /&gt;
+The sound structure obtained this way can be used as is in the construction of melodies and chords, or it can be liable to undergo microvariations and be modulated.&lt;br /&gt;
+&lt;br /&gt;
+For example, we can just bring a slight variation - hence an asymmetry - that momentarily but in a significant way destabilizes the strict &amp;quot;crystallinity&amp;quot; of the sound raising the note 1# for bend one eka (replace it by note 2):&lt;br /&gt;
+&lt;br /&gt;
 - 9 - 2 - 5 - 8 - 9 - 3&lt;br /&gt;
-Later, we can restore the perfect equilibrium and simmetry of sonor structure altering in equal sense and contrary the note 8 that balances the note 2 (the 8 so goes down - in diametrally opposite way - of one eka and so substituted with note 7#):&lt;br /&gt;
+&lt;br /&gt;
+Later, we can restore the perfect equilibrium and symmetry of the sound structure altering in equal sense and contrary motion the note 8 that balances the note 2 (the 8 so goes down - in diametrally opposite way - of one eka and so is replaced by note 7#):&lt;br /&gt;
+&lt;br /&gt;
 - 9 - 2 - 5 - 7# - 9 - 3&lt;br /&gt;
-The shown microvariation principle can be obviously applied also to more than a single note simultaneously.&lt;br /&gt;
-In other circumstances, we can integrate the original structure with the addition of new intervals and notes or changing radically the structure by employing different generator intervals.&lt;br /&gt;
 &lt;br /&gt;
+The shown microvariation principle can obviously be applied also to more than a single note simultaneously.&lt;br /&gt;
+&lt;br /&gt;
+In other circumstances, we can integrate the original structure with the addition of new intervals and notes or change the structure radically by employing different generator intervals.&lt;br /&gt;
 &lt;br /&gt;
-{ ! -- end of rough translation --}&lt;br /&gt;
 &lt;hr /&gt;
 Chapter 5: &lt;br /&gt;