Armodue harmony: Difference between revisions

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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-04-01 18:15:26 UTC</tt>.<br>

: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-04-01 18:21:27 UTC</tt>.<br>

: The original revision id was <tt>~~216349722~~</tt>.<br>

: The original revision id was <tt>216350794</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 27:

In Armodue (see [[16edo]]), in contrast, intervals corresponding to those formed by the fifth and seventh harmonic are rendered with greater fidelity of intonation. In this sense, Armodue increases the consonance of the higher harmonics; in particular, it renders the pitch of the seventh harmonic at maximum naturalness.

For this reason, especially important in Armodue are the ~~interval~~ of five eka (corresponding to the interval ratio given by the fifth harmonic) and the interval of 13 eka (corresponding to the interval ratio subsisting with the seventh harmonic). The circle of fifths which is the base of the dodecatonic system is replaced in Armodue by the cycle of 5 eka and the cycle of 13 eka, emphasizing the priority of the fifth and the [[7_4|seventh]] harmonic (7/4 Ratio).

For this reason, especially important in Armodue are the intervals of five eka (corresponding to the interval ratio given by the fifth harmonic) and the interval of 13 eka (corresponding to the interval ratio subsisting with the seventh harmonic). The circle of fifths which is the base of the dodecatonic system is replaced in Armodue by the cycle of 5 eka and the cycle of 13 eka, emphasizing the priority of the fifth and the [[7_4|seventh]] harmonic (7/4 Ratio).

==The triple mean of the double diagonal / side of the square==

Line 212:

Overall, we have 13 types of tetrachords and 10 types of pentachords at our disposition to create scales; the number of different realizable scales is therefore 23 (23 = 13 + 10) squared, that is something like 529 different scales (in the context of scales that are organized into two limiting intervals of seven eka with 2 eka between).

Each of these scales is transposable to any key (the possibilities are: 8464 scales; the product of 529 types of scales ~~****~~* 16 possible tonics).

Each of these scales is transposable to any key (the possibilities are: 8464 scales; the product of 529 types of scales * 16 possible tonics).

If for example we combine the tetrachord with formula 2, 2, 3 with the pentachord formula with 2,1,3,1 get the eight-note (octatonic) scale formed by the following notes (starting with note '1'):

Line 389:

In Armodue (see <a class="wiki_link" href="/16edo">16edo</a>), in contrast, intervals corresponding to those formed by the fifth and seventh harmonic are rendered with greater fidelity of intonation. In this sense, Armodue increases the consonance of the higher harmonics; in particular, it renders the pitch of the seventh harmonic at maximum naturalness.<br />

<br />

For this reason, especially important in Armodue are the ~~interval~~ of five eka (corresponding to the interval ratio given by the fifth harmonic) and the interval of 13 eka (corresponding to the interval ratio subsisting with the seventh harmonic). The circle of fifths which is the base of the dodecatonic system is replaced in Armodue by the cycle of 5 eka and the cycle of 13 eka, emphasizing the priority of the fifth and the <a class="wiki_link" href="/7_4">seventh</a> harmonic (7/4 Ratio).<br />

For this reason, especially important in Armodue are the intervals of five eka (corresponding to the interval ratio given by the fifth harmonic) and the interval of 13 eka (corresponding to the interval ratio subsisting with the seventh harmonic). The circle of fifths which is the base of the dodecatonic system is replaced in Armodue by the cycle of 5 eka and the cycle of 13 eka, emphasizing the priority of the fifth and the <a class="wiki_link" href="/7_4">seventh</a> harmonic (7/4 Ratio).<br />

<br />

<h2 id="toc2"><a name="Two theses supporting the system-The triple mean of the double diagonal / side of the square"></a>The triple mean of the double diagonal / side of the square</h2>

@@ 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:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-04-01 18:15:26 UTC</tt>.<br>
+: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-04-01 18:21:27 UTC</tt>.<br>
-: The original revision id was <tt>216349722</tt>.<br>
+: The original revision id was <tt>216350794</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 27: / Line 27: @@
 In Armodue (see [[16edo]]), in contrast, intervals corresponding to those formed by the fifth and seventh harmonic are rendered with greater fidelity of intonation. In this sense, Armodue increases the consonance of the higher harmonics; in particular, it renders the pitch of the seventh harmonic at maximum naturalness.
-For this reason, especially important in Armodue are the interval of five eka (corresponding to the interval ratio given by the fifth harmonic) and the interval of 13 eka (corresponding to the interval ratio subsisting with the seventh harmonic). The circle of fifths which is the base of the dodecatonic system is replaced in Armodue by the cycle of 5 eka and the cycle of 13 eka, emphasizing the priority of the fifth and the [[7_4|seventh]] harmonic (7/4 Ratio).
+For this reason, especially important in Armodue are the intervals of five eka (corresponding to the interval ratio given by the fifth harmonic) and the interval of 13 eka (corresponding to the interval ratio subsisting with the seventh harmonic). The circle of fifths which is the base of the dodecatonic system is replaced in Armodue by the cycle of 5 eka and the cycle of 13 eka, emphasizing the priority of the fifth and the [[7_4|seventh]] harmonic (7/4 Ratio).
 ==The triple mean of the double diagonal / side of the square==
@@ Line 212: / Line 212: @@
 Overall, we have 13 types of tetrachords and 10 types of pentachords at our disposition to create scales; the number of different realizable scales is therefore 23 (23 = 13 + 10) squared, that is something like 529 different scales (in the context of scales that are organized into two limiting intervals of seven eka with 2 eka between).
-Each of these scales is transposable to any key (the possibilities are: 8464 scales; the product of 529 types of scales ***** 16 possible tonics).
+Each of these scales is transposable to any key (the possibilities are: 8464 scales; the product of 529 types of scales * 16 possible tonics).
 If for example we combine the tetrachord with formula 2, 2, 3 with the pentachord formula with 2,1,3,1 get the eight-note (octatonic) scale formed by the following notes (starting with note '1'):
@@ Line 389: / Line 389: @@
 In Armodue (see &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;), in contrast, intervals corresponding to those formed by the fifth and seventh harmonic are rendered with greater fidelity of intonation. In this sense, Armodue increases the consonance of the higher harmonics; in particular, it renders the pitch of the seventh harmonic at maximum naturalness.&lt;br /&gt;
 &lt;br /&gt;
-For this reason, especially important in Armodue are the interval of five eka (corresponding to the interval ratio given by the fifth harmonic) and the interval of 13 eka (corresponding to the interval ratio subsisting with the seventh harmonic). The circle of fifths which is the base of the dodecatonic system is replaced in Armodue by the cycle of 5 eka and the cycle of 13 eka, emphasizing the priority of the fifth and the &lt;a class="wiki_link" href="/7_4"&gt;seventh&lt;/a&gt; harmonic (7/4 Ratio).&lt;br /&gt;
+For this reason, especially important in Armodue are the intervals of five eka (corresponding to the interval ratio given by the fifth harmonic) and the interval of 13 eka (corresponding to the interval ratio subsisting with the seventh harmonic). The circle of fifths which is the base of the dodecatonic system is replaced in Armodue by the cycle of 5 eka and the cycle of 13 eka, emphasizing the priority of the fifth and the &lt;a class="wiki_link" href="/7_4"&gt;seventh&lt;/a&gt; harmonic (7/4 Ratio).&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Two theses supporting the system-The triple mean of the double diagonal / side of the square"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;The triple mean of the double diagonal / side of the square&lt;/h2&gt;