SeventeenTheory: 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:

: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2006-07-11 12:07:39 UTC</tt>.

: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2006-07-11 12:14:23 UTC</tt>.

: The original revision id was <tt>~~860807~~</tt>.

: The original revision id was <tt>860847</tt>.

: The revision comment was: <tt>*%&##^ image transfer</tt>

: The revision comment was: <tt>clarity increase</tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

<h4>Original Wikitext content:</h4>

Line 12:

and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.

[[image:~~17fifths]][[image:space/showimage/~~17fifths]]

[[image:17fifths]]

The lines across indicate five fifths ("minor second") (1/17 of an octave). ~~Now~~ we ~~can~~ order ~~them ascendingly~~:

The lines across indicate five fifths ("minor second") (1/17 of an octave).

So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):

[[image:17versus12names width="1" height="1"]][[image:17versus12names]]

Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." These last two properties ~~are shared~~ with 24-equal (quartertones).

Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." These last two properties 17-equal shares with 24-equal (quartertones).

If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):

Line 32:

Line 34:

and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of &quot;flat/sharp&quot; is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.

<img src="/file/view/17fifths/30122064/17fifths" alt="17fifths" title="17fifths" />~~[[image:space/showimage/17fifths]]~~

<img src="/file/view/17fifths/30122064/17fifths" alt="17fifths" title="17fifths" />

The lines across indicate five fifths (&quot;minor second&quot;) (1/17 of an octave). ~~Now~~ we ~~can~~ order ~~them ascendingly~~:

The lines across indicate five fifths (&quot;minor second&quot;) (1/17 of an octave).

So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):

<img src="/file/view/17versus12names/30122065/1x1/17versus12names" alt="17versus12names" title="17versus12names" style="height: 1px; width: 1px;" /><img src="/file/view/17versus12names/30122065/17versus12names" alt="17versus12names" title="17versus12names" />

Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The &quot;half step&quot;/&quot;minor second&quot; in 17 is twice as small as the &quot;augmented unison&quot;/&quot;sharp&quot;/&quot;flat.&quot; Two sharp/flats add up to a minor third. Two &quot;neutral thirds&quot; add up to a &quot;perfect fifth.&quot; These last two properties ~~are shared~~ with 24-equal (quartertones).

Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The &quot;half step&quot;/&quot;minor second&quot; in 17 is twice as small as the &quot;augmented unison&quot;/&quot;sharp&quot;/&quot;flat.&quot; Two sharp/flats add up to a minor third. Two &quot;neutral thirds&quot; add up to a &quot;perfect fifth.&quot; These last two properties 17-equal shares with 24-equal (quartertones).

If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):

@@ 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:xenjacob|xenjacob]] and made on <tt>2006-07-11 12:07:39 UTC</tt>.<br>
+: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2006-07-11 12:14:23 UTC</tt>.<br>
-: The original revision id was <tt>860807</tt>.<br>
+: The original revision id was <tt>860847</tt>.<br>
-: The revision comment was: <tt>*%&##^ image transfer</tt><br>
+: The revision comment was: <tt>clarity increase</tt><br>
 The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 <h4>Original Wikitext content:</h4>
@@ Line 12: / Line 12: @@
 and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.
-[[image:17fifths]][[image:space/showimage/17fifths]]
+[[image:17fifths]]
-The lines across indicate five fifths ("minor second") (1/17 of an octave). Now we can order them ascendingly:
+The lines across indicate five fifths ("minor second") (1/17 of an octave).
+So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):
 [[image:17versus12names width="1" height="1"]][[image:17versus12names]]
-Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." These last two properties are shared with 24-equal (quartertones).
+Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." These last two properties 17-equal shares with 24-equal (quartertones).
 If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):
@@ Line 32: / Line 34: @@
 and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of &amp;quot;flat/sharp&amp;quot; is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:0:&amp;lt;img src=&amp;quot;/file/view/17fifths/30122064/17fifths&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/17fifths/30122064/17fifths" alt="17fifths" title="17fifths" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:0 --&gt;[[image:space/showimage/17fifths]]&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:0:&amp;lt;img src=&amp;quot;/file/view/17fifths/30122064/17fifths&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/17fifths/30122064/17fifths" alt="17fifths" title="17fifths" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:0 --&gt;&lt;br /&gt;
-The lines across indicate five fifths (&amp;quot;minor second&amp;quot;) (1/17 of an octave). Now we can order them ascendingly:&lt;br /&gt;
+The lines across indicate five fifths (&amp;quot;minor second&amp;quot;) (1/17 of an octave).&lt;br /&gt;
+&lt;br /&gt;
+So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because):&lt;br /&gt;
 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextLocalImageRule:1:&amp;lt;img src=&amp;quot;/file/view/17versus12names/30122065/1x1/17versus12names&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 1px; width: 1px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/17versus12names/30122065/1x1/17versus12names" alt="17versus12names" title="17versus12names" style="height: 1px; width: 1px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:1 --&gt;&lt;!-- ws:start:WikiTextLocalImageRule:2:&amp;lt;img src=&amp;quot;/file/view/17versus12names/30122065/17versus12names&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/17versus12names/30122065/17versus12names" alt="17versus12names" title="17versus12names" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:2 --&gt;&lt;br /&gt;
 &lt;br /&gt;
-Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The &amp;quot;half step&amp;quot;/&amp;quot;minor second&amp;quot; in 17 is twice as small as the &amp;quot;augmented unison&amp;quot;/&amp;quot;sharp&amp;quot;/&amp;quot;flat.&amp;quot; Two sharp/flats add up to a minor third. Two &amp;quot;neutral thirds&amp;quot; add up to a &amp;quot;perfect fifth.&amp;quot; These last two properties are shared with 24-equal (quartertones).&lt;br /&gt;
+Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The &amp;quot;half step&amp;quot;/&amp;quot;minor second&amp;quot; in 17 is twice as small as the &amp;quot;augmented unison&amp;quot;/&amp;quot;sharp&amp;quot;/&amp;quot;flat.&amp;quot; Two sharp/flats add up to a minor third. Two &amp;quot;neutral thirds&amp;quot; add up to a &amp;quot;perfect fifth.&amp;quot; These last two properties 17-equal shares with 24-equal (quartertones).&lt;br /&gt;
 &lt;br /&gt;
 If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):&lt;br /&gt;