Porcupine notation: Difference between revisions

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<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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-07-02 22:59:02 UTC</tt>.

: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-07-02 23:03:21 UTC</tt>.

: The original revision id was <tt>~~349915908~~</tt>.

: The original revision id was <tt>349916826</tt>.

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

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

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~ ~ ~

[[Paul Erlich]] commented: //I didn't come up with it but I like it because each of the four consonant triads in porcupine-7 gets a conventional spellings for its quality. D-F-A and E-G-B are minor, and F-A-C and G-B-D are major. Also the minor seventh chords D-F-A-C and E-G-B-D.//

//~ ~ ~//

Mike added:

//BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have "staff switches" in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you. ... Actually, forget staff changes, why not clef changes? 5 lines can accommodate 1 octave of both porcupine[7] and porcupine[8], so there you go.//

[[Paul Erlich]] commented: //I didn't come up with it but I like it because each of the four consonant triads in porcupine-7 gets a conventional spellings for its quality. D-F-A and E-G-B are minor, and F-A-C and G-B-D are major. Also the minor seventh chords D-F-A-C and E-G-B-D.//

~ ~ ~

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[[Andrew Heathwaite]] made the following diagram:

[[image:porcupine generator chain.png]]</pre></div>

[[image:porcupine generator chain.png]]

Andrew added:

//Yikes, so #v (sharp-down) is 40/39 and b^^ (flat-double-up) is 65/64 -- and in a 13-limit Porcupine musical setting, unless you're in 37edo, they're not the same, and they're both necessary if you want to spell your scales logically!//

//Let's say you want an 8:9:10:11:12:13:14 chord with letter names A B C D E F G. If you start it on Av, it's://

// Av B C D E Fb^ G//

// ...with the flat-up turning a 5/3 into 13/8 by subtracting 40/39.//

// But if I start it on A natural, I get://

// A B^ C^ D^ E^ Fb^^ G^//

// ...with the flat-double-up turning an 8/5 into 13/8 by adding 65/64!//

// To summarize://

// #v is the chroma in Porcupine[15].//

// In a 13-limit setting, it's 40/39.//

// In 15edo it's tempered out.//

// In 22edo, it's one degree, which would mean, for example, A#v=A^; so we don't need it to describe all the pitches.//

// In 37edo, it's one degree, but A#v != A^, because ^ is two degrees.//

// b^^ is the chroma in Porcupine[22].//

// In a 13-limit setting, it's 65/64.//

// In 15edo, it's equivalent to ^ and # and therefore totally unnecessary.//

// In 22edo, it's tempered out.//

// In 37edo, it's one degree, which means that #v and bvv are in fact the same, and only one accidental would be needed.//

// In other Porcupinefish systems (like 59edo, for instance), it's smaller than #v, and therefore needs a distinct and preferably smaller symbol.//

// That's my proposal for expanding the Porcupine notation [[https://www.facebook.com/MikeBattagliaMusic|Mike Battaglia]] has described into the 13-limit. Does this make sense to people?//

//BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have "staff switches" in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.//</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Porcupine Notation</title></head><body><a class="wiki_link" href="/Mike%20Battaglia">Mike Battaglia</a> posted the following description of a <a class="wiki_link" href="/Porcupine">Porcupine</a> notation to the Xenharmonic Alliance Facebook Group:

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~ ~ ~

<a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> commented: I didn't come up with it but I like it because each of the four consonant triads in porcupine-7 gets a conventional spellings for its quality. D-F-A and E-G-B are minor, and F-A-C and G-B-D are major. Also the minor seventh chords D-F-A-C and E-G-B-D.

~ ~ ~

Mike added:

BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have &quot;staff switches&quot; in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you. ... Actually, forget staff changes, why not clef changes? 5 lines can accommodate 1 octave of both porcupine[7] and porcupine[8], so there you go.

<a class="wiki_link" href="/Paul%20Erlich">Paul Erlich</a> commented: I didn't come up with it but I like it because each of the four consonant triads in porcupine-7 gets a conventional spellings for its quality. D-F-A and E-G-B are minor, and F-A-C and G-B-D are major. Also the minor seventh chords D-F-A-C and E-G-B-D.

~ ~ ~

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<a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> made the following diagram:

<img src="/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png" alt="porcupine generator chain.png" title="porcupine generator chain.png" /></body></html></pre></div>

<img src="/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png" alt="porcupine generator chain.png" title="porcupine generator chain.png" />

Andrew added:

Yikes, so #v (sharp-down) is 40/39 and b^^ (flat-double-up) is 65/64 -- and in a 13-limit Porcupine musical setting, unless you're in 37edo, they're not the same, and they're both necessary if you want to spell your scales logically!

Let's say you want an 8:9:10:11:12:13:14 chord with letter names A B C D E F G. If you start it on Av, it's:

Av B C D E Fb^ G

...with the flat-up turning a 5/3 into 13/8 by subtracting 40/39.

But if I start it on A natural, I get:

A B^ C^ D^ E^ Fb^^ G^

...with the flat-double-up turning an 8/5 into 13/8 by adding 65/64!

To summarize:

#v is the chroma in Porcupine[15].

In a 13-limit setting, it's 40/39.

In 15edo it's tempered out.

In 22edo, it's one degree, which would mean, for example, A#v=A^; so we don't need it to describe all the pitches.

In 37edo, it's one degree, but A#v != A^, because ^ is two degrees.

b^^ is the chroma in Porcupine[22].

In a 13-limit setting, it's 65/64.

In 15edo, it's equivalent to ^ and # and therefore totally unnecessary.

In 22edo, it's tempered out.

In 37edo, it's one degree, which means that #v and bvv are in fact the same, and only one accidental would be needed.

In other Porcupinefish systems (like 59edo, for instance), it's smaller than #v, and therefore needs a distinct and preferably smaller symbol.

That's my proposal for expanding the Porcupine notation <a class="wiki_link_ext" href="https://www.facebook.com/MikeBattagliaMusic" rel="nofollow">Mike Battaglia</a> has described into the 13-limit. Does this make sense to people?

BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have &quot;staff switches&quot; in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.</body></html></pre></div>

@@ 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-07-02 22:59:02 UTC</tt>.<br>
+: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2012-07-02 23:03:21 UTC</tt>.<br>
-: The original revision id was <tt>349915908</tt>.<br>
+: The original revision id was <tt>349916826</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 55: / Line 55: @@
 &lt;span class="messageBody"&gt;~ ~ ~&lt;/span&gt;
+&lt;span class="commentBody"&gt;[[Paul Erlich]] commented: //I didn't come up with it but I like it because each of the four consonant triads in porcupine-7 gets a conventional spellings for its quality. D-F-A and E-G-B are minor, and F-A-C and G-B-D are major. Also the minor seventh chords D-F-A-C and E-G-B-D.//&lt;/span&gt;
+&lt;span class="commentBody"&gt; &lt;/span&gt;
+&lt;span class="commentBody"&gt;//~ ~ ~//&lt;/span&gt;
+&lt;span class="commentBody"&gt; &lt;/span&gt;
+&lt;span class="commentBody"&gt;Mike added:&lt;/span&gt;
+//&lt;span class="commentBody"&gt;BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have "staff switches" in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you. ... Actually, forget staff changes, why not clef changes? 5 lines can accommodate 1 octave of both porcupine[7] and porcupine[8], so there you go.&lt;/span&gt;//
-&lt;span class="commentBody"&gt;[[Paul Erlich]] commented: //I didn't come up with it but I like it because each of the four consonant triads in porcupine-7 gets a conventional spellings for its quality. D-F-A and E-G-B are minor, and F-A-C and G-B-D are major. Also the minor seventh chords D-F-A-C and E-G-B-D.//&lt;/span&gt;
 &lt;span class="messageBody"&gt;~ ~ ~&lt;/span&gt;
@@ Line 62: / Line 68: @@
 &lt;span class="messageBody"&gt;[[Andrew Heathwaite]] made the following diagram:&lt;/span&gt;
-&lt;span class="messageBody"&gt;[[image:porcupine generator chain.png]]&lt;/span&gt;</pre></div>
+&lt;span class="messageBody"&gt;[[image:porcupine generator chain.png]]&lt;/span&gt;
+Andrew added:
+//Yikes, so #v (sharp-down) is 40/39 and b^^ (flat-double-up) is 65/64 -- and in a 13-limit Porcupine musical setting, unless you're in 37edo, they're not the same, and they're both necessary if you want to spell your scales logically!//
+//Let's&lt;span class="text_exposed_show"&gt; say you want an 8:9:10:11:12:13:14 chord with letter names A B C D E F G. If you start it on Av, it's:&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; Av B C D E Fb^ G&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; ...with the flat-up turning a 5/3 into 13/8 by subtracting 40/39.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; But if I start it on A natural, I get:&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; A B^ C^ D^ E^ Fb^^ G^&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; ...with the flat-double-up turning an 8/5 into 13/8 by adding 65/64!&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; To summarize:&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; #v is the chroma in Porcupine[15].&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; In a 13-limit setting, it's 40/39.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; In 15edo it's tempered out.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; In 22edo, it's one degree, which would mean, for example, A#v=A^; so we don't need it to describe all the pitches.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; In 37edo, it's one degree, but A#v != A^, because ^ is two degrees.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; b^^ is the chroma in Porcupine[22].&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; In a 13-limit setting, it's 65/64.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; In 15edo, it's equivalent to ^ and # and therefore totally unnecessary.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; In 22edo, it's tempered out.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; In 37edo, it's one degree, which means that #v and bvv are in fact the same, and only one accidental would be needed.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; In other Porcupinefish systems (like 59edo, for instance), it's smaller than #v, and therefore needs a distinct and preferably smaller symbol.&lt;/span&gt;//
+//&lt;span class="text_exposed_show"&gt; That's my proposal for expanding the Porcupine notation [[https://www.facebook.com/MikeBattagliaMusic|Mike Battaglia]] has described into the 13-limit. Does this make sense to people?&lt;/span&gt;//
+//&lt;span class="commentBody"&gt;BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have "staff switches" in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.&lt;/span&gt;//</pre></div>
 <h4>Original HTML content:</h4>
 <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Porcupine Notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Mike%20Battaglia"&gt;Mike Battaglia&lt;/a&gt; posted the following description of a &lt;a class="wiki_link" href="/Porcupine"&gt;Porcupine&lt;/a&gt; notation to the Xenharmonic Alliance Facebook Group:&lt;br /&gt;
@@ Line 113: / Line 154: @@
 &lt;span class="messageBody"&gt;~ ~ ~&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
+&lt;span class="commentBody"&gt;&lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt; commented: &lt;em&gt;I didn't come up with it but I like it because each of the four consonant triads in porcupine-7 gets a conventional spellings for its quality. D-F-A and E-G-B are minor, and F-A-C and G-B-D are major. Also the minor seventh chords D-F-A-C and E-G-B-D.&lt;/em&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; &lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt;&lt;em&gt;~ ~ ~&lt;/em&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt; &lt;/span&gt;&lt;br /&gt;
+&lt;span class="commentBody"&gt;Mike added:&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="commentBody"&gt;BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have &amp;quot;staff switches&amp;quot; in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you. ... Actually, forget staff changes, why not clef changes? 5 lines can accommodate 1 octave of both porcupine[7] and porcupine[8], so there you go.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span class="commentBody"&gt;&lt;a class="wiki_link" href="/Paul%20Erlich"&gt;Paul Erlich&lt;/a&gt; commented: &lt;em&gt;I didn't come up with it but I like it because each of the four consonant triads in porcupine-7 gets a conventional spellings for its quality. D-F-A and E-G-B are minor, and F-A-C and G-B-D are major. Also the minor seventh chords D-F-A-C and E-G-B-D.&lt;/em&gt;&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;span class="messageBody"&gt;~ ~ ~&lt;/span&gt;&lt;br /&gt;
@@ Line 120: / Line 167: @@
 &lt;span class="messageBody"&gt;&lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt; made the following diagram:&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span class="messageBody"&gt;&lt;!-- ws:start:WikiTextLocalImageRule:0:&amp;lt;img src=&amp;quot;/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png" alt="porcupine generator chain.png" title="porcupine generator chain.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:0 --&gt;&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+&lt;span class="messageBody"&gt;&lt;!-- ws:start:WikiTextLocalImageRule:0:&amp;lt;img src=&amp;quot;/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/porcupine%20generator%20chain.png/349915824/porcupine%20generator%20chain.png" alt="porcupine generator chain.png" title="porcupine generator chain.png" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:0 --&gt;&lt;/span&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
+Andrew added:&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;Yikes, so #v (sharp-down) is 40/39 and b^^ (flat-double-up) is 65/64 -- and in a 13-limit Porcupine musical setting, unless you're in 37edo, they're not the same, and they're both necessary if you want to spell your scales logically!&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;Let's&lt;span class="text_exposed_show"&gt; say you want an 8:9:10:11:12:13:14 chord with letter names A B C D E F G. If you start it on Av, it's:&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; Av B C D E Fb^ G&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; ...with the flat-up turning a 5/3 into 13/8 by subtracting 40/39.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; But if I start it on A natural, I get:&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; A B^ C^ D^ E^ Fb^^ G^&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; ...with the flat-double-up turning an 8/5 into 13/8 by adding 65/64!&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; To summarize:&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; #v is the chroma in Porcupine[15].&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; In a 13-limit setting, it's 40/39.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; In 15edo it's tempered out.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; In 22edo, it's one degree, which would mean, for example, A#v=A^; so we don't need it to describe all the pitches.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; In 37edo, it's one degree, but A#v != A^, because ^ is two degrees.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; b^^ is the chroma in Porcupine[22].&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; In a 13-limit setting, it's 65/64.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; In 15edo, it's equivalent to ^ and # and therefore totally unnecessary.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; In 22edo, it's tempered out.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; In 37edo, it's one degree, which means that #v and bvv are in fact the same, and only one accidental would be needed.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; In other Porcupinefish systems (like 59edo, for instance), it's smaller than #v, and therefore needs a distinct and preferably smaller symbol.&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;br /&gt;
+&lt;em&gt;&lt;span class="text_exposed_show"&gt; That's my proposal for expanding the Porcupine notation &lt;a class="wiki_link_ext" href="https://www.facebook.com/MikeBattagliaMusic" rel="nofollow"&gt;Mike Battaglia&lt;/a&gt; has described into the 13-limit. Does this make sense to people?&lt;/span&gt;&lt;/em&gt;&lt;br /&gt;
+&lt;em&gt;&lt;span class="commentBody"&gt;BTW with this notation system, one question is - how many lines do you use in a staff? I guess you'd have to have &amp;quot;staff switches&amp;quot; in the middle of a score if you want to switch into a porcupine[8]-oriented notation or what have you.&lt;/span&gt;&lt;/em&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>