Porcupine notation: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-28 06:52:54 UTC</tt>.

: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-28 06:58:31 UTC</tt>.

: The original revision id was <tt>~~602867982~~</tt>.

: The original revision id was <tt>602868058</tt>.

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

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For sharp-6 edos, simply double all ups and downs: P1 - vvM2 - ^^m3 - P4 - vv5... and C - Dvv - Eb^^ - F - Gvv...

This assumes a mapping of 5/4 that results in 250/243 mapping to zero edosteps. The obvious mapping often suffices, but sometimes the mapping needs tweaking, as with edos 36c, 43c, 57cc, 58c, 64ccc, 65c and 72cc. If the edo isn't tweaked, the generator won't map to 10/9, and two generators won't map to 6/5. (Arguably, the generated scale is still porcupine-like.)

This assumes a mapping of 5/4 that results in 250/243 mapping to zero edosteps. Since 10/9 should be vM2, 5/4 should be 10/9 + 9/8 = vM2 +M2 = vM3. The obvious mapping often suffices, but sometimes the mapping needs tweaking, as with edos 36c, 43c, 57cc, 58c, 64ccc, 65c and 72cc. If the edo isn't tweaked, the generator won't map to 10/9, and two generators won't map to 6/5. (Arguably, the generated scale is still porcupine-like.)

If we're not in an edo at all, but in a rank-2 tuning with a generator of indeterminate cents, use the sharp-3 notation.</pre></div>

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For sharp-6 edos, simply double all ups and downs: P1 - vvM2 - ^^m3 - P4 - vv5... and C - Dvv - Eb^^ - F - Gvv...

This assumes a mapping of 5/4 that results in 250/243 mapping to zero edosteps. The obvious mapping often suffices, but sometimes the mapping needs tweaking, as with edos 36c, 43c, 57cc, 58c, 64ccc, 65c and 72cc. If the edo isn't tweaked, the generator won't map to 10/9, and two generators won't map to 6/5. (Arguably, the generated scale is still porcupine-like.)

This assumes a mapping of 5/4 that results in 250/243 mapping to zero edosteps. Since 10/9 should be vM2, 5/4 should be 10/9 + 9/8 = vM2 +M2 = vM3. The obvious mapping often suffices, but sometimes the mapping needs tweaking, as with edos 36c, 43c, 57cc, 58c, 64ccc, 65c and 72cc. If the edo isn't tweaked, the generator won't map to 10/9, and two generators won't map to 6/5. (Arguably, the generated scale is still porcupine-like.)

If we're not in an edo at all, but in a rank-2 tuning with a generator of indeterminate cents, use the sharp-3 notation.</body></html></pre></div>

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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:<br>
-: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-28 06:52:54 UTC</tt>.<br>
+: This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-12-28 06:58:31 UTC</tt>.<br>
-: The original revision id was <tt>602867982</tt>.<br>
+: The original revision id was <tt>602868058</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 131: / Line 131: @@
 &lt;span class="commentBody"&gt;For sharp-6 edos, simply double all ups and downs: P1 - vvM2 - ^^m3 - P4 - vv5... and C - Dvv - Eb^^ - F - Gvv...&lt;/span&gt;
-&lt;span class="commentBody"&gt;This assumes a mapping of 5/4 that results in 250/243 mapping to zero edosteps. The obvious mapping often suffices, but sometimes the mapping needs tweaking, as with edos 36c, 43c, 57cc, 58c, 64ccc, 65c and 72cc. If the edo isn't tweaked, the generator won't map to 10/9, and two generators won't map to 6/5. (Arguabl&lt;/span&gt;y, the generated scale is still porcupine-like.)
+&lt;span class="commentBody"&gt;This assumes a mapping of 5/4 that results in 250/243 mapping to zero edosteps. Since 10/9 should be vM2, 5/4 should be 10/9 + 9/8 = vM2 +M2 = vM3. The obvious mapping often suffices, but sometimes the mapping needs tweaking, as with edos 36c, 43c, 57cc, 58c, 64ccc, 65c and 72cc. If the edo isn't tweaked, the generator won't map to 10/9, and two generators won't map to 6/5. (Arguabl&lt;/span&gt;y, the generated scale is still porcupine-like.)
 &lt;span class="commentBody"&gt; If we're not in an edo at all, but in a rank-2 tuning with a generator of indeterminate cents, use the sharp-3 notation.&lt;/span&gt;</pre></div>
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 &lt;span class="commentBody"&gt;For sharp-6 edos, simply double all ups and downs: P1 - vvM2 - ^^m3 - P4 - vv5... and C - Dvv - Eb^^ - F - Gvv...&lt;/span&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;span class="commentBody"&gt;This assumes a mapping of 5/4 that results in 250/243 mapping to zero edosteps. The obvious mapping often suffices, but sometimes the mapping needs tweaking, as with edos 36c, 43c, 57cc, 58c, 64ccc, 65c and 72cc. If the edo isn't tweaked, the generator won't map to 10/9, and two generators won't map to 6/5. (Arguabl&lt;/span&gt;y, the generated scale is still porcupine-like.)&lt;br /&gt;
+&lt;span class="commentBody"&gt;This assumes a mapping of 5/4 that results in 250/243 mapping to zero edosteps. Since 10/9 should be vM2, 5/4 should be 10/9 + 9/8 = vM2 +M2 = vM3. The obvious mapping often suffices, but sometimes the mapping needs tweaking, as with edos 36c, 43c, 57cc, 58c, 64ccc, 65c and 72cc. If the edo isn't tweaked, the generator won't map to 10/9, and two generators won't map to 6/5. (Arguabl&lt;/span&gt;y, the generated scale is still porcupine-like.)&lt;br /&gt;
 &lt;br /&gt;
 &lt;span class="commentBody"&gt; If we're not in an edo at all, but in a rank-2 tuning with a generator of indeterminate cents, use the sharp-3 notation.&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>