Porcupine temperament modal harmony: Difference between revisions
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-01 06: | : This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-11-01 06:40:41 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>270558284</tt>.<br> | ||
: The revision comment was: <tt></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> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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A MODMOS is "sharp-leaning" if it can be generated by a smaller number of "sharpening" alterations than it can by "flattening" alterations. As an analogy to meantone, C harmonic minor is sharp-leaning, because it's arrived at by sharpening the 7th degree of the aeolian mode of meantone[7] - or, in other words, it's meantone[7] 2|4 #7. You can also arrive at it by flattening the 3rd and 6th degrees of ionian, making it also meantone[7] 5|1 b3 b6, but since it's more simply represented as a single sharpening alteration, it is a "sharp-leaning" MODMOS. An example of a flat-leaning meantone MODMOS would be harmonic major, since it's either ionian b6 (5|1 b6) or aeolian #3 #7 (2|4 #3 #7), which is simpler to express as a single flattening alteration. | A MODMOS is "sharp-leaning" if it can be generated by a smaller number of "sharpening" alterations than it can by "flattening" alterations. As an analogy to meantone, C harmonic minor is sharp-leaning, because it's arrived at by sharpening the 7th degree of the aeolian mode of meantone[7] - or, in other words, it's meantone[7] 2|4 #7. You can also arrive at it by flattening the 3rd and 6th degrees of ionian, making it also meantone[7] 5|1 b3 b6, but since it's more simply represented as a single sharpening alteration, it is a "sharp-leaning" MODMOS. An example of a flat-leaning meantone MODMOS would be harmonic major, since it's either ionian b6 (5|1 b6) or aeolian #3 #7 (2|4 #3 #7), which is simpler to express as a single flattening alteration. | ||
**Porcupine[7] MOS:** | **Porcupine[7] MOS:** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 4333333 ||= ||= 6|0 || | ||= 4333333 ||= ||= 6|0 || | ||
| Line 31: | Line 31: | ||
||= 3333343 ||= ||= 5|1 || | ||= 3333343 ||= ||= 5|1 || | ||
||= 3333334 ||= ||= 6|0 || | ||= 3333334 ||= ||= 6|0 || | ||
**MODMOS with 1st note in generator chain flattened: #.......######** | **MODMOS with 1st note in generator chain flattened: #.......######** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 5333332 ||= ||= 6|0 b1 || | ||= 5333332 ||= ||= 6|0 b1 || | ||
| Line 44: | Line 41: | ||
||= 3333253 ||= ||= 1|5 b6 || | ||= 3333253 ||= ||= 1|5 b6 || | ||
||= 3333325 ||= ||= 0|6 b7 || | ||= 3333325 ||= ||= 0|6 b7 || | ||
**MODMOS with 2nd note in generator chain flattened: #.....#.#####** | **MODMOS with 2nd note in generator chain flattened: #.....#.#####** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 4333324 ||= ||= 6|0 b7 || | ||= 4333324 ||= ||= 6|0 b7 || | ||
| Line 56: | Line 51: | ||
||= 3332443 ||= ||= 1|5 b5 || | ||= 3332443 ||= ||= 1|5 b5 || | ||
||= 3333244 ||= ||= 0|6 b6 || | ||= 3333244 ||= ||= 0|6 b6 || | ||
**MODMOS with 3rd note in generator chain flattened: #....##.####** | **MODMOS with 3rd note in generator chain flattened: #....##.####** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 4333243 ||= ||= 6|0 b6 || | ||= 4333243 ||= ||= 6|0 b6 || | ||
| Line 68: | Line 61: | ||
||= 3324343 ||= ||= 1|5 b4 || | ||= 3324343 ||= ||= 1|5 b4 || | ||
||= 3332434 ||= ||= 0|6 b5 || | ||= 3332434 ||= ||= 0|6 b5 || | ||
**MODMOS with 4th note in generator chain flattened: #...###.###** | **MODMOS with 4th note in generator chain flattened: #...###.###** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 4332433 ||= ||= 6|0 b5 || | ||= 4332433 ||= ||= 6|0 b5 || | ||
| Line 80: | Line 71: | ||
||= 3243343 ||= ||= 1|5 b3 || | ||= 3243343 ||= ||= 1|5 b3 || | ||
||= 3324334 ||= ||= 0|6 b4 || | ||= 3324334 ||= ||= 0|6 b4 || | ||
**MODMOS with 5th note in generator chain flattened: #..####.##** | **MODMOS with 5th note in generator chain flattened: #..####.##** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 4324333 ||= ||= 6|0 b4 || | ||= 4324333 ||= ||= 6|0 b4 || | ||
| Line 92: | Line 81: | ||
||= 2433343 ||= ||= 1|5 b2 || | ||= 2433343 ||= ||= 1|5 b2 || | ||
||= 3243334 ||= ||= 0|6 b3 || | ||= 3243334 ||= ||= 0|6 b3 || | ||
**Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.#** | **Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.#** | ||
||= Step Pattern ||= ||= UDP Name #1 ||= UDP Name #2 || | ||= Step Pattern ||= ||= UDP Name #1 ||= UDP Name #2 || | ||
||= 4333342 ||= ||= 6|0 #7 ||= 1|5 b1 || | ||= 4333342 ||= ||= 6|0 #7 ||= 1|5 b1 || | ||
| Line 104: | Line 91: | ||
||= 3334243 ||= ||= 1|5 #5 ||= 3|3 b6 || | ||= 3334243 ||= ||= 1|5 #5 ||= 3|3 b6 || | ||
||= 3333424 ||= ||= 0|6 #6 ||= 2|4 b7 || | ||= 3333424 ||= ||= 0|6 #6 ||= 2|4 b7 || | ||
**MODMOS with 3rd note in generator chain sharpened: ##.####..#** | **MODMOS with 3rd note in generator chain sharpened: ##.####..#** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 4333423 ||= ||= 6|0 #6 || | ||= 4333423 ||= ||= 6|0 #6 || | ||
| Line 116: | Line 101: | ||
||= 3342343 ||= ||= 1|5 #4 || | ||= 3342343 ||= ||= 1|5 #4 || | ||
||= 3334234 ||= ||= 0|6 #5 || | ||= 3334234 ||= ||= 0|6 #5 || | ||
**MODMOS with 4th note in generator chain sharpened: ###.###...#** | **MODMOS with 4th note in generator chain sharpened: ###.###...#** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 4334233 ||= ||= 6|0 #5 || | ||= 4334233 ||= ||= 6|0 #5 || | ||
| Line 128: | Line 111: | ||
||= 3423343 ||= ||= 1|5 #3 || | ||= 3423343 ||= ||= 1|5 #3 || | ||
||= 3342334 ||= ||= 0|6 #4 || | ||= 3342334 ||= ||= 0|6 #4 || | ||
**MODMOS with 5th note in generator chain sharpened: ####.##....#** | **MODMOS with 5th note in generator chain sharpened: ####.##....#** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 4342333 ||= ||= 6|0 #4 || | ||= 4342333 ||= ||= 6|0 #4 || | ||
| Line 140: | Line 121: | ||
||= 4233343 ||= ||= 1|5 #2 || | ||= 4233343 ||= ||= 1|5 #2 || | ||
||= 3423334 ||= ||= 0|6 #3 || | ||= 3423334 ||= ||= 0|6 #3 || | ||
**MODMOS with 6th note in generator chain sharpened: #####.#.....#** | **MODMOS with 6th note in generator chain sharpened: #####.#.....#** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 4423333 ||= ||= 6|0 #3 || | ||= 4423333 ||= ||= 6|0 #3 || | ||
| Line 152: | Line 131: | ||
||= 2333344 ||= ||= 1|5 #1 || | ||= 2333344 ||= ||= 1|5 #1 || | ||
||= 4233334 ||= ||= 0|6 #2 || | ||= 4233334 ||= ||= 0|6 #2 || | ||
**MODMOS with 7th note in generator chain sharpened: ######.......#** | **MODMOS with 7th note in generator chain sharpened: ######.......#** | ||
||= Step Pattern ||= ||= UDP Name || | ||= Step Pattern ||= ||= UDP Name || | ||
||= 5233333 ||= ||= 6|0 #2 || | ||= 5233333 ||= ||= 6|0 #2 || | ||
| Line 164: | Line 141: | ||
||= 3333352 ||= ||= 1|5 #7 || | ||= 3333352 ||= ||= 1|5 #7 || | ||
||= 2333335 ||= ||= 0|6 #1 || | ||= 2333335 ||= ||= 0|6 #1 || | ||
</pre></div> | </pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
| Line 181: | Line 157: | ||
<br /> | <br /> | ||
A MODMOS is &quot;sharp-leaning&quot; if it can be generated by a smaller number of &quot;sharpening&quot; alterations than it can by &quot;flattening&quot; alterations. As an analogy to meantone, C harmonic minor is sharp-leaning, because it's arrived at by sharpening the 7th degree of the aeolian mode of meantone[7] - or, in other words, it's meantone[7] 2|4 #7. You can also arrive at it by flattening the 3rd and 6th degrees of ionian, making it also meantone[7] 5|1 b3 b6, but since it's more simply represented as a single sharpening alteration, it is a &quot;sharp-leaning&quot; MODMOS. An example of a flat-leaning meantone MODMOS would be harmonic major, since it's either ionian b6 (5|1 b6) or aeolian #3 #7 (2|4 #3 #7), which is simpler to express as a single flattening alteration.<br /> | A MODMOS is &quot;sharp-leaning&quot; if it can be generated by a smaller number of &quot;sharpening&quot; alterations than it can by &quot;flattening&quot; alterations. As an analogy to meantone, C harmonic minor is sharp-leaning, because it's arrived at by sharpening the 7th degree of the aeolian mode of meantone[7] - or, in other words, it's meantone[7] 2|4 #7. You can also arrive at it by flattening the 3rd and 6th degrees of ionian, making it also meantone[7] 5|1 b3 b6, but since it's more simply represented as a single sharpening alteration, it is a &quot;sharp-leaning&quot; MODMOS. An example of a flat-leaning meantone MODMOS would be harmonic major, since it's either ionian b6 (5|1 b6) or aeolian #3 #7 (2|4 #3 #7), which is simpler to express as a single flattening alteration.<br /> | ||
<br /> | |||
<br /> | <br /> | ||
<strong>Porcupine[7] MOS:</strong><br /> | <strong>Porcupine[7] MOS:</strong><br /> | ||
| Line 253: | Line 229: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 1st note in generator chain flattened: #.......######</strong><br /> | <strong>MODMOS with 1st note in generator chain flattened: #.......######</strong><br /> | ||
| Line 327: | Line 300: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 2nd note in generator chain flattened: #.....#.#####</strong><br /> | <strong>MODMOS with 2nd note in generator chain flattened: #.....#.#####</strong><br /> | ||
| Line 400: | Line 371: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 3rd note in generator chain flattened: #....##.####</strong><br /> | <strong>MODMOS with 3rd note in generator chain flattened: #....##.####</strong><br /> | ||
| Line 473: | Line 442: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 4th note in generator chain flattened: #...###.###</strong><br /> | <strong>MODMOS with 4th note in generator chain flattened: #...###.###</strong><br /> | ||
| Line 546: | Line 513: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 5th note in generator chain flattened: #..####.##</strong><br /> | <strong>MODMOS with 5th note in generator chain flattened: #..####.##</strong><br /> | ||
| Line 619: | Line 584: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.#</strong><br /> | <strong>Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.#</strong><br /> | ||
| Line 708: | Line 671: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 3rd note in generator chain sharpened: ##.####..#</strong><br /> | <strong>MODMOS with 3rd note in generator chain sharpened: ##.####..#</strong><br /> | ||
| Line 781: | Line 742: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 4th note in generator chain sharpened: ###.###...#</strong><br /> | <strong>MODMOS with 4th note in generator chain sharpened: ###.###...#</strong><br /> | ||
| Line 854: | Line 813: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 5th note in generator chain sharpened: ####.##....#</strong><br /> | <strong>MODMOS with 5th note in generator chain sharpened: ####.##....#</strong><br /> | ||
| Line 927: | Line 884: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 6th note in generator chain sharpened: #####.#.....#</strong><br /> | <strong>MODMOS with 6th note in generator chain sharpened: #####.#.....#</strong><br /> | ||
| Line 1,000: | Line 955: | ||
</table> | </table> | ||
<br /> | <br /> | ||
<strong>MODMOS with 7th note in generator chain sharpened: ######.......#</strong><br /> | <strong>MODMOS with 7th note in generator chain sharpened: ######.......#</strong><br /> | ||
| Line 1,073: | Line 1,026: | ||
</table> | </table> | ||
</body></html></pre></div> | |||
Revision as of 06:40, 1 November 2011
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author mbattaglia1 and made on 2011-11-01 06:40:41 UTC.
- The original revision id was 270558284.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
=Intro To Porcupine= We need an intro =Brief Intro to Modal Harmony and MODMOS's= We should have a brief intro to all that =Reasons Why Porcupine Will Make for The Best Modal Harmony Ever= Just summarize everything on Andrew H's page here =Porcupine[7] and its MODMOS's= The below mode names are given in [[Modal UDP Notation|UDP notation]]. For porcupine[7], the UDP-aligned generator is the 9/5, or the 11/6 if you prefer. All generators below refer to this generator, NOT the 10/9 one. A MODMOS is "sharp-leaning" if it can be generated by a smaller number of "sharpening" alterations than it can by "flattening" alterations. As an analogy to meantone, C harmonic minor is sharp-leaning, because it's arrived at by sharpening the 7th degree of the aeolian mode of meantone[7] - or, in other words, it's meantone[7] 2|4 #7. You can also arrive at it by flattening the 3rd and 6th degrees of ionian, making it also meantone[7] 5|1 b3 b6, but since it's more simply represented as a single sharpening alteration, it is a "sharp-leaning" MODMOS. An example of a flat-leaning meantone MODMOS would be harmonic major, since it's either ionian b6 (5|1 b6) or aeolian #3 #7 (2|4 #3 #7), which is simpler to express as a single flattening alteration. **Porcupine[7] MOS:** ||= Step Pattern ||= ||= UDP Name || ||= 4333333 ||= ||= 6|0 || ||= 3433333 ||= ||= 5|1 || ||= 3343333 ||= ||= 4|2 || ||= 3334333 ||= ||= 3|3 || ||= 3333433 ||= ||= 4|2 || ||= 3333343 ||= ||= 5|1 || ||= 3333334 ||= ||= 6|0 || **MODMOS with 1st note in generator chain flattened: #.......######** ||= Step Pattern ||= ||= UDP Name || ||= 5333332 ||= ||= 6|0 b1 || ||= 2533333 ||= ||= 5|1 b2 || ||= 3253333 ||= ||= 4|2 b3 || ||= 3325333 ||= ||= 3|3 b4 || ||= 3332533 ||= ||= 2|4 b5 || ||= 3333253 ||= ||= 1|5 b6 || ||= 3333325 ||= ||= 0|6 b7 || **MODMOS with 2nd note in generator chain flattened: #.....#.#####** ||= Step Pattern ||= ||= UDP Name || ||= 4333324 ||= ||= 6|0 b7 || ||= 4433332 ||= ||= 5|1 b1 || ||= 2443333 ||= ||= 4|2 b2 || ||= 3244333 ||= ||= 3|3 b3 || ||= 3324433 ||= ||= 2|4 b4 || ||= 3332443 ||= ||= 1|5 b5 || ||= 3333244 ||= ||= 0|6 b6 || **MODMOS with 3rd note in generator chain flattened: #....##.####** ||= Step Pattern ||= ||= UDP Name || ||= 4333243 ||= ||= 6|0 b6 || ||= 3433324 ||= ||= 5|1 b7 || ||= 4343332 ||= ||= 4|2 b1 || ||= 2434333 ||= ||= 3|3 b2 || ||= 3243433 ||= ||= 2|4 b3 || ||= 3324343 ||= ||= 1|5 b4 || ||= 3332434 ||= ||= 0|6 b5 || **MODMOS with 4th note in generator chain flattened: #...###.###** ||= Step Pattern ||= ||= UDP Name || ||= 4332433 ||= ||= 6|0 b5 || ||= 3433243 ||= ||= 5|1 b6 || ||= 3343324 ||= ||= 4|2 b7 || ||= 4334332 ||= ||= 3|3 b1 || ||= 2433433 ||= ||= 2|4 b2 || ||= 3243343 ||= ||= 1|5 b3 || ||= 3324334 ||= ||= 0|6 b4 || **MODMOS with 5th note in generator chain flattened: #..####.##** ||= Step Pattern ||= ||= UDP Name || ||= 4324333 ||= ||= 6|0 b4 || ||= 3432433 ||= ||= 5|1 b5 || ||= 3343243 ||= ||= 4|2 b6 || ||= 3334324 ||= ||= 3|3 b7 || ||= 4333432 ||= ||= 2|4 b1 || ||= 2433343 ||= ||= 1|5 b2 || ||= 3243334 ||= ||= 0|6 b3 || **Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.#** ||= Step Pattern ||= ||= UDP Name #1 ||= UDP Name #2 || ||= 4333342 ||= ||= 6|0 #7 ||= 1|5 b1 || ||= 2433334 ||= ||= 5|1 #1 ||= 0|6 b2 || ||= 4243333 ||= ||= 4|2 #2 ||= 6|0 b3 || ||= 3424333 ||= ||= 3|3 #3 ||= 5|1 b4 || ||= 3342433 ||= ||= 2|4 #4 ||= 4|2 b5 || ||= 3334243 ||= ||= 1|5 #5 ||= 3|3 b6 || ||= 3333424 ||= ||= 0|6 #6 ||= 2|4 b7 || **MODMOS with 3rd note in generator chain sharpened: ##.####..#** ||= Step Pattern ||= ||= UDP Name || ||= 4333423 ||= ||= 6|0 #6 || ||= 3433342 ||= ||= 5|1 #7 || ||= 2343334 ||= ||= 4|2 #1 || ||= 4234333 ||= ||= 3|3 #2 || ||= 3423433 ||= ||= 2|4 #3 || ||= 3342343 ||= ||= 1|5 #4 || ||= 3334234 ||= ||= 0|6 #5 || **MODMOS with 4th note in generator chain sharpened: ###.###...#** ||= Step Pattern ||= ||= UDP Name || ||= 4334233 ||= ||= 6|0 #5 || ||= 3433423 ||= ||= 5|1 #6 || ||= 3343342 ||= ||= 4|2 #7 || ||= 2334334 ||= ||= 3|3 #1 || ||= 4233433 ||= ||= 2|4 #2 || ||= 3423343 ||= ||= 1|5 #3 || ||= 3342334 ||= ||= 0|6 #4 || **MODMOS with 5th note in generator chain sharpened: ####.##....#** ||= Step Pattern ||= ||= UDP Name || ||= 4342333 ||= ||= 6|0 #4 || ||= 3434233 ||= ||= 5|1 #5 || ||= 3343423 ||= ||= 4|2 #6 || ||= 3334342 ||= ||= 3|3 #7 || ||= 2333434 ||= ||= 2|4 #1 || ||= 4233343 ||= ||= 1|5 #2 || ||= 3423334 ||= ||= 0|6 #3 || **MODMOS with 6th note in generator chain sharpened: #####.#.....#** ||= Step Pattern ||= ||= UDP Name || ||= 4423333 ||= ||= 6|0 #3 || ||= 3442333 ||= ||= 5|1 #4 || ||= 3344233 ||= ||= 4|2 #5 || ||= 3334423 ||= ||= 3|3 #6 || ||= 3333442 ||= ||= 2|4 #7 || ||= 2333344 ||= ||= 1|5 #1 || ||= 4233334 ||= ||= 0|6 #2 || **MODMOS with 7th note in generator chain sharpened: ######.......#** ||= Step Pattern ||= ||= UDP Name || ||= 5233333 ||= ||= 6|0 #2 || ||= 3523333 ||= ||= 5|1 #3 || ||= 3352333 ||= ||= 4|2 #4 || ||= 3335233 ||= ||= 3|3 #5 || ||= 3333523 ||= ||= 2|4 #6 || ||= 3333352 ||= ||= 1|5 #7 || ||= 2333335 ||= ||= 0|6 #1 ||
Original HTML content:
<html><head><title>Porcupine Temperament Modal Harmony</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Intro To Porcupine"></a><!-- ws:end:WikiTextHeadingRule:0 -->Intro To Porcupine</h1>
We need an intro<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Brief Intro to Modal Harmony and MODMOS's"></a><!-- ws:end:WikiTextHeadingRule:2 -->Brief Intro to Modal Harmony and MODMOS's</h1>
We should have a brief intro to all that<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h1> --><h1 id="toc2"><a name="Reasons Why Porcupine Will Make for The Best Modal Harmony Ever"></a><!-- ws:end:WikiTextHeadingRule:4 -->Reasons Why Porcupine Will Make for The Best Modal Harmony Ever</h1>
Just summarize everything on Andrew H's page here<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Porcupine[7] and its MODMOS's"></a><!-- ws:end:WikiTextHeadingRule:6 -->Porcupine[7] and its MODMOS's</h1>
<br />
The below mode names are given in <a class="wiki_link" href="/Modal%20UDP%20Notation">UDP notation</a>. For porcupine[7], the UDP-aligned generator is the 9/5, or the 11/6 if you prefer. All generators below refer to this generator, NOT the 10/9 one.<br />
<br />
A MODMOS is "sharp-leaning" if it can be generated by a smaller number of "sharpening" alterations than it can by "flattening" alterations. As an analogy to meantone, C harmonic minor is sharp-leaning, because it's arrived at by sharpening the 7th degree of the aeolian mode of meantone[7] - or, in other words, it's meantone[7] 2|4 #7. You can also arrive at it by flattening the 3rd and 6th degrees of ionian, making it also meantone[7] 5|1 b3 b6, but since it's more simply represented as a single sharpening alteration, it is a "sharp-leaning" MODMOS. An example of a flat-leaning meantone MODMOS would be harmonic major, since it's either ionian b6 (5|1 b6) or aeolian #3 #7 (2|4 #3 #7), which is simpler to express as a single flattening alteration.<br />
<br />
<br />
<strong>Porcupine[7] MOS:</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4333333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3433333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3343333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3334333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333433<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333343<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333334<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 1st note in generator chain flattened: #.......######</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">5333332<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 b1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2533333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 b2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3253333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 b3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3325333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 b4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3332533<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 b5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333253<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 b6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333325<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 b7<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 2nd note in generator chain flattened: #.....#.#####</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4333324<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 b7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4433332<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 b1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2443333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 b2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3244333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 b3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3324433<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 b4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3332443<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 b5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333244<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 b6<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 3rd note in generator chain flattened: #....##.####</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4333243<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 b6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3433324<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 b7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4343332<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 b1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2434333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 b2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3243433<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 b3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3324343<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 b4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3332434<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 b5<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 4th note in generator chain flattened: #...###.###</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4332433<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 b5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3433243<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 b6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3343324<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 b7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4334332<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 b1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2433433<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 b2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3243343<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 b3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3324334<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 b4<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 5th note in generator chain flattened: #..####.##</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4324333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 b4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3432433<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 b5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3343243<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 b6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3334324<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 b7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4333432<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 b1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2433343<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 b2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3243334<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 b3<br />
</td>
</tr>
</table>
<br />
<strong>Symmetrical MODMOS with 2nd note in generator chain sharpened or 6th note flattened: #.#####.#</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name #1<br />
</td>
<td style="text-align: center;">UDP Name #2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4333342<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 #7<br />
</td>
<td style="text-align: center;">1|5 b1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2433334<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 #1<br />
</td>
<td style="text-align: center;">0|6 b2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4243333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 #2<br />
</td>
<td style="text-align: center;">6|0 b3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3424333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 #3<br />
</td>
<td style="text-align: center;">5|1 b4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3342433<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 #4<br />
</td>
<td style="text-align: center;">4|2 b5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3334243<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 #5<br />
</td>
<td style="text-align: center;">3|3 b6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333424<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 #6<br />
</td>
<td style="text-align: center;">2|4 b7<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 3rd note in generator chain sharpened: ##.####..#</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4333423<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 #6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3433342<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 #7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2343334<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 #1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4234333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 #2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3423433<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 #3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3342343<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 #4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3334234<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 #5<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 4th note in generator chain sharpened: ###.###...#</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4334233<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 #5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3433423<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 #6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3343342<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 #7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2334334<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 #1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4233433<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 #2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3423343<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 #3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3342334<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 #4<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 5th note in generator chain sharpened: ####.##....#</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4342333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 #4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3434233<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 #5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3343423<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 #6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3334342<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 #7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2333434<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 #1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4233343<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 #2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3423334<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 #3<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 6th note in generator chain sharpened: #####.#.....#</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4423333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 #3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3442333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 #4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3344233<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 #5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3334423<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 #6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333442<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 #7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2333344<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 #1<br />
</td>
</tr>
<tr>
<td style="text-align: center;">4233334<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 #2<br />
</td>
</tr>
</table>
<br />
<strong>MODMOS with 7th note in generator chain sharpened: ######.......#</strong><br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Step Pattern<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">UDP Name<br />
</td>
</tr>
<tr>
<td style="text-align: center;">5233333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">6|0 #2<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3523333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">5|1 #3<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3352333<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">4|2 #4<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3335233<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">3|3 #5<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333523<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">2|4 #6<br />
</td>
</tr>
<tr>
<td style="text-align: center;">3333352<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">1|5 #7<br />
</td>
</tr>
<tr>
<td style="text-align: center;">2333335<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;">0|6 #1<br />
</td>
</tr>
</table>
</body></html>