5L 2s: 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:JosephRuhf|JosephRuhf]] and made on <tt>2014-06-04 14:39:51 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2014-06-04 23:03:21 UTC</tt>.

: The original revision id was <tt>~~512838698~~</tt>.

: The original revision id was <tt>512904622</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.

Line 69:

||= ||= ||= ||= ||= 19\45 ||= ||= 506.667 ||= 7 7 5 7 7 7 5 || 235.485 || 271.182 || 311.33 || 382.003 ||= ||

||= ||= ||= ||= ||= ||= 27\64 ||= 506.250 ||= 10 10 7 10 10 10 7 || 235.277 || 270.973 || 311.539 || 382.211 ||= ||

||= ||= ||= 8\19 ||= ||= ||= ||= 505.263 ||= 3 3 2 3 3 3 2 || || || 312.032 || 382.705 ||= Optimum rank range (L/s=3/2) diatonic ||

||= ||= ||= 8\19 ||= ||= ||= ||= 505.263 ||= 3 3 2 3 3 3 2 || 234.783 || 270.480 || 312.032 || 382.705 ||= Optimum rank range (L/s=3/2) diatonic ||

||= ||= ||= ||= ||= ||= 29\69 ||= 504.348 ||= 11 11 7 11 11 11 7 || || || 312.490 || 383.172 ||= ||

||= ||= ||= ||= ||= ||= 29\69 ||= 504.348 ||= 11 11 7 11 11 11 7 || 234.3255 || 270.022 || 312.490 || 383.172 ||= ||

||= ||= ||= ||= ||= 21\50 ||= ||= 504.000 ||= 8 8 5 8 8 8 5 || || || 312.664 || 383.336 ||= ||

||= ||= ||= ||= ||= 21\50 ||= ||= 504.000 ||= 8 8 5 8 8 8 5 || 234.152 || 269.848 || 312.664 || 383.336 ||= ||

||= ||= ||= ||= ||= ||= 34\81 ||= 503.704 ||= 13 13 8 13 13 13 8 || || || 312.811 || 383.485 ||= Golden meantone ||

||= ||= ||= ||= ||= ||= 34\81 ||= 503.704 ||= 13 13 8 13 13 13 8 || 234.003 || 269.700 || 312.811 || 383.485 ||= Golden meantone ||

||= ||= ||= ||= 13\31 ||= ||= ||= 503.226 ||= 5 5 3 5 5 5 3 || || || 313.051 || 383.723 ||= Meantone is in this region ||

||= ||= ||= ||= 13\31 ||= ||= ||= 503.226 ||= 5 5 3 5 5 5 3 || 233.7645 || 269.461 || 313.051 || 383.723 ||= Meantone is in this region ||

||= ||= ||= ||= ||= ||= 31\74 ||= 502.703 ||= 12 12 7 12 12 12 7 || || || 313.312 || 383.985 ||= ||

||= ||= ||= ||= ||= ||= 31\74 ||= 502.703 ||= 12 12 7 12 12 12 7 || 233.503 || 269.200 || 313.312 || 383.985 ||= ||

||= ||= ||= ||= ||= 18\43 ||= ||= 502.326 ||= 7 7 4 7 7 7 4 || || || 313.501 || 384.183 ||= ||

||= ||= ||= ||= ||= 18\43 ||= ||= 502.326 ||= 7 7 4 7 7 7 4 || 233.314 || 269.011 || 313.501 || 384.183 ||= ||

||= ||= ||= ||= ||= ||= 23\55 ||= 501.818 ||= 9 9 5 9 9 9 5 || || || 313.754 || 384.428 ||= ||

||= ||= ||= ||= ||= ||= 23\55 ||= 501.818 ||= 9 9 5 9 9 9 5 || 233.061 || 268.7575 || 313.754 || 384.428 ||= ||

||= ||= 5\12 ||= ||= ||= ||= ||= 500.000 ||= 2 2 1 2 2 2 1 || || || 314.664 || 385.336 ||= Boundary of propriety (generators

||= ||= 5\12 ||= ||= ||= ||= ||= 500.000 ||= 2 2 1 2 2 2 1 || 232.152 || 267.848 || 314.664 || 385.336 ||= Boundary of propriety (generators

larger than this are proper) ||

||= ||= ||= ||= ||= ||= 22\53 ||= 498.113 ||= 9 9 4 9 9 9 4 || || || 315.609 || 386.278 ||= Pythagorean is around here ||

||= ||= ||= ||= ||= ||= 22\53 ||= 498.113 ||= 9 9 4 9 9 9 4 || 231.208 || 266.905 || 315.609 || 386.278 ||= Pythagorean is around here ||

||= ||= ||= ||= ||= 17\41 ||= ||= 497.591 ||= 7 7 3 7 7 7 3 || || || 315.883 || 386.556 ||= ||

||= ||= ||= ||= ||= 17\41 ||= ||= 497.591 ||= 7 7 3 7 7 7 3 || 230.932 || 266.629 || 315.883 || 386.556 ||= ||

||= ||= ||= ||= ||= ||= 29\70 ||= 497.143 ||= 12 12 5 12 12 12 5 || || || 316.092 || 386.765 ||= ||

||= ||= ||= ||= ||= ||= 29\70 ||= 497.143 ||= 12 12 5 12 12 12 5 || 230.723 || 266.420 || 316.092 || 386.765 ||= ||

||= ||= ||= ||= 12\29 ||= ||= ||= 496.552 ||= 5 5 2 5 5 5 2 || || || 316.388 || 387.061 ||= ||

||= ||= ||= ||= 12\29 ||= ||= ||= 496.552 ||= 5 5 2 5 5 5 2 || 230.4275 || 266.124 || 316.388 || 387.061 ||= ||

||= ||= ||= ||= ||= ||= 31\75 ||= 496.000 ||= 13 13 5 13 13 13 5 || || || 316.664 || 387.336 ||= ||

||= ||= ||= ||= ||= ||= 31\75 ||= 496.000 ||= 13 13 5 13 13 13 5 || 230.152 || 265.848 || 316.664 || 387.336 ||= ||

||= ||= ||= ||= ||= 19\46 ||= ||= 495.652 ||= 8 8 3 8 8 8 3 || || || 316.837 || 387.511 ||= ||

||= ||= ||= ||= ||= 19\46 ||= ||= 495.652 ||= 8 8 3 8 8 8 3 || 229.978 || 265.6745 || 316.837 || 387.511 ||= ||

||= ||= ||= ||= ||= ||= 26\63 ||= 495.238 ||= 11 11 4 11 11 11 4 || || || 317.045 || 387.717 ||= ||

||= ||= ||= ||= ||= ||= 26\63 ||= 495.238 ||= 11 11 4 11 11 11 4 || 229.771 || 265.4675 || 317.045 || 387.717 ||= ||

||= ||= ||= 7\17 ||= ||= ||= ||= 494.118 ||= 3 3 1 3 3 3 1 || || || 317.596 || 388.286 ||= L/s = 3 ||

||= ||= ||= 7\17 ||= ||= ||= ||= 494.118 ||= 3 3 1 3 3 3 1 || 229.210 || 264.907 || 317.596 || 388.286 ||= L/s = 3 ||

||= ||= ||= ||= ||= ||= 23\56 ||= 492.857 ||= 10 10 3 10 10 10 3 || || || 318.235 || 388.908 ||= ||

||= ||= ||= ||= ||= ||= 23\56 ||= 492.857 ||= 10 10 3 10 10 10 3 || 228.580 || 264.277 || 318.235 || 388.908 ||= ||

||= ||= ||= ||= ||= 16\39 ||= ||= 492.308 ||= 7 7 2 7 7 7 2 || || || 318.51 || 389.182 ||= ||

||= ||= ||= ||= ||= 16\39 ||= ||= 492.308 ||= 7 7 2 7 7 7 2 || 228.305 || 264.002 || 318.51 || 389.182 ||= ||

||= ||= ||= ||= ||= ||= 25\61 ||= 491.803 ||= 11 11 3 11 11 11 3 || || || 318.761 || 389.436 ||= ||

||= ||= ||= ||= ||= ||= 25\61 ||= 491.803 ||= 11 11 3 11 11 11 3 || 228.053 || 263.750 || 318.761 || 389.436 ||= ||

||= ||= ||= ||= 9\22 ||= ||= ||= 490.909 ||= 4 4 1 4 4 4 1 || || || 319.209 || 389.882 ||= (No-5's) superpyth is in this region

||= ||= ||= ||= 9\22 ||= ||= ||= 490.909 ||= 4 4 1 4 4 4 1 || 227.606 || 263.303 || 319.209 || 389.882 ||= (No-5's) superpyth is in this region

L/s = 4 ||

||= ||= ||= ||= ||= ||= 20\49 ||= 489.796 ||= 9 9 2 9 9 9 2 || || || 319.766 || 390.438 ||= ||

||= ||= ||= ||= ||= ||= 20\49 ||= 489.796 ||= 9 9 2 9 9 9 2 || 227.050 || 262.746 || 319.766 || 390.438 ||= ||

||= ||= ||= ||= ||= 11\27 ||= ||= 488.889 ||= 5 5 1 5 5 5 1 || || || 320.219 || 390.892 ||= ||

||= ||= ||= ||= ||= 11\27 ||= ||= 488.889 ||= 5 5 1 5 5 5 1 || 226.596 || 262.293 || 320.219 || 390.892 ||= ||

||= ||= ||= ||= ||= ||= 13\32 ||= 487.500 ||= 6 6 1 6 6 6 1 || || || 320.914 || 391.596 ||= ||

||= ||= ||= ||= ||= ||= 13\32 ||= 487.500 ||= 6 6 1 6 6 6 1 || 225.9015 || 261.598 || 320.914 || 391.596 ||= ||

||= 2\5 ||= ||= ||= ||= ||= ||= 480.000 ||= 1 1 0 1 1 1 0 || || || 324.664 || 395.336 ||= ||

||= 2\5 ||= ||= ||= ||= ||= ||= 480.000 ||= 1 1 0 1 1 1 0 || 222.152 || 257.848 || 324.664 || 395.336 ||= ||

Temperaments above 5\12 on this chart are called "negative temperaments" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 8\19) and 1/4-comma (close to 13\31). As these tunings approach 3\7, the majors become flatter and the minors become sharper.

Line 441:

<td style="text-align: center;">3 3 2 3 3 3 2

</td>

<td>

<td>234.783

</td>

<td>

<td>270.480

</td>

<td>312.032

Line 469:

<td style="text-align: center;">11 11 7 11 11 11 7

</td>

<td>

<td>234.3255

</td>

<td>

<td>270.022

</td>

<td>312.490

Line 497:

<td style="text-align: center;">8 8 5 8 8 8 5

</td>

<td>

<td>234.152

</td>

<td>

<td>269.848

</td>

<td>312.664

Line 525:

<td style="text-align: center;">13 13 8 13 13 13 8

</td>

<td>

<td>234.003

</td>

<td>

<td>269.700

</td>

<td>312.811

Line 553:

<td style="text-align: center;">5 5 3 5 5 5 3

</td>

<td>

<td>233.7645

</td>

<td>

<td>269.461

</td>

<td>313.051

Line 581:

<td style="text-align: center;">12 12 7 12 12 12 7

</td>

<td>

<td>233.503

</td>

<td>

<td>269.200

</td>

<td>313.312

Line 609:

<td style="text-align: center;">7 7 4 7 7 7 4

</td>

<td>

<td>233.314

</td>

<td>

<td>269.011

</td>

<td>313.501

Line 637:

<td style="text-align: center;">9 9 5 9 9 9 5

</td>

<td>

<td>233.061

</td>

<td>

<td>268.7575

</td>

<td>313.754

Line 665:

<td style="text-align: center;">2 2 1 2 2 2 1

</td>

<td>

<td>232.152

</td>

<td>

<td>267.848

</td>

<td>314.664

Line 694:

<td style="text-align: center;">9 9 4 9 9 9 4

</td>

<td>

<td>231.208

</td>

<td>

<td>266.905

</td>

<td>315.609

Line 722:

<td style="text-align: center;">7 7 3 7 7 7 3

</td>

<td>

<td>230.932

</td>

<td>

<td>266.629

</td>

<td>315.883

Line 750:

<td style="text-align: center;">12 12 5 12 12 12 5

</td>

<td>

<td>230.723

</td>

<td>

<td>266.420

</td>

<td>316.092

Line 778:

<td style="text-align: center;">5 5 2 5 5 5 2

</td>

<td>

<td>230.4275

</td>

<td>

<td>266.124

</td>

<td>316.388

Line 806:

<td style="text-align: center;">13 13 5 13 13 13 5

</td>

<td>

<td>230.152

</td>

<td>

<td>265.848

</td>

<td>316.664

Line 834:

<td style="text-align: center;">8 8 3 8 8 8 3

</td>

<td>

<td>229.978

</td>

<td>

<td>265.6745

</td>

<td>316.837

Line 862:

<td style="text-align: center;">11 11 4 11 11 11 4

</td>

<td>

<td>229.771

</td>

<td>

<td>265.4675

</td>

<td>317.045

Line 890:

<td style="text-align: center;">3 3 1 3 3 3 1

</td>

<td>

<td>229.210

</td>

<td>

<td>264.907

</td>

<td>317.596

Line 918:

<td style="text-align: center;">10 10 3 10 10 10 3

</td>

<td>

<td>228.580

</td>

<td>

<td>264.277

</td>

<td>318.235

Line 946:

<td style="text-align: center;">7 7 2 7 7 7 2

</td>

<td>

<td>228.305

</td>

<td>

<td>264.002

</td>

<td>318.51

Line 974:

<td style="text-align: center;">11 11 3 11 11 11 3

</td>

<td>

<td>228.053

</td>

<td>

<td>263.750

</td>

<td>318.761

Line 1,002:

<td style="text-align: center;">4 4 1 4 4 4 1

</td>

<td>

<td>227.606

</td>

<td>

<td>263.303

</td>

<td>319.209

Line 1,031:

<td style="text-align: center;">9 9 2 9 9 9 2

</td>

<td>

<td>227.050

</td>

<td>

<td>262.746

</td>

<td>319.766

Line 1,059:

<td style="text-align: center;">5 5 1 5 5 5 1

</td>

<td>

<td>226.596

</td>

<td>

<td>262.293

</td>

<td>320.219

Line 1,087:

<td style="text-align: center;">6 6 1 6 6 6 1

</td>

<td>

<td>225.9015

</td>

<td>

<td>261.598

</td>

<td>320.914

Line 1,115:

<td style="text-align: center;">1 1 0 1 1 1 0

</td>

<td>

<td>222.152

</td>

<td>

<td>257.848

</td>

<td>324.664

@@ 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:JosephRuhf|JosephRuhf]] and made on <tt>2014-06-04 14:39:51 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2014-06-04 23:03:21 UTC</tt>.<br>
-: The original revision id was <tt>512838698</tt>.<br>
+: The original revision id was <tt>512904622</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 69: / Line 69: @@
 ||=   ||=   ||=   ||=   ||= 19\45 ||=   ||= 506.667 ||= 7 7 5 7 7 7 5 || 235.485 || 271.182 || 311.33 || 382.003 ||=   ||
 ||=   ||=   ||=   ||=   ||=   ||= 27\64 ||= 506.250 ||= 10 10 7 10 10 10 7 || 235.277 || 270.973 || 311.539 || 382.211 ||=   ||
-||=   ||=   ||= 8\19 ||=   ||=   ||=   ||= 505.263 ||= 3 3 2 3 3 3 2 ||   ||   || 312.032 || 382.705 ||= Optimum rank range (L/s=3/2) diatonic ||
+||=   ||=   ||= 8\19 ||=   ||=   ||=   ||= 505.263 ||= 3 3 2 3 3 3 2 || 234.783 || 270.480 || 312.032 || 382.705 ||= Optimum rank range (L/s=3/2) diatonic ||
-||=   ||=   ||=   ||=   ||=   ||= 29\69 ||= 504.348 ||= 11 11 7 11 11 11 7 ||   ||   || 312.490 || 383.172 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 29\69 ||= 504.348 ||= 11 11 7 11 11 11 7 || 234.3255 || 270.022 || 312.490 || 383.172 ||=   ||
-||=   ||=   ||=   ||=   ||= 21\50 ||=   ||= 504.000 ||= 8 8 5 8 8 8 5 ||   ||   || 312.664 || 383.336 ||=   ||
+||=   ||=   ||=   ||=   ||= 21\50 ||=   ||= 504.000 ||= 8 8 5 8 8 8 5 || 234.152 || 269.848 || 312.664 || 383.336 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 34\81 ||= 503.704 ||= 13 13 8 13 13 13 8 ||   ||   || 312.811 || 383.485 ||= Golden meantone ||
+||=   ||=   ||=   ||=   ||=   ||= 34\81 ||= 503.704 ||= 13 13 8 13 13 13 8 || 234.003 || 269.700 || 312.811 || 383.485 ||= Golden meantone ||
-||=   ||=   ||=   ||= 13\31 ||=   ||=   ||= 503.226 ||= 5 5 3 5 5 5 3 ||   ||   || 313.051 || 383.723 ||= Meantone is in this region ||
+||=   ||=   ||=   ||= 13\31 ||=   ||=   ||= 503.226 ||= 5 5 3 5 5 5 3 || 233.7645 || 269.461 || 313.051 || 383.723 ||= Meantone is in this region ||
-||=   ||=   ||=   ||=   ||=   ||= 31\74 ||= 502.703 ||= 12 12 7 12 12 12 7 ||   ||   || 313.312 || 383.985 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 31\74 ||= 502.703 ||= 12 12 7 12 12 12 7 || 233.503 || 269.200 || 313.312 || 383.985 ||=   ||
-||=   ||=   ||=   ||=   ||= 18\43 ||=   ||= 502.326 ||= 7 7 4 7 7 7 4 ||   ||   || 313.501 || 384.183 ||=   ||
+||=   ||=   ||=   ||=   ||= 18\43 ||=   ||= 502.326 ||= 7 7 4 7 7 7 4 || 233.314 || 269.011 || 313.501 || 384.183 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 23\55 ||= 501.818 ||= 9 9 5 9 9 9 5 ||   ||   || 313.754 || 384.428 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 23\55 ||= 501.818 ||= 9 9 5 9 9 9 5 || 233.061 || 268.7575 || 313.754 || 384.428 ||=   ||
-||=   ||= 5\12 ||=   ||=   ||=   ||=   ||= 500.000 ||= 2 2 1 2 2 2 1 ||   ||   || 314.664 || 385.336 ||= Boundary of propriety (generators
+||=   ||= 5\12 ||=   ||=   ||=   ||=   ||= 500.000 ||= 2 2 1 2 2 2 1 || 232.152 || 267.848 || 314.664 || 385.336 ||= Boundary of propriety (generators
 larger than this are proper) ||
-||=   ||=   ||=   ||=   ||=   ||= 22\53 ||= 498.113 ||= 9 9 4 9 9 9 4 ||   ||   || 315.609 || 386.278 ||= Pythagorean is around here ||
+||=   ||=   ||=   ||=   ||=   ||= 22\53 ||= 498.113 ||= 9 9 4 9 9 9 4 || 231.208 || 266.905 || 315.609 || 386.278 ||= Pythagorean is around here ||
-||=   ||=   ||=   ||=   ||= 17\41 ||=   ||= 497.591 ||= 7 7 3 7 7 7 3 ||   ||   || 315.883 || 386.556 ||=   ||
+||=   ||=   ||=   ||=   ||= 17\41 ||=   ||= 497.591 ||= 7 7 3 7 7 7 3 || 230.932 || 266.629 || 315.883 || 386.556 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 29\70 ||= 497.143 ||= 12 12 5 12 12 12 5 ||   ||   || 316.092 || 386.765 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 29\70 ||= 497.143 ||= 12 12 5 12 12 12 5 || 230.723 || 266.420 || 316.092 || 386.765 ||=   ||
-||=   ||=   ||=   ||= 12\29 ||=   ||=   ||= 496.552 ||= 5 5 2 5 5 5 2 ||   ||   || 316.388 || 387.061 ||=   ||
+||=   ||=   ||=   ||= 12\29 ||=   ||=   ||= 496.552 ||= 5 5 2 5 5 5 2 || 230.4275 || 266.124 || 316.388 || 387.061 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 31\75 ||= 496.000 ||= 13 13 5 13 13 13 5 ||   ||   || 316.664 || 387.336 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 31\75 ||= 496.000 ||= 13 13 5 13 13 13 5 || 230.152 || 265.848 || 316.664 || 387.336 ||=   ||
-||=   ||=   ||=   ||=   ||= 19\46 ||=   ||= 495.652 ||= 8 8 3 8 8 8 3 ||   ||   || 316.837 || 387.511 ||=   ||
+||=   ||=   ||=   ||=   ||= 19\46 ||=   ||= 495.652 ||= 8 8 3 8 8 8 3 || 229.978 || 265.6745 || 316.837 || 387.511 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 26\63 ||= 495.238 ||= 11 11 4 11 11 11 4 ||   ||   || 317.045 || 387.717 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 26\63 ||= 495.238 ||= 11 11 4 11 11 11 4 || 229.771 || 265.4675 || 317.045 || 387.717 ||=   ||
-||=   ||=   ||= 7\17 ||=   ||=   ||=   ||= 494.118 ||= 3 3 1 3 3 3 1 ||   ||   || 317.596 || 388.286 ||= L/s = 3 ||
+||=   ||=   ||= 7\17 ||=   ||=   ||=   ||= 494.118 ||= 3 3 1 3 3 3 1 || 229.210 || 264.907 || 317.596 || 388.286 ||= L/s = 3 ||
-||=   ||=   ||=   ||=   ||=   ||= 23\56 ||= 492.857 ||= 10 10 3 10 10 10 3 ||   ||   || 318.235 || 388.908 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 23\56 ||= 492.857 ||= 10 10 3 10 10 10 3 || 228.580 || 264.277 || 318.235 || 388.908 ||=   ||
-||=   ||=   ||=   ||=   ||= 16\39 ||=   ||= 492.308 ||= 7 7 2 7 7 7 2 ||   ||   || 318.51 || 389.182 ||=   ||
+||=   ||=   ||=   ||=   ||= 16\39 ||=   ||= 492.308 ||= 7 7 2 7 7 7 2 || 228.305 || 264.002 || 318.51 || 389.182 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 25\61 ||= 491.803 ||= 11 11 3 11 11 11 3 ||   ||   || 318.761 || 389.436 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 25\61 ||= 491.803 ||= 11 11 3 11 11 11 3 || 228.053 || 263.750 || 318.761 || 389.436 ||=   ||
-||=   ||=   ||=   ||= 9\22 ||=   ||=   ||= 490.909 ||= 4 4 1 4 4 4 1 ||   ||   || 319.209 || 389.882 ||= (No-5's) superpyth is in this region
+||=   ||=   ||=   ||= 9\22 ||=   ||=   ||= 490.909 ||= 4 4 1 4 4 4 1 || 227.606 || 263.303 || 319.209 || 389.882 ||= (No-5's) superpyth is in this region
 L/s = 4 ||
-||=   ||=   ||=   ||=   ||=   ||= 20\49 ||= 489.796 ||= 9 9 2 9 9 9 2 ||   ||   || 319.766 || 390.438 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 20\49 ||= 489.796 ||= 9 9 2 9 9 9 2 || 227.050 || 262.746 || 319.766 || 390.438 ||=   ||
-||=   ||=   ||=   ||=   ||= 11\27 ||=   ||= 488.889 ||= 5 5 1 5 5 5 1 ||   ||   || 320.219 || 390.892 ||=   ||
+||=   ||=   ||=   ||=   ||= 11\27 ||=   ||= 488.889 ||= 5 5 1 5 5 5 1 || 226.596 || 262.293 || 320.219 || 390.892 ||=   ||
-||=   ||=   ||=   ||=   ||=   ||= 13\32 ||= 487.500 ||= 6 6 1 6 6 6 1 ||   ||   || 320.914 || 391.596 ||=   ||
+||=   ||=   ||=   ||=   ||=   ||= 13\32 ||= 487.500 ||= 6 6 1 6 6 6 1 || 225.9015 || 261.598 || 320.914 || 391.596 ||=   ||
-||= 2\5 ||=   ||=   ||=   ||=   ||=   ||= 480.000 ||= 1 1 0 1 1 1 0 ||   ||   || 324.664 || 395.336 ||=   ||
+||= 2\5 ||=   ||=   ||=   ||=   ||=   ||= 480.000 ||= 1 1 0 1 1 1 0 || 222.152 || 257.848 || 324.664 || 395.336 ||=   ||
 Temperaments above 5\12 on this chart are called "negative temperaments" (as they lessen the size of the fifth) and include meantone systems such as 1/3-comma (close to 8\19) and 1/4-comma (close to 13\31). As these tunings approach 3\7, the majors become flatter and the minors become sharper.
@@ Line 441: / Line 441: @@
          &lt;td style="text-align: center;"&gt;3 3 2 3 3 3 2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;234.783&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;270.480&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;312.032&lt;br /&gt;
@@ Line 469: / Line 469: @@
          &lt;td style="text-align: center;"&gt;11 11 7 11 11 11 7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;234.3255&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;270.022&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;312.490&lt;br /&gt;
@@ Line 497: / Line 497: @@
          &lt;td style="text-align: center;"&gt;8 8 5 8 8 8 5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;234.152&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;269.848&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;312.664&lt;br /&gt;
@@ Line 525: / Line 525: @@
          &lt;td style="text-align: center;"&gt;13 13 8 13 13 13 8&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;234.003&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;269.700&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;312.811&lt;br /&gt;
@@ Line 553: / Line 553: @@
          &lt;td style="text-align: center;"&gt;5 5 3 5 5 5 3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;233.7645&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;269.461&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;313.051&lt;br /&gt;
@@ Line 581: / Line 581: @@
          &lt;td style="text-align: center;"&gt;12 12 7 12 12 12 7&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;233.503&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;269.200&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;313.312&lt;br /&gt;
@@ Line 609: / Line 609: @@
          &lt;td style="text-align: center;"&gt;7 7 4 7 7 7 4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;233.314&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;269.011&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;313.501&lt;br /&gt;
@@ Line 637: / Line 637: @@
          &lt;td style="text-align: center;"&gt;9 9 5 9 9 9 5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;233.061&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;268.7575&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;313.754&lt;br /&gt;
@@ Line 665: / Line 665: @@
          &lt;td style="text-align: center;"&gt;2 2 1 2 2 2 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;232.152&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;267.848&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;314.664&lt;br /&gt;
@@ Line 694: / Line 694: @@
          &lt;td style="text-align: center;"&gt;9 9 4 9 9 9 4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;231.208&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;266.905&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;315.609&lt;br /&gt;
@@ Line 722: / Line 722: @@
          &lt;td style="text-align: center;"&gt;7 7 3 7 7 7 3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;230.932&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;266.629&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;315.883&lt;br /&gt;
@@ Line 750: / Line 750: @@
          &lt;td style="text-align: center;"&gt;12 12 5 12 12 12 5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;230.723&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;266.420&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;316.092&lt;br /&gt;
@@ Line 778: / Line 778: @@
          &lt;td style="text-align: center;"&gt;5 5 2 5 5 5 2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;230.4275&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;266.124&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;316.388&lt;br /&gt;
@@ Line 806: / Line 806: @@
          &lt;td style="text-align: center;"&gt;13 13 5 13 13 13 5&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;230.152&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;265.848&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;316.664&lt;br /&gt;
@@ Line 834: / Line 834: @@
          &lt;td style="text-align: center;"&gt;8 8 3 8 8 8 3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;229.978&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;265.6745&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;316.837&lt;br /&gt;
@@ Line 862: / Line 862: @@
          &lt;td style="text-align: center;"&gt;11 11 4 11 11 11 4&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;229.771&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;265.4675&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;317.045&lt;br /&gt;
@@ Line 890: / Line 890: @@
          &lt;td style="text-align: center;"&gt;3 3 1 3 3 3 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;229.210&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;264.907&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;317.596&lt;br /&gt;
@@ Line 918: / Line 918: @@
          &lt;td style="text-align: center;"&gt;10 10 3 10 10 10 3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;228.580&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;264.277&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;318.235&lt;br /&gt;
@@ Line 946: / Line 946: @@
          &lt;td style="text-align: center;"&gt;7 7 2 7 7 7 2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;228.305&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;264.002&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;318.51&lt;br /&gt;
@@ Line 974: / Line 974: @@
          &lt;td style="text-align: center;"&gt;11 11 3 11 11 11 3&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;228.053&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;263.750&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;318.761&lt;br /&gt;
@@ Line 1,002: / Line 1,002: @@
          &lt;td style="text-align: center;"&gt;4 4 1 4 4 4 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;227.606&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;263.303&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;319.209&lt;br /&gt;
@@ Line 1,031: / Line 1,031: @@
          &lt;td style="text-align: center;"&gt;9 9 2 9 9 9 2&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;227.050&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;262.746&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;319.766&lt;br /&gt;
@@ Line 1,059: / Line 1,059: @@
          &lt;td style="text-align: center;"&gt;5 5 1 5 5 5 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;226.596&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;262.293&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;320.219&lt;br /&gt;
@@ Line 1,087: / Line 1,087: @@
          &lt;td style="text-align: center;"&gt;6 6 1 6 6 6 1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;225.9015&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;261.598&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;320.914&lt;br /&gt;
@@ Line 1,115: / Line 1,115: @@
          &lt;td style="text-align: center;"&gt;1 1 0 1 1 1 0&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;222.152&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;257.848&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;324.664&lt;br /&gt;