Phoenix: Difference between revisions
Wikispaces>MasonGreen1 **Imported revision 567829531 - Original comment: ** |
Wikispaces>MasonGreen1 **Imported revision 567829659 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-26 02: | : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2015-11-26 02:54:53 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>567829659</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext 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;white-space: pre-wrap ! important" class="old-revision-html">The **phoenix** tuning continuum ranges consists of a range of equally-tempered scales ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see [[11edf]] | <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;white-space: pre-wrap ! important" class="old-revision-html">The **phoenix** tuning continuum ranges consists of a range of equally-tempered scales ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see [[11edf]]). All of these scales stretch the octave by around 8 to 12 cents. A distinctive feature of phoenix-tuned scales is that prime-numbered harmonics are, on average, approximated more reliably than composite ones. Concentrating the error around composites provides greater overall benefit to tempering. | ||
I (Mason Green) chose the name phoenix because these scales approximate most small intervals reasonably well, but they have a noticeable weakness at the 8th harmonic ratio (8:1) which falls almost exactly between two scale degrees; the 9:1, 10:1 and 12:1 are also not approximated well. There is also a long stretch of missed harmonics from 24 (or 25) to 31. Figuratively, the scale, like a phoenix, "dies" at 24 and rises from the ashes again at 31 or 32. | I (Mason Green) chose the name phoenix because these scales approximate most small intervals reasonably well, but they have a noticeable weakness at the 8th harmonic ratio (8:1) which falls almost exactly between two scale degrees; the 9:1, 10:1 and 12:1 are also not approximated well. There is also a long stretch of missed harmonics from 24 (or 25) to 31. Figuratively, the scale, like a phoenix, "dies" at 24 and rises from the ashes again at 31 or 32. | ||
| Line 26: | Line 26: | ||
Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic. Pianos are good instruments for phoenix because they have stretched octaves already. | Phoenix scales are best used over only a finite range of around five octaves; harmonics larger than this range are once again matched poorly. A phoenix piano could be built and would have around 97 keys on it (which is only slightly more than an ordinary piano); pianos are especially good instruments for phoenix because they have built-in octave stretching already. Another option though is to end at 87 keys (one fewer than an ordinary piano) since there the largest interval here is the 24th harmonic. Pianos are good instruments for phoenix because they have stretched octaves already. | ||
|| Interval || Width in steps || 16ed9:5 width cents (min) || 11edf width cents | || Interval || Width in steps || 16ed9:5 width cents (min) || 11edf width cents (max) || Equivalencies (closest listed first) || | ||
|| Chromatic semitone || 1 || || 63.814 | || Chromatic semitone || 1 || || 63.814 || 28:27, 25:24, 33:32 || | ||
|| Diatonic semitone || 2 || || 127.628 | || Diatonic semitone || 2 || || 127.628 || 15:14, 16:15 || | ||
|| Whole tone || 3 || || 191.442 | || Whole tone || 3 || || 191.442 || 10:9, 9:8, 8:7(//functional//) || | ||
|| Subminor third || 4 || || 255.256 | || Subminor third || 4 || || 255.256 || 7:6, 8:7 || | ||
|| Minor third || 5 || || 319.070 | || Minor third || 5 || || 319.070 || 6:5 || | ||
|| Major third || 6 || || 382.884 | || Major third || 6 || || 382.884 || 5:4 || | ||
|| Supermajor third || 7 || || 446.699 | || Supermajor third || 7 || || 446.699 || 9:7 || | ||
|| Perfect fourth || 8 || || 510.513 | || Perfect fourth || 8 || || 510.513 || 4:3 || | ||
|| Augmented fourth || 9 || || 574.327 | || Augmented fourth || 9 || || 574.327 || 7:5 || | ||
|| Diminished fifth || 10 || || 638.141 || || | || Diminished fifth || 10 || || 638.141 || || | ||
|| Perfect fifth || 11 || || 701.955 | || Perfect fifth || 11 || || 701.955 || 3:2 || | ||
|| Subminor sixth || 12 || || 765.769 | || Subminor sixth || 12 || || 765.769 || 14:9 || | ||
|| Minor sixth || 13 || || 829.583 | || Minor sixth || 13 || || 829.583 || 8:5 || | ||
|| Major sixth || 14 || || 893.397 | || Major sixth || 14 || || 893.397 || 5:3 || | ||
|| Subminor seventh || 15 || || 957.211 | || Subminor seventh || 15 || || 957.211 || 7:4 || | ||
|| Minor seventh || 16 || || 1021.025 | || Minor seventh || 16 || || 1021.025 || 9:5 || | ||
|| Major seventh || 17 || || 1084.840 | || Major seventh || 17 || || 1084.840 || 15:8 || | ||
|| Diminished octave || 18 || || 1148.654 | || Diminished octave || 18 || || 1148.654 || 11:6 || | ||
|| Octave (stretched) || 19 || || 1212.468 | || Octave (stretched) || 19 || || 1212.468 || 2:1 || | ||
|| Chromatic minor ninth || 20 || || 1276.282 | || Chromatic minor ninth || 20 || || 1276.282 || || | ||
|| Diatonic minor ninth || 21 || || 1340.096 | || Diatonic minor ninth || 21 || || 1340.096 || 13:6 || | ||
|| Major ninth || 22 || || 1403.910 | || Major ninth || 22 || || 1403.910 || 9:4 || | ||
|| Subminor tenth || 23 || || 1467.724 | || Subminor tenth || 23 || || 1467.724 || 7:3 || | ||
|| Minor tenth || 24 || || 1531.538 | || Minor tenth || 24 || || 1531.538 || 17:7, 12:5 || | ||
|| Major tenth || 25 || || 1595.352 | || Major tenth || 25 || || 1595.352 || 5:2, 19:8 || | ||
|| Minor eleventh || 26 || || 1659.167 | || Minor eleventh || 26 || || 1659.167 || 13:5 || | ||
|| Perfect eleventh || 27 || || 1722.980 | || Perfect eleventh || 27 || || 1722.980 || 8:3 || | ||
|| Augmented eleventh, diminished twelfth || 28 || || 1786.795 | || Augmented eleventh, diminished twelfth || 28 || || 1786.795 || 14:15 || | ||
|| Minor twelfth || 29 || || 1850.609 | || Minor twelfth || 29 || || 1850.609 || || | ||
|| Perfect twelfth, tritave, 3rd harmonic || 30 || || 1914.423 | || Perfect twelfth, tritave, 3rd harmonic || 30 || || 1914.423 || 3:1 || | ||
|| Minor || 31 || || 1978.237 | || Minor || 31 || || 1978.237 || || | ||
|| Neutral thirteenth || 32 || || 2042.051 | || Neutral thirteenth || 32 || || 2042.051 || 13:4 || | ||
|| Major thirteenth || 33 || || 2105.865 | || Major thirteenth || 33 || || 2105.865 || 10:3, 27:8 || | ||
|| Subminor fourteenth || 34 || || 2169.680 | || Subminor fourteenth || 34 || || 2169.680 || 7:2 || | ||
|| Minor fourteenth || 35 || || 2233.493 | || Minor fourteenth || 35 || || 2233.493 || 18:5, 11:3 || | ||
|| Major fourteenth || 36 || || 2297.307 | || Major fourteenth || 36 || || 2297.307 || 15:4 || | ||
|| Double octave, fifteenth (flat) || 37 || || 2361.121 | || Double octave, fifteenth (flat) || 37 || || 2361.121 || || | ||
|| Double octave, fifteenth (sharp) || 38 || || 2424.935 | || Double octave, fifteenth (sharp) || 38 || || 2424.935 || 4:1 || | ||
|| Minor sixteenth || 39 || || 2488.750 | || Minor sixteenth || 39 || || 2488.750 || 19:9 || | ||
|| Neutral sixteenth || 40 || || 2552.564 | || Neutral sixteenth || 40 || || 2552.564 || 13:4 || | ||
|| Major sixteenth || 41 || || 2616.378 | || Major sixteenth || 41 || || 2616.378 || 9:2 || | ||
|| Minor seventeenth || 42 || || 2680.192 | || Minor seventeenth || 42 || || 2680.192 || 14:3 || | ||
|| Neutral seventeenth || 43 || || 2744.006 | || Neutral seventeenth || 43 || || 2744.006 || || | ||
|| Major seventeenth; fifth harmonic || 44 || || 2807.82 | || Major seventeenth; fifth harmonic || 44 || || 2807.82 || 5:1 || | ||
|| Minor eighteenth || 45 || || 2871.634 | || Minor eighteenth || 45 || || 2871.634 || 21:4 || | ||
|| Major eighteenth || 46 || || 2935.448 | || Major eighteenth || 46 || || 2935.448 || 11:2 (flat) || | ||
|| Augmented eighteenth; diminished nineteenth || 47 || || 2999.262 | || Augmented eighteenth; diminished nineteenth || 47 || || 2999.262 || 11:2 (sharp) || | ||
|| Minor nineteenth || 48 || || 3063.076 | || Minor nineteenth || 48 || || 3063.076 || || | ||
|| Perfect nineteenth, sixth harmonic || 49 || || 3126.890 | || Perfect nineteenth, sixth harmonic || 49 || || 3126.890 || 6:1 || | ||
|| Minor twentieth || 50 || || 3190.705 | || Minor twentieth || 50 || || 3190.705 || 19:3 || | ||
|| Neutral twentieth || 51 || || 3254.519 | || Neutral twentieth || 51 || || 3254.519 || 13:2 || | ||
|| Major twentieth || 52 || || 3318.333 | || Major twentieth || 52 || || 3318.333 || 27:4 || | ||
|| (Sub)minor twenty-first; 7th harmonic || 53 || || 3382.147 | || (Sub)minor twenty-first; 7th harmonic || 53 || || 3382.147 || 7:1 || | ||
|| Minor/neutral twenty-first || 54 || || 3445.961 | || Minor/neutral twenty-first || 54 || || 3445.961 || 22:3 || | ||
|| Major twenty-first || 55 || || 3509.775 | || Major twenty-first || 55 || || 3509.775 || 15:2 || | ||
|| Twenty-second, triple octave, 8th harmonic (flat) || 56 || || 3573.589 | || Twenty-second, triple octave, 8th harmonic (flat) || 56 || || 3573.589 || 8:1 (flat) || | ||
|| Twenty-second, triple octave, 8th harmonic (sharp) || 57 || || 3637.403 | || Twenty-second, triple octave, 8th harmonic (sharp) || 57 || || 3637.403 || 8:1 (sharp) || | ||
|| Minor twenty-third || 58 || || 3701.217 | || Minor twenty-third || 58 || || 3701.217 || 17:2 || | ||
|| Neutral twenty-third || 59 || || 3765.031 | || Neutral twenty-third || 59 || || 3765.031 || || | ||
|| Major twenty-third; 9th harmonic || 60 || || 3828.845 | || Major twenty-third; 9th harmonic || 60 || || 3828.845 || 9:1 || | ||
|| Minor twenty-fourth || 61 || || 3892.659 | || Minor twenty-fourth || 61 || || 3892.659 || 19:2 || | ||
|| Neutral twenty-fourth || 62 || || 3956.474 | || Neutral twenty-fourth || 62 || || 3956.474 || 29:3 || | ||
|| Major twenty-fourth, decade || 63 || || 4020.288 | || Major twenty-fourth, decade || 63 || || 4020.288 || 10:1 (sharp), 31:3 (flat) || | ||
|| Twenty-fifth || 64 || || 4084.102 | || Twenty-fifth || 64 || || 4084.102 || 21:2 || | ||
|| Half-augmented twenty-fifth; 11th harmonic || 65 || || 4147.916 | || Half-augmented twenty-fifth; 11th harmonic || 65 || || 4147.916 || 11:1 || | ||
|| Diminished twenty-sixth || 66 || || 4211.730 | || Diminished twenty-sixth || 66 || || 4211.730 || 34:3 || | ||
|| Minor twenty-sixth || 67 || || 4275.544 | || Minor twenty-sixth || 67 || || 4275.544 || 12:1 (flat) || | ||
|| Major twenty-sixth || 68 || || 4339.358 | || Major twenty-sixth || 68 || || 4339.358 || 12:1 (sharp) || | ||
|| Minor twenty-seventh || 69 || || 4403.172 | || Minor twenty-seventh || 69 || || 4403.172 || || | ||
|| Neutral twenty-seventh, thirteenth harmonic || 70 || || 4466.986 | || Neutral twenty-seventh, thirteenth harmonic || 70 || || 4466.986 || 13:1 || | ||
|| Major twenty-seventh || 71 || || 4530.800 | || Major twenty-seventh || 71 || || 4530.800 || 27:2 || | ||
|| Minor twenty-eighth, 14th harmonic || 72 || || 4594.615 | || Minor twenty-eighth, 14th harmonic || 72 || || 4594.615 || 14:1 || | ||
|| Neutral twenty-eighth || 73 || || 4658.429 | || Neutral twenty-eighth || 73 || || 4658.429 || 15:1 (flat) || | ||
|| Major twenty-eighth || 74 || || 4722.243 | || Major twenty-eighth || 74 || || 4722.243 || 15:1 (sharp) || | ||
|| Twenty-ninth; quadruple octave, 16th harmonic || 75 || || 4786.057 | || Twenty-ninth; quadruple octave, 16th harmonic || 75 || || 4786.057 || 16:1 || | ||
|| Half-augmented twenty-ninth || 76 || || 4849.871 | || Half-augmented twenty-ninth || 76 || || 4849.871 || 33:2 || | ||
|| Minor thirtieth, 17th harmonic || 77 || || 4913.685 | || Minor thirtieth, 17th harmonic || 77 || || 4913.685 || 17:1 || | ||
|| Chromatic major thirtieth || 78 || || 4977.499 | || Chromatic major thirtieth || 78 || || 4977.499 || 35:2 || | ||
|| Diatonic major thirtieth || 79 || || 5041.313 | || Diatonic major thirtieth || 79 || || 5041.313 || 37:2 || | ||
|| Minor thirty-first, 19th harmonic || 80 || || 5105.127 | || Minor thirty-first, 19th harmonic || 80 || || 5105.127 || 19:1 || | ||
|| Neutral thirty-first || 81 || || 5168.941 | || Neutral thirty-first || 81 || || 5168.941 || || | ||
|| Major thirty-first || 82 || || 5232.755 | || Major thirty-first || 82 || || 5232.755 || 41:2 || | ||
|| Thirty-second, 21st harmonic || 83 || || 5296.570 | || Thirty-second, 21st harmonic || 83 || || 5296.570 || 21:1 || | ||
|| Half-augmented thirty-second, 22nd harmonic || 84 || || 5360.384 | || Half-augmented thirty-second, 22nd harmonic || 84 || || 5360.384 || 22:1 || | ||
|| 23rd harmonic || 85 || || 5424.198 | || 23rd harmonic || 85 || || 5424.198 || 23:1 || | ||
|| Thirty-third || 86 | || Thirty-third || 86 || || || 24:1, 47:2 * || | ||
|| Half-augmented thirty-third || 87 || || 5551.826 | || Half-augmented thirty-third || 87 || || 5551.826 || 49:2 || | ||
|| Minor thirty-fourth || 88 || || 5615.640 | || Minor thirty-fourth || 88 || || 5615.640 || 51:2 || | ||
|| Major thirty-fourth || 89 || || 5679.454 | || Major thirty-fourth || 89 || || 5679.454 || 53:2 || | ||
|| Supermajor thirty-fourth || 90 || || 5743.268 | || Supermajor thirty-fourth || 90 || || 5743.268 || 55:2 || | ||
|| Minor thirty-fifth || 91 || || 5807.082 | || Minor thirty-fifth || 91 || || 5807.082 || 57:2 || | ||
|| Neutral/major thirty-fifth || 92 || || 5870.896 | || Neutral/major thirty-fifth || 92 || || 5870.896 || || | ||
|| 31st harmonic || 93 || || 5934.710 | || 31st harmonic || 93 || || 5934.710 || 31:1 (wide-end only) || | ||
|| 32nd harmonic || 94 || || 5998.52 | || 32nd harmonic || 94 || || 5998.52 || 32:1 || | ||
|| 33rd harmonic || 95 || || 6062.339 | || 33rd harmonic || 95 || || 6062.339 || 33:1 || | ||
|| 34th harmonic || 96 || || 6126.153 | || 34th harmonic || 96 || || 6126.153 || 34:1 (narrow-end only) || | ||
Harmonics beyond the 34th are not matched well. | Harmonics beyond the 34th are not matched well. | ||
The wide end of the phoenix continuum matches 86 scale degrees to the 24th harmonic, whereas the narrow end matches 86 degrees to 47:2. The wide end of the continuum matches the 31st harmonic, the narrow end does not. On the other hand, the narrow end of the continuum matches the 34th harmonic, unlike the wide end.</pre></div> | The wide end of the phoenix continuum matches 86 scale degrees to the 24th harmonic, whereas the narrow end matches 86 degrees to 47:2. The wide end of the continuum matches the 31st harmonic, the narrow end does not. On the other hand, the narrow end of the continuum matches the 34th harmonic, unlike the wide end.</pre></div> | ||
<h4>Original HTML content:</h4> | <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>Phoenix</title></head><body>The <strong>phoenix</strong> tuning continuum ranges consists of a range of equally-tempered scales ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see <a class="wiki_link" href="/11edf">11edf</a> | <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>Phoenix</title></head><body>The <strong>phoenix</strong> tuning continuum ranges consists of a range of equally-tempered scales ranging from 63.5998 cents (which divides the just 9:5 interval into 16 equal parts), through 63.8141 cents (which divides the just perfect fifth into 11 equal parts, see <a class="wiki_link" href="/11edf">11edf</a>). All of these scales stretch the octave by around 8 to 12 cents. A distinctive feature of phoenix-tuned scales is that prime-numbered harmonics are, on average, approximated more reliably than composite ones. Concentrating the error around composites provides greater overall benefit to tempering.<br /> | ||
<br /> | <br /> | ||
I (Mason Green) chose the name phoenix because these scales approximate most small intervals reasonably well, but they have a noticeable weakness at the 8th harmonic ratio (8:1) which falls almost exactly between two scale degrees; the 9:1, 10:1 and 12:1 are also not approximated well. There is also a long stretch of missed harmonics from 24 (or 25) to 31. Figuratively, the scale, like a phoenix, &quot;dies&quot; at 24 and rises from the ashes again at 31 or 32.<br /> | I (Mason Green) chose the name phoenix because these scales approximate most small intervals reasonably well, but they have a noticeable weakness at the 8th harmonic ratio (8:1) which falls almost exactly between two scale degrees; the 9:1, 10:1 and 12:1 are also not approximated well. There is also a long stretch of missed harmonics from 24 (or 25) to 31. Figuratively, the scale, like a phoenix, &quot;dies&quot; at 24 and rises from the ashes again at 31 or 32.<br /> | ||
| Line 157: | Line 157: | ||
<td>16ed9:5 width cents (min)<br /> | <td>16ed9:5 width cents (min)<br /> | ||
</td> | </td> | ||
<td>11edf width cents | <td>11edf width cents (max)<br /> | ||
</td> | </td> | ||
<td>Equivalencies (closest listed first)<br /> | <td>Equivalencies (closest listed first)<br /> | ||
| Line 172: | Line 170: | ||
</td> | </td> | ||
<td>63.814<br /> | <td>63.814<br /> | ||
</td> | </td> | ||
<td>28:27, 25:24, 33:32<br /> | <td>28:27, 25:24, 33:32<br /> | ||
| Line 186: | Line 182: | ||
</td> | </td> | ||
<td>127.628<br /> | <td>127.628<br /> | ||
</td> | </td> | ||
<td>15:14, 16:15<br /> | <td>15:14, 16:15<br /> | ||
| Line 200: | Line 194: | ||
</td> | </td> | ||
<td>191.442<br /> | <td>191.442<br /> | ||
</td> | </td> | ||
<td>10:9, 9:8, 8:7(<em>functional</em>)<br /> | <td>10:9, 9:8, 8:7(<em>functional</em>)<br /> | ||
| Line 214: | Line 206: | ||
</td> | </td> | ||
<td>255.256<br /> | <td>255.256<br /> | ||
</td> | </td> | ||
<td>7:6, 8:7<br /> | <td>7:6, 8:7<br /> | ||
| Line 228: | Line 218: | ||
</td> | </td> | ||
<td>319.070<br /> | <td>319.070<br /> | ||
</td> | </td> | ||
<td>6:5<br /> | <td>6:5<br /> | ||
| Line 242: | Line 230: | ||
</td> | </td> | ||
<td>382.884<br /> | <td>382.884<br /> | ||
</td> | </td> | ||
<td>5:4<br /> | <td>5:4<br /> | ||
| Line 256: | Line 242: | ||
</td> | </td> | ||
<td>446.699<br /> | <td>446.699<br /> | ||
</td> | </td> | ||
<td>9:7<br /> | <td>9:7<br /> | ||
| Line 270: | Line 254: | ||
</td> | </td> | ||
<td>510.513<br /> | <td>510.513<br /> | ||
</td> | </td> | ||
<td>4:3<br /> | <td>4:3<br /> | ||
| Line 284: | Line 266: | ||
</td> | </td> | ||
<td>574.327<br /> | <td>574.327<br /> | ||
</td> | </td> | ||
<td>7:5<br /> | <td>7:5<br /> | ||
| Line 298: | Line 278: | ||
</td> | </td> | ||
<td>638.141<br /> | <td>638.141<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 312: | Line 290: | ||
</td> | </td> | ||
<td>701.955<br /> | <td>701.955<br /> | ||
</td> | </td> | ||
<td>3:2<br /> | <td>3:2<br /> | ||
| Line 326: | Line 302: | ||
</td> | </td> | ||
<td>765.769<br /> | <td>765.769<br /> | ||
</td> | </td> | ||
<td>14:9<br /> | <td>14:9<br /> | ||
| Line 340: | Line 314: | ||
</td> | </td> | ||
<td>829.583<br /> | <td>829.583<br /> | ||
</td> | </td> | ||
<td>8:5<br /> | <td>8:5<br /> | ||
| Line 354: | Line 326: | ||
</td> | </td> | ||
<td>893.397<br /> | <td>893.397<br /> | ||
</td> | </td> | ||
<td>5:3<br /> | <td>5:3<br /> | ||
| Line 368: | Line 338: | ||
</td> | </td> | ||
<td>957.211<br /> | <td>957.211<br /> | ||
</td> | </td> | ||
<td>7:4<br /> | <td>7:4<br /> | ||
| Line 382: | Line 350: | ||
</td> | </td> | ||
<td>1021.025<br /> | <td>1021.025<br /> | ||
</td> | </td> | ||
<td>9:5<br /> | <td>9:5<br /> | ||
| Line 396: | Line 362: | ||
</td> | </td> | ||
<td>1084.840<br /> | <td>1084.840<br /> | ||
</td> | </td> | ||
<td>15:8<br /> | <td>15:8<br /> | ||
| Line 410: | Line 374: | ||
</td> | </td> | ||
<td>1148.654<br /> | <td>1148.654<br /> | ||
</td> | </td> | ||
<td>11:6<br /> | <td>11:6<br /> | ||
| Line 424: | Line 386: | ||
</td> | </td> | ||
<td>1212.468<br /> | <td>1212.468<br /> | ||
</td> | </td> | ||
<td>2:1<br /> | <td>2:1<br /> | ||
| Line 438: | Line 398: | ||
</td> | </td> | ||
<td>1276.282<br /> | <td>1276.282<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 452: | Line 410: | ||
</td> | </td> | ||
<td>1340.096<br /> | <td>1340.096<br /> | ||
</td> | </td> | ||
<td>13:6<br /> | <td>13:6<br /> | ||
| Line 466: | Line 422: | ||
</td> | </td> | ||
<td>1403.910<br /> | <td>1403.910<br /> | ||
</td> | </td> | ||
<td>9:4<br /> | <td>9:4<br /> | ||
| Line 480: | Line 434: | ||
</td> | </td> | ||
<td>1467.724<br /> | <td>1467.724<br /> | ||
</td> | </td> | ||
<td>7:3<br /> | <td>7:3<br /> | ||
| Line 494: | Line 446: | ||
</td> | </td> | ||
<td>1531.538<br /> | <td>1531.538<br /> | ||
</td> | </td> | ||
<td>17:7, 12:5<br /> | <td>17:7, 12:5<br /> | ||
| Line 508: | Line 458: | ||
</td> | </td> | ||
<td>1595.352<br /> | <td>1595.352<br /> | ||
</td> | </td> | ||
<td>5:2, 19:8<br /> | <td>5:2, 19:8<br /> | ||
| Line 522: | Line 470: | ||
</td> | </td> | ||
<td>1659.167<br /> | <td>1659.167<br /> | ||
</td> | </td> | ||
<td>13:5<br /> | <td>13:5<br /> | ||
| Line 536: | Line 482: | ||
</td> | </td> | ||
<td>1722.980<br /> | <td>1722.980<br /> | ||
</td> | </td> | ||
<td>8:3<br /> | <td>8:3<br /> | ||
| Line 550: | Line 494: | ||
</td> | </td> | ||
<td>1786.795<br /> | <td>1786.795<br /> | ||
</td> | </td> | ||
<td>14:15<br /> | <td>14:15<br /> | ||
| Line 564: | Line 506: | ||
</td> | </td> | ||
<td>1850.609<br /> | <td>1850.609<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 578: | Line 518: | ||
</td> | </td> | ||
<td>1914.423<br /> | <td>1914.423<br /> | ||
</td> | </td> | ||
<td>3:1<br /> | <td>3:1<br /> | ||
| Line 592: | Line 530: | ||
</td> | </td> | ||
<td>1978.237<br /> | <td>1978.237<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 606: | Line 542: | ||
</td> | </td> | ||
<td>2042.051<br /> | <td>2042.051<br /> | ||
</td> | </td> | ||
<td>13:4<br /> | <td>13:4<br /> | ||
| Line 620: | Line 554: | ||
</td> | </td> | ||
<td>2105.865<br /> | <td>2105.865<br /> | ||
</td> | </td> | ||
<td>10:3, 27:8<br /> | <td>10:3, 27:8<br /> | ||
| Line 634: | Line 566: | ||
</td> | </td> | ||
<td>2169.680<br /> | <td>2169.680<br /> | ||
</td> | </td> | ||
<td>7:2<br /> | <td>7:2<br /> | ||
| Line 648: | Line 578: | ||
</td> | </td> | ||
<td>2233.493<br /> | <td>2233.493<br /> | ||
</td> | </td> | ||
<td>18:5, 11:3<br /> | <td>18:5, 11:3<br /> | ||
| Line 662: | Line 590: | ||
</td> | </td> | ||
<td>2297.307<br /> | <td>2297.307<br /> | ||
</td> | </td> | ||
<td>15:4<br /> | <td>15:4<br /> | ||
| Line 676: | Line 602: | ||
</td> | </td> | ||
<td>2361.121<br /> | <td>2361.121<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 690: | Line 614: | ||
</td> | </td> | ||
<td>2424.935<br /> | <td>2424.935<br /> | ||
</td> | </td> | ||
<td>4:1<br /> | <td>4:1<br /> | ||
| Line 704: | Line 626: | ||
</td> | </td> | ||
<td>2488.750<br /> | <td>2488.750<br /> | ||
</td> | </td> | ||
<td>19:9<br /> | <td>19:9<br /> | ||
| Line 718: | Line 638: | ||
</td> | </td> | ||
<td>2552.564<br /> | <td>2552.564<br /> | ||
</td> | </td> | ||
<td>13:4<br /> | <td>13:4<br /> | ||
| Line 732: | Line 650: | ||
</td> | </td> | ||
<td>2616.378<br /> | <td>2616.378<br /> | ||
</td> | </td> | ||
<td>9:2<br /> | <td>9:2<br /> | ||
| Line 746: | Line 662: | ||
</td> | </td> | ||
<td>2680.192<br /> | <td>2680.192<br /> | ||
</td> | </td> | ||
<td>14:3<br /> | <td>14:3<br /> | ||
| Line 760: | Line 674: | ||
</td> | </td> | ||
<td>2744.006<br /> | <td>2744.006<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 774: | Line 686: | ||
</td> | </td> | ||
<td>2807.82<br /> | <td>2807.82<br /> | ||
</td> | </td> | ||
<td>5:1<br /> | <td>5:1<br /> | ||
| Line 788: | Line 698: | ||
</td> | </td> | ||
<td>2871.634<br /> | <td>2871.634<br /> | ||
</td> | </td> | ||
<td>21:4<br /> | <td>21:4<br /> | ||
| Line 802: | Line 710: | ||
</td> | </td> | ||
<td>2935.448<br /> | <td>2935.448<br /> | ||
</td> | </td> | ||
<td>11:2 (flat)<br /> | <td>11:2 (flat)<br /> | ||
| Line 816: | Line 722: | ||
</td> | </td> | ||
<td>2999.262<br /> | <td>2999.262<br /> | ||
</td> | </td> | ||
<td>11:2 (sharp)<br /> | <td>11:2 (sharp)<br /> | ||
| Line 830: | Line 734: | ||
</td> | </td> | ||
<td>3063.076<br /> | <td>3063.076<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 844: | Line 746: | ||
</td> | </td> | ||
<td>3126.890<br /> | <td>3126.890<br /> | ||
</td> | </td> | ||
<td>6:1<br /> | <td>6:1<br /> | ||
| Line 858: | Line 758: | ||
</td> | </td> | ||
<td>3190.705<br /> | <td>3190.705<br /> | ||
</td> | </td> | ||
<td>19:3<br /> | <td>19:3<br /> | ||
| Line 872: | Line 770: | ||
</td> | </td> | ||
<td>3254.519<br /> | <td>3254.519<br /> | ||
</td> | </td> | ||
<td>13:2<br /> | <td>13:2<br /> | ||
| Line 886: | Line 782: | ||
</td> | </td> | ||
<td>3318.333<br /> | <td>3318.333<br /> | ||
</td> | </td> | ||
<td>27:4<br /> | <td>27:4<br /> | ||
| Line 900: | Line 794: | ||
</td> | </td> | ||
<td>3382.147<br /> | <td>3382.147<br /> | ||
</td> | </td> | ||
<td>7:1<br /> | <td>7:1<br /> | ||
| Line 914: | Line 806: | ||
</td> | </td> | ||
<td>3445.961<br /> | <td>3445.961<br /> | ||
</td> | </td> | ||
<td>22:3<br /> | <td>22:3<br /> | ||
| Line 928: | Line 818: | ||
</td> | </td> | ||
<td>3509.775<br /> | <td>3509.775<br /> | ||
</td> | </td> | ||
<td>15:2<br /> | <td>15:2<br /> | ||
| Line 942: | Line 830: | ||
</td> | </td> | ||
<td>3573.589<br /> | <td>3573.589<br /> | ||
</td> | </td> | ||
<td>8:1 (flat)<br /> | <td>8:1 (flat)<br /> | ||
| Line 956: | Line 842: | ||
</td> | </td> | ||
<td>3637.403<br /> | <td>3637.403<br /> | ||
</td> | </td> | ||
<td>8:1 (sharp)<br /> | <td>8:1 (sharp)<br /> | ||
| Line 970: | Line 854: | ||
</td> | </td> | ||
<td>3701.217<br /> | <td>3701.217<br /> | ||
</td> | </td> | ||
<td>17:2<br /> | <td>17:2<br /> | ||
| Line 984: | Line 866: | ||
</td> | </td> | ||
<td>3765.031<br /> | <td>3765.031<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 998: | Line 878: | ||
</td> | </td> | ||
<td>3828.845<br /> | <td>3828.845<br /> | ||
</td> | </td> | ||
<td>9:1<br /> | <td>9:1<br /> | ||
| Line 1,012: | Line 890: | ||
</td> | </td> | ||
<td>3892.659<br /> | <td>3892.659<br /> | ||
</td> | </td> | ||
<td>19:2<br /> | <td>19:2<br /> | ||
| Line 1,026: | Line 902: | ||
</td> | </td> | ||
<td>3956.474<br /> | <td>3956.474<br /> | ||
</td> | </td> | ||
<td>29:3<br /> | <td>29:3<br /> | ||
| Line 1,040: | Line 914: | ||
</td> | </td> | ||
<td>4020.288<br /> | <td>4020.288<br /> | ||
</td> | </td> | ||
<td>10:1 (sharp), 31:3 (flat)<br /> | <td>10:1 (sharp), 31:3 (flat)<br /> | ||
| Line 1,054: | Line 926: | ||
</td> | </td> | ||
<td>4084.102<br /> | <td>4084.102<br /> | ||
</td> | </td> | ||
<td>21:2<br /> | <td>21:2<br /> | ||
| Line 1,068: | Line 938: | ||
</td> | </td> | ||
<td>4147.916<br /> | <td>4147.916<br /> | ||
</td> | </td> | ||
<td>11:1<br /> | <td>11:1<br /> | ||
| Line 1,082: | Line 950: | ||
</td> | </td> | ||
<td>4211.730<br /> | <td>4211.730<br /> | ||
</td> | </td> | ||
<td>34:3<br /> | <td>34:3<br /> | ||
| Line 1,096: | Line 962: | ||
</td> | </td> | ||
<td>4275.544<br /> | <td>4275.544<br /> | ||
</td> | </td> | ||
<td>12:1 (flat)<br /> | <td>12:1 (flat)<br /> | ||
| Line 1,110: | Line 974: | ||
</td> | </td> | ||
<td>4339.358<br /> | <td>4339.358<br /> | ||
</td> | </td> | ||
<td>12:1 (sharp)<br /> | <td>12:1 (sharp)<br /> | ||
| Line 1,124: | Line 986: | ||
</td> | </td> | ||
<td>4403.172<br /> | <td>4403.172<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,138: | Line 998: | ||
</td> | </td> | ||
<td>4466.986<br /> | <td>4466.986<br /> | ||
</td> | </td> | ||
<td>13:1<br /> | <td>13:1<br /> | ||
| Line 1,152: | Line 1,010: | ||
</td> | </td> | ||
<td>4530.800<br /> | <td>4530.800<br /> | ||
</td> | </td> | ||
<td>27:2<br /> | <td>27:2<br /> | ||
| Line 1,166: | Line 1,022: | ||
</td> | </td> | ||
<td>4594.615<br /> | <td>4594.615<br /> | ||
</td> | </td> | ||
<td>14:1<br /> | <td>14:1<br /> | ||
| Line 1,180: | Line 1,034: | ||
</td> | </td> | ||
<td>4658.429<br /> | <td>4658.429<br /> | ||
</td> | </td> | ||
<td>15:1 (flat)<br /> | <td>15:1 (flat)<br /> | ||
| Line 1,194: | Line 1,046: | ||
</td> | </td> | ||
<td>4722.243<br /> | <td>4722.243<br /> | ||
</td> | </td> | ||
<td>15:1 (sharp)<br /> | <td>15:1 (sharp)<br /> | ||
| Line 1,208: | Line 1,058: | ||
</td> | </td> | ||
<td>4786.057<br /> | <td>4786.057<br /> | ||
</td> | </td> | ||
<td>16:1<br /> | <td>16:1<br /> | ||
| Line 1,222: | Line 1,070: | ||
</td> | </td> | ||
<td>4849.871<br /> | <td>4849.871<br /> | ||
</td> | </td> | ||
<td>33:2<br /> | <td>33:2<br /> | ||
| Line 1,236: | Line 1,082: | ||
</td> | </td> | ||
<td>4913.685<br /> | <td>4913.685<br /> | ||
</td> | </td> | ||
<td>17:1<br /> | <td>17:1<br /> | ||
| Line 1,250: | Line 1,094: | ||
</td> | </td> | ||
<td>4977.499<br /> | <td>4977.499<br /> | ||
</td> | </td> | ||
<td>35:2<br /> | <td>35:2<br /> | ||
| Line 1,264: | Line 1,106: | ||
</td> | </td> | ||
<td>5041.313<br /> | <td>5041.313<br /> | ||
</td> | </td> | ||
<td>37:2<br /> | <td>37:2<br /> | ||
| Line 1,278: | Line 1,118: | ||
</td> | </td> | ||
<td>5105.127<br /> | <td>5105.127<br /> | ||
</td> | </td> | ||
<td>19:1<br /> | <td>19:1<br /> | ||
| Line 1,292: | Line 1,130: | ||
</td> | </td> | ||
<td>5168.941<br /> | <td>5168.941<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,306: | Line 1,142: | ||
</td> | </td> | ||
<td>5232.755<br /> | <td>5232.755<br /> | ||
</td> | </td> | ||
<td>41:2<br /> | <td>41:2<br /> | ||
| Line 1,320: | Line 1,154: | ||
</td> | </td> | ||
<td>5296.570<br /> | <td>5296.570<br /> | ||
</td> | </td> | ||
<td>21:1<br /> | <td>21:1<br /> | ||
| Line 1,334: | Line 1,166: | ||
</td> | </td> | ||
<td>5360.384<br /> | <td>5360.384<br /> | ||
</td> | </td> | ||
<td>22:1<br /> | <td>22:1<br /> | ||
| Line 1,348: | Line 1,178: | ||
</td> | </td> | ||
<td>5424.198<br /> | <td>5424.198<br /> | ||
</td> | </td> | ||
<td>23:1<br /> | <td>23:1<br /> | ||
| Line 1,358: | Line 1,186: | ||
</td> | </td> | ||
<td>86<br /> | <td>86<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,376: | Line 1,202: | ||
</td> | </td> | ||
<td>5551.826<br /> | <td>5551.826<br /> | ||
</td> | </td> | ||
<td>49:2<br /> | <td>49:2<br /> | ||
| Line 1,390: | Line 1,214: | ||
</td> | </td> | ||
<td>5615.640<br /> | <td>5615.640<br /> | ||
</td> | </td> | ||
<td>51:2<br /> | <td>51:2<br /> | ||
| Line 1,404: | Line 1,226: | ||
</td> | </td> | ||
<td>5679.454<br /> | <td>5679.454<br /> | ||
</td> | </td> | ||
<td>53:2<br /> | <td>53:2<br /> | ||
| Line 1,418: | Line 1,238: | ||
</td> | </td> | ||
<td>5743.268<br /> | <td>5743.268<br /> | ||
</td> | </td> | ||
<td>55:2<br /> | <td>55:2<br /> | ||
| Line 1,432: | Line 1,250: | ||
</td> | </td> | ||
<td>5807.082<br /> | <td>5807.082<br /> | ||
</td> | </td> | ||
<td>57:2<br /> | <td>57:2<br /> | ||
| Line 1,446: | Line 1,262: | ||
</td> | </td> | ||
<td>5870.896<br /> | <td>5870.896<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,460: | Line 1,274: | ||
</td> | </td> | ||
<td>5934.710<br /> | <td>5934.710<br /> | ||
</td> | </td> | ||
<td>31:1 (wide-end only)<br /> | <td>31:1 (wide-end only)<br /> | ||
| Line 1,474: | Line 1,286: | ||
</td> | </td> | ||
<td>5998.52<br /> | <td>5998.52<br /> | ||
</td> | </td> | ||
<td>32:1<br /> | <td>32:1<br /> | ||
| Line 1,488: | Line 1,298: | ||
</td> | </td> | ||
<td>6062.339<br /> | <td>6062.339<br /> | ||
</td> | </td> | ||
<td>33:1<br /> | <td>33:1<br /> | ||
| Line 1,502: | Line 1,310: | ||
</td> | </td> | ||
<td>6126.153<br /> | <td>6126.153<br /> | ||
</td> | </td> | ||
<td>34:1 (narrow-end only)<br /> | <td>34:1 (narrow-end only)<br /> | ||