19edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 593016010 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 597506530 - Original comment: ** |
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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: | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-10-30 18:18:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>597506530</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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However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[xenharmonic/Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[xenharmonic/The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]]. It is less successful with [[xenharmonic/7-limit|7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[xenharmonic/7_6|7/6]]), and a septimal whole tone ([[xenharmonic/8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[xenharmonic/Graham complexity|Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles and 13 for sensi. | However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[xenharmonic/Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[xenharmonic/The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|zeta integral edo]]. It is less successful with [[xenharmonic/7-limit|7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[xenharmonic/7_6|7/6]]), and a septimal whole tone ([[xenharmonic/8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The [[xenharmonic/Graham complexity|Graham complexity]] of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles and 13 for sensi. | ||
Being a zeta integral tuning, the 13-limit is represented relatively well, and practically [[19edo|19-edo]] can be used //adaptively// on instruments which | Being a zeta integral tuning, the 13-limit is represented relatively well, and practically [[19edo|19-edo]] can be used //adaptively// on instruments which allow you to bend notes up: by different amounts, the 3rd, 5th, 7th and 13th harmonics are all tuned flat. The same cannot be said of 12edo, in which the 5th and 7th are - not only farther than they are in 19, but fairly sharp already. Another option would be to use a stretched octave; the [[The Riemann Zeta Function and Tuning|zeta function]]-optimal tuning has an octave of roughly 1203 cents. Stringed instruments, in particular the piano, are frequently tuned with stretched octaves anyway due to the inharmonicity inherent in strings, which makes 19edo a promising option for them. | ||
=As a means of extending harmony= | =As a means of extending harmony= | ||
Because 19 EDO allows for more blended, consonant harmonies than 12 EDO does, it can be a much better candidate for using alternate forms of harmony such as quartal, | Because 19 EDO allows for more blended, consonant harmonies than 12 EDO does, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. William Lynch suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non diatonic chord extensions which tend to clash in 12 EDO blend much better in 19 EDO. | ||
In addition, Joseph Yasser talks about the idea of a 12 tone supra diatonic scale where the 7 tone major scale in 19 EDO becomes akin to the pentatonic of western music; as it would sound to a future generation, ambiguous and not tonally fortified. As paraphrased "A system in which the undeniable laws of tonal gravity exist, yet in a much more complex tonal universe. " Yasser believed that music would eventually move to a 19 tone system with a 12 note supra diatonic scale would become the standard. While this has yet to happen, Yasser's concept of supra-diatonicity is intriguing and worth exploring for those wanting to extend ton<span style="line-height: 15.6px;">l</span><span style="line-height: 1.5;">aity without sounding too alien.</span> | In addition, Joseph Yasser talks about the idea of a 12 tone supra diatonic scale where the 7 tone major scale in 19 EDO becomes akin to the pentatonic of western music; as it would sound to a future generation, ambiguous and not tonally fortified. As paraphrased "A system in which the undeniable laws of tonal gravity exist, yet in a much more complex tonal universe. " Yasser believed that music would eventually move to a 19 tone system with a 12 note supra diatonic scale would become the standard. While this has yet to happen, Yasser's concept of supra-diatonicity is intriguing and worth exploring for those wanting to extend ton<span style="line-height: 15.6px;">l</span><span style="line-height: 1.5;">aity without sounding too alien.</span> | ||
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Since 19 is prime, all rank two temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate. | Since 19 is prime, all rank two temperaments in 19edo have one period per octave. Therefore you can make a correspondence between intervals and the linear temperaments they generate. | ||
||~ Degrees of 19edo ||~ Solfege ||~ Diatonic Category ||~ Dodecatonic category ||~ Cents ||||~ Ratios* ||~ Generator for || | ||~ Degrees of 19edo ||~ Solfege ||~ Diatonic Category ||~ Dodecatonic category ||~ Cents coarse/fine ||||~ Ratios* ||~ Generator for || | ||
|| 0 || do || P1 || P1 ||= 0 |||| 1 || || | || 0 || do || P1 || P1 ||= 0 |||| 1 || || | ||
|| 1 || di || A1, d2 || A1, m2 || 63.1579 |||| 25/24, 21/20, 28/27, 26/25, 27/26 || Unicorn/rhinocerus || | || 1 || di || A1, d2 || A1, m2 || 63.1579 | ||
|| 2 || ra || m2 || M2, m3 || 126.326 |||| 15/14, 16/15, 13/12, 14/13 || [[xenharmonic/Negri|Negri]] || | 75.7895 |||| 25/24, 21/20, 28/27, 26/25, 27/26 || Unicorn/rhinocerus || | ||
|| 3 || re || M2 || M3 || 189.474 |||| 9/8, 10/9 || Deutone (2-meantone) / spell || | || 2 || ra || m2 || M2, m3 || 126.326 | ||
|| 4 || ri/ma || A2, d3 || m4, a3 || 252.632 |||| 7/6, 8/7, 15/13 || [[xenharmonic/Godzilla|Godzilla]] || | 151.579 |||| 15/14, 16/15, 13/12, 14/13 || [[xenharmonic/Negri|Negri]] || | ||
|| 5 || me || m3 || M4, m5 || 315. | || 3 || re || M2 || M3 || 189.474 | ||
|| 6 || mi || M3 || M5 || 378.947 |||| 5/4, 16/13, 26/21 || [[xenharmonic/Magic|Magic]]/charisma/glamour || | 227.368 |||| 9/8, 10/9 || Deutone (2-meantone) / spell || | ||
|| 7 || mo || A3, d4 || A5, d6 || 442.105 |||| 32/25, 9/7, 13/10 || [[xenharmonic/Sensi|Sensi]] || | || 4 || ri/ma || A2, d3 || m4, a3 || 252.632 | ||
|| 8 || fa || P4 || P6 || 505.263 |||| 4/3 || [[xenharmonic/Meantone|Meantone]]/[[xenharmonic/flattone|flattone]]/[[xenharmonic/meanennedecal|meanenneadecal]]/[[xenharmonic/meanpop|meanpop]] || | 303.158 |||| 7/6, 8/7, 15/13 || [[xenharmonic/Godzilla|Godzilla]] || | ||
|| 9 || fi || A4 || A6, m7 || 568.421 |||| 25/18, 7/5, 18/13 || [[xenharmonic/Liese|Liese]]/[[xenharmonic/Triton|triton]]/lisa || | || 5 || me || m3 || M4, m5 || 315.7895 | ||
|| 10 || se || d5 || M7, d8 || 631.579 |||| 36/25, 10/7, 13/9 || Liese/triton/lisa || | 378.947 |||| 6/5, 25/21 || [[xenharmonic/Kleismic|Kleismic]] ([[xenharmonic/hanson|hanson]], [[xenharmonic/keemun|keemun]], [[xenharmonic/catakleismic|catakleismic]]) || | ||
|| 11 || sol || P5 || P8 || 694.737 |||| 3/2 || Meantone || | || 6 || mi || M3 || M5 || 378.947 | ||
|| 12 || lo || A5 || A8, m9 || 757.895 |||| 25/16, 14/9, <span style="line-height: 1.5;">20/13</span> || Sensi || | 454.737 |||| 5/4, 16/13, 26/21 || [[xenharmonic/Magic|Magic]]/charisma/glamour || | ||
|| 13 || le || m6 || M9, m10 || 821.053 |||| 8/5, <span style="line-height: 1.5;">13/8, 21/13</span> || Magic || | || 7 || mo || A3, d4 || A5, d6 || 442.105 | ||
|| 14 || la || M6 || M10 || 884. | 530.526 |||| 32/25, 9/7, 13/10 || [[xenharmonic/Sensi|Sensi]] || | ||
|| 15 || li/ta || A6, d7 || m11, A10 || 947.368 |||| 7/4, 12/7, 26/15 || Godzilla || | || 8 || fa || P4 || P6 || 505.263 | ||
|| 16 || te || m7 || M11, m12 || 1010.53 |||| 9/5, 16/9 || Deutone / spell || | 606.316 |||| 4/3 || [[xenharmonic/Meantone|Meantone]]/[[xenharmonic/flattone|flattone]]/[[xenharmonic/meanennedecal|meanenneadecal]]/[[xenharmonic/meanpop|meanpop]] || | ||
|| 17 || ti || M7 || M12 || 1073.68 |||| 15/8, 13/7, <span style="line-height: 1.5;">28/15, 24/13</span> || Negri || | || 9 || fi || A4 || A6, m7 || 568.421 | ||
|| 18 || da || A7, d8 || A12, d13 || 1136.84 |||| <span style="line-height: 1.5;">48/25, </span>40/21, 27/14, <span style="line-height: 1.5;">25/13, 52/27</span> || Unicorn/rhinocerus || | 682.105 |||| 25/18, 7/5, 18/13 || [[xenharmonic/Liese|Liese]]/[[xenharmonic/Triton|triton]]/lisa || | ||
|| 10 || se || d5 || M7, d8 || 631.579 | |||
757.895 |||| 36/25, 10/7, 13/9 || Liese/triton/lisa || | |||
|| 11 || sol || P5 || P8 || 694.737 | |||
833.684 |||| 3/2 || Meantone || | |||
|| 12 || lo || A5 || A8, m9 || 757.895 | |||
909.484 |||| 25/16, 14/9, <span style="line-height: 1.5;">20/13</span> || Sensi || | |||
|| 13 || le || m6 || M9, m10 || 821.053 | |||
985.263 |||| 8/5, <span style="line-height: 1.5;">13/8, 21/13</span> || Magic || | |||
|| 14 || la || M6 || M10 || 884.2105 | |||
1061.05 |||| 5/3, 42/25 || Kleismic (hanson, keemun, catakleismic) || | |||
|| 15 || li/ta || A6, d7 || m11, A10 || 947.368 | |||
1136.84 |||| 7/4, 12/7, 26/15 || Godzilla || | |||
|| 16 || te || m7 || M11, m12 || 1010.53 | |||
1212.63 |||| 9/5, 16/9 || Deutone / spell || | |||
|| 17 || ti || M7 || M12 || 1073.68 | |||
1288.42 |||| 15/8, 13/7, <span style="line-height: 1.5;">28/15, 24/13</span> || Negri || | |||
|| 18 || da || A7, d8 || A12, d13 || 1136.84 | |||
1364.21 |||| <span style="line-height: 1.5;">48/25, </span>40/21, 27/14, <span style="line-height: 1.5;">25/13, 52/27</span> || Unicorn/rhinocerus || | |||
*based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible. | *based on treating 19-EDO as a 2.3.5.7.13 subgroup temperament; other approaches are possible. | ||
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||= 78732/78125 ||< | 2 9 -7 > ||> 13.40 ||= Medium Semicomma, <span style="line-height: 1.5;">Sensipent Comma</span> || | ||= 78732/78125 ||< | 2 9 -7 > ||> 13.40 ||= Medium Semicomma, <span style="line-height: 1.5;">Sensipent Comma</span> || | ||
||= 15625/15552 ||< | -6 -5 6 > ||> 8.11 ||= Kleisma, <span style="line-height: 1.5;">Semicomma Majeur</span> || | ||= 15625/15552 ||< | -6 -5 6 > ||> 8.11 ||= Kleisma, <span style="line-height: 1.5;">Semicomma Majeur</span> || | ||
||= | ||= ||< | 8 14 -13 > ||> 5.29 ||= Parakleisma || | ||
||= | ||= ||< | -14 -19 19 > ||> 2.82 ||= Enneadeca, <span style="line-height: 1.5;">19-Tone-Comma</span> || | ||
||= 1029/1000 ||< | -3 1 -3 3 > ||> 49.49 ||= Keega || | ||= 1029/1000 ||< | -3 1 -3 3 > ||> 49.49 ||= Keega || | ||
||= 525/512 ||< | -9 1 2 1 > ||> 43.41 ||= Avicennma, <span style="line-height: 1.5;">Avicenna's Enharmonic Diesis</span> || | ||= 525/512 ||< | -9 1 2 1 > ||> 43.41 ||= Avicennma, <span style="line-height: 1.5;">Avicenna's Enharmonic Diesis</span> || | ||
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||= 10976/10935 ||< | 5 -7 -1 3 > ||> 6.48 ||= Hemimage || | ||= 10976/10935 ||< | 5 -7 -1 3 > ||> 6.48 ||= Hemimage || | ||
||= 3136/3125 ||< | 6 0 -5 2 > ||> 6.08 ||= Hemimean || | ||= 3136/3125 ||< | 6 0 -5 2 > ||> 6.08 ||= Hemimean || | ||
||= 703125/702464 ||< | -11 2 7 -3 > ||> 1.63 ||= Meter || | ||= [[tel:703125/702464|703125/702464]] ||< | -11 2 7 -3 > ||> 1.63 ||= Meter || | ||
||= 4375/4374 ||< | -1 -7 4 1 > ||> 0.40 ||= Ragisma || | ||= 4375/4374 ||< | -1 -7 4 1 > ||> 0.40 ||= Ragisma || | ||
||= [[xenharmonic/100_99|100/99]] ||< | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma || | ||= [[xenharmonic/100_99|100/99]] ||< | 2 -2 2 0 -1 > ||> 17.40 ||= Ptolemisma || | ||
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However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>. It is less successful with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8_7">8/7</a>). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Graham%20complexity">Graham complexity</a> of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles and 13 for sensi.<br /> | However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Harmonic%20Limit">5-limit</a> music in a tolerable manner, and is the fifth (after 12) <a class="wiki_link" href="http://xenharmonic.wikispaces.com/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">zeta integral edo</a>. It is less successful with <a class="wiki_link" href="http://xenharmonic.wikispaces.com/7-limit">7-limit</a> (but still better than 12-et), as it eliminates the distinction between a septimal minor third (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_6">7/6</a>), and a septimal whole tone (<a class="wiki_link" href="http://xenharmonic.wikispaces.com/8_7">8/7</a>). 19-EDO also has the advantage of being excellent for negri, keemun, godzilla, magic/muggles and triton/liese, and fairly decent for sensi. Keemun and Negri are of particular note for being very simple 7-limit temperaments, with their MOS scales in 19-EDO offering a great abundance of septimal tetrads. The <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Graham%20complexity">Graham complexity</a> of a 7-limit tetrad is 6 for keemun, 7 for negri, 8 for godzilla, 10 for meantone, 11 for triton, 12 for magic/muggles and 13 for sensi.<br /> | ||
<br /> | <br /> | ||
Being a zeta integral tuning, the 13-limit is represented relatively well, and practically <a class="wiki_link" href="/19edo">19-edo</a> can be used <em>adaptively</em> on instruments which | Being a zeta integral tuning, the 13-limit is represented relatively well, and practically <a class="wiki_link" href="/19edo">19-edo</a> can be used <em>adaptively</em> on instruments which allow you to bend notes up: by different amounts, the 3rd, 5th, 7th and 13th harmonics are all tuned flat. The same cannot be said of 12edo, in which the 5th and 7th are - not only farther than they are in 19, but fairly sharp already. Another option would be to use a stretched octave; the <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning">zeta function</a>-optimal tuning has an octave of roughly 1203 cents. Stringed instruments, in particular the piano, are frequently tuned with stretched octaves anyway due to the inharmonicity inherent in strings, which makes 19edo a promising option for them.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="As a means of extending harmony"></a><!-- ws:end:WikiTextHeadingRule:6 -->As a means of extending harmony</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="As a means of extending harmony"></a><!-- ws:end:WikiTextHeadingRule:6 -->As a means of extending harmony</h1> | ||
Because 19 EDO allows for more blended, consonant harmonies than 12 EDO does, it can be a much better candidate for using alternate forms of harmony such as quartal, | Because 19 EDO allows for more blended, consonant harmonies than 12 EDO does, it can be a much better candidate for using alternate forms of harmony such as quartal, secundal, and poly chords. William Lynch suggests the use of seventh chords of various types to be the fundamental sonorities with a triad deemed as incomplete. Higher extensions involving the 7th harmonic as well as other non diatonic chord extensions which tend to clash in 12 EDO blend much better in 19 EDO.<br /> | ||
<br /> | <br /> | ||
In addition, Joseph Yasser talks about the idea of a 12 tone supra diatonic scale where the 7 tone major scale in 19 EDO becomes akin to the pentatonic of western music; as it would sound to a future generation, ambiguous and not tonally fortified. As paraphrased &quot;A system in which the undeniable laws of tonal gravity exist, yet in a much more complex tonal universe. &quot; Yasser believed that music would eventually move to a 19 tone system with a 12 note supra diatonic scale would become the standard. While this has yet to happen, Yasser's concept of supra-diatonicity is intriguing and worth exploring for those wanting to extend ton<span style="line-height: 15.6px;">l</span><span style="line-height: 1.5;">aity without sounding too alien.</span><br /> | In addition, Joseph Yasser talks about the idea of a 12 tone supra diatonic scale where the 7 tone major scale in 19 EDO becomes akin to the pentatonic of western music; as it would sound to a future generation, ambiguous and not tonally fortified. As paraphrased &quot;A system in which the undeniable laws of tonal gravity exist, yet in a much more complex tonal universe. &quot; Yasser believed that music would eventually move to a 19 tone system with a 12 note supra diatonic scale would become the standard. While this has yet to happen, Yasser's concept of supra-diatonicity is intriguing and worth exploring for those wanting to extend ton<span style="line-height: 15.6px;">l</span><span style="line-height: 1.5;">aity without sounding too alien.</span><br /> | ||
| Line 222: | Line 240: | ||
<th>Dodecatonic category<br /> | <th>Dodecatonic category<br /> | ||
</th> | </th> | ||
<th>Cents<br /> | <th>Cents coarse/fine<br /> | ||
</th> | </th> | ||
<th colspan="2">Ratios*<br /> | <th colspan="2">Ratios*<br /> | ||
| Line 255: | Line 273: | ||
</td> | </td> | ||
<td>63.1579<br /> | <td>63.1579<br /> | ||
75.7895<br /> | |||
</td> | </td> | ||
<td colspan="2">25/24, 21/20, 28/27, 26/25, 27/26<br /> | <td colspan="2">25/24, 21/20, 28/27, 26/25, 27/26<br /> | ||
| Line 271: | Line 290: | ||
</td> | </td> | ||
<td>126.326<br /> | <td>126.326<br /> | ||
151.579<br /> | |||
</td> | </td> | ||
<td colspan="2">15/14, 16/15, 13/12, 14/13<br /> | <td colspan="2">15/14, 16/15, 13/12, 14/13<br /> | ||
| Line 287: | Line 307: | ||
</td> | </td> | ||
<td>189.474<br /> | <td>189.474<br /> | ||
227.368<br /> | |||
</td> | </td> | ||
<td colspan="2">9/8, 10/9<br /> | <td colspan="2">9/8, 10/9<br /> | ||
| Line 303: | Line 324: | ||
</td> | </td> | ||
<td>252.632<br /> | <td>252.632<br /> | ||
303.158<br /> | |||
</td> | </td> | ||
<td colspan="2">7/6, 8/7, 15/13<br /> | <td colspan="2">7/6, 8/7, 15/13<br /> | ||
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<td>M4, m5<br /> | <td>M4, m5<br /> | ||
</td> | </td> | ||
<td>315. | <td>315.7895<br /> | ||
378.947<br /> | |||
</td> | </td> | ||
<td colspan="2">6/5, 25/21<br /> | <td colspan="2">6/5, 25/21<br /> | ||
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</td> | </td> | ||
<td>378.947<br /> | <td>378.947<br /> | ||
454.737<br /> | |||
</td> | </td> | ||
<td colspan="2">5/4, 16/13, 26/21<br /> | <td colspan="2">5/4, 16/13, 26/21<br /> | ||
| Line 351: | Line 375: | ||
</td> | </td> | ||
<td>442.105<br /> | <td>442.105<br /> | ||
530.526<br /> | |||
</td> | </td> | ||
<td colspan="2">32/25, 9/7, 13/10<br /> | <td colspan="2">32/25, 9/7, 13/10<br /> | ||
| Line 367: | Line 392: | ||
</td> | </td> | ||
<td>505.263<br /> | <td>505.263<br /> | ||
606.316<br /> | |||
</td> | </td> | ||
<td colspan="2">4/3<br /> | <td colspan="2">4/3<br /> | ||
| Line 383: | Line 409: | ||
</td> | </td> | ||
<td>568.421<br /> | <td>568.421<br /> | ||
682.105<br /> | |||
</td> | </td> | ||
<td colspan="2">25/18, 7/5, 18/13<br /> | <td colspan="2">25/18, 7/5, 18/13<br /> | ||
| Line 399: | Line 426: | ||
</td> | </td> | ||
<td>631.579<br /> | <td>631.579<br /> | ||
757.895<br /> | |||
</td> | </td> | ||
<td colspan="2">36/25, 10/7, 13/9<br /> | <td colspan="2">36/25, 10/7, 13/9<br /> | ||
| Line 415: | Line 443: | ||
</td> | </td> | ||
<td>694.737<br /> | <td>694.737<br /> | ||
833.684<br /> | |||
</td> | </td> | ||
<td colspan="2">3/2<br /> | <td colspan="2">3/2<br /> | ||
| Line 431: | Line 460: | ||
</td> | </td> | ||
<td>757.895<br /> | <td>757.895<br /> | ||
909.484<br /> | |||
</td> | </td> | ||
<td colspan="2">25/16, 14/9, <span style="line-height: 1.5;">20/13</span><br /> | <td colspan="2">25/16, 14/9, <span style="line-height: 1.5;">20/13</span><br /> | ||
| Line 447: | Line 477: | ||
</td> | </td> | ||
<td>821.053<br /> | <td>821.053<br /> | ||
985.263<br /> | |||
</td> | </td> | ||
<td colspan="2">8/5, <span style="line-height: 1.5;">13/8, 21/13</span><br /> | <td colspan="2">8/5, <span style="line-height: 1.5;">13/8, 21/13</span><br /> | ||
| Line 462: | Line 493: | ||
<td>M10<br /> | <td>M10<br /> | ||
</td> | </td> | ||
<td>884. | <td>884.2105<br /> | ||
1061.05<br /> | |||
</td> | </td> | ||
<td colspan="2">5/3, 42/25<br /> | <td colspan="2">5/3, 42/25<br /> | ||
| Line 479: | Line 511: | ||
</td> | </td> | ||
<td>947.368<br /> | <td>947.368<br /> | ||
1136.84<br /> | |||
</td> | </td> | ||
<td colspan="2">7/4, 12/7, 26/15<br /> | <td colspan="2">7/4, 12/7, 26/15<br /> | ||
| Line 495: | Line 528: | ||
</td> | </td> | ||
<td>1010.53<br /> | <td>1010.53<br /> | ||
1212.63<br /> | |||
</td> | </td> | ||
<td colspan="2">9/5, 16/9<br /> | <td colspan="2">9/5, 16/9<br /> | ||
| Line 511: | Line 545: | ||
</td> | </td> | ||
<td>1073.68<br /> | <td>1073.68<br /> | ||
1288.42<br /> | |||
</td> | </td> | ||
<td colspan="2">15/8, 13/7, <span style="line-height: 1.5;">28/15, 24/13</span><br /> | <td colspan="2">15/8, 13/7, <span style="line-height: 1.5;">28/15, 24/13</span><br /> | ||
| Line 527: | Line 562: | ||
</td> | </td> | ||
<td>1136.84<br /> | <td>1136.84<br /> | ||
1364.21<br /> | |||
</td> | </td> | ||
<td colspan="2"><span style="line-height: 1.5;">48/25, </span>40/21, 27/14, <span style="line-height: 1.5;">25/13, 52/27</span><br /> | <td colspan="2"><span style="line-height: 1.5;">48/25, </span>40/21, 27/14, <span style="line-height: 1.5;">25/13, 52/27</span><br /> | ||
| Line 764: | Line 800: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| 8 14 -13 &gt;<br /> | <td style="text-align: left;">| 8 14 -13 &gt;<br /> | ||
| Line 774: | Line 810: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;"> | <td style="text-align: center;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -14 -19 19 &gt;<br /> | <td style="text-align: left;">| -14 -19 19 &gt;<br /> | ||
| Line 894: | Line 930: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">703125/702464<br /> | <td style="text-align: center;">[[tel:703125/702464|703125/702464]]<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">| -11 2 7 -3 &gt;<br /> | <td style="text-align: left;">| -11 2 7 -3 &gt;<br /> | ||