Gallery of just intervals: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 254136840 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 255057426 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09- | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2011-09-17 12:04:16 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>255057426</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> | ||
| Line 20: | Line 20: | ||
=Gallery of Just Intervals= | =Gallery of Just Intervals= | ||
See also [[http://www.huygens-fokker.org/docs/intervals.html|List of intervals (Huygens-Fokker foundation)]] | See also [[List of Superparticular Intervals]] and [[http://www.huygens-fokker.org/docs/intervals.html|List of intervals (Huygens-Fokker foundation)]] | ||
||~ frequency ratio ||~ cents value (three decimal places) ||~ some common names || | ||~ frequency ratio ||~ cents value (three decimal places) ||~ some common names || | ||
|| [[1_1|1/1]] || 0.000 || (perfect) unison, unity, perfect prime, tonic || | || [[1_1|1/1]] || 0.000 || (perfect) unison, unity, perfect prime, tonic || | ||
|| [[100_99|100/99]] || 17.344 || | || [[100_99|100/99]] || 17.344 || Ptolemy's comma || | ||
|| [[81_80|81/80]] || 21.506 || syntonic comma, Didymus comma || | || [[81_80|81/80]] || 21.506 || syntonic comma, Didymus comma || | ||
|| [[65_64|65/64]] || 26.841 || 13th-partial chroma || | || [[65_64|65/64]] || 26.841 || 13th-partial chroma || | ||
| Line 34: | Line 34: | ||
|| [[28_27|28/27]] || 62.961 || septimal chroma, small septimal chromatic semitone || | || [[28_27|28/27]] || 62.961 || septimal chroma, small septimal chromatic semitone || | ||
|| [[25_24|25/24]] || 70.672 || chroma, chromatic semitone, Zarlinian semitone || | || [[25_24|25/24]] || 70.672 || chroma, chromatic semitone, Zarlinian semitone || | ||
|| [[22_21|22/21]] || 80.537 || | || [[22_21|22/21]] || 80.537 || undecimal minor semitone || | ||
|| [[21_20|21/20]] || 84.467 || minor semitone, large septimal chromatic semitone || | || [[21_20|21/20]] || 84.467 || minor semitone, large septimal chromatic semitone || | ||
|| [[256_243|256/243]] || 90.225 || Pythagorean limma, Pythagorean minor second || | || [[256_243|256/243]] || 90.225 || Pythagorean limma, Pythagorean minor second || | ||
|| [[135_128|135/128]] || 92.179 || major limma || | || [[135_128|135/128]] || 92.179 || major limma || | ||
|| [[18_17|18/17]] || 98.955 || | || [[18_17|18/17]] || 98.955 || Arabic lute index finger || | ||
|| [[17_16|17/16]] || 104.955 || | || [[17_16|17/16]] || 104.955 || 17th harmonic (octave reduced) || | ||
|| [[16_15|16/15]] || 111.713 || diatonic semitone, classic minor second, 15th subharmonic (octave reduced) || | || [[16_15|16/15]] || 111.713 || diatonic semitone, classic minor second, 15th subharmonic (octave reduced) || | ||
|| [[2187_2048|2187/2048]] || 113.685 || apotome || | || [[2187_2048|2187/2048]] || 113.685 || apotome || | ||
| Line 45: | Line 45: | ||
|| [[14_13|14/13]] || 128.298 || 2/3-tone, trienthird || | || [[14_13|14/13]] || 128.298 || 2/3-tone, trienthird || | ||
|| [[27_25|27/25]] || 133.238 || large limma || | || [[27_25|27/25]] || 133.238 || large limma || | ||
|| [[13_12|13/12]] || 138.573 || | || [[13_12|13/12]] || 138.573 || tridecimal 2/3-tone || | ||
|| [[12_11|12/11]] || 150.637 || (small) (undecimal) neutral second, 3/4-tone || | || [[12_11|12/11]] || 150.637 || (small) (undecimal) neutral second, 3/4-tone || | ||
|| [[35_32|35/32]] || 155.14 || septimal neutral second || | || [[35_32|35/32]] || 155.14 || septimal neutral second || | ||
| Line 52: | Line 52: | ||
|| [[10_9|10/9]] || 182.404 || classic (whole) tone, classic major second, minor whole tone || | || [[10_9|10/9]] || 182.404 || classic (whole) tone, classic major second, minor whole tone || | ||
|| [[9_8|9/8]] || 203.910 || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) || | || [[9_8|9/8]] || 203.910 || (Pythagorean) (whole) tone, Pythagorean major second, major whole tone, 9th harmonic or harmonic ninth (octave reduced) || | ||
|| [[17_15|17/15]] || 216.687 || | || [[17_15|17/15]] || 216.687 || septendecimal whole tone || | ||
|| [[8_7|8/7]] || 231.174 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic || | || [[8_7|8/7]] || 231.174 || (septimal) supermajor second, septimal whole tone, diminished third, 7th subharmonic || | ||
|| [[15_13|15/13]] || 247.741 || semifourth || | || [[15_13|15/13]] || 247.741 || semifourth || | ||
|| [[7_6|7/6]] || 266.871 || (septimal) subminor third, septimal minor third, augmented second || | || [[7_6|7/6]] || 266.871 || (septimal) subminor third, septimal minor third, augmented second || | ||
|| [[20_17|20/17]] || 281.358 || | || [[20_17|20/17]] || 281.358 || septendecimal augmented second || | ||
|| [[13_11|13/11]] || 289.210 || tridecimal minor third || | || [[13_11|13/11]] || 289.210 || tridecimal minor third || | ||
|| [[32_27|32/27]] || 294.135 || Pythagorean minor third, 27th subharmonic (octave reduced) || | || [[32_27|32/27]] || 294.135 || Pythagorean minor third, 27th subharmonic (octave reduced) || | ||
|| [[6_5|6/5]] || 315.641 || (classic) minor third || | || [[6_5|6/5]] || 315.641 || (classic) minor third || | ||
|| [[17_14|17/14]] || 336.130 || | || [[17_14|17/14]] || 336.130 || (septendecimal) supraminor third || | ||
|| [[11_9|11/9]] || 347.408 || (undecimal) neutral third || | || [[11_9|11/9]] || 347.408 || (undecimal) neutral third || | ||
|| [[16_13|16/13]] || 359.472 || tridecimal neutral third || | || [[16_13|16/13]] || 359.472 || tridecimal neutral third || | ||
| Line 66: | Line 66: | ||
|| [[14_11|14/11]] || 417.508 || (undecimal) supermajor third, undecimal major third, (undecimal) diminished fourth || | || [[14_11|14/11]] || 417.508 || (undecimal) supermajor third, undecimal major third, (undecimal) diminished fourth || | ||
|| [[9_7|9/7]] || 435.084 || (septimal) supermajor third, septimal major third, BP third, (septimal) diminished fourth || | || [[9_7|9/7]] || 435.084 || (septimal) supermajor third, septimal major third, BP third, (septimal) diminished fourth || | ||
|| [[22_17|22/17]] || 446.363 || | || [[22_17|22/17]] || 446.363 || septendecimal supermajor third || | ||
|| [[13_10|13/10]] || 454.214 || Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth || | || [[13_10|13/10]] || 454.214 || Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third || | ||
|| [[17_13|17/13]] || 464.428 || | || [[17_13|17/13]] || 464.428 || septendecimal sub-fourth || | ||
|| [[21_16|21/16]] || 470.781 || sub-fourth, narrow fourth, augmented third, 21st harmonic or septimal 11th (octave reduced) || | || [[21_16|21/16]] || 470.781 || sub-fourth, narrow fourth, augmented third, 21st harmonic or septimal 11th (octave reduced) || | ||
|| [[4_3|4/3]] || 498.045 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron || | || [[4_3|4/3]] || 498.045 || perfect fourth, 3rd subharmonic (octave reduced), diatessaron || | ||
| Line 75: | Line 75: | ||
|| [[48_35|48/35]] || 546.815 || septimal super-fourth || | || [[48_35|48/35]] || 546.815 || septimal super-fourth || | ||
|| [[11_8|11/8]] || 551.318 || super-fourth, undecimal semi-augmented fourth, 11th harmonic or harmonic 11th (octave reduced) || | || [[11_8|11/8]] || 551.318 || super-fourth, undecimal semi-augmented fourth, 11th harmonic or harmonic 11th (octave reduced) || | ||
|| [[18_13|18/13]] || 563.382 || | || [[18_13|18/13]] || 563.382 || tridecimal augmented fourth || | ||
|| [[7_5|7/5]] || 582.512 || augmented fourth, septimal tritone, Huygen's tritone, BP fourth, subdiminished fifth || | || [[7_5|7/5]] || 582.512 || augmented fourth, septimal tritone, Huygen's tritone, BP fourth, subdiminished fifth || | ||
|| [[24_17|24/17]] || 597.000 || | || [[24_17|24/17]] || 597.000 || 1st septendecimal tritone || | ||
|| [[17_12|17/12]] || 603.000 || | || [[17_12|17/12]] || 603.000 || 2nd septendecimal tritone || | ||
|| [[10_7|10/7]] || 617.488 || diminished fifth, Euler's tritone, superaugmented fourth || | || [[10_7|10/7]] || 617.488 || diminished fifth, Euler's tritone, superaugmented fourth || | ||
|| [[13_9|13/9]] || 636.618 || | || [[13_9|13/9]] || 636.618 || tridecimal diminished fifth || | ||
|| [[16_11|16/11]] || 648.682 || sub-fifth, undecimal semi-diminished fifth, 11th subharmonic (octave reduced) || | || [[16_11|16/11]] || 648.682 || sub-fifth, undecimal semi-diminished fifth, 11th subharmonic (octave reduced) || | ||
|| [[35_24|35/24]] || 653.185 || septimal sub-fifth || | || [[35_24|35/24]] || 653.185 || septimal sub-fifth || | ||
| Line 87: | Line 87: | ||
|| [[Just perfect fifth|3/2]] || 701.955 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente || | || [[Just perfect fifth|3/2]] || 701.955 || [[perfect fifth]], 3rd harmonic (octave reduced), diapente || | ||
|| [[32_21|32/21]] || 729.219 || super-fifth, wide fifth, diminished sixth, 21st subharmonic (octave reduced) || | || [[32_21|32/21]] || 729.219 || super-fifth, wide fifth, diminished sixth, 21st subharmonic (octave reduced) || | ||
|| [[20_13|20/13]] || 745.786 || Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth || | || [[26_17|26/17]] || 735.572 || septendecimal super-fifth || | ||
|| [[17_11|17/11]] || 753.637 || | || [[20_13|20/13]] || 745.786 || Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth || | ||
|| [[17_11|17/11]] || 753.637 || septendecimal subminor sixth || | |||
|| [[14_9|14/9]] || 764.916 || (septimal) subminor sixth, septimal minor sixth, augmented fifth || | || [[14_9|14/9]] || 764.916 || (septimal) subminor sixth, septimal minor sixth, augmented fifth || | ||
|| [[11_7|11/7]] || 782.492 || (undecimal) subminor sixth, undecimal augmented fifth || | || [[11_7|11/7]] || 782.492 || (undecimal) subminor sixth, undecimal augmented fifth || | ||
| Line 97: | Line 98: | ||
|| [[27_16|27/16]] || 905.865 || Pythagorean major sixth, 27th harmonic (octave reduced) || | || [[27_16|27/16]] || 905.865 || Pythagorean major sixth, 27th harmonic (octave reduced) || | ||
|| [[22_13|22/13]] || 910.790 || tridecimal major sixth || | || [[22_13|22/13]] || 910.790 || tridecimal major sixth || | ||
|| [[17_10|17/10]] || 918.642 || | || [[17_10|17/10]] || 918.642 || septendecimal diminished seventh || | ||
|| [[12_7|12/7]] || 933.129 || (septimal) supermajor sixth, septimal major sixth, diminished seventh || | || [[12_7|12/7]] || 933.129 || (septimal) supermajor sixth, septimal major sixth, diminished seventh || | ||
|| [[26_15|26/15]] || 952.259 || semitwelfth || | || [[26_15|26/15]] || 952.259 || semitwelfth || | ||
|| [[7_4|7/4]] || 968.826 || (septimal) subminor seventh, harmonic seventh, augmented sixth, 7th harmonic (octave reduced) || | || [[7_4|7/4]] || 968.826 || (septimal) subminor seventh, harmonic seventh, augmented sixth, 7th harmonic (octave reduced) || | ||
|| [[225_128|225/128]] || 976.537 || marvel five-limit harmonic seventh || | || [[225_128|225/128]] || 976.537 || marvel five-limit harmonic seventh || | ||
|| [[30_17|30/17]] || 983.313 || | || [[30_17|30/17]] || 983.313 || septendecimal minor seventh || | ||
|| [[16_9|16/9]] || 996.090 || (Pythagorean) minor seventh, 9th subharmonic (octave reduced) || | || [[16_9|16/9]] || 996.090 || (Pythagorean) minor seventh, 9th subharmonic (octave reduced) || | ||
|| [[9_5|9/5]] || 1017.596 || (classic) minor seventh, just minor seventh, BP seventh || | || [[9_5|9/5]] || 1017.596 || (classic) minor seventh, just minor seventh, BP seventh || | ||
|| [[20_11|20/11]] || 1034.996 || (small) undecimal neutral seventh, large minor seventh || | || [[20_11|20/11]] || 1034.996 || (small) undecimal neutral seventh, large minor seventh || | ||
|| [[11_6|11/6]] || 1049.363 || (large) (undecimal) neutral seventh, 21/4-tone || | || [[11_6|11/6]] || 1049.363 || (large) (undecimal) neutral seventh, 21/4-tone || | ||
|| [[24_13|24/13]] || 1061.427 || | || [[24_13|24/13]] || 1061.427 || tridecimal neutral seventh || | ||
|| [[13_7|13/7]] || 1071.702 || | || [[13_7|13/7]] || 1071.702 || 16/3-tone || | ||
|| [[28_15|28/15]] || 1080.557 || | || [[28_15|28/15]] || 1080.557 || grave major seventh || | ||
|| [[15_8|15/8]] || 1088.269 || (classic) major seventh, 15th harmonic (octave reduced) || | || [[15_8|15/8]] || 1088.269 || (classic) major seventh, 15th harmonic (octave reduced) || | ||
|| [[32_17|32/17]] || 1095.045 || | || [[32_17|32/17]] || 1095.045 || 17th subharmonic (octave-reduced) || | ||
|| [[40_21|40/21]] || 1115.533 || acute major seventh || | || [[40_21|40/21]] || 1115.533 || acute major seventh || | ||
|| [[64_33|64/33]] || 1146.727 || 33rd subharmonic (octave reduced) || | || [[64_33|64/33]] || 1146.727 || 33rd subharmonic (octave reduced) || | ||
| Line 134: | Line 135: | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Gallery of Just Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Gallery of Just Intervals</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Gallery of Just Intervals"></a><!-- ws:end:WikiTextHeadingRule:2 -->Gallery of Just Intervals</h1> | ||
<br /> | <br /> | ||
See also <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow">List of intervals (Huygens-Fokker foundation)</a><br /> | See also <a class="wiki_link" href="/List%20of%20Superparticular%20Intervals">List of Superparticular Intervals</a> and <a class="wiki_link_ext" href="http://www.huygens-fokker.org/docs/intervals.html" rel="nofollow">List of intervals (Huygens-Fokker foundation)</a><br /> | ||
<br /> | <br /> | ||
| Line 160: | Line 161: | ||
<td>17.344<br /> | <td>17.344<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Ptolemy's comma<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 240: | Line 241: | ||
<td>80.537<br /> | <td>80.537<br /> | ||
</td> | </td> | ||
<td><br /> | <td>undecimal minor semitone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 272: | Line 273: | ||
<td>98.955<br /> | <td>98.955<br /> | ||
</td> | </td> | ||
<td><br /> | <td>Arabic lute index finger<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 280: | Line 281: | ||
<td>104.955<br /> | <td>104.955<br /> | ||
</td> | </td> | ||
<td><br /> | <td>17th harmonic (octave reduced)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 328: | Line 329: | ||
<td>138.573<br /> | <td>138.573<br /> | ||
</td> | </td> | ||
<td><br /> | <td>tridecimal 2/3-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 384: | Line 385: | ||
<td>216.687<br /> | <td>216.687<br /> | ||
</td> | </td> | ||
<td><br /> | <td>septendecimal whole tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 416: | Line 417: | ||
<td>281.358<br /> | <td>281.358<br /> | ||
</td> | </td> | ||
<td><br /> | <td>septendecimal augmented second<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 448: | Line 449: | ||
<td>336.130<br /> | <td>336.130<br /> | ||
</td> | </td> | ||
<td><br /> | <td>(septendecimal) supraminor third<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 496: | Line 497: | ||
<td>446.363<br /> | <td>446.363<br /> | ||
</td> | </td> | ||
<td><br /> | <td>septendecimal supermajor third<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 504: | Line 505: | ||
<td>454.214<br /> | <td>454.214<br /> | ||
</td> | </td> | ||
<td>Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth<br /> | <td>Barbados third, tridecimal 9/4 tone, tridecimal semidiminished fourth, tridecimal ultramajor third<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 512: | Line 513: | ||
<td>464.428<br /> | <td>464.428<br /> | ||
</td> | </td> | ||
<td><br /> | <td>septendecimal sub-fourth<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 568: | Line 569: | ||
<td>563.382<br /> | <td>563.382<br /> | ||
</td> | </td> | ||
<td><br /> | <td>tridecimal augmented fourth<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 584: | Line 585: | ||
<td>597.000<br /> | <td>597.000<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1st septendecimal tritone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 592: | Line 593: | ||
<td>603.000<br /> | <td>603.000<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2nd septendecimal tritone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 608: | Line 609: | ||
<td>636.618<br /> | <td>636.618<br /> | ||
</td> | </td> | ||
<td><br /> | <td>tridecimal diminished fifth<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 657: | Line 658: | ||
</td> | </td> | ||
<td>super-fifth, wide fifth, diminished sixth, 21st subharmonic (octave reduced)<br /> | <td>super-fifth, wide fifth, diminished sixth, 21st subharmonic (octave reduced)<br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td><a class="wiki_link" href="/26_17">26/17</a><br /> | |||
</td> | |||
<td>735.572<br /> | |||
</td> | |||
<td>septendecimal super-fifth<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 664: | Line 673: | ||
<td>745.786<br /> | <td>745.786<br /> | ||
</td> | </td> | ||
<td>Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth<br /> | <td>Barbados sixth, ratwolf wolf fifth, tridecimal semi-augmented fifth, tridecimal ultraminor sixth<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 672: | Line 681: | ||
<td>753.637<br /> | <td>753.637<br /> | ||
</td> | </td> | ||
<td><br /> | <td>septendecimal subminor sixth<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 744: | Line 753: | ||
<td>918.642<br /> | <td>918.642<br /> | ||
</td> | </td> | ||
<td><br /> | <td>septendecimal diminished seventh<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 784: | Line 793: | ||
<td>983.313<br /> | <td>983.313<br /> | ||
</td> | </td> | ||
<td><br /> | <td>septendecimal minor seventh<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 824: | Line 833: | ||
<td>1061.427<br /> | <td>1061.427<br /> | ||
</td> | </td> | ||
<td><br /> | <td>tridecimal neutral seventh<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 832: | Line 841: | ||
<td>1071.702<br /> | <td>1071.702<br /> | ||
</td> | </td> | ||
<td><br /> | <td>16/3-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 840: | Line 849: | ||
<td>1080.557<br /> | <td>1080.557<br /> | ||
</td> | </td> | ||
<td><br /> | <td>grave major seventh<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 856: | Line 865: | ||
<td>1095.045<br /> | <td>1095.045<br /> | ||
</td> | </td> | ||
<td><br /> | <td>17th subharmonic (octave-reduced)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||