15edo: Difference between revisions
Wikispaces>TallKite **Imported revision 600698084 - Original comment: ** |
Wikispaces>TallKite **Imported revision 600700440 - 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:TallKite|TallKite]] and made on <tt>2016-11-29 | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2016-11-29 01:56:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>600700440</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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"In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the [[octave]] into 15 equal steps. Each step represents a frequency ratio of 2^(1/15), or 80 [[cent]]s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of [[5edo|5 equal divisions of the octave]] (or five scales of [[3edo]])." | "In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the [[octave]] into 15 equal steps. Each step represents a frequency ratio of 2^(1/15), or 80 [[cent]]s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of [[5edo|5 equal divisions of the octave]] (or five scales of [[3edo]])." | ||
15-edo can be seen as a [[7-limit]] temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to [[11-limit]] intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15-edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, | 15-edo can be seen as a [[7-limit]] temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to [[11-limit]] intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15-edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, 6/5, and their octave inverses) that has a positive [[81_80|syntonic comma]]. | ||
In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. | In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo. | ||
| Line 75: | Line 75: | ||
*based on treating 15-EDO as an 11-limit temperament; other approaches are possible | *based on treating 15-EDO as an 11-limit temperament; other approaches are possible | ||
In [[Ups and Downs Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs|ups and downs notation]], which is fifth-generated, every 15edo note has at least three names. 15edo can be notated without ups and downs by using the [[Ups and Downs Notation#Natural%20Generators|natural generator]], which is not the 9\15 5th but the 2\15 2nd, also known as porcupine notation. The 15edo porcupine genchain is: | |||
...A6 - A7 - A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 - d8 - d2 - d3... | |||
||= EDOstep ||= cents ||= ups and downs | ||= EDOstep ||= cents ||= ups and downs | ||
relative notation ||= ups and downs | relative notation ||= ups and downs | ||
absolute notation ||= porcupine | absolute notation ||= porcupine | ||
relative ||= porcupine | relative notation ||= porcupine | ||
absolute || | absolute notation || | ||
||= 0 ||= | ||= 0 ||= 0¢ ||= unison, min 2nd ||= C# / D / Eb ||= unison ||= D || | ||
||= 1 ||= | ||= 1 ||= 80¢ ||= up-unison, upminor 2nd ||= C#^ / D^ / Eb^ ||= aug unison, dim 2nd ||= D# / Eb || | ||
||= 2 ||= | ||= 2 ||= 160¢ ||= downaug 1, downmajor 2nd, downminor 3rd ||= D#v / Ev / Fv / Gbv ||= perf 2nd ||= E || | ||
||= 3 ||= | ||= 3 ||= 240¢ ||= aug 1, maj 2nd, min 3rd, dim 4th ||= D# / E / F / Gb ||= aug 2nd, dim 3rd ||= E# / Fb || | ||
||= 4 ||= | ||= 4 ||= 320¢ ||= upaug 1, upmaj 2nd, upmin 3rd, updim 4th ||= D#^ / E^ / F^ / Gb^ ||= min 3rd ||= F || | ||
||= 5 ||= | ||= 5 ||= 400¢ ||= downmaj 3rd, down 4th, downdim 5th ||= F#v / Gv / Abv ||= maj 3rd ||= F# / Gb || | ||
||= 6 ||= | ||= 6 ||= 480¢ ||= maj 3rd, perf 4th, dim 5th ||= F# / G / Ab ||= min 4th ||= G || | ||
||= 7 ||= | ||= 7 ||= 560¢ ||= upmaj 3rd, up 4th, updim 5th ||= F#^ / G^ / Ab^ ||= maj 4th ||= G# / Abb || | ||
||= 8 ||= | ||= 8 ||= 640¢ ||= downaug 4th, down 5th, downmin 6th ||= G#v / Av / Bbv ||= min 5th ||= Gx / Ab || | ||
||= 9 ||= | ||= 9 ||= 720¢ ||= aug 4th, perf 5th, min 6th ||= G# / A / Bb ||= maj 5th ||= A || | ||
||= 10 ||= | ||= 10 ||= 800¢ ||= upaug 4th, up 5th, upmin 6th ||= G#^ / A^ / Bb^ ||= min 6th ||= A# / Bb || | ||
||= 11 ||= | ||= 11 ||= 880¢ ||= downaug 5th, downmaj 6th, downmin 7th ||= A#v / Bv / Cv / Dbv ||= maj 6th ||= B || | ||
||= 12 ||= | ||= 12 ||= 960¢ ||= aug 5th, maj 6th, min 7th, dim 8ve ||= A# / B / C / Db ||= aug 6th, dim 7th ||= B# / Cb || | ||
||= 13 ||= | ||= 13 ||= 1040¢ ||= upmaj 6th, upmin 7th, updim 8ve ||= A#^ / B^ / C^ / Db^ ||= perf 7th ||= C || | ||
||= 14 ||= | ||= 14 ||= 1120¢ ||= downmaj 7th, down octave, downmin 9th ||= C#v / Dv / Ebv ||= aug 7th, dim 8ve ||= C# / Db || | ||
||= 15 ||= | ||= 15 ||= 1200¢ ||= maj 7th, octave, min 9th ||= C# / D / Eb ||= 8ve ||= D || | ||
15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by [[IgliashonJones|Igliashon Jones]] in the paper "[[http://www.cityoftheasleep.com/etc/5nEDOs.pdf|Five is Not an Odd Number]]". For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see [[@Harmony in 15edo Blacksmith|Harmony in 15edo Blacksmith[10]]]. | 15-EDO offers some minor improvements over 12-TET in ratios of 5 (particularly in 6/5 and 5/3), and has a much better approximation to the 7th and 11th harmonics, but its approximation to the 3rd harmonic is rather off. However, the particular way in which this approximation is off is as much a feature as it is a bug, for it allows the construction of a 5L5s MOS scale wherein every note of the scale can serve as a root for a 7-limit otonal or utonal tetrad, as well as either a 5-limit major or minor 7th chord. This is known as Blackwood temperament, named after Easley Blackwood, Jr., who is the first to document its existence. It has also been written on extensively by [[IgliashonJones|Igliashon Jones]] in the paper "[[http://www.cityoftheasleep.com/etc/5nEDOs.pdf|Five is Not an Odd Number]]". For an in-depth treatment of harmony in 15-edo based on this temperament (and its 7- and 11-limit extensions), see [[@Harmony in 15edo Blacksmith|Harmony in 15edo Blacksmith[10]]]. | ||
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&quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 15 equal steps. Each step represents a frequency ratio of 2^(1/15), or 80 <a class="wiki_link" href="/cent">cent</a>s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of <a class="wiki_link" href="/5edo">5 equal divisions of the octave</a> (or five scales of <a class="wiki_link" href="/3edo">3edo</a>).&quot;<br /> | &quot;In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the <a class="wiki_link" href="/octave">octave</a> into 15 equal steps. Each step represents a frequency ratio of 2^(1/15), or 80 <a class="wiki_link" href="/cent">cent</a>s. Because 15 factors into 3 times 5, it can be seen as being made up of three scales of <a class="wiki_link" href="/5edo">5 equal divisions of the octave</a> (or five scales of <a class="wiki_link" href="/3edo">3edo</a>).&quot;<br /> | ||
<br /> | <br /> | ||
15-edo can be seen as a <a class="wiki_link" href="/7-limit">7-limit</a> temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to <a class="wiki_link" href="/11-limit">11-limit</a> intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15-edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, | 15-edo can be seen as a <a class="wiki_link" href="/7-limit">7-limit</a> temperament because of its ability to approximate some septimal intervals, but it also contains some fairly obvious approximations to <a class="wiki_link" href="/11-limit">11-limit</a> intervals, so it can reasonably be described as an 11-limit temperament; however, due to its rather distant approximation of the 3rd harmonic (and therefore the 9th harmonic as well), those seeking to approximate JI with 15-edo would be best advised to avoid chords requiring those harmonics (or to at least treat them with sensitivity). 15-edo is also notable for being the smallest edo with recognizable, distinct representations of 5-odd limit intervals (3/2, 5/4, 6/5, and their octave inverses) that has a positive <a class="wiki_link" href="/81_80">syntonic comma</a>.<br /> | ||
<br /> | <br /> | ||
In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo.<br /> | In the 15-edo system, major thirds cannot be divided perfectly into two, and coupled with the lack of a standard tritone, this tuning at first can be disorienting. However, because the guitar can be tuned symmetrically, from E to e (6th to 1st strings) unlike the 12-tone system on guitars, the learning curve is very manageable. All chords look the same modulated anywhere, and minor arpeggios are vertically stacked, making them very easy to play. 15-tone may be a promising start for anyone interested in superior harmony and xenharmony, a manageable number of tones, and the sonic fingerprint of multiples of 5-edo.<br /> | ||
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*based on treating 15-EDO as an 11-limit temperament; other approaches are possible<br /> | *based on treating 15-EDO as an 11-limit temperament; other approaches are possible<br /> | ||
<br /> | <br /> | ||
In <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Summary%20of%20EDO%20notation-%22Pentatonic%22%20EDOs">ups and downs notation</a>, which is fifth-generated, every 15edo note has at least three names. 15edo can be notated without ups and downs by using the <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Natural%20Generators">natural generator</a>, which is not the 9\15 5th but the 2\15 2nd, also known as porcupine notation. The 15edo porcupine genchain is:<br /> | |||
...A6 - A7 - A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 - d8 - d2 - d3...<br /> | |||
<br /> | <br /> | ||
| Line 661: | Line 661: | ||
</td> | </td> | ||
<td style="text-align: center;">porcupine<br /> | <td style="text-align: center;">porcupine<br /> | ||
relative<br /> | relative notation<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">porcupine <br /> | <td style="text-align: center;">porcupine <br /> | ||
absolute<br /> | absolute notation<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 670: | Line 670: | ||
<td style="text-align: center;">0<br /> | <td style="text-align: center;">0<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">0¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">unison, min 2nd<br /> | <td style="text-align: center;">unison, min 2nd<br /> | ||
| Line 676: | Line 676: | ||
<td style="text-align: center;">C# / D / Eb<br /> | <td style="text-align: center;">C# / D / Eb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">unison<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||
| Line 684: | Line 684: | ||
<td style="text-align: center;">1<br /> | <td style="text-align: center;">1<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">80¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">up-unison, upminor 2nd<br /> | <td style="text-align: center;">up-unison, upminor 2nd<br /> | ||
| Line 690: | Line 690: | ||
<td style="text-align: center;">C#^ / D^ / Eb^<br /> | <td style="text-align: center;">C#^ / D^ / Eb^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">aug unison, dim 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D# / Eb<br /> | <td style="text-align: center;">D# / Eb<br /> | ||
| Line 698: | Line 698: | ||
<td style="text-align: center;">2<br /> | <td style="text-align: center;">2<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">160¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">downaug 1, downmajor 2nd, downminor 3rd<br /> | <td style="text-align: center;">downaug 1, downmajor 2nd, downminor 3rd<br /> | ||
| Line 704: | Line 704: | ||
<td style="text-align: center;">D#v / Ev / Fv / Gbv<br /> | <td style="text-align: center;">D#v / Ev / Fv / Gbv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">perf 2nd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E<br /> | <td style="text-align: center;">E<br /> | ||
| Line 712: | Line 712: | ||
<td style="text-align: center;">3<br /> | <td style="text-align: center;">3<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">240¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">aug 1, maj 2nd, min 3rd, dim 4th<br /> | <td style="text-align: center;">aug 1, maj 2nd, min 3rd, dim 4th<br /> | ||
| Line 718: | Line 718: | ||
<td style="text-align: center;">D# / E / F / Gb<br /> | <td style="text-align: center;">D# / E / F / Gb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">aug 2nd, dim 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">E# / Fb<br /> | <td style="text-align: center;">E# / Fb<br /> | ||
| Line 726: | Line 726: | ||
<td style="text-align: center;">4<br /> | <td style="text-align: center;">4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">320¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">upaug 1, upmaj 2nd, upmin 3rd, updim 4th<br /> | <td style="text-align: center;">upaug 1, upmaj 2nd, upmin 3rd, updim 4th<br /> | ||
| Line 732: | Line 732: | ||
<td style="text-align: center;">D#^ / E^ / F^ / Gb^<br /> | <td style="text-align: center;">D#^ / E^ / F^ / Gb^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">min 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F<br /> | <td style="text-align: center;">F<br /> | ||
| Line 740: | Line 740: | ||
<td style="text-align: center;">5<br /> | <td style="text-align: center;">5<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">400¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">downmaj 3rd, down 4th, downdim 5th<br /> | <td style="text-align: center;">downmaj 3rd, down 4th, downdim 5th<br /> | ||
| Line 746: | Line 746: | ||
<td style="text-align: center;">F#v / Gv / Abv<br /> | <td style="text-align: center;">F#v / Gv / Abv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">maj 3rd<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">F# / Gb<br /> | <td style="text-align: center;">F# / Gb<br /> | ||
| Line 754: | Line 754: | ||
<td style="text-align: center;">6<br /> | <td style="text-align: center;">6<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">480¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">maj 3rd, perf 4th, dim 5th<br /> | <td style="text-align: center;">maj 3rd, perf 4th, dim 5th<br /> | ||
| Line 760: | Line 760: | ||
<td style="text-align: center;">F# / G / Ab<br /> | <td style="text-align: center;">F# / G / Ab<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">min 4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G<br /> | <td style="text-align: center;">G<br /> | ||
| Line 768: | Line 768: | ||
<td style="text-align: center;">7<br /> | <td style="text-align: center;">7<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">560¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">upmaj 3rd, up 4th, updim 5th<br /> | <td style="text-align: center;">upmaj 3rd, up 4th, updim 5th<br /> | ||
| Line 774: | Line 774: | ||
<td style="text-align: center;">F#^ / G^ / Ab^<br /> | <td style="text-align: center;">F#^ / G^ / Ab^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">maj 4th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">G# / Abb<br /> | <td style="text-align: center;">G# / Abb<br /> | ||
| Line 782: | Line 782: | ||
<td style="text-align: center;">8<br /> | <td style="text-align: center;">8<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">640¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">downaug 4th, down 5th, downmin 6th<br /> | <td style="text-align: center;">downaug 4th, down 5th, downmin 6th<br /> | ||
| Line 788: | Line 788: | ||
<td style="text-align: center;">G#v / Av / Bbv<br /> | <td style="text-align: center;">G#v / Av / Bbv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">min 5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">Gx / Ab<br /> | <td style="text-align: center;">Gx / Ab<br /> | ||
| Line 796: | Line 796: | ||
<td style="text-align: center;">9<br /> | <td style="text-align: center;">9<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">720¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">aug 4th, perf 5th, min 6th<br /> | <td style="text-align: center;">aug 4th, perf 5th, min 6th<br /> | ||
| Line 802: | Line 802: | ||
<td style="text-align: center;">G# / A / Bb<br /> | <td style="text-align: center;">G# / A / Bb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">maj 5th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A<br /> | <td style="text-align: center;">A<br /> | ||
| Line 810: | Line 810: | ||
<td style="text-align: center;">10<br /> | <td style="text-align: center;">10<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">800¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">upaug 4th, up 5th, upmin 6th<br /> | <td style="text-align: center;">upaug 4th, up 5th, upmin 6th<br /> | ||
| Line 816: | Line 816: | ||
<td style="text-align: center;">G#^ / A^ / Bb^<br /> | <td style="text-align: center;">G#^ / A^ / Bb^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">min 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A# / Bb<br /> | <td style="text-align: center;">A# / Bb<br /> | ||
| Line 824: | Line 824: | ||
<td style="text-align: center;">11<br /> | <td style="text-align: center;">11<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">880¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">downaug 5th, downmaj 6th, downmin 7th<br /> | <td style="text-align: center;">downaug 5th, downmaj 6th, downmin 7th<br /> | ||
| Line 830: | Line 830: | ||
<td style="text-align: center;">A#v / Bv / Cv / Dbv<br /> | <td style="text-align: center;">A#v / Bv / Cv / Dbv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">maj 6th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B<br /> | <td style="text-align: center;">B<br /> | ||
| Line 838: | Line 838: | ||
<td style="text-align: center;">12<br /> | <td style="text-align: center;">12<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">960¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">aug 5th, maj 6th, min 7th, dim 8ve<br /> | <td style="text-align: center;">aug 5th, maj 6th, min 7th, dim 8ve<br /> | ||
| Line 844: | Line 844: | ||
<td style="text-align: center;">A# / B / C / Db<br /> | <td style="text-align: center;">A# / B / C / Db<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">aug 6th, dim 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">B# / Cb<br /> | <td style="text-align: center;">B# / Cb<br /> | ||
| Line 852: | Line 852: | ||
<td style="text-align: center;">13<br /> | <td style="text-align: center;">13<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1040¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">upmaj 6th, upmin 7th, updim 8ve<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">A#^ / B^ / C^ / Db^<br /> | <td style="text-align: center;">A#^ / B^ / C^ / Db^<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">perf 7th<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C<br /> | <td style="text-align: center;">C<br /> | ||
| Line 866: | Line 866: | ||
<td style="text-align: center;">14<br /> | <td style="text-align: center;">14<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1120¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">downmaj 7th, down octave, downmin 9th<br /> | <td style="text-align: center;">downmaj 7th, down octave, downmin 9th<br /> | ||
| Line 872: | Line 872: | ||
<td style="text-align: center;">C#v / Dv / Ebv<br /> | <td style="text-align: center;">C#v / Dv / Ebv<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">aug 7th, dim 8ve<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">C# / Db<br /> | <td style="text-align: center;">C# / Db<br /> | ||
| Line 880: | Line 880: | ||
<td style="text-align: center;">15<br /> | <td style="text-align: center;">15<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"> | <td style="text-align: center;">1200¢<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">maj 7th, octave, min 9th<br /> | <td style="text-align: center;">maj 7th, octave, min 9th<br /> | ||
| Line 886: | Line 886: | ||
<td style="text-align: center;">C# / D / Eb<br /> | <td style="text-align: center;">C# / D / Eb<br /> | ||
</td> | </td> | ||
<td style="text-align: center;"><br /> | <td style="text-align: center;">8ve<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">D<br /> | <td style="text-align: center;">D<br /> | ||