47edo: Difference between revisions
Wikispaces>TallKite **Imported revision 617219405 - Original comment: ** |
Wikispaces>TallKite **Imported revision 617220635 - 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>2017-09-05 15: | : This revision was by author [[User:TallKite|TallKite]] and made on <tt>2017-09-05 15:22:27 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>617220635</tt>.<br> | ||
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47edo is a [[Ups and Downs Notation#Other%20EDOs|regular]] edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2. | 47edo is a [[Ups and Downs Notation#Other%20EDOs|regular]] edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2. | ||
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a | A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a roughly 7edo-ish scale: | ||
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D | D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D | ||
D# is next to D. This notation requires triple, quadruple and | D# is next to D. This notation requires triple, quadruple and in some keys, quintuple sharps and flats. For example, a 0-15-27-38 chord (an approximate 4:5:6:7) on the note three edosteps above D would be spelled either as D#<span style="font-size: 90%; vertical-align: super;">3</span> - F#<span style="font-size: 90%; vertical-align: super;">5</span> - A#<span style="font-size: 90%; vertical-align: super;">3</span> - C# or as Eb<span style="font-size: 90%; vertical-align: super;">4</span> - Gbb - Ab<span style="font-size: 90%; vertical-align: super;">4</span> - Db<span style="font-size: 90%; vertical-align: super;">6</span>. | ||
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a | Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep: | ||
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D | D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D | ||
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats. | D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats. | ||
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==Intervals of 47edo== | ==Intervals of 47edo== | ||
||~ Degree ||~ Size (Cents) ||~ relative notation | ||~ Degree ||~ Size (Cents) ||||~ relative notation ||~ absolute notation || | ||
||= 0 ||> 0.0000 ||= perfect unison ||= P1 ||= D || | ||= 0 ||> 0.0000 ||= perfect unison ||= P1 ||= D || | ||
||= 1 ||> 25.5319 ||= aug 1sn ||= A1 ||= D# || | ||= 1 ||> 25.5319 ||= aug 1sn ||= A1 ||= D# || | ||
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47edo is a <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Other%20EDOs">regular</a> edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2.<br /> | 47edo is a <a class="wiki_link" href="/Ups%20and%20Downs%20Notation#Other%20EDOs">regular</a> edo because its 5th falls between 4\7 = 686¢ and 3\5 = 720¢. (Its alternate 5th does as well.) 47edo is the most difficult regular edo to notate, because no other regular edo's 5th is as far off from a just 3/2.<br /> | ||
<br /> | <br /> | ||
A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a | A notation using the best 5th has major and minor 2nds of 7 and 6 edosteps respectively, with the naturals creating a roughly 7edo-ish scale:<br /> | ||
D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D<br /> | D * * * * * * E * * * * * F * * * * * * G * * * * * * A * * * * * * B * * * * * C * * * * * * D<br /> | ||
D# is next to D. This notation requires triple, quadruple and | D# is next to D. This notation requires triple, quadruple and in some keys, quintuple sharps and flats. For example, a 0-15-27-38 chord (an approximate 4:5:6:7) on the note three edosteps above D would be spelled either as D#<span style="font-size: 90%; vertical-align: super;">3</span> - F#<span style="font-size: 90%; vertical-align: super;">5</span> - A#<span style="font-size: 90%; vertical-align: super;">3</span> - C# or as Eb<span style="font-size: 90%; vertical-align: super;">4</span> - Gbb - Ab<span style="font-size: 90%; vertical-align: super;">4</span> - Db<span style="font-size: 90%; vertical-align: super;">6</span>.<br /> | ||
<br /> | <br /> | ||
Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a | Using the 2nd best 5th is even more awkward. The major 2nd is 9 edosteps and the minor is only one. The naturals create a roughly 5edo-ish scale, with two of the notes inflected by a comma-sized edostep:<br /> | ||
D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D<br /> | D * * * * * * * * E F * * * * * * * * G * * * * * * * * A * * * * * * * * B C * * * * * * * * D<br /> | ||
D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.<br /> | D# is next to E. This notation requires quadruple, quintuple, and even sextuple ups and downs, as well as single sharps and flats.<br /> | ||
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<th>Size (Cents)<br /> | <th>Size (Cents)<br /> | ||
</th> | </th> | ||
<th>relative notation | <th colspan="2">relative notation<br /> | ||
</th> | </th> | ||
<th>absolute notation<br /> | <th>absolute notation<br /> | ||