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Wikispaces>xenjacob **Imported revision 860783 - Original comment: ** |
Wikispaces>xenjacob **Imported revision 860807 - Original comment: *%&##^ image transfer** |
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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:xenjacob|xenjacob]] and made on <tt>2006-07-11 12: | : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2006-07-11 12:07:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>860807</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>*%&##^ image transfer</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> | ||
| Line 10: | Line 10: | ||
Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# | Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# | ||
and then wrap it into a circle of the desired size | and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function. | ||
[[image:space/showimage/17fifths]] | [[image:17fifths]][[image:space/showimage/17fifths]] | ||
The lines across indicate five fifths ("minor second") (1/17 of an octave). Now we can order them ascendingly: | The lines across indicate five fifths ("minor second") (1/17 of an octave). Now we can order them ascendingly: | ||
[[image: | |||
[[image:17versus12names width="1" height="1"]][[image:17versus12names]] | |||
Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." These last two properties are shared with 24-equal (quartertones). | Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." These last two properties are shared with 24-equal (quartertones). | ||
If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):[[image: | If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step): | ||
[[image:17versus12cents]] | |||
and in pitch/interval classes: | and in pitch/interval classes: | ||
[[image: | |||
[[image:17versus12pcs]][[image:17versus12pcs width="1" height="1"]]</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>SeventeenTheory</title></head><body>17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonics, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<br /> | <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>SeventeenTheory</title></head><body>17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonics, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<br /> | ||
| Line 26: | Line 30: | ||
Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#<br /> | Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#<br /> | ||
<br /> | <br /> | ||
and then wrap it into a circle of the desired size | and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of &quot;flat/sharp&quot; is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.<br /> | ||
<br /> | <br /> | ||
[[image:space/showimage/17fifths]]<br /> | <!-- ws:start:WikiTextLocalImageRule:0:&lt;img src=&quot;/file/view/17fifths/30122064/17fifths&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17fifths/30122064/17fifths" alt="17fifths" title="17fifths" /><!-- ws:end:WikiTextLocalImageRule:0 -->[[image:space/showimage/17fifths]]<br /> | ||
The lines across indicate five fifths (&quot;minor second&quot;) (1/17 of an octave). Now we can order them ascendingly:<br /> | The lines across indicate five fifths (&quot;minor second&quot;) (1/17 of an octave). Now we can order them ascendingly:<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextLocalImageRule:1:&lt;img src=&quot;/file/view/17versus12names/30122065/1x1/17versus12names&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1px; width: 1px;&quot; /&gt; --><img src="/file/view/17versus12names/30122065/1x1/17versus12names" alt="17versus12names" title="17versus12names" style="height: 1px; width: 1px;" /><!-- ws:end:WikiTextLocalImageRule:1 --><!-- ws:start:WikiTextLocalImageRule:2:&lt;img src=&quot;/file/view/17versus12names/30122065/17versus12names&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17versus12names/30122065/17versus12names" alt="17versus12names" title="17versus12names" /><!-- ws:end:WikiTextLocalImageRule:2 --><br /> | |||
<br /> | <br /> | ||
Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The &quot;half step&quot;/&quot;minor second&quot; in 17 is twice as small as the &quot;augmented unison&quot;/&quot;sharp&quot;/&quot;flat.&quot; Two sharp/flats add up to a minor third. Two &quot;neutral thirds&quot; add up to a &quot;perfect fifth.&quot; These last two properties are shared with 24-equal (quartertones).<br /> | Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The &quot;half step&quot;/&quot;minor second&quot; in 17 is twice as small as the &quot;augmented unison&quot;/&quot;sharp&quot;/&quot;flat.&quot; Two sharp/flats add up to a minor third. Two &quot;neutral thirds&quot; add up to a &quot;perfect fifth.&quot; These last two properties are shared with 24-equal (quartertones).<br /> | ||
<br /> | <br /> | ||
If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step): | If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextLocalImageRule:3:&lt;img src=&quot;/file/view/17versus12cents/30122071/17versus12cents&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17versus12cents/30122071/17versus12cents" alt="17versus12cents" title="17versus12cents" /><!-- ws:end:WikiTextLocalImageRule:3 --><br /> | |||
and in pitch/interval classes:<br /> | and in pitch/interval classes:<br /> | ||
<br /> | |||
<!-- ws:start:WikiTextLocalImageRule:4:&lt;img src=&quot;/file/view/17versus12pcs/30122074/17versus12pcs&quot; alt=&quot;&quot; title=&quot;&quot; /&gt; --><img src="/file/view/17versus12pcs/30122074/17versus12pcs" alt="17versus12pcs" title="17versus12pcs" /><!-- ws:end:WikiTextLocalImageRule:4 --><!-- ws:start:WikiTextLocalImageRule:5:&lt;img src=&quot;/file/view/17versus12pcs/30122074/1x1/17versus12pcs&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 1px; width: 1px;&quot; /&gt; --><img src="/file/view/17versus12pcs/30122074/1x1/17versus12pcs" alt="17versus12pcs" title="17versus12pcs" style="height: 1px; width: 1px;" /><!-- ws:end:WikiTextLocalImageRule:5 --></body></html></pre></div> | |||
Revision as of 12:07, 11 July 2006
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author xenjacob and made on 2006-07-11 12:07:39 UTC.
- The original revision id was 860807.
- The revision comment was: *%&##^ image transfer
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonics, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:
Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#
and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.
[[image:17fifths]][[image:space/showimage/17fifths]]
The lines across indicate five fifths ("minor second") (1/17 of an octave). Now we can order them ascendingly:
[[image:17versus12names width="1" height="1"]][[image:17versus12names]]
Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." These last two properties are shared with 24-equal (quartertones).
If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):
[[image:17versus12cents]]
and in pitch/interval classes:
[[image:17versus12pcs]][[image:17versus12pcs width="1" height="1"]]Original HTML content:
<html><head><title>SeventeenTheory</title></head><body>17-tone equal tuning has fifths very close to just-intonation (and 12-equal) fifths. Consequently we use the usual circle-of-fifths on a five-line-staff notation, with a twist of new enharmonics, caused by the accumulation of the difference in the size of the fifth. To figure out the enharmonic names of any closed circle of fifths, write out a portion of it, like:<br /> <br /> Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#<br /> <br /> and then wrap it into a circle of the desired size. If you do this with 17, you will notice that Cb = A#...that's how big the value of "flat/sharp" is in 17. The closer two notes are in the circle, the more familiar to us their harmonic function.<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:0:<img src="/file/view/17fifths/30122064/17fifths" alt="" title="" /> --><img src="/file/view/17fifths/30122064/17fifths" alt="17fifths" title="17fifths" /><!-- ws:end:WikiTextLocalImageRule:0 -->[[image:space/showimage/17fifths]]<br /> The lines across indicate five fifths ("minor second") (1/17 of an octave). Now we can order them ascendingly:<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:1:<img src="/file/view/17versus12names/30122065/1x1/17versus12names" alt="" title="" style="height: 1px; width: 1px;" /> --><img src="/file/view/17versus12names/30122065/1x1/17versus12names" alt="17versus12names" title="17versus12names" style="height: 1px; width: 1px;" /><!-- ws:end:WikiTextLocalImageRule:1 --><!-- ws:start:WikiTextLocalImageRule:2:<img src="/file/view/17versus12names/30122065/17versus12names" alt="" title="" /> --><img src="/file/view/17versus12names/30122065/17versus12names" alt="17versus12names" title="17versus12names" /><!-- ws:end:WikiTextLocalImageRule:2 --><br /> <br /> Note that C# is HIGHER than Db; note that none of the intervals save the octave/unison are exactly the same as in 12. Note that The "half step"/"minor second" in 17 is twice as small as the "augmented unison"/"sharp"/"flat." Two sharp/flats add up to a minor third. Two "neutral thirds" add up to a "perfect fifth." These last two properties are shared with 24-equal (quartertones).<br /> <br /> If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:3:<img src="/file/view/17versus12cents/30122071/17versus12cents" alt="" title="" /> --><img src="/file/view/17versus12cents/30122071/17versus12cents" alt="17versus12cents" title="17versus12cents" /><!-- ws:end:WikiTextLocalImageRule:3 --><br /> and in pitch/interval classes:<br /> <br /> <!-- ws:start:WikiTextLocalImageRule:4:<img src="/file/view/17versus12pcs/30122074/17versus12pcs" alt="" title="" /> --><img src="/file/view/17versus12pcs/30122074/17versus12pcs" alt="17versus12pcs" title="17versus12pcs" /><!-- ws:end:WikiTextLocalImageRule:4 --><!-- ws:start:WikiTextLocalImageRule:5:<img src="/file/view/17versus12pcs/30122074/1x1/17versus12pcs" alt="" title="" style="height: 1px; width: 1px;" /> --><img src="/file/view/17versus12pcs/30122074/1x1/17versus12pcs" alt="17versus12pcs" title="17versus12pcs" style="height: 1px; width: 1px;" /><!-- ws:end:WikiTextLocalImageRule:5 --></body></html>