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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
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| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2006-07-11 12:07:39 UTC</tt>.<br>
| | | en = SeventeenTheory |
| : The original revision id was <tt>860807</tt>.<br>
| | | es = |
| : The revision comment was: <tt>*%&##^ image transfer</tt><br>
| | | ja = 17音理論 |
| 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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| <h4>Original Wikitext content:</h4>
| | [[17edo|17-tone equal tuning]] has fifths very close to [[just intonation|just-intonation]] (and [[12edo|12-equal]]) fifths. Consequently we use the usual [[Circle of fifths|circle-of-fifths]] on a five-line-staff [[notation]], with a twist of new [[enharmonic]] equivalents, 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: |
| <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;white-space: pre-wrap ! important" class="old-revision-html">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:
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| 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# |
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| 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. | | 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. |
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| [[image:17fifths]][[image:space/showimage/17fifths]] | | [[File:17fifths-withext.jpg|alt=17fifths|17fifths]] |
| The lines across indicate five fifths ("minor second") (1/17 of an octave). Now we can order them ascendingly:
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| [[image:17versus12names width="1" height="1"]][[image:17versus12names]]
| | The lines across indicate five fourths = "minor second" = 1/17 of an octave. (We know this because 17's perfect fourth is 7/17 of an [[octave]], and 7*5 modulo 17 = 1.) |
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| 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).
| | So if we re-wrap the circle according to these lines, we should get the 17 notes of the scale in ascending/descending order (I moved A to the top just because): |
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| If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step): | | [[File:17versus12names-withext.jpg|alt=17versus12names|17versus12names]] |
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| | 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." 17 shares this last property with the quartertone scale ([[24-EDO]]). |
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| | If the old notation is bothering you, here it is in [[cents]] (hundredths of a 12-equal half step): |
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| | [[File:17versus12cents-withext.jpg|alt=17versus12cents|17versus12cents]] |
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| [[image:17versus12cents]]
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| and in pitch/interval classes: | | and in pitch/interval classes: |
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| [[image:17versus12pcs]][[image:17versus12pcs width="1" height="1"]]</pre></div> | | [[File:17versus12pcs-withext.jpg|alt=17versus12pcs|17versus12pcs]] |
| <h4>Original HTML content:</h4>
| | [[Category:17edo]] |
| <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 />
| | [[Category:EDO theory pages]] |
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| Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E#<br />
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| 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 />
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| <!-- 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 />
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| The lines across indicate five fifths (&quot;minor second&quot;) (1/17 of an octave). Now we can order them ascendingly:<br />
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| <!-- 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 />
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| 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 />
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| If the old notation is bothering you, here it is in cents (hundredths of a 12-equal half step):<br />
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| <!-- 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 />
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| and in pitch/interval classes:<br />
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| <!-- 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>
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