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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | {{Infobox Interval |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| | | Name = septendecimal supraminor sixth |
| : This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-12-28 14:08:06 UTC</tt>.<br>
| | | Color name = 17or6, soru 6th |
| : The original revision id was <tt>602876782</tt>.<br>
| | | Sound = ji-34-21-csound-foscil-220hz.mp3 |
| : 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>
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| <h4>Original Wikitext content:</h4>
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| <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">**34/21**
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| | 1 -1 0 -1 0 0 1> | |
| 834.1745 cents
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| [[media type="file" key="ji-34-21-csound-foscil-220hz.mp3"]] [[file:xenharmonic/ji-34-21-csound-foscil-220hz.mp3|sound sample]]
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| The **septendecimal supraminor sixth**. Its inverse is the septendecimal submajor third [[21_17|21/17]].
| | '''34/21''' is the '''septendecimal supraminor sixth'''. |
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| See [[Gallery of Just Intervals]]</pre></div>
| | This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the [[Acoustic phi|acoustic golden ratio]]. In this case, 34/21 is ~1.1 [[cent|¢]] sharp of the golden ratio. Two fall short of [[21/8]] and three of them fall short of [[17/4]] by [[9261/9248]], which becomes particularly significant in [[Sephiroth]] temperament. |
| <h4>Original HTML content:</h4>
| | == Approximation == |
| <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>34_21</title></head><body><strong>34/21</strong><br />
| | {{Interval edo approximation|21/17}} |
| | 1 -1 0 -1 0 0 1&gt;<br />
| | == See also == |
| 834.1745 cents<br />
| | * [[21/17]] – its [[octave complement]] |
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| | * [[Gallery of just intervals]] |
| <br />
| | |
| The <strong>septendecimal supraminor sixth</strong>. Its inverse is the septendecimal submajor third <a class="wiki_link" href="/21_17">21/17</a>.<br />
| | [[Category:Sixth]] |
| <br />
| | [[Category:Supraminor sixth]] |
| See <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">Gallery of Just Intervals</a></body></html></pre></div>
| | [[Category:Golden ratio approximations]] |
| | {{todo|expand}} |
34/21 is the septendecimal supraminor sixth.
This interval is a ratio of two consecutive Fibonacci numbers, therefore it approximates the acoustic golden ratio. In this case, 34/21 is ~1.1 ¢ sharp of the golden ratio. Two fall short of 21/8 and three of them fall short of 17/4 by 9261/9248, which becomes particularly significant in Sephiroth temperament.
Approximation
Edo approximations for 34/21 (834.17 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 3 |
2\3 |
800.00 |
-34.17 |
-8.54
|
| 10 |
7\10 |
840.00 |
+5.83 |
+4.85
|
| 13 |
9\13 |
830.77 |
-3.41 |
-3.69
|
| 20 |
14\20 |
840.00 |
+5.83 |
+9.71
|
| 23 |
16\23 |
834.78 |
+0.61 |
+1.17
|
| 26 |
18\26 |
830.77 |
-3.41 |
-7.38
|
| 33 |
23\33 |
836.36 |
+2.19 |
+6.02
|
| 36 |
25\36 |
833.33 |
-0.84 |
-2.52
|
| 46 |
32\46 |
834.78 |
+0.61 |
+2.33
|
| 49 |
34\49 |
832.65 |
-1.52 |
-6.21
|
| 56 |
39\56 |
835.71 |
+1.54 |
+7.19
|
| 59 |
41\59 |
833.90 |
-0.28 |
-1.36
|
| 62 |
43\62 |
832.26 |
-1.92 |
-9.90
|
| 69 |
48\69 |
834.78 |
+0.61 |
+3.50
|
| 72 |
50\72 |
833.33 |
-0.84 |
-5.05
|
| 79 |
55\79 |
835.44 |
+1.27 |
+8.35
|
See also