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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 = septimal neutral second |
| : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 13:16:46 UTC</tt>.<br>
| | | Color name = zy2, zoyo 2nd |
| : The original revision id was <tt>300949110</tt>.<br>
| | | Sound = jid_35_32_pluck_adu_dr220.mp3 |
| : The revision comment was: <tt></tt><br>
| | | Comma = no |
| 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>
| | |
| <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">**35/32**, the **septimal neutral second**, is approximately half of a [[6_5|6/5]] just minor third; (6/5)/(35/32)^2 = 6144/6125, the [[porwell comma]]. It is the interval between [[8_7|8/7]] and [[5_4|5/4]]. It is 385/384 sharp of 12/11, and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to [[keenanismic chords]], interpreting [[48_35|48/35]] as [[11_8|11/8]]. It is also 176/175 flat of 11/10, and tempering that out instead leads to [[valinorsmic chords]] and interprets 48/35 as [[15_11|15/11]].</pre></div>
| | '''35/32''', the '''septimal neutral second''', is approximately half of a [[6/5]] just minor third; (6/5)/(35/32)<sup>2</sup> = [[6144/6125]], the porwell comma. It is the interval between [[8/7]] and [[5/4]]. It is 385/384 sharp of [[12/11]], and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to [[keenanismic chords]], interpreting [[48/35]] as [[11/8]]. It is also [[176/175]] flat of [[11/10]], and tempering that out instead leads to [[valinorsmic chords]] and interprets 48/35 as [[15/11]]. |
| <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>35_32</title></head><body><strong>35/32</strong>, the <strong>septimal neutral second</strong>, is approximately half of a <a class="wiki_link" href="/6_5">6/5</a> just minor third; (6/5)/(35/32)^2 = 6144/6125, the <a class="wiki_link" href="/porwell%20comma">porwell comma</a>. It is the interval between <a class="wiki_link" href="/8_7">8/7</a> and <a class="wiki_link" href="/5_4">5/4</a>. It is 385/384 sharp of 12/11, and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to <a class="wiki_link" href="/keenanismic%20chords">keenanismic chords</a>, interpreting <a class="wiki_link" href="/48_35">48/35</a> as <a class="wiki_link" href="/11_8">11/8</a>. It is also 176/175 flat of 11/10, and tempering that out instead leads to <a class="wiki_link" href="/valinorsmic%20chords">valinorsmic chords</a> and interprets 48/35 as <a class="wiki_link" href="/15_11">15/11</a>.</body></html></pre></div>
| | It is very closely approximated by [[31edo|4\31]], being just 0.3 [[cents]] sharp of that interval. |
| | == Approximation == |
| | {{Interval edo approximation|35/32}} |
| | == See also == |
| | * [[64/35]] – its [[octave complement]] |
| | * [[Gallery of just intervals]] |
| | |
| | [[Category:Second]] |
| | [[Category:Neutral second]] |
| | [[Category:Mint]] |
35/32, the septimal neutral second, is approximately half of a 6/5 just minor third; (6/5)/(35/32)2 = 6144/6125, the porwell comma. It is the interval between 8/7 and 5/4. It is 385/384 sharp of 12/11, and tempering it out makes the interval from 8/7 to 5/4 a 12/11, and leads to keenanismic chords, interpreting 48/35 as 11/8. It is also 176/175 flat of 11/10, and tempering that out instead leads to valinorsmic chords and interprets 48/35 as 15/11.
It is very closely approximated by 4\31, being just 0.3 cents sharp of that interval.
Approximation
Edo approximations for 35/32 (155.14 ¢)
≤ 80edo, relative error ≤ 10%
| Edo |
Step size |
Cents (¢) |
Absolute error (¢) |
Relative error (%)
|
| 7 |
1\7 |
171.43 |
+16.29 |
+9.50
|
| 8 |
1\8 |
150.00 |
-5.14 |
-3.43
|
| 15 |
2\15 |
160.00 |
+4.86 |
+6.08
|
| 16 |
2\16 |
150.00 |
-5.14 |
-6.85
|
| 23 |
3\23 |
156.52 |
+1.38 |
+2.65
|
| 31 |
4\31 |
154.84 |
-0.30 |
-0.78
|
| 38 |
5\38 |
157.89 |
+2.76 |
+8.72
|
| 39 |
5\39 |
153.85 |
-1.29 |
-4.20
|
| 46 |
6\46 |
156.52 |
+1.38 |
+5.30
|
| 47 |
6\47 |
153.19 |
-1.95 |
-7.63
|
| 54 |
7\54 |
155.56 |
+0.42 |
+1.87
|
| 62 |
8\62 |
154.84 |
-0.30 |
-1.55
|
| 69 |
9\69 |
156.52 |
+1.38 |
+7.95
|
| 70 |
9\70 |
154.29 |
-0.85 |
-4.98
|
| 77 |
10\77 |
155.84 |
+0.70 |
+4.52
|
| 78 |
10\78 |
153.85 |
-1.29 |
-8.41
|
See also