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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox ET}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
'''[[Ed5|Division of the 5th harmonic]] into 17 equal parts''' (17ED5) is a good [[hyperpyth]] tuning. The step size is about 163.9008 cents, corresponding to 7.3215 [[EDO]].
: This revision was by author [[User:guest|guest]] and made on <tt>2011-12-31 21:40:59 UTC</tt>.<br>
: The original revision id was <tt>288945041</tt>.<br>
: 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>
<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">=Division of the 5/1 into 17 tones=


A hyperpyth tuning, 17ed5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. However, in hyperpyth, 21/5 isn't necessarily represented, at least not as well. In 17ed5, the 21/5 is represented about as well as the 9/5 is, although that's not too good. Luckily, 27, 29, and 39 do a fair job of it. Nevertheless it's the simplest equal hyperpyth after 5ed5, and quite consonant. I imagine it to be the traditional tonality of the tiny creatures living on subatomic particles.
== Division of the 5/1 into 17 tones ==
A hyperpyth tuning, 17ED5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. However, in hyperpyth, 21/5 isn't necessarily represented, at least not as well. In 17ED5, the 21/5 is represented about as well as the 9/5 is, although that's not too good. Luckily, 27, 29, and 39 do a fair job of it. Nevertheless it's the simplest equal hyperpyth after 5ED5, and quite consonant. I imagine it to be the traditional tonality of the tiny creatures living on subatomic particles.


But wait, an interesting pattern emerges:
But wait, an interesting pattern emerges:


22ed5 focuses on 9/5
[[22ed5|22ED5]] focuses on 9/5
27ed5 focuses on 13/5
 
29ed5 focuses on 17/5
[[27ed5|27ED5]] focuses on 13/5
 
[[29ed5|29ED5]] focuses on 17/5
 
(and 34=17*2)
(and 34=17*2)


so: 22+27+29=78=39*2
so: 22+27+29=78=39*2
and behold, of the lot, 39ed5 offers the best balance between those intervals.


|| 0: 0.000 cents || 1/1 ||  ||
and behold, of the lot, [[39ed5|39ED5]] offers the best balance between those intervals.
|| 1: 163.901 ||  ||  ||
|| 2: 327.802 ||  ||  ||
|| 3: 491.702 ||  ||  ||
|| 4: 655.603 ||  ||  ||
|| 5: 819.504 ||  ||  ||
|| 6: 983.405 || 9/5, 16/9, 7/4 || 1017 ||
|| 7: 1147.306 ||  ||  ||
|| 8: 1311.206 ||  ||  ||
|| 9: 1475.107 ||  ||  ||
|| 10: 1639.008 || 13/5 || 1654 ||
|| 11: 1802.909 ||  ||  ||
|| 12: 1966.810 ||  ||  ||
|| 13: 2130.710 || 17/5 || 2118 ||
|| 14: 2294.611 ||  ||  ||
|| 15: 2458.512 || (21/5) || 2486 ||
|| 16: 2622.413 ||  ||  ||
|| 17: 2786.314 || 5/1 ||  ||</pre></div>
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;17ed5&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Division of the 5/1 into 17 tones"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Division of the 5/1 into 17 tones&lt;/h1&gt;
&lt;br /&gt;
A hyperpyth tuning, 17ed5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. However, in hyperpyth, 21/5 isn't necessarily represented, at least not as well. In 17ed5, the 21/5 is represented about as well as the 9/5 is, although that's not too good. Luckily, 27, 29, and 39 do a fair job of it. Nevertheless it's the simplest equal hyperpyth after 5ed5, and quite consonant. I imagine it to be the traditional tonality of the tiny creatures living on subatomic particles.&lt;br /&gt;
&lt;br /&gt;
But wait, an interesting pattern emerges:&lt;br /&gt;
&lt;br /&gt;
22ed5 focuses on 9/5&lt;br /&gt;
27ed5 focuses on 13/5&lt;br /&gt;
29ed5 focuses on 17/5&lt;br /&gt;
(and 34=17*2)&lt;br /&gt;
&lt;br /&gt;
so: 22+27+29=78=39*2&lt;br /&gt;
and behold, of the lot, 39ed5 offers the best balance between those intervals.&lt;br /&gt;
&lt;br /&gt;


{| class="wikitable"
|-
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
| | 0
| | 0.000
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 163.901
| | [[11/10]]
| |
|-
| | 2
| | 327.802
| | [[6/5]]
| |
|-
| | 3
| | 491.702
| | [[4/3]]
| |
|-
| | 4
| | 655.603
| | [[16/11]], [[19/13]], <br>[[22/15]]
| |
|-
| | 5
| | 819.504
| | [[8/5]]
| |
|-
| | 6
| | 983.405
| | [[7/4]], [[9/5]], [[16/9]]
| |
|-
| | 7
| | 1147.306
| | [[25/13]], [[27/14]], <br>[[35/18]], [[64/33]]
| |
|-
| | 8
| | 1311.206
| | [[16/15|32/15]]
| |
|-
| | 9
| | 1475.107
| | [[75/64|75/32]]
| |
|-
| | 10
| | 1639.008
| | [[13/5]], [[9/7|18/7]]
| |
|-
| | 11
| | 1802.909
| | [[17/12|17/6]]
| |
|-
| | 12
| | 1966.810
| | [[14/9|28/9]]
| |
|-
| | 13
| | 2130.710
| | [[17/10|17/5]], [[12/7|24/7]]
| |
|-
| | 14
| | 2294.611
| | [[19/10|19/5]], [[32/17|64/17]]
| |
|-
| | 15
| | 2458.512
| | [[21/20|21/5]], [[25/24|25/6]], <br>[[33/32|33/8]]
| |
|-
| | 16
| | 2622.413
| | [[17/15|68/15]]
| |
|-
| | 17
| | 2786.314
| | '''exact [[5/1]]'''
| | just major third plus two octaves
|}


&lt;table class="wiki_table"&gt;
== Harmonics ==
    &lt;tr&gt;
{{Harmonics in equal
        &lt;td&gt;0: 0.000 cents&lt;br /&gt;
| steps = 17
&lt;/td&gt;
| num = 5
        &lt;td&gt;1/1&lt;br /&gt;
| denom = 1
&lt;/td&gt;
}}
        &lt;td&gt;&lt;br /&gt;
{{Harmonics in equal
&lt;/td&gt;
| steps = 17
    &lt;/tr&gt;
| num = 5
    &lt;tr&gt;
| denom = 1
        &lt;td&gt;1: 163.901&lt;br /&gt;
| start = 12
&lt;/td&gt;
| collapsed = 1
        &lt;td&gt;&lt;br /&gt;
}}
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2: 327.802&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3: 491.702&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;4: 655.603&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5: 819.504&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;6: 983.405&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/5, 16/9, 7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1017&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7: 1147.306&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;8: 1311.206&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9: 1475.107&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;10: 1639.008&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1654&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11: 1802.909&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;12: 1966.810&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13: 2130.710&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2118&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;14: 2294.611&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15: 2458.512&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;(21/5)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2486&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;16: 2622.413&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17: 2786.314&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:Hyperpyth]]
[[Category:Todo:add sound example]]
Retrieved from "https://en.xen.wiki/w/17ed5"