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9edt: Difference between revisions

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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>
{{ED intro}}
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-09-04 12:44:58 UTC</tt>.<br>
 
: The original revision id was <tt>250623624</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
It has a decent seventh harmonic ([[7/1]]) which is 12.4¢ sharp, and an excellent [[13/1]] inherited from [[3edt]] which is only 2.6{{c}} flat. However, the [[5/1]] is 39{{c}} flat, thus 13 steps of 9edt (approximating the 5/1) can be described as a neutral seventeenth—or if tritave-reduced to 4 steps, a neutral sixth (approximating the 5/3). This neutral sixth has a size of 845{{c}}, which is between [[8/5]] and [[5/3]]; if this interval is also taken as an approximation to [[13/8]], it would temper out [[40/39]]—making 9edt an exotemperament in the 8.3.5.13 subgroup. Though, 9edt is more well behaved on the 3.7.13 [[subgroup]], of which it tempers out [[351/343]] and [[2197/2187]].
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>
Following [[4edt]], this is the next edt that supports [[BPS]] temperament. For small edts, this property is virtually the same as supporting a [[4L 5s (3/1-equivalent)|3/1-equivalent "lambda" scale]], of which 9edt offers the "equalized" interpretation of {{nowrap|L {{=}} s}}, analogous to [[7edo]] in diatonic ([[5L&nbsp;2s]]) music.
<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">The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a third, it would count as a neutral third. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more a 13/8, though this is allegedly a no-twos tuning. The 3.7.13 subgroup tempers out 351/343 and 2197/2187. 9edt is the third [[The Riemann Zeta Function and Tuning#Removing primes|no-twos zeta peak edt]].</pre></div>
 
<h4>Original HTML content:</h4>
9edt is the third [[the Riemann zeta function and tuning#Removing primes|no-twos zeta peak edt]].
<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;9edt&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The 9 equal division of 3, the tritave, divides it into 9 equal steps of size 211.328 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a third, it would count as a neutral third. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more a 13/8, though this is allegedly a no-twos tuning. The 3.7.13 subgroup tempers out 351/343 and 2197/2187. 9edt is the third &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Removing primes"&gt;no-twos zeta peak edt&lt;/a&gt;.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
=== Relation to edos ===
9edt is related to [[17edo]], by which it may be approximated by playing every third step (the 17edo non-octave whole-tone scale), the discrepancy is only about four cents when it gets to [[3/1]].
 
=== Harmonics ===
{{Harmonics in equal|9|3|1|}}
{{Harmonics in equal|9|3|1|intervals=prime}}
 
{| class="wikitable"
|-
! rowspan="2" | Steps
! colspan="2" | Size
! rowspan="2" | Comparable intervals (¢)
|-
! Cents
! [[Hekt]]s
|-
! colspan="3" | 0
| [[1/1]]
|-
| 1
| 211.328
| 144.444
| [[9/8]] (204)
|-
| 2
| 422.657
| 288.889
| [[9/7]] (435)
|-
| 3
| 633.985
| 433.333
| [[13/9]] (637)
|-
| 4
| 845.313
| 577.778
| [[13/8]] (841), [[5/3]] (884), [[8/5]] (814)
|-
| 5
| 1056.642
| 722.222
| [[9/5]] (1018), [[11/6]] (1049)
|-
| 6
| 1267.970
| 866.667
| [[27/13]] (1265)
|-
| 7
| 1479.298
| 1011.111
| [[7/3]] (1467)
|-
| 8
| 1690.627
| 1155.556
| [[8/3]] (1698)
|-
| 9
| 1901.955
| 1300
| [[3/1]]
|}
 
== Music ==
* [https://www.youtube.com/watch?v=sEQP1AtjPrA Far Away From Them / Spazzystackers] by [[Mandrake]]
 
[[Category:Macrotonal]]
Retrieved from "https://en.xen.wiki/w/9edt"