7edf: 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:Kosmorsky|Kosmorsky]] and made on <tt>2011-12-26 16:33:51 UTC</tt>.<br>
 
: The original revision id was <tt>288517542</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
7edf is related to [[12edo]], but with the 3/2 rather than the 2/1 being just, which stretches the octave by 3.3514{{c}}. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13. It forms as a decent approximation to stretched-octave tuning on pianos, since pianos' strings have overtones that tend slightly sharp and are thus often tuned with stretched octaves.
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>
=== Harmonics ===
<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">Lookalikes: [[12edo]], [[19ed3]]</pre></div>
{{Harmonics in equal|7|3|2|prec=2|columns=15}}
<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;7edf&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Lookalikes: &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;, &lt;a class="wiki_link" href="/19ed3"&gt;19ed3&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Subsets and supersets ===
7edf is the 4th [[prime equal division|prime edf]], after [[5edf]] and before [[11edf]].
 
== Intervals ==
{| class="wikitable center-1 right-2 center-3"
|-
! #
! Cents
! Approximate ratios
! 12edo notation
|-
| 0
| 0
| exact 1/1
| C
|-
| 1
| 100.3
| 18/17, 17/16
| C#, Db
|-
| 2
| 200.6
| 9/8
| D
|-
| 3
| 300.8
| 19/16, 44/37
| D#, Eb
|-
| 4
| 401.1
| 63/50
| E
|-
| 5
| 501.4
|4/3
| F
|-
| 6
| 601.7
| 64/45
| F#, Gb
|-
| 7
| 702.0
| exact 3/2
| G
|-
| 8
| 802.2
| 100/63
| G#, Ab
|-
| 9
| 902.5
| 27/16
| A
|-
| 10
| 1002.8
| 16/9
| A#, Bb
|-
| 11
| 1103.1
| 17/9
| B
|-
| 12
| 1203.4
| 2/1
| C
|-
| 13
| 1303.6
| 17/8
| C#, Db
|-
| 14
| 1403.9
| exact 9/4
| D
|}
 
== See also ==
* [[12edo]] – relative edo
* [[19edt]] – relative edt
* [[28ed5]] – relative ed5
* [[31ed6]] – relative ed6
* [[34ed7]] – relative ed7
* [[40ed10]] – relative ed10
* [[43ed12]] – relative ed12
* [[76ed80]] – close to the zeta-optimized tuning for 12edo
* [[1ed18/17|AS18/17]] – relative [[AS|ambitonal sequence]]
 
{{Todo|expand}}
 
[[Category:12edo]]

Latest revision as of 13:26, 10 June 2025

← 6edf 7edf 8edf →
Prime factorization 7 (prime)
Step size 100.279 ¢ 
Octave 12\7edf (1203.35 ¢)
(convergent)
Twelfth 19\7edf (1905.31 ¢)
(convergent)
Consistency limit 10
Distinct consistency limit 6

7 equal divisions of the perfect fifth (abbreviated 7edf or 7ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 7 equal parts of about 100 ¢ each. Each step represents a frequency ratio of (3/2)1/7, or the 7th root of 3/2.

Theory

7edf is related to 12edo, but with the 3/2 rather than the 2/1 being just, which stretches the octave by 3.3514 ¢. The patent val has a generally sharp tendency for harmonics up to 21, with the exception for 11 and 13. It forms as a decent approximation to stretched-octave tuning on pianos, since pianos' strings have overtones that tend slightly sharp and are thus often tuned with stretched octaves.

Harmonics

Approximation of harmonics in 7edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Error Absolute (¢) +3.35 +3.35 +6.70 +21.51 +6.70 +40.67 +10.05 +6.70 +24.86 -39.87 +10.05 -28.24 +44.02 +24.86 +13.41
Relative (%) +3.3 +3.3 +6.7 +21.4 +6.7 +40.6 +10.0 +6.7 +24.8 -39.8 +10.0 -28.2 +43.9 +24.8 +13.4
Steps
(reduced) 		12
(5) 		19
(5) 		24
(3) 		28
(0) 		31
(3) 		34
(6) 		36
(1) 		38
(3) 		40
(5) 		41
(6) 		43
(1) 		44
(2) 		46
(4) 		47
(5) 		48
(6)

Subsets and supersets

7edf is the 4th prime edf, after 5edf and before 11edf.

Intervals

# Cents Approximate ratios 12edo notation
0 0 exact 1/1 C
1 100.3 18/17, 17/16 C#, Db
2 200.6 9/8 D
3 300.8 19/16, 44/37 D#, Eb
4 401.1 63/50 E
5 501.4 4/3 F
6 601.7 64/45 F#, Gb
7 702.0 exact 3/2 G
8 802.2 100/63 G#, Ab
9 902.5 27/16 A
10 1002.8 16/9 A#, Bb
11 1103.1 17/9 B
12 1203.4 2/1 C
13 1303.6 17/8 C#, Db
14 1403.9 exact 9/4 D

See also

Retrieved from "https://en.xen.wiki/index.php?title=7edf&oldid=199125"