12:15:18:20: Difference between revisions

Chord information
Harmonics	12:15:18:20
Subharmonics	1/(15:12:10:9)
Intervals from root	1/1–5/4–3/2–5/3
Cents from root	0¢–386¢–702¢–884¢
Step intervals	5/4, 6/5, 10/9
Step cents	386¢, 316¢, 182¢
Color name	yo-6 or y6
Prime limit	5
Genus	32⋅5 (45)
Intervallic odd limit	9
Otonal odd limit	15
Utonal odd limit	15
Consistent edos (d ≥ 2)	12edo, 19edo, 34edo, 38edo*, …
	* 2 ≤ d < 4; 4 ≤ d < 8; * 8 ≤ d < 16; …

VisualWikitext

Latest revision as of 04:53, 26 May 2026

12:15:18:20, the just, classical, or ptolemaic major sixth chord, is a major sixth chord in the 5-limit, with steps 5/4, 6/5, and 10/9. It is an anomalous saturated suspension in the 9-odd-limit.

Edo approximations for 12:15:18:20 ▶
*intervals: 5/4, 3/2, 5/3 · ≤ 60edo, RMS rel. error ≤ 15%*
	Edo	Steps	Cents (¢)	Absolute errors (¢)	RMS (¢)	RMS (%)
▶	7	`0 2 4 5`	`0.00 342.86 685.71 857.14`	`0.00 -43.46 -16.24 -27.22`	15.85	9.24
▶	12	`0 4 7 9`	`0.00 400.00 700.00 900.00`	`0.00 +13.69 -1.96 +15.64`	7.88	7.88
▶	15	`0 5 9 11`	`0.00 400.00 720.00 880.00`	`0.00 +13.69 +18.04 -4.36`	9.28	11.60
▶	19	`0 6 11 14`	`0.00 378.95 694.74 884.21`	`0.00 -7.37 -7.22 -0.15`	3.61	5.72
▶	22	`0 7 13 16`	`0.00 381.82 709.09 872.73`	`0.00 -4.50 +7.14 -11.63`	6.82	12.51
▶	26	`0 8 15 19`	`0.00 369.23 692.31 876.92`	`0.00 -17.08 -9.65 -7.44`	6.09	13.20
▶	27	`0 9 16 20`	`0.00 400.00 711.11 888.89`	`0.00 +13.69 +9.16 +4.53`	5.11	11.49
▶	31	`0 10 18 23`	`0.00 387.10 696.77 890.32`	`0.00 +0.78 -5.18 +5.96`	3.95	10.20
▶	34	`0 11 20 25`	`0.00 388.24 705.88 882.35`	`0.00 +1.92 +3.93 -2.01`	2.20	6.25
▶	38	`0 12 22 28`	`0.00 378.95 694.74 884.21`	`0.00 -7.37 -7.22 -0.15`	3.61	11.43
▶	41	`0 13 24 30`	`0.00 380.49 702.44 878.05`	`0.00 -5.83 +0.48 -6.31`	3.16	10.81
▶	46	`0 15 27 34`	`0.00 391.30 704.35 886.96`	`0.00 +4.99 +2.39 +2.60`	1.77	6.77
▶	50	`0 16 29 37`	`0.00 384.00 696.00 888.00`	`0.00 -2.31 -5.96 +3.64`	3.49	14.54
▶	53	`0 17 31 39`	`0.00 384.91 701.89 883.02`	`0.00 -1.41 -0.07 -1.34`	0.67	2.96
▶	58	`0 19 34 43`	`0.00 393.10 703.45 889.66`	`0.00 +6.79 +1.49 +5.30`	2.75	13.30
▶	60	`0 19 35 44`	`0.00 380.00 700.00 880.00`	`0.00 -6.31 -1.96 -4.36`	2.39	11.94

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-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Infobox Chord|12:15:18:20|ColorName=yo-6 or y6}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+'''12:15:18:20''', the ''just'', ''classical'', or ''ptolemaic major sixth chord'', is a [[major sixth chord]] in the [[5-limit]], with steps [[5/4]], [[6/5]], and [[10/9]]. It is an [[anomalous saturated suspension]] in the [[9-odd-limit]].
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-08-01 17:43:24 UTC</tt>.<br>
-: The original revision id was <tt>243785559</tt>.<br>
-: The revision comment was: <tt></tt><br>
+{{chord edo approximation}}
-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">The //just added sixth chord// is a 5-prime-limit, 9-odd-limit chord of just intonation which is an "ASS", or [[Dyadic chord|anomalous saturated suspension]]. In close position, it is 1-5/4-3/2-5/3, with steps 5/4-6/5-10/9-6/5. </pre></div>
+== See also ==
-<h4>Original HTML content:</h4>
+* Its [[chord homonym|homonym]] [[10:12:15:18]] (1/1–6/5–3/2–9/5), a [[minor seventh chord]].
-<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;just added sixth chord&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The &lt;em&gt;just added sixth chord&lt;/em&gt; is a 5-prime-limit, 9-odd-limit chord of just intonation which is an &amp;quot;ASS&amp;quot;, or &lt;a class="wiki_link" href="/Dyadic%20chord"&gt;anomalous saturated suspension&lt;/a&gt;. In close position, it is 1-5/4-3/2-5/3, with steps 5/4-6/5-10/9-6/5.&lt;/body&gt;&lt;/html&gt;</pre></div>
+{{Todo|expand}}
+[[Category:Tetrads]]

12:15:18:20: Difference between revisions

Latest revision as of 04:53, 26 May 2026

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