28/25: Difference between revisions

Interval information
Ratio	28/25
Factorization	22 × 5-2 × 7
Monzo	[2 0 -2 1⟩
Size in cents	196.1985¢
Names	(septimal) middle major second,; (septimal) middle whole tone
Color name	zgg3, zogugu 3rd
FJS name	[math]\displaystyle{ \text{d3}^{7}_{5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	9.45121
Weil norm (log2 max(n, d))	9.61471
Wilson norm (sopfr(nd))	21
	https://en.xen.wiki/w/File:Jid_28_25_pluck_adu_dr220.mp3; [sound info]
	Open this interval in xen-calc

VisualWikitext

Latest revision as of 02:27, 2 June 2026

28/25, the (septimal) middle whole tone, is the interval between 5/4 and 7/5, and is intermediate in size between 10/9, of which it is 126/125 sharp, and 9/8, of which it is 225/224 flat. It's actually the mediant of 19/17 and 9/8. A meantone where the tone is tuned to be exactly 28/25 has a fifth of size 2√14/5, or 698.099 ¢, which is closely approximated by 55edo (however, 55edo in its patent val maps this interval inconsistently to 8\55 instead of 9\55; 55d is required for proper mapping).

Approximation

Edo approximations for 28/25 (196.20 ¢)
*≤ 80edo, relative error ≤ 10%*
Edo	Step size	Cents (¢)	Absolute error (¢)	Relative error (%)
6	1\6	200.00	+3.80	+1.90
12	2\12	200.00	+3.80	+3.80
18	3\18	200.00	+3.80	+5.70
24	4\24	200.00	+3.80	+7.60
25	4\25	192.00	-4.20	-8.75
30	5\30	200.00	+3.80	+9.50
31	5\31	193.55	-2.65	-6.85
37	6\37	194.59	-1.60	-4.95
43	7\43	195.35	-0.85	-3.04
49	8\49	195.92	-0.28	-1.14
55	9\55	196.36	+0.17	+0.76
61	10\61	196.72	+0.52	+2.66
67	11\67	197.01	+0.82	+4.56
73	12\73	197.26	+1.06	+6.46
74	12\74	194.59	-1.60	-9.89
79	13\79	197.47	+1.27	+8.36
80	13\80	195.00	-1.20	-7.99

@@ Line 1: / Line 1: @@
-<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) middle major second, (septimal) middle whole tone
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-02-12 19:26:00 UTC</tt>.<br>
+| Color name = zgg3, zogugu 3rd
-: The original revision id was <tt>301034568</tt>.<br>
+| Sound = jid_28_25_pluck_adu_dr220.mp3
-: 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>
+'''28/25''', the '''(septimal) middle whole tone''', is the interval between [[5/4]] and [[7/5]], and is intermediate in size between [[10/9]], of which it is [[126/125]] sharp, and [[9/8]], of which it is [[225/224]] flat. It's actually the [[mediant]] of [[19/17]] and [[9/8]]. A [[meantone]] where the tone is tuned to be exactly 28/25 has a fifth of size 2√14/5, or 698.099{{cent}}, which is closely approximated by [[55edo]] (however, 55edo in its patent val maps this interval inconsistently to 8\55 instead of 9\55; 55d is required for proper mapping).
-<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 middle second, 28/25, is the interval between [[5_4/5/4]] and [[7_5|7/5]], and is intermediate in size between [[10_9|10/9]], which it is 126/125 sharp of, and [[9_8|9/8]], which it is 225/224 flat of. A meantone where the tone is tuned to be exactly 28/25 has a fifth of size 2 √14/5, or 698.099 cents.</pre></div>
+== Approximation ==
-<h4>Original HTML content:</h4>
+{{Interval edo approximation|28/25}}
-<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;28_25&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The middle second, 28/25, is the interval between [[5_4/5/4]] and &lt;a class="wiki_link" href="/7_5"&gt;7/5&lt;/a&gt;, and is intermediate in size between &lt;a class="wiki_link" href="/10_9"&gt;10/9&lt;/a&gt;, which it is 126/125 sharp of, and &lt;a class="wiki_link" href="/9_8"&gt;9/8&lt;/a&gt;, which it is 225/224 flat of. A meantone where the tone is tuned to be exactly 28/25 has a fifth of size 2 √14/5, or 698.099 cents.&lt;/body&gt;&lt;/html&gt;</pre></div>
+== See also ==
+* [[25/14]] – its [[octave complement]]
+* [[25/21]] – its [[fourth complement]]
+* [[29/26]] – a co-mediant interval
+* [[Gallery of just intervals]]
+* [[25-odd-limit]]
+[[Category:Second]]
+[[Category:Whole tone]]

28/25: Difference between revisions

Latest revision as of 02:27, 2 June 2026

Approximation

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