22/19: Difference between revisions

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<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 = undevicesimal semifourth, minimal minor third, godzilla semifourth
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-06-01 16:42:28 UTC</tt>.<br>
| Color name = 19u1o2, nulo 2nd
: The original revision id was <tt>341892948</tt>.<br>
| Sound = jid_22_19_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>
 
<h4>Original Wikitext content:</h4>
'''22/19''', the '''undevicesimal semifourth''', is a [[19-limit]] [[interseptimal]] interval measuring about 254 [[cent]]s. It is classified as a [[major second]] in [[FJS]] and [[HEJI]], sharp of the [[9/8|Pythagorean major second]] by [[176/171]], which is the difference between [[33/32]] and [[513/512]]. [[Margo Schulter]] has called it the ''minimal minor third'' instead, in which case it is flat of the [[32/27|Pythagorean minor third]] by [[304/297]]. A stack of two 22/19's exceeds [[4/3]] by [[363/361]].
<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">Margo Schulter has called 22/19 the minimal minor third; since it is a good tuning for the godzilla generator in the 11 and 13 limits, it can also be called the godzilla third: in godzilla, it serves for both 8/7 and 7/6.</pre></div>
 
<h4>Original HTML content:</h4>
Since it is a good tuning for the [[godzilla]] generator in the [[11-limit]] and [[13-limit]], it can also be called the ''godzilla semifourth'': in godzilla, it serves for both [[8/7]] and [[7/6]].
<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;22_19&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Margo Schulter has called 22/19 the minimal minor third; since it is a good tuning for the godzilla generator in the 11 and 13 limits, it can also be called the godzilla third: in godzilla, it serves for both 8/7 and 7/6.&lt;/body&gt;&lt;/html&gt;</pre></div>
 
== Approximation ==
{{Interval edo approximation|22/19}}
 
== See also ==
* [[19/11]] – its [[octave complement]]
* [[Gallery of just intervals]]
 
[[Category:Interseptimal intervals]]
[[Category:Semifourth]]
[[Category:Second]]
[[Category:Supermajor second]]
[[Category:Third]]
[[Category:Subminor third]]

Latest revision as of 07:54, 11 April 2026

Interval information
Ratio 22/19
Factorization 2 × 11 × 19-1
Monzo [1 0 0 0 1 0 0 -1⟩
Size in cents 253.8049¢
Names undevicesimal semifourth,
minimal minor third,
godzilla semifourth
Color name 19u1o2, nulo 2nd
FJS name [math]\displaystyle{ \text{M2}^{11}_{19} }[/math]
Special properties reduced
Tenney norm (log2 nd) 8.70736
Weil norm (log2 max(n, d)) 8.91886
Wilson norm (sopfr(nd)) 32

[sound info]
Open this interval in xen-calc

22/19, the undevicesimal semifourth, is a 19-limit interseptimal interval measuring about 254 cents. It is classified as a major second in FJS and HEJI, sharp of the Pythagorean major second by 176/171, which is the difference between 33/32 and 513/512. Margo Schulter has called it the minimal minor third instead, in which case it is flat of the Pythagorean minor third by 304/297. A stack of two 22/19's exceeds 4/3 by 363/361.

Since it is a good tuning for the godzilla generator in the 11-limit and 13-limit, it can also be called the godzilla semifourth: in godzilla, it serves for both 8/7 and 7/6.

Approximation

Edo approximations for 22/19 (253.80 ¢)
≤ 80edo, relative error ≤ 10%
Edo Step size Cents (¢) Absolute error (¢) Relative error (%)
5 1\5 240.00 -13.80 -5.75
9 2\9 266.67 +12.86 +9.65
14 3\14 257.14 +3.34 +3.89
19 4\19 252.63 -1.17 -1.86
24 5\24 250.00 -3.80 -7.61
28 6\28 257.14 +3.34 +7.79
33 7\33 254.55 +0.74 +2.04
38 8\38 252.63 -1.17 -3.72
43 9\43 251.16 -2.64 -9.47
47 10\47 255.32 +1.51 +5.93
52 11\52 253.85 +0.04 +0.18
57 12\57 252.63 -1.17 -5.57
61 13\61 255.74 +1.93 +9.82
66 14\66 254.55 +0.74 +4.07
71 15\71 253.52 -0.28 -1.68
76 16\76 252.63 -1.17 -7.43
80 17\80 255.00 +1.20 +7.97

See also

Retrieved from "https://en.xen.wiki/index.php?title=22/19&oldid=227612"