11L 4s: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Infobox MOS
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| Other names =  
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-10-26 14:30:00 UTC</tt>.<br>
| Periods = 1
: The original revision id was <tt>563957907</tt>.<br>
| nLargeSteps = 11
: The revision comment was: <tt></tt><br>
| nSmallSteps = 4
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| Equalized = 4
<h4>Original Wikitext content:</h4>
| Collapsed = 3
<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 interval which generates this MOS is a sharp 6/5 of height 4/15edo (320 cents) to 3/11edo (327 3/11). At its harmonic entropy minimum, 7 equals +3 generators.
| Pattern = LLLLLsLLLLLs
|| 4/15 ||  ||  ||  ||  || 320 ||
}}
||  ||  ||  ||  || 19/71 || 321.127 ||
{{MOS intro}}
||  ||  ||  || 15/56 ||  || 321.429 ||
The bright generator represents a minor third slightly sharp of [[6/5]] (315.6¢), though this MOS is most reasonably interpreted in the 2.7.11 [[orgone]] temperament where it is identified as ~[[77/64]]. At its harmonic entropy minimum, the octave-reduced 7th [[harmonic]] (about 968¢) equals 3 of these generators.
||  ||  ||  ||  || 26/97 || 321.6495 ||
||  ||  || 11/41 ||  ||  || 321.951 ||
||  ||  ||  ||  ||  || 322.146 ||
||  ||  ||  ||  || 29/108 || 322.222 ||
||  ||  ||  ||  ||  || 322.268 ||
||  ||  ||  || 18/67 ||  || 322.388 ||
||  ||  ||  ||  || 25/93 || 322.581 ||
||  || 7/26 ||  ||  ||  || 323.077 ||
||  ||  ||  ||  || 24/89 || 323.5955 ||
||  ||  ||  || 17/63 ||  || 323.8095 ||
||  ||  ||  ||  ||  || 323.947 ||
||  ||  ||  ||  || 27/100 || 324 ||
||  ||  ||  ||  ||  || 324.055 ||
||  ||  || 10/37 ||  ||  || 324.324 ||
||  ||  ||  ||  ||  || 324.443 ||
||  ||  ||  ||  || 23/85 || 324.706 ||
||  ||  ||  || 13/48 ||  || 325 ||
||  ||  ||  ||  || 16/59 || 325.424 ||
|| 3/11 ||  ||  ||  ||  || 327.273 ||</pre></div>
<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;11L 4s&lt;/title&gt;&lt;/head&gt;&lt;body&gt;The interval which generates this MOS is a sharp 6/5 of height 4/15edo (320 cents) to 3/11edo (327 3/11). At its harmonic entropy minimum, 7 equals +3 generators.&lt;br /&gt;


== Modes==
{{MOS modes}}


&lt;table class="wiki_table"&gt;
== Intervals ==
    &lt;tr&gt;
{{MOS intervals}}
        &lt;td&gt;4/15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;320&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;19/71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;321.127&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;15/56&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;321.429&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26/97&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;321.6495&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11/41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;321.951&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;322.146&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;29/108&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;322.222&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;322.268&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;18/67&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;322.388&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/93&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;322.581&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/26&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;323.077&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;24/89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;323.5955&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;17/63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;323.8095&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;323.947&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;27/100&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324.055&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;10/37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324.324&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324.443&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;23/85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;324.706&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13/48&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;325&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;16/59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;325.424&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3/11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;327.273&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
== Scale tree ==
{{MOS tuning spectrum
| 13/8 = Golden superklesimic
| 10/7 = [[Superkleismic]]
| 9/5 = [[Senator]]
| 9/4 = [[Orgone]]
| 5/2 = [[Hyperkleismic]]
| 5/1 = [[Oregon]]
| 6/1 = [[Ork]]/[[Orca]]}}
 
[[Category:15-tone scales]]

Latest revision as of 00:01, 18 June 2025

↖ 10L 3s ↑ 11L 3s 12L 3s ↗
← 10L 4s 11L 4s 12L 4s →
↙ 10L 5s ↓ 11L 5s 12L 5s ↘ 
┌╥╥╥┬╥╥╥┬╥╥╥┬╥╥┬┐
│║║║│║║║│║║║│║║││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLsLLLsLLs
sLLsLLLsLLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\15 to 3\11 (320.0 ¢ to 327.3 ¢)
Dark 8\11 to 11\15 (872.7 ¢ to 880.0 ¢)
TAMNAMS information
Related to 4L 3s (smitonic)
With tunings 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 4L 7s
Sister 4L 11s
Daughters 15L 11s, 11L 15s
Neutralized 7L 8s
2-Flought 26L 4s, 11L 19s
Equal tunings
Equalized (L:s = 1:1) 4\15 (320.0 ¢)
Supersoft (L:s = 4:3) 15\56 (321.4 ¢)
Soft (L:s = 3:2) 11\41 (322.0 ¢)
Semisoft (L:s = 5:3) 18\67 (322.4 ¢)
Basic (L:s = 2:1) 7\26 (323.1 ¢)
Semihard (L:s = 5:2) 17\63 (323.8 ¢)
Hard (L:s = 3:1) 10\37 (324.3 ¢)
Superhard (L:s = 4:1) 13\48 (325.0 ¢)
Collapsed (L:s = 1:0) 3\11 (327.3 ¢)

11L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 4 small steps, repeating every octave. 11L 4s is a grandchild scale of 4L 3s, expanding it by 8 tones. Generators that produce this scale range from 320 ¢ to 327.3 ¢, or from 872.7 ¢ to 880 ¢. The bright generator represents a minor third slightly sharp of 6/5 (315.6¢), though this MOS is most reasonably interpreted in the 2.7.11 orgone temperament where it is identified as ~77/64. At its harmonic entropy minimum, the octave-reduced 7th harmonic (about 968¢) equals 3 of these generators.

Modes

Modes of 11L 4s
UDP Cyclic
order		 Step
pattern
14|0 1 LLLsLLLsLLLsLLs
13|1 5 LLLsLLLsLLsLLLs
12|2 9 LLLsLLsLLLsLLLs
11|3 13 LLsLLLsLLLsLLLs
10|4 2 LLsLLLsLLLsLLsL
9|5 6 LLsLLLsLLsLLLsL
8|6 10 LLsLLsLLLsLLLsL
7|7 14 LsLLLsLLLsLLLsL
6|8 3 LsLLLsLLLsLLsLL
5|9 7 LsLLLsLLsLLLsLL
4|10 11 LsLLsLLLsLLLsLL
3|11 15 sLLLsLLLsLLLsLL
2|12 4 sLLLsLLLsLLsLLL
1|13 8 sLLLsLLsLLLsLLL
0|14 12 sLLsLLLsLLLsLLL

Intervals

Intervals of 11L 4s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 80.0 ¢
Major 1-mosstep M1ms L 80.0 ¢ to 109.1 ¢
2-mosstep Minor 2-mosstep m2ms L + s 109.1 ¢ to 160.0 ¢
Major 2-mosstep M2ms 2L 160.0 ¢ to 218.2 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 218.2 ¢ to 240.0 ¢
Major 3-mosstep M3ms 3L 240.0 ¢ to 327.3 ¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 218.2 ¢ to 320.0 ¢
Perfect 4-mosstep P4ms 3L + s 320.0 ¢ to 327.3 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 327.3 ¢ to 400.0 ¢
Major 5-mosstep M5ms 4L + s 400.0 ¢ to 436.4 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 436.4 ¢ to 480.0 ¢
Major 6-mosstep M6ms 5L + s 480.0 ¢ to 545.5 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 545.5 ¢ to 560.0 ¢
Major 7-mosstep M7ms 6L + s 560.0 ¢ to 654.5 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 545.5 ¢ to 640.0 ¢
Major 8-mosstep M8ms 6L + 2s 640.0 ¢ to 654.5 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 654.5 ¢ to 720.0 ¢
Major 9-mosstep M9ms 7L + 2s 720.0 ¢ to 763.6 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 763.6 ¢ to 800.0 ¢
Major 10-mosstep M10ms 8L + 2s 800.0 ¢ to 872.7 ¢
11-mosstep Perfect 11-mosstep P11ms 8L + 3s 872.7 ¢ to 880.0 ¢
Augmented 11-mosstep A11ms 9L + 2s 880.0 ¢ to 981.8 ¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 872.7 ¢ to 960.0 ¢
Major 12-mosstep M12ms 9L + 3s 960.0 ¢ to 981.8 ¢
13-mosstep Minor 13-mosstep m13ms 9L + 4s 981.8 ¢ to 1040.0 ¢
Major 13-mosstep M13ms 10L + 3s 1040.0 ¢ to 1090.9 ¢
14-mosstep Minor 14-mosstep m14ms 10L + 4s 1090.9 ¢ to 1120.0 ¢
Major 14-mosstep M14ms 11L + 3s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 11L + 4s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 11L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\15 320.000 880.000 1:1 1.000 Equalized 11L 4s
23\86 320.930 879.070 6:5 1.200
19\71 321.127 878.873 5:4 1.250
34\127 321.260 878.740 9:7 1.286
15\56 321.429 878.571 4:3 1.333 Supersoft 11L 4s
41\153 321.569 878.431 11:8 1.375
26\97 321.649 878.351 7:5 1.400
37\138 321.739 878.261 10:7 1.429 Superkleismic
11\41 321.951 878.049 3:2 1.500 Soft 11L 4s
40\149 322.148 877.852 11:7 1.571
29\108 322.222 877.778 8:5 1.600
47\175 322.286 877.714 13:8 1.625 Golden superklesimic
18\67 322.388 877.612 5:3 1.667 Semisoft 11L 4s
43\160 322.500 877.500 12:7 1.714
25\93 322.581 877.419 7:4 1.750
32\119 322.689 877.311 9:5 1.800 Senator
7\26 323.077 876.923 2:1 2.000 Basic 11L 4s
Scales with tunings softer than this are proper
31\115 323.478 876.522 9:4 2.250 Orgone
24\89 323.596 876.404 7:3 2.333
41\152 323.684 876.316 12:5 2.400
17\63 323.810 876.190 5:2 2.500 Semihard 11L 4s
Hyperkleismic
44\163 323.926 876.074 13:5 2.600
27\100 324.000 876.000 8:3 2.667
37\137 324.088 875.912 11:4 2.750
10\37 324.324 875.676 3:1 3.000 Hard 11L 4s
33\122 324.590 875.410 10:3 3.333
23\85 324.706 875.294 7:2 3.500
36\133 324.812 875.188 11:3 3.667
13\48 325.000 875.000 4:1 4.000 Superhard 11L 4s
29\107 325.234 874.766 9:2 4.500
16\59 325.424 874.576 5:1 5.000 Oregon
19\70 325.714 874.286 6:1 6.000 Ork/Orca
3\11 327.273 872.727 1:0 → ∞ Collapsed 11L 4s
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