User:BudjarnLambeth/SimHue: Difference between revisions

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'''SimHue 11''' is intended as a simple heuristic for comparing how good EDOs are relative to each other at approximating the [[11-limit]].
{{Editable user page}}
'''SimHue 11''' is intended as a simple heuristic for comparing how good [[Edo|EDOs (ed2s)]] are relative to their size at approximating the [[11-limit]].


It could be easily adapted into ''SimHue N'' for the N-prime-limit, or ''SimHue A.B.C'' for the subgroup A.B.C where A, B, C can be any harmonic or interval.
It could be easily adapted into ''SimHue N'' for the [[Prime-limit|N-prime-limit]], or ''SimHue A.B.C'' for the [[subgroup]] A.B.C where A, B, C can be any [[harmonic]] or [[interval]].


=== Definition ===
=== Definition ===
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For each ed2, let N(ed2) be the number of steps that ed2 has.  
For each ed2, let N(ed2) be the number of steps that ed2 has.  


Let N(ed3) be the number of steps its nearest ed3 has per 1200 cents.
Let N(ed3) be the number of steps its nearest [[ed3]] has per 1200 [[cents]].


Let N(ed5) be the number of steps its nearest ed5 has per 1200 cents.
Let N(ed5) be the number of steps its nearest [[ed5]] has per 1200 cents.


And so on.
And so on.


<math>S(\mathrm{ed2}) = \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed3})\right|}{3} + \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed5})\right|}{5} + \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed7})\right|}{7} + \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed11})\right|}{11}</math>
<math display="block">
\begin{aligned}
S(\mathrm{ed2}) &= \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed3})\right|}{3} + \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed5})\right|}{5} + \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed7})\right|}{7} + \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed11})\right|}{11} \\
&\quad + \frac{\left|N(\mathrm{ed3}) - N(\mathrm{ed5})\right|}{5} + \frac{\left|N(\mathrm{ed3}) - N(\mathrm{ed7})\right|}{7} + \frac{\left|N(\mathrm{ed3}) - N(\mathrm{ed11})\right|}{11} \\
&\quad + \frac{\left|N(\mathrm{ed5}) - N(\mathrm{ed7})\right|}{7} + \frac{\left|N(\mathrm{ed5}) - N(\mathrm{ed11})\right|}{11} \\
&\quad + \frac{\left|N(\mathrm{ed7}) - N(\mathrm{ed11})\right|}{11}
\end{aligned}
</math>


S(ed2) is the SimHue 11 score for the edo. Lower S(ed2) is better.
S(ed2) is the SimHue 11 score for the ed2. Lower S(ed2) is better.


=== SimHue 11 scores for every EDO 1-100 ===
=== SimHue 11 scores for every EDO 1-100 ===


{| class="wikitable sortable"
{| class="wikitable sortable" style="table-layout: fixed; width: 48em;"
! ed2 !! S(ed2)!! Nearest ed3 !! Nearest ed5 !! Nearest ed7 !! Nearest ed11  
! ed2 !! S(ed2) !! Nearest ed3 !! Nearest ed5 !! Nearest ed7 !! Nearest ed11
|-
|-
| data-sort-value="1" | 1ed2 || 0.1369|| data-sort-value="2" | 2ed3 || data-sort-value="2" | 2ed5 || data-sort-value="3" | 3ed7 || data-sort-value="3" | 3ed11  
| data-sort-value="1" | 1ed2 || 0.3289 || data-sort-value="2" | 2ed3 || data-sort-value="2" | 2ed5 || data-sort-value="3" | 3ed7 || data-sort-value="3" | 3ed11
|-
|-
| data-sort-value="2" | 2ed2 || 0.0882|| data-sort-value="3" | 3ed3 || data-sort-value="5" | 5ed5 || data-sort-value="6" | 6ed7 || data-sort-value="7" | 7ed11  
| data-sort-value="2" | 2ed2 || 0.2115 || data-sort-value="3" | 3ed3 || data-sort-value="5" | 5ed5 || data-sort-value="6" | 6ed7 || data-sort-value="7" | 7ed11
|-
|-
| data-sort-value="3" | 3ed2 || 0.0859|| data-sort-value="5" | 5ed3 || data-sort-value="7" | 7ed5 || data-sort-value="8" | 8ed7 || data-sort-value="10" | 10ed11  
| data-sort-value="3" | 3ed2 || 0.2201 || data-sort-value="5" | 5ed3 || data-sort-value="7" | 7ed5 || data-sort-value="8" | 8ed7 || data-sort-value="10" | 10ed11
|-
|-
| data-sort-value="4" | 4ed2 || 0.1122|| data-sort-value="6" | 6ed3 || data-sort-value="9" | 9ed5 || data-sort-value="11" | 11ed7 || data-sort-value="14" | 14ed11  
| data-sort-value="4" | 4ed2 || 0.2063 || data-sort-value="6" | 6ed3 || data-sort-value="9" | 9ed5 || data-sort-value="11" | 11ed7 || data-sort-value="14" | 14ed11
|-
|-
| data-sort-value="5" | 5ed2 || 0.0591|| data-sort-value="8" | 8ed3 || data-sort-value="12" | 12ed5 || data-sort-value="14" | 14ed7 || data-sort-value="17" | 17ed11  
| data-sort-value="5" | 5ed2 || 0.1596 || data-sort-value="8" | 8ed3 || data-sort-value="12" | 12ed5 || data-sort-value="14" | 14ed7 || data-sort-value="17" | 17ed11
|-
|-
| data-sort-value="6" | 6ed2 || 0.1233|| data-sort-value="10" | 10ed3 || data-sort-value="14" | 14ed5 || data-sort-value="17" | 17ed7 || data-sort-value="21" | 21ed11  
| data-sort-value="6" | 6ed2 || 0.2460 || data-sort-value="10" | 10ed3 || data-sort-value="14" | 14ed5 || data-sort-value="17" | 17ed7 || data-sort-value="21" | 21ed11
|-
|-
| data-sort-value="7" | 7ed2 || 0.0652|| data-sort-value="11" | 11ed3 || data-sort-value="16" | 16ed5 || data-sort-value="20" | 20ed7 || data-sort-value="24" | 24ed11  
| data-sort-value="7" | 7ed2 || 0.1561 || data-sort-value="11" | 11ed3 || data-sort-value="16" | 16ed5 || data-sort-value="20" | 20ed7 || data-sort-value="24" | 24ed11
|-
|-
| data-sort-value="8" | 8ed2 || 0.1358|| data-sort-value="13" | 13ed3 || data-sort-value="19" | 19ed5 || data-sort-value="22" | 22ed7 || data-sort-value="28" | 28ed11  
| data-sort-value="8" | 8ed2 || 0.2827 || data-sort-value="13" | 13ed3 || data-sort-value="19" | 19ed5 || data-sort-value="22" | 22ed7 || data-sort-value="28" | 28ed11
|-
|-
| data-sort-value="9" | 9ed2 || 0.0816|| data-sort-value="14" | 14ed3 || data-sort-value="21" | 21ed5 || data-sort-value="25" | 25ed7 || data-sort-value="31" | 31ed11  
| data-sort-value="9" | 9ed2 || 0.1783 || data-sort-value="14" | 14ed3 || data-sort-value="21" | 21ed5 || data-sort-value="25" | 25ed7 || data-sort-value="31" | 31ed11
|-
|-
| data-sort-value="10" | 10ed2 || 0.0649|| data-sort-value="16" | 16ed3 || data-sort-value="23" | 23ed5 || data-sort-value="28" | 28ed7 || data-sort-value="35" | 35ed11  
| data-sort-value="10" | 10ed2 || 0.1641 || data-sort-value="16" | 16ed3 || data-sort-value="23" | 23ed5 || data-sort-value="28" | 28ed7 || data-sort-value="35" | 35ed11
|-
|-
| data-sort-value="11" | 11ed2 || 0.1384|| data-sort-value="17" | 17ed3 || data-sort-value="26" | 26ed5 || data-sort-value="31" | 31ed7 || data-sort-value="38" | 38ed11  
| data-sort-value="11" | 11ed2 || 0.3483 || data-sort-value="17" | 17ed3 || data-sort-value="26" | 26ed5 || data-sort-value="31" | 31ed7 || data-sort-value="38" | 38ed11
|-
|-
| data-sort-value="12" | 12ed2 || 0.0446|| data-sort-value="19" | 19ed3 || data-sort-value="28" | 28ed5 || data-sort-value="34" | 34ed7 || data-sort-value="42" | 42ed11  
| data-sort-value="12" | 12ed2 || 0.1079 || data-sort-value="19" | 19ed3 || data-sort-value="28" | 28ed5 || data-sort-value="34" | 34ed7 || data-sort-value="42" | 42ed11
|-
|-
| data-sort-value="13" | 13ed2 || 0.1251|| data-sort-value="21" | 21ed3 || data-sort-value="30" | 30ed5 || data-sort-value="36" | 36ed7 || data-sort-value="45" | 45ed11  
| data-sort-value="13" | 13ed2 || 0.3123 || data-sort-value="21" | 21ed3 || data-sort-value="30" | 30ed5 || data-sort-value="36" | 36ed7 || data-sort-value="45" | 45ed11
|-
|-
| data-sort-value="14" | 14ed2 || 0.1091|| data-sort-value="22" | 22ed3 || data-sort-value="33" | 33ed5 || data-sort-value="39" | 39ed7 || data-sort-value="48" | 48ed11  
| data-sort-value="14" | 14ed2 || 0.2556 || data-sort-value="22" | 22ed3 || data-sort-value="33" | 33ed5 || data-sort-value="39" | 39ed7 || data-sort-value="48" | 48ed11
|-
|-
| data-sort-value="15" | 15ed2 || 0.0706|| data-sort-value="24" | 24ed3 || data-sort-value="35" | 35ed5 || data-sort-value="42" | 42ed7 || data-sort-value="52" | 52ed11  
| data-sort-value="15" | 15ed2 || 0.1468 || data-sort-value="24" | 24ed3 || data-sort-value="35" | 35ed5 || data-sort-value="42" | 42ed7 || data-sort-value="52" | 52ed11
|-
|-
| data-sort-value="16" | 16ed2 || 0.1020|| data-sort-value="25" | 25ed3 || data-sort-value="37" | 37ed5 || data-sort-value="45" | 45ed7 || data-sort-value="55" | 55ed11  
| data-sort-value="16" | 16ed2 || 0.2110 || data-sort-value="25" | 25ed3 || data-sort-value="37" | 37ed5 || data-sort-value="45" | 45ed7 || data-sort-value="55" | 55ed11
|-
|-
| data-sort-value="17" | 17ed2 || 0.0714|| data-sort-value="27" | 27ed3 || data-sort-value="39" | 39ed5 || data-sort-value="48" | 48ed7 || data-sort-value="59" | 59ed11  
| data-sort-value="17" | 17ed2 || 0.2004 || data-sort-value="27" | 27ed3 || data-sort-value="39" | 39ed5 || data-sort-value="48" | 48ed7 || data-sort-value="59" | 59ed11
|-
|-
| data-sort-value="18" | 18ed2 || 0.1476|| data-sort-value="29" | 29ed3 || data-sort-value="42" | 42ed5 || data-sort-value="51" | 51ed7 || data-sort-value="62" | 62ed11  
| data-sort-value="18" | 18ed2 || 0.2905 || data-sort-value="29" | 29ed3 || data-sort-value="42" | 42ed5 || data-sort-value="51" | 51ed7 || data-sort-value="62" | 62ed11
|-
|-
| data-sort-value="19" | 19ed2 || 0.0585|| data-sort-value="30" | 30ed3 || data-sort-value="44" | 44ed5 || data-sort-value="53" | 53ed7 || data-sort-value="66" | 66ed11  
| data-sort-value="19" | 19ed2 || 0.1234 || data-sort-value="30" | 30ed3 || data-sort-value="44" | 44ed5 || data-sort-value="53" | 53ed7 || data-sort-value="66" | 66ed11
|-
|-
| data-sort-value="20" | 20ed2 || 0.1135|| data-sort-value="32" | 32ed3 || data-sort-value="46" | 46ed5 || data-sort-value="56" | 56ed7 || data-sort-value="69" | 69ed11  
| data-sort-value="20" | 20ed2 || 0.2779 || data-sort-value="32" | 32ed3 || data-sort-value="46" | 46ed5 || data-sort-value="56" | 56ed7 || data-sort-value="69" | 69ed11
|-
|-
| data-sort-value="21" | 21ed2 || 0.0920|| data-sort-value="33" | 33ed3 || data-sort-value="49" | 49ed5 || data-sort-value="59" | 59ed7 || data-sort-value="73" | 73ed11  
| data-sort-value="21" | 21ed2 || 0.2223 || data-sort-value="33" | 33ed3 || data-sort-value="49" | 49ed5 || data-sort-value="59" | 59ed7 || data-sort-value="73" | 73ed11
|-
|-
| data-sort-value="22" | 22ed2 || 0.0496|| data-sort-value="35" | 35ed3 || data-sort-value="51" | 51ed5 || data-sort-value="62" | 62ed7 || data-sort-value="76" | 76ed11  
| data-sort-value="22" | 22ed2 || 0.1120 || data-sort-value="35" | 35ed3 || data-sort-value="51" | 51ed5 || data-sort-value="62" | 62ed7 || data-sort-value="76" | 76ed11
|-
|-
| data-sort-value="23" | 23ed2 || 0.1636|| data-sort-value="36" | 36ed3 || data-sort-value="53" | 53ed5 || data-sort-value="65" | 65ed7 || data-sort-value="80" | 80ed11  
| data-sort-value="23" | 23ed2 || 0.3630 || data-sort-value="36" | 36ed3 || data-sort-value="53" | 53ed5 || data-sort-value="65" | 65ed7 || data-sort-value="80" | 80ed11
|-
|-
| data-sort-value="24" | 24ed2 || 0.0517|| data-sort-value="38" | 38ed3 || data-sort-value="56" | 56ed5 || data-sort-value="67" | 67ed7 || data-sort-value="83" | 83ed11  
| data-sort-value="24" | 24ed2 || 0.1563 || data-sort-value="38" | 38ed3 || data-sort-value="56" | 56ed5 || data-sort-value="67" | 67ed7 || data-sort-value="83" | 83ed11
|-
|-
| data-sort-value="25" | 25ed2 || 0.1053|| data-sort-value="40" | 40ed3 || data-sort-value="58" | 58ed5 || data-sort-value="70" | 70ed7 || data-sort-value="86" | 86ed11  
| data-sort-value="25" | 25ed2 || 0.2586 || data-sort-value="40" | 40ed3 || data-sort-value="58" | 58ed5 || data-sort-value="70" | 70ed7 || data-sort-value="86" | 86ed11
|-
|-
| data-sort-value="26" | 26ed2 || 0.0777|| data-sort-value="41" | 41ed3 || data-sort-value="60" | 60ed5 || data-sort-value="73" | 73ed7 || data-sort-value="90" | 90ed11  
| data-sort-value="26" | 26ed2 || 0.1563 || data-sort-value="41" | 41ed3 || data-sort-value="60" | 60ed5 || data-sort-value="73" | 73ed7 || data-sort-value="90" | 90ed11
|-
|-
| data-sort-value="27" | 27ed2 || 0.0907|| data-sort-value="43" | 43ed3 || data-sort-value="63" | 63ed5 || data-sort-value="76" | 76ed7 || data-sort-value="93" | 93ed11  
| data-sort-value="27" | 27ed2 || 0.1706 || data-sort-value="43" | 43ed3 || data-sort-value="63" | 63ed5 || data-sort-value="76" | 76ed7 || data-sort-value="93" | 93ed11
|-
|-
| data-sort-value="28" | 28ed2 || 0.1045|| data-sort-value="44" | 44ed3 || data-sort-value="65" | 65ed5 || data-sort-value="79" | 79ed7 || data-sort-value="97" | 97ed11  
| data-sort-value="28" | 28ed2 || 0.2649 || data-sort-value="44" | 44ed3 || data-sort-value="65" | 65ed5 || data-sort-value="79" | 79ed7 || data-sort-value="97" | 97ed11
|-
|-
| data-sort-value="29" | 29ed2 || 0.0661|| data-sort-value="46" | 46ed3 || data-sort-value="67" | 67ed5 || data-sort-value="81" | 81ed7 || data-sort-value="100" | 100ed11  
| data-sort-value="29" | 29ed2 || 0.1443 || data-sort-value="46" | 46ed3 || data-sort-value="67" | 67ed5 || data-sort-value="81" | 81ed7 || data-sort-value="100" | 100ed11
|-
|-
| data-sort-value="30" | 30ed2 || 0.1413|| data-sort-value="48" | 48ed3 || data-sort-value="70" | 70ed5 || data-sort-value="84" | 84ed7 || data-sort-value="104" | 104ed11  
| data-sort-value="30" | 30ed2 || 0.2936 || data-sort-value="48" | 48ed3 || data-sort-value="70" | 70ed5 || data-sort-value="84" | 84ed7 || data-sort-value="104" | 104ed11
|-
|-
| data-sort-value="31" | 31ed2 || 0.0377|| data-sort-value="49" | 49ed3 || data-sort-value="72" | 72ed5 || data-sort-value="87" | 87ed7 || data-sort-value="107" | 107ed11  
| data-sort-value="31" | 31ed2 || 0.0836 || data-sort-value="49" | 49ed3 || data-sort-value="72" | 72ed5 || data-sort-value="87" | 87ed7 || data-sort-value="107" | 107ed11
|-
|-
| data-sort-value="32" | 32ed2 || 0.1013|| data-sort-value="51" | 51ed3 || data-sort-value="74" | 74ed5 || data-sort-value="90" | 90ed7 || data-sort-value="111" | 111ed11  
| data-sort-value="32" | 32ed2 || 0.2372 || data-sort-value="51" | 51ed3 || data-sort-value="74" | 74ed5 || data-sort-value="90" | 90ed7 || data-sort-value="111" | 111ed11
|-
|-
| data-sort-value="33" | 33ed2 || 0.1187|| data-sort-value="52" | 52ed3 || data-sort-value="77" | 77ed5 || data-sort-value="93" | 93ed7 || data-sort-value="114" | 114ed11  
| data-sort-value="33" | 33ed2 || 0.2880 || data-sort-value="52" | 52ed3 || data-sort-value="77" | 77ed5 || data-sort-value="93" | 93ed7 || data-sort-value="114" | 114ed11
|-
|-
| data-sort-value="34" | 34ed2 || 0.0610|| data-sort-value="54" | 54ed3 || data-sort-value="79" | 79ed5 || data-sort-value="95" | 95ed7 || data-sort-value="118" | 118ed11  
| data-sort-value="34" | 34ed2 || 0.1655 || data-sort-value="54" | 54ed3 || data-sort-value="79" | 79ed5 || data-sort-value="95" | 95ed7 || data-sort-value="118" | 118ed11
|-
|-
| data-sort-value="35" | 35ed2 || 0.1379|| data-sort-value="55" | 55ed3 || data-sort-value="81" | 81ed5 || data-sort-value="98" | 98ed7 || data-sort-value="121" | 121ed11  
| data-sort-value="35" | 35ed2 || 0.2472 || data-sort-value="55" | 55ed3 || data-sort-value="81" | 81ed5 || data-sort-value="98" | 98ed7 || data-sort-value="121" | 121ed11
|-
|-
| data-sort-value="36" | 36ed2 || 0.0631|| data-sort-value="57" | 57ed3 || data-sort-value="84" | 84ed5 || data-sort-value="101" | 101ed7 || data-sort-value="125" | 125ed11  
| data-sort-value="36" | 36ed2 || 0.1700 || data-sort-value="57" | 57ed3 || data-sort-value="84" | 84ed5 || data-sort-value="101" | 101ed7 || data-sort-value="125" | 125ed11
|-
|-
| data-sort-value="37" | 37ed2 || 0.0891|| data-sort-value="59" | 59ed3 || data-sort-value="86" | 86ed5 || data-sort-value="104" | 104ed7 || data-sort-value="128" | 128ed11  
| data-sort-value="37" | 37ed2 || 0.1811 || data-sort-value="59" | 59ed3 || data-sort-value="86" | 86ed5 || data-sort-value="104" | 104ed7 || data-sort-value="128" | 128ed11
|-
|-
| data-sort-value="38" | 38ed2 || 0.0965|| data-sort-value="60" | 60ed3 || data-sort-value="88" | 88ed5 || data-sort-value="107" | 107ed7 || data-sort-value="131" | 131ed11  
| data-sort-value="38" | 38ed2 || 0.1992 || data-sort-value="60" | 60ed3 || data-sort-value="88" | 88ed5 || data-sort-value="107" | 107ed7 || data-sort-value="131" | 131ed11
|-
|-
| data-sort-value="39" | 39ed2 || 0.1045|| data-sort-value="62" | 62ed3 || data-sort-value="91" | 91ed5 || data-sort-value="109" | 109ed7 || data-sort-value="135" | 135ed11  
| data-sort-value="39" | 39ed2 || 0.2547 || data-sort-value="62" | 62ed3 || data-sort-value="91" | 91ed5 || data-sort-value="109" | 109ed7 || data-sort-value="135" | 135ed11
|-
|-
| data-sort-value="40" | 40ed2 || 0.1193|| data-sort-value="63" | 63ed3 || data-sort-value="93" | 93ed5 || data-sort-value="112" | 112ed7 || data-sort-value="138" | 138ed11  
| data-sort-value="40" | 40ed2 || 0.2517 || data-sort-value="63" | 63ed3 || data-sort-value="93" | 93ed5 || data-sort-value="112" | 112ed7 || data-sort-value="138" | 138ed11
|-
|-
| data-sort-value="41" | 41ed2 || 0.0301|| data-sort-value="65" | 65ed3 || data-sort-value="95" | 95ed5 || data-sort-value="115" | 115ed7 || data-sort-value="142" | 142ed11  
| data-sort-value="41" | 41ed2 || 0.0861 || data-sort-value="65" | 65ed3 || data-sort-value="95" | 95ed5 || data-sort-value="115" | 115ed7 || data-sort-value="142" | 142ed11
|-
|-
| data-sort-value="42" | 42ed2 || 0.1444|| data-sort-value="67" | 67ed3 || data-sort-value="98" | 98ed5 || data-sort-value="118" | 118ed7 || data-sort-value="145" | 145ed11  
| data-sort-value="42" | 42ed2 || 0.2865 || data-sort-value="67" | 67ed3 || data-sort-value="98" | 98ed5 || data-sort-value="118" | 118ed7 || data-sort-value="145" | 145ed11
|-
|-
| data-sort-value="43" | 43ed2 || 0.0667|| data-sort-value="68" | 68ed3 || data-sort-value="100" | 100ed5 || data-sort-value="121" | 121ed7 || data-sort-value="149" | 149ed11  
| data-sort-value="43" | 43ed2 || 0.1508 || data-sort-value="68" | 68ed3 || data-sort-value="100" | 100ed5 || data-sort-value="121" | 121ed7 || data-sort-value="149" | 149ed11
|-
|-
| data-sort-value="44" | 44ed2 || 0.0991|| data-sort-value="70" | 70ed3 || data-sort-value="102" | 102ed5 || data-sort-value="124" | 124ed7 || data-sort-value="152" | 152ed11  
| data-sort-value="44" | 44ed2 || 0.2239 || data-sort-value="70" | 70ed3 || data-sort-value="102" | 102ed5 || data-sort-value="124" | 124ed7 || data-sort-value="152" | 152ed11
|-
|-
| data-sort-value="45" | 45ed2 || 0.1353|| data-sort-value="71" | 71ed3 || data-sort-value="104" | 104ed5 || data-sort-value="126" | 126ed7 || data-sort-value="156" | 156ed11  
| data-sort-value="45" | 45ed2 || 0.2358 || data-sort-value="71" | 71ed3 || data-sort-value="104" | 104ed5 || data-sort-value="126" | 126ed7 || data-sort-value="156" | 156ed11
|-
|-
| data-sort-value="46" | 46ed2 || 0.0463|| data-sort-value="73" | 73ed3 || data-sort-value="107" | 107ed5 || data-sort-value="129" | 129ed7 || data-sort-value="159" | 159ed11  
| data-sort-value="46" | 46ed2 || 0.1061 || data-sort-value="73" | 73ed3 || data-sort-value="107" | 107ed5 || data-sort-value="129" | 129ed7 || data-sort-value="159" | 159ed11
|-
|-
| data-sort-value="47" | 47ed2 || 0.1284|| data-sort-value="74" | 74ed3 || data-sort-value="109" | 109ed5 || data-sort-value="132" | 132ed7 || data-sort-value="163" | 163ed11  
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SimHue 11 is intended as a simple heuristic for comparing how good EDOs (ed2s) are relative to their size at approximating the 11-limit.

It could be easily adapted into SimHue N for the N-prime-limit, or SimHue A.B.C for the subgroup A.B.C where A, B, C can be any harmonic or interval.

Definition

For each ed2, let N(ed2) be the number of steps that ed2 has.

Let N(ed3) be the number of steps its nearest ed3 has per 1200 cents.

Let N(ed5) be the number of steps its nearest ed5 has per 1200 cents.

And so on.

[math]\displaystyle{ \begin{aligned} S(\mathrm{ed2}) &= \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed3})\right|}{3} + \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed5})\right|}{5} + \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed7})\right|}{7} + \frac{\left|N(\mathrm{ed2}) - N(\mathrm{ed11})\right|}{11} \\ &\quad + \frac{\left|N(\mathrm{ed3}) - N(\mathrm{ed5})\right|}{5} + \frac{\left|N(\mathrm{ed3}) - N(\mathrm{ed7})\right|}{7} + \frac{\left|N(\mathrm{ed3}) - N(\mathrm{ed11})\right|}{11} \\ &\quad + \frac{\left|N(\mathrm{ed5}) - N(\mathrm{ed7})\right|}{7} + \frac{\left|N(\mathrm{ed5}) - N(\mathrm{ed11})\right|}{11} \\ &\quad + \frac{\left|N(\mathrm{ed7}) - N(\mathrm{ed11})\right|}{11} \end{aligned} }[/math]

S(ed2) is the SimHue 11 score for the ed2. Lower S(ed2) is better.

SimHue 11 scores for every EDO 1-100

ed2 S(ed2) Nearest ed3 Nearest ed5 Nearest ed7 Nearest ed11
1ed2 0.3289 2ed3 2ed5 3ed7 3ed11
2ed2 0.2115 3ed3 5ed5 6ed7 7ed11
3ed2 0.2201 5ed3 7ed5 8ed7 10ed11
4ed2 0.2063 6ed3 9ed5 11ed7 14ed11
5ed2 0.1596 8ed3 12ed5 14ed7 17ed11
6ed2 0.2460 10ed3 14ed5 17ed7 21ed11
7ed2 0.1561 11ed3 16ed5 20ed7 24ed11
8ed2 0.2827 13ed3 19ed5 22ed7 28ed11
9ed2 0.1783 14ed3 21ed5 25ed7 31ed11
10ed2 0.1641 16ed3 23ed5 28ed7 35ed11
11ed2 0.3483 17ed3 26ed5 31ed7 38ed11
12ed2 0.1079 19ed3 28ed5 34ed7 42ed11
13ed2 0.3123 21ed3 30ed5 36ed7 45ed11
14ed2 0.2556 22ed3 33ed5 39ed7 48ed11
15ed2 0.1468 24ed3 35ed5 42ed7 52ed11
16ed2 0.2110 25ed3 37ed5 45ed7 55ed11
17ed2 0.2004 27ed3 39ed5 48ed7 59ed11
18ed2 0.2905 29ed3 42ed5 51ed7 62ed11
19ed2 0.1234 30ed3 44ed5 53ed7 66ed11
20ed2 0.2779 32ed3 46ed5 56ed7 69ed11
21ed2 0.2223 33ed3 49ed5 59ed7 73ed11
22ed2 0.1120 35ed3 51ed5 62ed7 76ed11
23ed2 0.3630 36ed3 53ed5 65ed7 80ed11
24ed2 0.1563 38ed3 56ed5 67ed7 83ed11
25ed2 0.2586 40ed3 58ed5 70ed7 86ed11
26ed2 0.1563 41ed3 60ed5 73ed7 90ed11
27ed2 0.1706 43ed3 63ed5 76ed7 93ed11
28ed2 0.2649 44ed3 65ed5 79ed7 97ed11
29ed2 0.1443 46ed3 67ed5 81ed7 100ed11
30ed2 0.2936 48ed3 70ed5 84ed7 104ed11
31ed2 0.0836 49ed3 72ed5 87ed7 107ed11
32ed2 0.2372 51ed3 74ed5 90ed7 111ed11
33ed2 0.2880 52ed3 77ed5 93ed7 114ed11
34ed2 0.1655 54ed3 79ed5 95ed7 118ed11
35ed2 0.2472 55ed3 81ed5 98ed7 121ed11
36ed2 0.1700 57ed3 84ed5 101ed7 125ed11
37ed2 0.1811 59ed3 86ed5 104ed7 128ed11
38ed2 0.1992 60ed3 88ed5 107ed7 131ed11
39ed2 0.2547 62ed3 91ed5 109ed7 135ed11
40ed2 0.2517 63ed3 93ed5 112ed7 138ed11
41ed2 0.0861 65ed3 95ed5 115ed7 142ed11
42ed2 0.2865 67ed3 98ed5 118ed7 145ed11
43ed2 0.1508 68ed3 100ed5 121ed7 149ed11
44ed2 0.2239 70ed3 102ed5 124ed7 152ed11
45ed2 0.2358 71ed3 104ed5 126ed7 156ed11
46ed2 0.1061 73ed3 107ed5 129ed7 159ed11
47ed2 0.3012 74ed3 109ed5 132ed7 163ed11
48ed2 0.1873 76ed3 111ed5 135ed7 166ed11
49ed2 0.1769 78ed3 114ed5 138ed7 170ed11
50ed2 0.1515 79ed3 116ed5 140ed7 173ed11
51ed2 0.2209 81ed3 118ed5 143ed7 176ed11
52ed2 0.2793 82ed3 121ed5 146ed7 180ed11
53ed2 0.0881 84ed3 123ed5 149ed7 183ed11
54ed2 0.3378 86ed3 125ed5 152ed7 187ed11
55ed2 0.2076 87ed3 128ed5 154ed7 190ed11
56ed2 0.1749 89ed3 130ed5 157ed7 194ed11
57ed2 0.1996 90ed3 132ed5 160ed7 197ed11
58ed2 0.1068 92ed3 135ed5 163ed7 201ed11
59ed2 0.2773 94ed3 137ed5 166ed7 204ed11
60ed2 0.1796 95ed3 139ed5 168ed7 208ed11
61ed2 0.2374 97ed3 142ed5 171ed7 211ed11
62ed2 0.1671 98ed3 144ed5 174ed7 214ed11
63ed2 0.1595 100ed3 146ed5 177ed7 218ed11
64ed2 0.3687 101ed3 149ed5 180ed7 221ed11
65ed2 0.1242 103ed3 151ed5 182ed7 225ed11
66ed2 0.2812 105ed3 153ed5 185ed7 228ed11
67ed2 0.2299 106ed3 156ed5 188ed7 232ed11
68ed2 0.1422 108ed3 158ed5 191ed7 235ed11
69ed2 0.2667 109ed3 160ed5 194ed7 239ed11
70ed2 0.1869 111ed3 163ed5 197ed7 242ed11
71ed2 0.3092 113ed3 165ed5 199ed7 246ed11
72ed2 0.0694 114ed3 167ed5 202ed7 249ed11
73ed2 0.2000 116ed3 170ed5 205ed7 253ed11
74ed2 0.2129 117ed3 172ed5 208ed7 256ed11
75ed2 0.1980 119ed3 174ed5 211ed7 259ed11
76ed2 0.2703 120ed3 176ed5 213ed7 263ed11
77ed2 0.1253 122ed3 179ed5 216ed7 266ed11
78ed2 0.2197 124ed3 181ed5 219ed7 270ed11
79ed2 0.2076 125ed3 183ed5 222ed7 273ed11
80ed2 0.1194 127ed3 186ed5 225ed7 277ed11
81ed2 0.2101 128ed3 188ed5 227ed7 280ed11
82ed2 0.1721 130ed3 190ed5 230ed7 284ed11
83ed2 0.2603 132ed3 193ed5 233ed7 287ed11
84ed2 0.1352 133ed3 195ed5 236ed7 291ed11
85ed2 0.2679 135ed3 197ed5 239ed7 294ed11
86ed2 0.2970 136ed3 200ed5 241ed7 298ed11
87ed2 0.0995 138ed3 202ed5 244ed7 301ed11
88ed2 0.2600 139ed3 204ed5 247ed7 304ed11
89ed2 0.1370 141ed3 207ed5 250ed7 308ed11
90ed2 0.2353 143ed3 209ed5 253ed7 311ed11
91ed2 0.1707 144ed3 211ed5 255ed7 315ed11
92ed2 0.2122 146ed3 214ed5 258ed7 318ed11
93ed2 0.2418 147ed3 216ed5 261ed7 322ed11
94ed2 0.1053 149ed3 218ed5 264ed7 325ed11
95ed2 0.2252 151ed3 221ed5 267ed7 329ed11
96ed2 0.1869 152ed3 223ed5 270ed7 332ed11
97ed2 0.2401 154ed3 225ed5 272ed7 336ed11
98ed2 0.2911 155ed3 228ed5 275ed7 339ed11
99ed2 0.1055 157ed3 230ed5 278ed7 342ed11
100ed2 0.3115 158ed3 232ed5 281ed7 346ed11
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