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Nice edos to start with are 7edo, 9edo, 10edo, 12edo, 15edo, 17edo, 19edo, 22edo, 26edo, 29edo, 31edo, 34edo, 41edo, 43edo, 46edo, 48edo, 50edo, 53edo, 55edo and 60edo. They offer nice approximations to some of the intervals.
<span style="font-family: 'Consolas';"><div><big>''Do not ban this user''</big></div>


Meantone: 7edo, 12edo, 19edo, 26edo, 31edo, 43edo, 50edo, 55edo. These allow unambiguous notation and have a generally familiar diatonic scale, except for 7edo which is slightly out of tune.
<div><big>''He did nothing wrong''</big></div>


Superpyth: 10edo, 15edo, 17edo, 22edo. These edos are worthy of mention avoiding the 81/80 comma instead sharpening the fifth to temper out the 64/63 comma. The diatonic scale will sound out of tune, and it's harder to notate, but the xenharmonic musical possibilities may help.
Edos are for calculating approximate logarithms in mathematics. The right choice of an edo (such as [[53edo]] or even [[612edo]] for 5-limit numbers) would give accurate results.


Schismic: 12edo, 17edo, 29edo, 41edo, 53edo. These edos go eight fifths down to get the 5/4 ratio, which potentially allows greater accuracy in both 3/2 and 5/4 than meantone, as 53edo shows.
<pre>Which number is the biggest?
A. 81^56
B. 9^100
C. 27^72
D. 2^224</pre>


Modified 12edo: 48edo, 60edo. These offer the intervals of 12edo, while also offering more accurate 5 and 7, detaching from meantone and schismic instead into different temperaments.
53log₂(81^56)≈18816<br>
53log₂(9^100)≈16800<br>
53log₂(27^72)≈18144<br>
53log₂(2^224)=11872


9edo is a macrotonal edo that accurately represents 7/6.
<b>A.</b>


34edo is notable for its 5–limit accuracy.
(calculated successfully with [[53edo]])


46edo is notable for its 13–simit accuracy.
<pre>³√(2 7/9)÷³√(3/5) rounded to the nearest integer is
A. 1
B. 2
C. 3
D. 4</pre>
 
53log₂(³√(25/9)÷³√(3/5))≈39
 
2^(39÷53)≈5÷3
 
round(5÷3)=2
 
<b>B.</b>
 
(calculated successfully with [[53edo]])
 
<pre>Which number is the smallest?
A. 5√3
B. 4√7
C. 8√2
D. 3√11</pre>
 
41log₂(5√3)≈127.5<br>
41log₂(4√7)≈139.5<br>
41log₂(8√2)=143.5<br>
41log₂(3√11)≈136
 
<b>A.</b>
 
(calculated successfully with [[41edo]])
 
</span>
 
<!--For information about me, see [[Editor PiotrGrochowski]]
 
<span style="font-family: 'Consolas';">'''DO NOT MOVE [[Editor PiotrGrochowski]] HERE. THIS IS A PERSONAL [[SandBox]].'''</span>
 
 
 
making up interval names
 
0\94 0 unison
 
1\94 12.766
 
2\94 25.532
 
3\94 38.298
 
4\94 51.064
 
5\94 63.830
 
6\94 76.596
 
7\94 89.362
 
8\94 102.128
 
9\94 114.894
 
10\94 127.660
 
11\94 140.426
 
12\94 153.191
 
13\94 165.957
 
14\94 178.723
 
15\94 191.489
 
16\94 204.255
 
experimenting with 94edo version of partch (I like to keep using 94edo for everything...)
 
1/1
 
144/143
 
81/80
 
49/48
 
36/35
 
25/24
 
 
 
 
 
Will write down the commas of 15–odd–limit below
 
{{list
|[[16/15]], [[15/8]]
|[[15/14]], [[28/15]]
|[[14/13]], [[13/7]]
|[[13/12]], [[24/13]]
|[[12/11]], [[11/6]]
|[[11/10]], [[20/11]]
|[[10/9]], [[9/5]]
|[[9/8]], [[16/9]]
|[[8/7]], [[7/4]]
|[[15/13]], [[26/15]]
|[[7/6]], [[12/7]]
|[[13/11]], [[22/13]]
|[[6/5]], [[5/3]]
|[[11/9]], [[18/11]]
|[[16/13]], [[13/8]]
|[[5/4]], [[8/5]]
|[[14/11]], [[11/7]]
|[[9/7]], [[14/9]]
|[[13/10]], [[20/13]]
|[[4/3]], [[3/2]]
|[[15/11]], [[22/15]]
|[[11/8]], [[16/11]]
|[[18/13]], [[13/9]]
|[[7/5]], [[10/7]]
}}
 
<pre>16/15 and 15/14 — '''225/224'''
16/15 and 14/13 — '''105/104'''
16/15 and 13/12 — '''65/64'''
16/15 and 12/11 — '''45/44'''
16/15 and 11/10 — '''33/32'''
16/15 and 10/9 — '''25/24'''
16/15 and 9/8 — '''135/128'''
15/14 and 14/13 — '''196/195'''
15/14 and 13/12 — '''91/90'''
15/14 and 12/11 — '''56/55'''
15/14 and 11/10 — '''77/75'''
15/14 and 10/9 — '''28/27'''
15/14 and 9/8 — '''21/20'''
14/13 and 13/12 — '''169/168'''
-->
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