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First of all, sometimes music I ''can'' play on the piano may sound better in a different tuning. A well known example is that music based on the diatonic scale can be rendered in any meantone temperament, and not just 12-EDO. Baroque and Renaissance music in particular generally will sound better in tunings ranging from about sixth comma meantone (~55EDO) to quarte-comma meantone (~31edo). Indeed this was what was used when these styles were the hot new thing in Europe. I have tried my hand at this style, and I find my compositions to sound better in these tunings as well.  
First of all, sometimes music I ''can'' play on the piano may sound better in a different tuning. A well known example is that music based on the diatonic scale can be rendered in any meantone temperament, and not just 12-EDO. Baroque and Renaissance music in particular generally will sound better in tunings ranging from about sixth comma meantone (~55EDO) to quarte-comma meantone (~31edo). Indeed this was what was used when these styles were the hot new thing in Europe. I have tried my hand at this style, and I find my compositions to sound better in these tunings as well.  


Here is a short fugue I wrote in the Phrygian mode rendered in 55 EDO:
Here are two short fugues I wrote in Phrygian and Mixolydian mode, respectively. Each is rendered in my favorite meantone tuning for that piece, as well as 12 EDO for comparison.  
[[File:Phrygian Fugue.mp3|thumb|none|Phrygian Fugue in 55 EDO]]


And here it is in 12 EDO:
<table style="width:100%">
[[File:Phrygian Fugue 12edo.mp3|thumb|none|Phrygian Fugue in 12EDO]]
  <tr>
    <td>Phrygian Fugue in 55 and 12 EDO</td>
    <td>[[File:Phrygian Fugue.mp3|thumb|none|Phrygian Fugue in 55 EDO]]</td>
    <td>[[File:Phrygian Fugue 12edo.mp3|thumb|none|Phrygian Fugue in 12 EDO]]</td>
  </tr>
  <tr>
    <td>Mixolydian Fugue in 31 and 12 EDO</td>
    <td>[[File:Mixolydian fugue.mp3|thumb|none|Mixolydian Fugue in 31 EDO]]</td>
    <td>[[File:Mixolydian_fugue_12edo.mp3|thumb|none|Mixolydian Fugue in 12 EDO]]</td>
  </tr>
</table>


I don't know about you, but the 55EDO version sounds better to me.
In each case, I prefer the non-12EDO version.
 
Here's another short, fugue, this time in Mixolydian and 31 EDO:
[[File:Mixolydian fugue.mp3|thumb|none|Mixolydian Fugue in 31 EDO]]
 
And in 12 EDO:
[[File:Mixolydian_fugue_12edo.mp3|thumb|none|Mixolydian Fugue in 12 EDO]]
 
Again, I prefer the non-12EDO version.