View source for User:BudjarnLambeth/Table of stretched 42edo tunings

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[[42edo]] has almost 50% relative error on harmonics 3/1 and 5/1. This means that whether one [[Octave stretch|stretches]] or [[Octave shrinking|compresses]] the octave, either way it will improve 42edo’s approximations of [[JI]], but in opposite directions.

This table provides a detailed comparison of three stretched- and three compressed-octave tunings for 42edo.

{| class="wikitable"
|+
!Tuning
! '''[[42ed257/128]]'''
! [[1ed28.7c|'''APS720jot''']]
! [[zpi|'''189zpi''']]
! [[42edo]]
! [[1ed28.5c|APS715jot]]
! [[191zpi]]
! [[ed255/128#42ed255/128|42ed255/128]]
|-
! Steps / octave
| ~41.77
| ~41.81
| ~41.83
| '''42.00'''
| ~42.10
| ~42.19
| ~42.24
|-
! Step size
| ~28.73¢
| ~28.70¢
| ~28.69¢
| '''~28.57¢'''
| ~28.50¢
| ~28.44¢
| ~28.41¢
|-
! Overview
| <small>ex: 5 <br>gd: 2, 3, 7 <br>ok: <br>ba: 11, 13</small>
| <small>ex: 5 <br>gd: 2, 3 <br>ok: 7, 11, 13 <br>ba:</small>
| <small>ex: 5 <br>gd: 2, 13 <br>ok: 3, 11 <br>ba: 7</small>
| '''<small>ex: 2, 7 <br>gd: <br>ok: 11 <br>ba: 3, 5, 13</small>'''
| <small>ex: 2 <br>gd: 5, 7, 13 <br>ok: 3, 11 <br>ba:</small>
| <small>ex: 5, 11, 13 <br>gd: 2, 3 <br>ok: <br>ba: 7</small>
| <small>ex: 3, 5, 11 <br>gd: 2 <br>ok: 13 <br>ba: 7</small>
|-
! 2/1 error
| +23.5% <br>(6.7¢)
| +19.0% <br>(5.5¢)
| +17.2% <br>(4.9¢)
| '''0.0% <br>(0.0¢)'''
| -10.2% <br>(2.9¢)
| −18.8% <br>(5.3¢)
| −23.9% <br>(6.8¢)
|-
! 3/1 error
| −19.6% <br>(5.6¢)
| −26.7% <br>(7.7¢)
| −29.6% <br>(8.5¢)
| '''+43.2% <br>(12.3¢)'''
| +27.0% <br>(7.7¢)
| +13.4% <br>(3.8¢)
| +5.4% <br>(1.5¢)
|-
! 5/1 error
| +2.4% <br>(0.7¢)
| −7.9% <br>(2.3¢)
| −12.2% <br>(3.5¢)
| '''+47.9% <br>(13.7¢)'''
| +24.2% <br>(6.9¢)
| +4.3% <br>(1.2¢)
| −7.5% <br>(2.1¢)
|-
! 7/1 error
| −24.9% <br>(7.2¢)
| −37.5% <br>(10.8¢)
| −42.6% <br>(12.2¢)
| '''+9.1% <br>(2.6¢)'''
| -19.6% <br>(5.6¢)
| −43.6% <br>(12.4¢)
| +42.2% <br>(12.0¢)
|-
! 11/1 error
| −48.3% <br>(13.9¢)
| +36.2% <br>(10.4¢)
| +29.8% <br>(8.6¢)
| '''−29.6% <br>(8.5¢)'''
| +35.1% <br>(10.0¢)
| +5.5% <br>(1.6¢)
| −12.1% <br>(3.4¢)
|-
! 13/1 error
| +45.1% <br>(13.0¢)
| +28.6% <br>(8.2¢)
| +21.7% <br>(6.2¢)
| '''−41.8% <br>(12.0¢)'''
| +20.4% <br>(5.8¢)
| −11.3% <br>(3.2¢)
| −30.1% <br>(8.6¢)
|-
! 17/1 error
| +28.7% <br>(8.2¢)
| +10.4% <br>(3.0¢)
| +2.9% <br>(0.8¢)
| '''+32.7% <br>(9.3¢)'''
| -9.1% <br>(2.5¢)
| -44.0% <br>(12.5¢)
| +35.2% <br>(10.0¢)
|-
! 2/1 val <br>(& reduced)
| 42 <br>(0)
| 42 <br>(0)
| 42 <br>(0)
| '''42 <br>(0)'''
| 42 <br>(0)
| 42 <br>(0)
| 42 <br>(0)
|-
! 3/1 val
| 66 <br>(24)
| 66 <br>(24)
| 66 <br>(24)
| '''67 <br>(25)'''
| 67 <br>(25)
| 67 <br>(25)
| 67 <br>(25)
|-
! 5/1 val
| 97 <br>(13)
| 97 <br>(13)
| 97 <br>(13)
| '''98 <br>(14)'''
| 98 <br>(14)
| 98 <br>(14)
| 98 <br>(14)
|-
! 7/1 val
| 117 <br>(33)
| 117 <br>(33)
| 117 <br>(33)
| '''118 <br>(34)'''
| 118 <br>(34)
| 118 <br>(34)
| 118 <br>(34)
|-
! 11/1 val
| 144 <br>(18)
| 145 <br>(19)
| 145 <br>(19)
| '''145 <br>(19)'''
| 146 <br>(20)
| 146 <br>(20)
| 146 <br>(20)
|-
! 13/1 val
| 155 <br>(29)
| 155 <br>(29)
| 155 <br>(29)
| '''155 <br>(29)'''
| 156 <br>(30)
| 156 <br>(30)
| 156 <br>(30)
|-
! 17/1 val
| 171 <br>(3)
| 171 <br>(3)
| 171 <br>(3)
| '''172 <br>(4)'''
| 172 <br>(4)
| 172 <br>(4)
| 173 <br>(5)
|-
| colspan="8" | <small><div style="text-align: center;">''ex = “excellent”, 0-13% relative error • gd = “good”, 13-27% • ok = “okay”, 27-40% • bd = “bad”, 40-50%''</div></small>
|}

[[Category:42edo]][[Category:Tables]]