42edo: Difference between revisions

BudjarnLambeth (talk | contribs)
BudjarnLambeth (talk | contribs)
Octave stretch: Moved most of the table out to its own page to avoid overloading this Edo page
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42edo’s inaccurate 3rd and 5th harmonics can be greatly improved through [[octave stretching]] or [[octave shrinking]]. Both approaches work about equally well but in opposite directions, giving two quite different flavors of tuning to play with.  
42edo’s inaccurate 3rd and 5th harmonics can be greatly improved through [[octave stretching]] or [[octave shrinking]]. Both approaches work about equally well but in opposite directions, giving two quite different flavors of tuning to play with.  


Click “expand” for a table comparing the properties of three stretched and two compressed tunings of 42edo:
The following table compares three stretched and two compressed tunings of 42edo:


{| class="wikitable mw-collapsible mw-collapsed"
{| class="wikitable"
|+
|+
!Tuning
!Tuning
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| great: 5, 11, 13 <br>good: 2, 3 <br>okay: <br>bad: 7
| great: 5, 11, 13 <br>good: 2, 3 <br>okay: <br>bad: 7
| great: 3, 5, 11 <br>good: 2 <br>okay: 13 <br>bad: 7
| great: 3, 5, 11 <br>good: 2 <br>okay: 13 <br>bad: 7
|-
! 2/1 error
| +23.5% (6.7¢)
| +19.0% (5.5¢)
| +17.2% (4.9¢)
| 0.0% (0.0¢)
| −18.8% (5.3¢)
| −23.9% (6.8¢)
|-
! 3/1 error
| −19.6% (5.6¢)
| −26.7% (7.7¢)
| −29.6% (8.5¢)
| +43.2% (12.3¢)
| +13.4% (3.8¢)
| +5.4% (1.5¢)
|-
! 5/1 error
| +2.4% (0.7¢)
| −7.9% (2.3¢)
| −12.2% (3.5¢)
| +47.9% (13.7¢)
| +4.3% (1.2¢)
| −7.5% (2.1¢)
|-
! 7/1 error
| −24.9% (7.2¢)
| −37.5% (10.8¢)
| −42.6% (12.2¢)
| +9.1% (2.6¢)
| −43.6% (12.4¢)
| +42.2% (12.0¢)
|-
! 11/1 error
| −48.3% (13.9¢)
| +36.2% (10.4¢)
| +29.8% (8.6¢)
| −29.6% (8.5¢)
| +5.5% (1.6¢)
| −12.1% (3.4¢)
|-
! 13/1 error
| +45.1% (13.0¢)
| +28.6% (8.2¢)
| +21.7% (6.2¢)
| −41.8% (12.0¢)
| −11.3% (3.2¢)
| −30.1% (8.6¢)
|-
|-
| colspan="7" | <small><div style="text-align: center;">''“great” = 0-12.5% relative error • “good” = 12.5-27.5% • “okay” = 27.5-40% • “bad” = 40-50%''</div></small>
| colspan="7" | <small><div style="text-align: center;">''“great” = 0-12.5% relative error • “good” = 12.5-27.5% • “okay” = 27.5-40% • “bad” = 40-50%''</div></small>
|}
|}
For a more detailed comparison see [[Table of stretched 42edo tunings]].


==Intervals==
==Intervals==