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42edo: Difference between revisions

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=== Octave stretch ===
=== Octave stretch ===
42edo’s poor 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 poor 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.
Spectrum of octave stretch:
* [[Ed257/128#42ed257/128|42ed257/128]]


Stretched versions of 42edo include:
Stretched versions of 42edo include:
* [[zpi|189zpi]] (~41.83edo)
* [[Ed257/128#42ed257/128|42ed257/128]] (~41.77edo, improves harmonics 3 & 5 at the expense of harmonic 11)
* [[Ed257/128#42ed257/128|42ed257/128]]
* [[zpi|189zpi]] (~41.83edo) (~41.77edo, improves harmonics 3 & 5 at the expense of harmonics 7 & 11)
Stretching improves 3/1 and 5/1 at the cost of worsening 11/1.


Compressed versions of 42edo include:
Compressed versions of 42edo include:
* [[zpi|191zpi]] (~42.19edo)
* [[zpi|191zpi]] (~42.19edo, improves harmonics 3, 5 & 13 at the expense of harmonic 7)
* [[Ed255/128#42ed255/128|42ed255/128]]
* [[Ed255/128#42ed255/128|42ed255/128]] (~42.24edo, improves harmonics 3, 5 & 13 at the expense of harmonic 7)
Compression improves 3/1, 5/1 and 13/1 at the cost of worsening 7/1.


Expand the following table for a comparison of relative error in stretched vs regular vs compressed 42edo:
{| class="wikitable sortable mw-collapsible"
{| class="wikitable sortable mw-collapsible mw-collapsed"
|+
|+
!Relative error of
!Relative error of
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