https://en.xen.wiki/index.php?action=history&feed=atom&title=User%3ABudjarnLambeth%2F149zpi 2026-07-05T11:07:01Z Revision history for this page on the wiki MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=User:BudjarnLambeth/149zpi&diff=207163&oldid=prev 2025-08-16T06:26:50Z

<p>Second-last one of these I&#039;m going to make. The last one will be 161zpi</p> <p><b>New page</b></p><div>{{Editable user page}}<br /> <br /> &#039;&#039;&#039;149zpi&#039;&#039;&#039;, the 149th [[zeta peak index]], is a [[Octave shrinking|compressed-octaves]] version of [[35edo]]. It can be thought of as &#039;&#039;&#039;35ed1202.564&#039;&#039;&#039; or as &#039;&#039;&#039;34.358cet&#039;&#039;&#039;. <br /> <br /> It has a step size of 34.358 [[cent]]s, and the [[octave]] ([[2/1]]) is tuned slightly impurely to 1202.564 cents.<br /> <br /> 35edo tunes almost all simple [[harmonic]]s slightly flat by roughly the same amount, so 149zpi is one possible way of correcting for this.<br /> <br /> ==Prime harmonics==<br /> {{Harmonics in cet|34.358|columns=7|intervals=prime|title=Approximation of prime harmonics in 149zpi}}<br /> {{Harmonics in cet|34.358|columns=7|start=8|intervals=prime|title=Approximation of prime harmonics in 149zpi}}<br /> <br /> For [[prime]]s up to 43:<br /> <br /> 435zpi approximates these with less than 7 cents error (&lt;20% relative error):<br /> * 2, 5, 7, 11, 23, 31, 37, 41<br /> <br /> ...these with 7-14 cents error (20-40% relative error):<br /> * 3, 13, 17, 19, 29<br /> <br /> ...and these with more than 14 cents error (&gt;40% relative error):<br /> * 43<br /> <br /> This makes it usable as a full [[41-limit]] tuning, or as a more accurate no-3s [[11-limit]] tuning.<br /> <br /> ==Scales==<br /> Any [[35edo#Scales|scales from 35edo]] should also be useable here.<br /> <br /> ==Instruments==<br /> All instruments listed under [[35edo#Instruments]] also work for 149zpi.<br /> <br /> [[Category:Zeta peak indexes]] [[Category:35edo]]</div>

BudjarnLambeth