(32 intermediate revisions by the same user not shown)
Line 1:
Line 1:
This is a page where I will draft edits before making them on the actual page. This may possibly include drafting a new page to be created. If you have something to add to any of them, or any concerns, please suggest them on the talk page. If a template is set to debug, make sure to remove that setting when editing the target page.
This is a page where I will draft edits before making them on the actual page. This may possibly include drafting a new page to be created. If you have something to add to any of them, or any concerns, please suggest them on the talk page. If a template is set to debug, make sure to remove that setting when editing the target page.
= Planned new section to 12edo =
= Pajara =
== History ==
There are two different mappings of the 11-limit. One is just called ''pajara'' and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. It is best tuned flat of 22edo. The other, called ''pajarous'' to avoid confusion, maps the 11th harmonic slightly simpler, but 22edo is the only [[11-odd-limit]] [[diamond monotone]] tuning, where primes [[3/1|3]] and [[5/1|5]] are less accurate than in optimal tunings of canonical 11-limit pajara.
Pythagoreas stacking fifths, Thirds being treated as consonant, Meantone tunings, Well temperaments, equal temperament for equal use in all keys (make this into actual paragraphs)
In the following tables, odd harmonics 1–11 and their inverses are in '''bold'''.
The [[Xenharmonic Wiki]] is an open resource dedicated to musical [[tuning system]]s, focusing on [[xenharmonic music]] while also documenting [[historical tunings]] and tuning practices from [[world musical traditions|world traditions]]. It covers the [[theory]] and [[practice|practical applications]] of these systems.
For a lengthier introduction, see [[Xenharmonic Wiki: Introduction]].
[[File:Pts-2-3-5-e2-twtop-tlin.jpg|thumb|right]]
== If you are new to musical tuning ==
* [[Why use alternative tunings?]]
* [[Microtonal music|What are microtonal and xenharmonic music]]?
* [[Listen]] to alternatively tuned music, in case you're wondering what it all sounds like.
* [[List of approaches to musical tuning|Discover approaches to musical tuning]]
* [[Links|Explore links]] to xenharmonic websites
* [[The Library|Browse the library]] of published works about microtonal/xenharmonic music
* Learn about the [[Xenharmonic Alliance]], a social group of xenharmonic musicians
== Popular topics ==
* [[Just intonation]] – Tuning based on [[interval]]s with {{W|rational number}} [[frequency ratio]]s
* [[EDO|Equal divisions of the octave]] and other [[equal-step tuning]]s
* [[MOS scale|Moment of Symmetry (MOS) scales]] – Scales with at most two distinct sizes (e.g. {{w|major and minor}}) for each interval class, [[MOS scale#Equivalent definitions and generalizations|among many other things]]
* [[Regular temperaments]] – Tuning systems that appear the same everywhere, excellent for free modulation; [[equal temperament]]s are a basic example
* [[Historical temperaments]] – such as [[Pythagorean tuning]], [[meantone]] temperaments, and [[well temperament]]s
== Practical xenharmonics ==
* [[List of music software]]
* [[List of microtonal software plugins]]
* [[Instruments]]
* [[Guides]]
== Contributing to the Xenharmonic Wiki ==
This wiki is created by volunteers. It is a perpetual work in progress, depending on members of the community to help us develop it. We welcome relevant new content and constructive updates to existing pages, so please feel free to [[Help: How to get your Xenharmonic Wiki account|sign up and contribute]]!
Latest revision as of 23:34, 18 February 2026
This is a page where I will draft edits before making them on the actual page. This may possibly include drafting a new page to be created. If you have something to add to any of them, or any concerns, please suggest them on the talk page. If a template is set to debug, make sure to remove that setting when editing the target page.
There are two different mappings of the 11-limit. One is just called pajara and is slightly more complex but suffers almost no loss of accuracy compared to the 7-limit. It is best tuned flat of 22edo. The other, called pajarous to avoid confusion, maps the 11th harmonic slightly simpler, but 22edo is the only 11-odd-limitdiamond monotone tuning, where primes 3 and 5 are less accurate than in optimal tunings of canonical 11-limit pajara.
In the following tables, odd harmonics 1–11 and their inverses are in bold.
This wiki is created by volunteers. It is a perpetual work in progress, depending on members of the community to help us develop it. We welcome relevant new content and constructive updates to existing pages, so please feel free to sign up and contribute!
