User:CompactStar/Ordinal interval notation: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
CompactStar (talk | contribs)
5,020 edits
No edit summary
CompactStar (talk | contribs)
5,020 edits
Tag: Redirect target changed
 
(56 intermediate revisions by the same user not shown)
Line 1: Line 1:
'''Lefts and rights notation''' is a notation for [[just intonation]] developed by [[User:CompactStar|CompactStar]].
#redirect [[User:CompactStar/Lefts and rights notation]]
== Explanation ==
Regular interval names corresponds to [[Pythagorean]] intervals, e.g. [[32/27]] is a minor third. To name non-Pythagorean intervals, they are given the name of a nearby Pythagorean interval (see [[#Mapping non-Pythagorean intervals]]), then prefixed with a sequence of lefts and rights (abbreviated as < and > respectively). Left and right have the following meaning (where X is any left/right sequence, and Y is a regular interval category like "major third"):
* Xleft Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is flatter than X Y
* Xright Y = the simplest (with respect to [[Tenney height]]) Y whose left/right sequence starts with X and is sharper than X Y
 
More simply, left means to find the simplest flatter interval, and right means to find the simplest sharper interval, with each new left/right having less and less of an impact. Here are some examples with major thirds:
* Leftmajor third = [[5/4]], since it is the simplest major third flatter than 81/64
* Rightmajor third = [[9/7]], since it is the simplest major third sharper than 81/64
* Leftleftmajor third = [[16/13]], since it is the simplest major third flatter than 5/4
* Leftrightmajor third = [[24/19]], since it is the simplest major third between 5/4 and 81/64
* Rightleftmajor third = [[14/11]], since it is the simplest major third between 81/64 and 9/7
* Rightrightmajor third = [[22/17]], since it is the simplest major third sharper than 9/7
 
This system c
=== Mapping non-Pythagorean intervals ===
To map non-Pythagorean intervals to Pythagorean intervals, each prime harmonic above 3 is mapped to the lowest-complexity Pythagorean interval that is within √([[2187/2048]]) (57 cents) of it.

Latest revision as of 03:31, 2 January 2024

Redirect to:

Retrieved from "https://en.xen.wiki/index.php?title=User:CompactStar/Ordinal_interval_notation&oldid=130316"