Very low accuracy temperaments: Difference between revisions

Below are listed some '''very low accuracy temperaments'''. Temperaments with exceedingly low accuracy such as these tend to temper out very large intervals such as 9/8, 10/9, 32/27, or 15/14, equating wildly different interval sizes with [[semitone (interval size measure)|semitone]]-level or even greater [[error]]s. As a result, all of them are right on or even beyond the edge of what can be sensibly called a temperament at all; that is to say, they are [[exotemperament]]s.

This temperament is characterized by [[9/8]] being tempering out, and has been termed a "troll temperament" by its namers. It is named on account of 4/3 and 3/2 both being represented by the 600 cent half octave, which, in terms of diatonic function, serves as an antitonic. Surprisingly, it has extensions all the way up to the 11-limit, as confirmed by the data from [http://x31eq.com/cgi-bin/rt.cgi?limit=11&ets=2_4p&tuning=po x31eq]. The original 5-limit is basically the 3-limit music of [[2edo]] with the addition of harmonic 5 represented by an independent generator.  

=== 7-limit ===

Alteraugment is like [[augmented]], but the generator provides 5/4 instead of 3/2. [[User:VectorGraphics|Vector Graphics]] suggests the name ''kinsborough'' for this temperament.

== Yo (2c & 3)  ==

This temperament family is characterized by the [[color notation|yo 2nd]] [[10/9]] being tempering out.

* WE: ~2 = 1189.201{{c}}, ~3/2 = 978.002{{c}}

* CWE: ~2 = 1200.000{{c}}, ~3/2 = 983.918{{c}}

Involution was named by [[User:CompactStar|CompactStar]] in 2023.  

: error map: {{val| +65.405 -84.203 -94.789 }}

<!-- * [[CTE]]: ~3 = 1901.955{{c}}, ~5/3 = 701.863{{c}}

: [[error map]]: {{val| 0.000 -182.496 -266.779 }} -->

: error map: {{val| +86.594 -78.085 -111.407 }}

* [[CWE]]: ~3 = 1901.995{{c}}, ~5/3 = 691.468{{c}}

 

This temperament was named by [[User:Jerdle|Jerdle]] as an abbreviation of "co-decimal", as it resembles [[decimal]] in many ways, but exchanges the roles of 5's and 7's. While decimal equates [[8/7]] and [[7/6]], as well as [[6/5]] and [[5/4]], this equates [[10/9]] and [[6/5]], as well as [[7/6]] and [[9/7]]. It is an extension of [[bug]] and [[54/49|mujannabic]] in the same way decimal is of [[semaphore]] and [[dicot]].  

[[Comma list]]: [[27/25]], [[54/49]]

: error map: {{val| -2.821 -31.998 +18.621 +34.699 }}

{{Optimal ET sequence|legend=1| 1c, …, 6bcd, 7d }}

* WE: ~2 = 1268.274{{c}}, ~3/2 = 612.921{{c}}

: error map: {{val| +68.274 -20.760 -249.765 }}

* CWE: ~2 = 1200.000{{c}}, ~3/2 = 614.055{{c}}