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Map of rank-2 temperaments: Difference between revisions

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See also: [[Pythagorean family]]
See also: [[Pythagorean family]]


Temperaments in this family are interesting because they can be thought of as [[12edo]] with microtonal alterations.
{| class="wikitable"
! colspan="7" |Generator!!Cents!!Comments
|-
|0\12|| || || ||
|
| ||0||
|-
|
|
|
|
|1\636
|
|
|1.887
|
|-
|
|
|
|
|1\624
|
|
|1.923
|
|-
|
|
|
|
|
|2\1236
|
|1.942
|[[Atomic]]
|-
|
|
|
|
|
|
|3\1848
|1.948
|Atomic
|-
|
|
|
|
|1\612
|
|
|1.961
|Atomic
|-
|
|
|
|
|1\600
|
|
|2
|
|-
|
|
|
|
|1\588
|
|
|2.041
|
|-
|
|
|
|
|1\576
|
|
|2.083
|
|-
|
|
|
|
|...
|
|
|...
|
|-
|
|
|
|
|1\108
|
|
|11.111
|
|-
|
|
|
|
|1\96
|
|
|12.5
|[[Compton]]
|-
|
|
|
|
|1\84
|
|
|14.286
|Compton
|-
|
|
|
|
|
|
|3\240
|15
|Compton
|-
|
|
|
|
|
|2\156
|
|15.385
|Compton
|-
|
|
|
|
|
|
|3\228
|15.789
|Compton
|-
|
|
|
|
|1\72
|
|
|16.667
|Compton
|-
|
|
|
|1\60
|
|
|
|20
|Compton
|-
|
|
|
|
|2\108
|
|
|22.222
|
|-
|
|
|1\48
|
|
|
|
|25
|[[Catler]]
|-
|
|
|
|
|3\132
|
|
| 27.273
|Catler
|-
|
|
|
| 2\84
|
|
|
|28.571
|Catler
|-
|
|
|
|
|3\120
|
|
|30
|Catler
|-
|
|1\36
|
|
|
|
|
|33.333
|Catler/[[Catnip]]
|-
|
|
|
|
|4\132
|
|
|36.364
|Catnip
|-
|
|
|
|3\96
|
|
|
|37.5
| Catnip
|-
|
|
|
|
|5\156
|
|
|38.462
|Catnip
|-
|
|
|2\60
|
|
|
|
|40
|Catnip
|-
|
|
|
|
|5\144
|
|
|41.667
|
|-
|
|
|
|3\84
|
|
|
| 42.857
|
|-
|
|
|
|
|4\108
|
|
|44.444
|
|-
|1\24
|
|
|
|
|
|
| 50
|
|}


<ul><li>[[Compton]] - 3-limit as in 12edo; intervals of 5 are off by one generator. In the 7-limit (sometimes called [[waage]]), intervals of 7 are off by two generators. In the 11-limit, intervals of 11 are off by 3 generators. Thinking of [[72edo]] might make this more concrete.</li><li>[[Catler]] - 5-limit as in 12edo; intervals of 7 are off by one generator.</li><li>[[Atomic]] - Does not temper out the schisma, so 3/2 is one schisma sharp of its 12edo value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the Pythagorean comma is twelve schismas, and hence 81/80, the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.</li></ul>
== See also ==


==See also==
*[[Fractional-octave temperaments]]: Lists dozens more temperaments that have not yet been listed here.
 
*[[Fractional-octave temperaments]]: Lists dozens of temperaments that have not yet been listed here.


[[Category:Rank 2]]
[[Category:Rank 2]]
[[Category:Lists of temperaments]]
[[Category:Lists of temperaments]]
Retrieved from "https://en.xen.wiki/w/Map_of_rank-2_temperaments"