45edo: Difference between revisions

m Make table notes appear under their respective tables
BudjarnLambeth (talk | contribs)
m Octave stretch: temporary improvement until the roll out
 
(One intermediate revision by one other user not shown)
Line 14: Line 14:


=== Octave stretch ===
=== Octave stretch ===
45edo's approximations of 3/1, 5/1, 7/1, 11/1, 13/1 and 17/1 are all improved by [[Gallery of arithmetic pitch sequences #APS of farabs|APS3.21farab]], a [[Octave stretch|stretched-octave]] version of 45edo. The trade-off is a slightly worse 2/1.
45edo's approximations of 3/1, 5/1, 7/1, 11/1, 13/1 and 17/1 are all improved by [[equal tuning|13ed11/9]], a [[Octave stretch|stretched-octave]] version of 45edo. The trade-off is a slightly worse 2/1.


The tuning [[126ed7]] may be used for this purpose too, it improves 3/1, 5/1, 7/1, 11/1 and 13/1, at the cost of a slightly worse 2/1.
The tuning [[126ed7]] may be used for this purpose too, it improves 3/1, 5/1, 7/1, 11/1 and 13/1, at the cost of a slightly worse 2/1.
Line 497: Line 497:


In the following diagrams, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
In the following diagrams, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this EDO.
== Approximation to JI ==
=== Zeta peak index ===
{{ZPI
| zpi = 207
| steps = 44.8397488079316
| step size = 26.7619697233392
| tempered height = 5.252141
| pure height = 1.593330
| integral = 0.837163
| gap = 14.719415
| octave = 1204.28863755026
| consistent = 7
| distinct = 7
}}


== Regular temperament properties ==
== Regular temperament properties ==