3125edo: Difference between revisions

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3125edo is distinctly [[consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.

~~The fact that~~ 3125 = 55 ~~makes curious notations possible based on~~ the ~~symmetric base 5 positional number system, by converting~~ the ~~number to base 5 with digits {-2, -1, 0, 1, 2}~~. ~~3125 has~~ subset edos 5, 25, 125, and 625.

3125 = 55 , and as such it is the 5th edo of the form x^x. It hhas subset edos 5, 25, 125, and 625.

In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.

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=== Prime harmonics ===

=== Miscellaneous properties ===

The fact that 3125 = 55 makes curious notations possible based on the symmetric base 5 positional number system, by converting the number to base 5 with digits {-2, -1, 0, 1, 2}.

== Regular temperament properties ==

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! Associated Ratio

! Temperaments

|-

|1

|139\3125

|53.376

|33/32

|[[Prequartismic]]

|-

| 1

@@ Line 5: / Line 5: @@
 edo is distinctly [[consistent]] through the [[15-odd-limit]]. A basis for its 7-limit commas is 78125000/78121827, 645700815/645657712 and 281484423828125/281474976710656. In the 11-limit, 151263/151250, 820125/819896, 21437500/21434787 and [[Quartisma|117440512/117406179]] are tempered out – it should be noted this edo is so far the only one [https://en.xen.wiki/index.php?title=3125edo&oldid=7860 known to have been confirmed] as tempering out 117440512/117406179 prior to the independent discovery of this comma's significance as the difference between a stack of five [[33/32]] quartertones and one [[7/6]] subminor third. In the 13-limit, 6656/6655, 123201/123200, 140625/140608, 151263/151250 and 1399680/1399489 are all tempered out.
-The fact that 3125 = 5<sup>5</sup> makes curious notations possible based on the symmetric base 5 positional number system, by converting the number to base 5 with digits {-2, -1, 0, 1, 2}. 3125 has subset edos 5, 25, 125, and 625.
+= 5<sup>5</sup> , and as such it is the 5th edo of the form x^x. It hhas subset edos 5, 25, 125, and 625.
 In the 2.5.11.13.19.23.29.31 subgroup, it supports a temperament called estates general, described as 1789 & 3125.
@@ Line 11: / Line 11: @@
 === Prime harmonics ===
 {{Harmonics in equal|3125|columns=11}}
+=== Miscellaneous properties ===
+The fact that 3125 = 5<sup>5</sup> makes curious notations possible based on the symmetric base 5 positional number system, by converting the number to base 5 with digits {-2, -1, 0, 1, 2}.
 == Regular temperament properties ==
@@ Line 22: / Line 25: @@
 ! Associated<br>Ratio
 ! Temperaments
+|-
+|1
+|139\3125
+|53.376
+|33/32
+|[[Prequartismic]]
 |-
 | 1