171edo: Difference between revisions

Line 25:

=== 7-prime-limited odd-limit analysis ===

171edo is ''distinctly'' [[consistent]] and monotone up to the 7-prime-limited 45-odd-limit~~, i.e.~~

171edo is ''distinctly'' [[consistent]] and monotone up to the 7-prime-limited 45-odd-limit:

* when tempered using the patent val, the relative sizes of any two intervals are never conflated ''or'' reversed

* the direct approximation is equal to the approximation given by stacking patent val prime approximations, thus every interval has absolute error < 3.509c.

{{Databox

|collapse=true

Line 36:

Line 34:

7-PL 45-OL odds:

1 3 5 7 9 15 21 25 27 35 45

Mapping Ratio

Mapping Ratio Error

*)

(* 7\171*) 36/35

(* 7\171*) 36/35 (* +.352c *)

(* 9\171*) 28/27

(* 9\171*) 28/27 (* +.197c *)

(* 10\171*) 25/24

(* 10\171*) 25/24 (* -.497c *)

(* 12\171*) 21/20

(* 12\171*) 21/20 (* -.257c *)

(* 16\171*) 16/15

(* 16\171*) 16/15 (* +.549c *)

(* 17\171*) 15/14

(* 17\171*) 15/14 (* -.145c *)

(* 19\171*) 27/25

(* 19\171*) 27/25 (* +.096c *)

(* 22\171*) 35/32

(* 22\171*) 35/32 (* -.754c *)

(* 26\171*) 10/9

(* 26\171*) 10/9 (* +.052c *)

(* 28\171*) 28/25

(* 28\171*) 28/25 (* +.293c *)

(* 29\171*) 9/8

(* 29\171*) 9/8 (* -.401c *)

(* 33\171*) 8/7

(* 33\171*) 8/7 (* -.405c *)

(* 38\171*) 7/6

(* 38\171*) 7/6 (* -.204c *)

(* 42\171*) 32/27

(* 42\171*) 32/27 (* +.602c *)

(* 43\171*) 25/21

(* 43\171*) 25/21 (* -.092c *)

(* 45\171*) 6/5

(* 45\171*) 6/5 (* +.148c *)

(* 54\171*) 56/45

(* 54\171*) 56/45 (* +.345c *)

(* 55\171*) 5/4

(* 55\171*) 5/4 (* -.349c *)

(* 61\171*) 32/25

(* 61\171*) 32/25 (* +.698c *)

(* 62\171*) 9/7

(* 62\171*) 9/7 (* +.004c *)

(* 64\171*) 35/27

(* 64\171*) 35/27 (* -.152c *)

(* 67\171*) 21/16

(* 67\171*) 21/16 (* -.605c *)

(* 71\171*) 4/3

(* 71\171*) 4/3 (* +.201c *)

(* 74\171*) 27/20

(* 74\171*) 27/20 (* -.253c *)

(* 78\171*) 48/35

(* 78\171*) 48/35 (* +.553c *)

(* 81\171*) 25/18

(* 81\171*) 25/18 (* -.296c *)

(* 83\171*) 7/5

(* 83\171*) 7/5 (* -.056c *)

(* 84\171*) 45/32

(* 84\171*) 45/32 (* -.750c *)

(* 87\171*) 64/45

(* 88\171*) 10/7

@@ Line 25: / Line 25: @@
 === 7-prime-limited odd-limit analysis ===
-edo is ''distinctly'' [[consistent]] and monotone up to the 7-prime-limited 45-odd-limit, i.e.
+edo is ''distinctly'' [[consistent]] and monotone up to the 7-prime-limited 45-odd-limit:
-* when tempered using the patent val, the relative sizes of any two intervals are never conflated ''or'' reversed
-* the direct approximation is equal to the approximation given by stacking patent val prime approximations, thus every interval has absolute error < 3.509c.
 {{Databox
 |collapse=true
@@ Line 36: / Line 34: @@
 -PL 45-OL odds:
 3 5 7 9 15 21 25 27 35 45
-   Mapping   Ratio
+   Mapping   Ratio    Error
 *)
-(*  7\171*) 36/35
+(*  7\171*) 36/35 (* +.352c *)
-(*  9\171*) 28/27
+(*  9\171*) 28/27 (* +.197c *)
-(* 10\171*) 25/24
+(* 10\171*) 25/24 (* -.497c *)
-(* 12\171*) 21/20
+(* 12\171*) 21/20 (* -.257c *)
-(* 16\171*) 16/15
+(* 16\171*) 16/15 (* +.549c *)
-(* 17\171*) 15/14
+(* 17\171*) 15/14 (* -.145c *)
-(* 19\171*) 27/25
+(* 19\171*) 27/25 (* +.096c *)
-(* 22\171*) 35/32
+(* 22\171*) 35/32 (* -.754c *)
-(* 26\171*) 10/9
+(* 26\171*) 10/9  (* +.052c *)
-(* 28\171*) 28/25
+(* 28\171*) 28/25 (* +.293c *)
-(* 29\171*) 9/8
+(* 29\171*) 9/8   (* -.401c *)
-(* 33\171*) 8/7
+(* 33\171*) 8/7   (* -.405c *)
-(* 38\171*) 7/6
+(* 38\171*) 7/6   (* -.204c *)
-(* 42\171*) 32/27
+(* 42\171*) 32/27 (* +.602c *)
-(* 43\171*) 25/21
+(* 43\171*) 25/21 (* -.092c *)
-(* 45\171*) 6/5
+(* 45\171*) 6/5   (* +.148c *)
-(* 54\171*) 56/45
+(* 54\171*) 56/45 (* +.345c *)
-(* 55\171*) 5/4
+(* 55\171*) 5/4   (* -.349c *)
-(* 61\171*) 32/25
+(* 61\171*) 32/25 (* +.698c *)
-(* 62\171*) 9/7
+(* 62\171*) 9/7   (* +.004c *)
-(* 64\171*) 35/27
+(* 64\171*) 35/27 (* -.152c *)
-(* 67\171*) 21/16
+(* 67\171*) 21/16 (* -.605c *)
-(* 71\171*) 4/3
+(* 71\171*) 4/3   (* +.201c *)
-(* 74\171*) 27/20
+(* 74\171*) 27/20 (* -.253c *)
-(* 78\171*) 48/35
+(* 78\171*) 48/35 (* +.553c *)
-(* 81\171*) 25/18
+(* 81\171*) 25/18 (* -.296c *)
-(* 83\171*) 7/5
+(* 83\171*) 7/5   (* -.056c *)
-(* 84\171*) 45/32
+(* 84\171*) 45/32 (* -.750c *)
 (* 87\171*) 64/45
 (* 88\171*) 10/7