171edo: Difference between revisions
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=== 7-prime-limited odd-limit analysis === | |||
171edo is ''distinctly'' [[consistent]] and monotone up to the 7-prime-limited 45-odd-limit: | |||
{{Databox | |||
|collapse=true | |||
|title=The 7-prime-limited 45-odd-limit, by 171edo mapping (SW3 format) | |||
|text= | |||
<pre> | |||
(* | |||
7-PL 45-OL odds: | |||
1 3 5 7 9 15 21 25 27 35 45 | |||
Mapping Ratio Error | |||
*) | |||
(* 7\171*) 36/35 (* +.352c *) | |||
(* 9\171*) 28/27 (* +.197c *) | |||
(* 10\171*) 25/24 (* -.497c *) | |||
(* 12\171*) 21/20 (* -.257c *) | |||
(* 16\171*) 16/15 (* +.549c *) | |||
(* 17\171*) 15/14 (* -.145c *) | |||
(* 19\171*) 27/25 (* +.096c *) | |||
(* 22\171*) 35/32 (* -.754c *) | |||
(* 26\171*) 10/9 (* +.052c *) | |||
(* 28\171*) 28/25 (* +.293c *) | |||
(* 29\171*) 9/8 (* -.401c *) | |||
(* 33\171*) 8/7 (* -.405c *) | |||
(* 38\171*) 7/6 (* -.204c *) | |||
(* 42\171*) 32/27 (* +.602c *) | |||
(* 43\171*) 25/21 (* -.092c *) | |||
(* 45\171*) 6/5 (* +.148c *) | |||
(* 54\171*) 56/45 (* +.345c *) | |||
(* 55\171*) 5/4 (* -.349c *) | |||
(* 61\171*) 32/25 (* +.698c *) | |||
(* 62\171*) 9/7 (* +.004c *) | |||
(* 64\171*) 35/27 (* -.152c *) | |||
(* 67\171*) 21/16 (* -.605c *) | |||
(* 71\171*) 4/3 (* +.201c *) | |||
(* 74\171*) 27/20 (* -.253c *) | |||
(* 78\171*) 48/35 (* +.553c *) | |||
(* 81\171*) 25/18 (* -.296c *) | |||
(* 83\171*) 7/5 (* -.056c *) | |||
(* 84\171*) 45/32 (* -.750c *) | |||
(* 87\171*) 64/45 | |||
(* 88\171*) 10/7 | |||
(* 90\171*) 36/25 | |||
(* 93\171*) 35/24 | |||
(* 97\171*) 40/27 | |||
(*100\171*) 3/2 | |||
(*104\171*) 32/21 | |||
(*107\171*) 54/35 | |||
(*109\171*) 14/9 | |||
(*110\171*) 25/16 | |||
(*116\171*) 8/5 | |||
(*117\171*) 45/28 | |||
(*126\171*) 5/3 | |||
(*128\171*) 42/25 | |||
(*129\171*) 27/16 | |||
(*133\171*) 12/7 | |||
(*138\171*) 7/4 | |||
(*142\171*) 16/9 | |||
(*143\171*) 25/14 | |||
(*145\171*) 9/5 | |||
(*149\171*) 64/35 | |||
(*152\171*) 50/27 | |||
(*154\171*) 28/15 | |||
(*155\171*) 15/8 | |||
(*159\171*) 40/21 | |||
(*161\171*) 48/25 | |||
(*162\171*) 27/14 | |||
(*164\171*) 35/18 | |||
(*171\171*) 2/1 | |||
</pre> | |||
}} | |||
The 7-prime-limited 49-odd-limit is where non-distinctness first shows up: namely, ~49/48 = ~50/49 (this is characteristic of all ennealimmal tunings). However, 171edo remains consistent up to much higher 7-prime-limited odd-limits (much higher than even [[99edo]]). | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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| 2.88 | | 2.88 | ||
|} | |} | ||
* 171et is lower in relative error than any previous equal temperaments in the 7-limit | * 171et is lower in relative error than any previous equal temperaments in the 7-limit. Not until [[441edo|441]] do we find a better equal temperaments in terms of absolute error, and not until [[3125edo|3125]] do we find one in terms of relative error. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
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| 182.46 | | 182.46 | ||
| 10/9 | | 10/9 | ||
| [[ | | [[Mitonic]] / mineral (171) / ore (171e) / goldmine (171ef) | ||
|- | |- | ||
| 1 | | 1 | ||
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| 498.25 | | 498.25 | ||
| 4/3 | | 4/3 | ||
| [[ | | [[Pontiac]] | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 272: | Line 346: | ||
| 182.46 | | 182.46 | ||
| 10/9 | | 10/9 | ||
| [[ | | [[Domain (temperament)|Domain]] | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 290: | Line 364: | ||
| 315.79<br>(49.12) | | 315.79<br>(49.12) | ||
| 6/5<br>(36/35) | | 6/5<br>(36/35) | ||
| [[Ennealimmal]] ( | | [[Ennealimmal]] / enneabiotic (171ef) / ennealympic (171) / ennealimnic (171) / ennealiminal (171ef) | ||
|- | |- | ||
| 9 | | 9 | ||