171edo: Difference between revisions
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[[684edo]], which quadruples it, achieves [[17-odd-limit]] consistency. | [[684edo]], which quadruples it, achieves [[17-odd-limit]] consistency. | ||
=== 7-prime-limited odd-limit analysis === | |||
171edo is ''distinctly'' [[consistent]] and monotone up to the 7-prime-limited 45-odd-limit, i.e. | |||
* 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 | |||
|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*) | |||
(* 7\171*) 36/35 | |||
(* 9\171*) 28/27 | |||
(* 10\171*) 25/24 | |||
(* 12\171*) 21/20 | |||
(* 16\171*) 16/15 | |||
(* 17\171*) 15/14 | |||
(* 19\171*) 27/25 | |||
(* 22\171*) 35/32 | |||
(* 26\171*) 10/9 | |||
(* 28\171*) 28/25 | |||
(* 29\171*) 9/8 | |||
(* 33\171*) 8/7 | |||
(* 38\171*) 7/6 | |||
(* 42\171*) 32/27 | |||
(* 43\171*) 25/21 | |||
(* 45\171*) 6/5 | |||
(* 54\171*) 56/45 | |||
(* 55\171*) 5/4 | |||
(* 61\171*) 32/25 | |||
(* 62\171*) 9/7 | |||
(* 64\171*) 35/27 | |||
(* 67\171*) 21/16 | |||
(* 71\171*) 4/3 | |||
(* 74\171*) 27/20 | |||
(* 78\171*) 48/35 | |||
(* 81\171*) 25/18 | |||
(* 83\171*) 7/5 | |||
(* 84\171*) 45/32 | |||
(* 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. | |||
== Intervals == | == Intervals == | ||