171edo: Difference between revisions

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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]]).
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
|}
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* 171et is lower in relative error than any previous equal temperaments in the 7-limit and in the [[9-odd-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.
* 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
| [[Minortone]] / [[mitonic]] / mineral (171) / ore (171e) / goldmine (171ef)
| [[Mitonic]] / mineral (171) / ore (171e) / goldmine (171ef)
|-
|-
| 1
| 1
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| 498.25
| 498.25
| 4/3
| 4/3
| [[Helmholtz (temperament)|Helmholtz]] / [[pontiac]]
| [[Pontiac]]
|-
|-
| 1
| 1
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| 182.46
| 182.46
| 10/9
| 10/9
| [[Terrain]] / [[domain]]
| [[Domain (temperament)|Domain]]
|-
|-
| 3
| 3
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| 315.79<br>(49.12)
| 315.79<br>(49.12)
| 6/5<br>(36/35)
| 6/5<br>(36/35)
| [[Ennealimmal]] (171e) / ennealimmia (171) / ennealimnic (171) / ennealiminal (171ef)
| [[Ennealimmal]] / enneabiotic (171ef) / ennealympic (171) / ennealimnic (171) / ennealiminal (171ef)
|-
|-
| 9
| 9