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 | 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 | * 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 | ||
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| 182.46 | | 182.46 | ||
| 10/9 | | 10/9 | ||
| [[ | | [[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]] ( | | [[Ennealimmal]] / enneabiotic (171ef) / ennealympic (171) / ennealimnic (171) / ennealiminal (171ef) | ||
|- | |- | ||
| 9 | | 9 | ||