152edo: Difference between revisions

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It has two reasonable mappings for [[13/1|13]], with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The optimal tuning of this temperament is [[consistent]] in the [[integer limit|15-integer-limit]]. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the [[13-limit]] rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]].

Extending it beyond the 13-limit can be tricky, as the approximated [[17/1|harmonic 17]] is almost 1/3-edostep flat of just, which does not blend well with the sharp tendency from the lower harmonics. The 152fg val in turn gives you an alternative that is more than 2/3-edostep sharp. However, if we skip prime 17 altogether, we can treat 152edo as a no-17 [[23-limit]] system with the 152f val, where it is strong and almost consistent to the no-17 [[23-odd-limit]] with the sole exception of [[13/8]] and its [[octave complement]]. It tempers out [[400/399]] and [[495/494]] in the [[19-limit]] and [[484/483]] and [[576/575]] in the 23-limit.

Extending it beyond the 13-limit can be tricky, as the approximated [[17/1|harmonic 17]] is almost 1/3-edostep flat of just, which does not blend well with the sharp tendency from the lower harmonics. The 152fg val in turn gives you an alternative that is more than 2/3-edostep sharp. However, if we skip prime 17 altogether, we can treat 152edo as a no-17 [[23-limit]] system with the 152f val, where it is strong and almost consistent to the no-17 [[23-odd-limit]] with the sole exception of [[13/8]] and its [[octave complement]]. It tempers out [[400/399]] and [[495/494]] in the [[19-limit]] and [[300/299]], [[484/483]] and [[576/575]] in the 23-limit.

[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].

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=== Subsets and supersets ===

Since 152 factors into 2<sup>3</sup> × 19, 152edo has subset edos {{EDOs| 2, 4, 8, 19, 38, 76 }}.

Since 152 factors into primes as {{nowrap| 2<sup>3</sup> × 19 }}, 152edo has subset edos {{EDOs| 2, 4, 8, 19, 38, 76 }}.

== Approximation to JI ==

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 It has two reasonable mappings for [[13/1|13]], with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The optimal tuning of this temperament is [[consistent]] in the [[integer limit|15-integer-limit]]. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the [[13-limit]] rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]].
-Extending it beyond the 13-limit can be tricky, as the approximated [[17/1|harmonic 17]] is almost 1/3-edostep flat of just, which does not blend well with the sharp tendency from the lower harmonics. The 152fg val in turn gives you an alternative that is more than 2/3-edostep sharp. However, if we skip prime 17 altogether, we can treat 152edo as a no-17 [[23-limit]] system with the 152f val, where it is strong and almost consistent to the no-17 [[23-odd-limit]] with the sole exception of [[13/8]] and its [[octave complement]]. It tempers out [[400/399]] and [[495/494]] in the [[19-limit]] and [[484/483]] and [[576/575]] in the 23-limit.
+Extending it beyond the 13-limit can be tricky, as the approximated [[17/1|harmonic 17]] is almost 1/3-edostep flat of just, which does not blend well with the sharp tendency from the lower harmonics. The 152fg val in turn gives you an alternative that is more than 2/3-edostep sharp. However, if we skip prime 17 altogether, we can treat 152edo as a no-17 [[23-limit]] system with the 152f val, where it is strong and almost consistent to the no-17 [[23-odd-limit]] with the sole exception of [[13/8]] and its [[octave complement]]. It tempers out [[400/399]] and [[495/494]] in the [[19-limit]] and [[300/299]], [[484/483]] and [[576/575]] in the 23-limit.
 [[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].
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 === Subsets and supersets ===
-Since 152 factors into 2<sup>3</sup> × 19, 152edo has subset edos {{EDOs| 2, 4, 8, 19, 38, 76 }}.
+Since 152 factors into primes as {{nowrap| 2<sup>3</sup> × 19 }}, 152edo has subset edos {{EDOs| 2, 4, 8, 19, 38, 76 }}.
 == Approximation to JI ==