BPS: Difference between revisions

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=== Strong extensions ===

While strong 11-limit extensions can be proposed, tempering out [[77/75]] in the ~~flatter~~ range (i.e. ~~flat~~ of [[13edt|3\13edt]]) and [[1375/1323]] in the ~~sharper~~ range, neither of these are of particular accuracy; more accurate extensions would be of considerably higher complexity. However, one could argue for the canonicity of the latter extension by being the no-twos retraction of 11-limit [[hedgehog]] temperament (which, as a member of the [[porcupine family]], makes more sense to consider with prime 11 in mind than without it).

While strong 11-limit extensions can be proposed, tempering out [[77/75]] in the sharper range (i.e. sharp of [[13edt|3\13edt]]) and [[1375/1323]] in the flatter range, neither of these are of particular accuracy; more accurate extensions would be of considerably higher complexity. However, one could argue for the canonicity of the latter extension by being the no-twos retraction of 11-limit [[hedgehog]] temperament (which, as a member of the [[porcupine family]], makes more sense to consider with prime 11 in mind than without it).

In the 13-limit, sharp tunings can generally map the 13th harmonic by tempering out [[637/625]] and identifying (25/21)<sup>2</sup> with [[13/9]], which is optimal near the 30edt tuning. For flat tunings, it is more accurate to temper out [[65/63]] instead.

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 === Strong extensions ===
-While strong 11-limit extensions can be proposed, tempering out [[77/75]] in the flatter range (i.e. flat of [[13edt|3\13edt]]) and [[1375/1323]] in the sharper range, neither of these are of particular accuracy; more accurate extensions would be of considerably higher complexity. However, one could argue for the canonicity of the latter extension by being the no-twos retraction of 11-limit [[hedgehog]] temperament (which, as a member of the [[porcupine family]], makes more sense to consider with prime 11 in mind than without it).
+While strong 11-limit extensions can be proposed, tempering out [[77/75]] in the sharper range (i.e. sharp of [[13edt|3\13edt]]) and [[1375/1323]] in the flatter range, neither of these are of particular accuracy; more accurate extensions would be of considerably higher complexity. However, one could argue for the canonicity of the latter extension by being the no-twos retraction of 11-limit [[hedgehog]] temperament (which, as a member of the [[porcupine family]], makes more sense to consider with prime 11 in mind than without it).
 In the 13-limit, sharp tunings can generally map the 13th harmonic by tempering out [[637/625]] and identifying (25/21)<sup>2</sup> with [[13/9]], which is optimal near the 30edt tuning. For flat tunings, it is more accurate to temper out [[65/63]] instead.