Talk:31st-octave temperaments: Difference between revisions
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Cmloegcmluin (talk | contribs) unhyphenate "comma basis" |
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Trying to understand this statement in the '''Birds''' section: "It also tempers out the 31-7 comma, but sadly, combining the two commas leads to torsion." | Trying to understand this statement in the '''Birds''' section: "It also tempers out the 31-7 comma, but sadly, combining the two commas leads to torsion." | ||
When the commas listed — 3136/3125 and 823543/819200 — are expressed as the comma | When the commas listed — 3136/3125 and 823543/819200 — are expressed as the comma basis for this temperament, we get {{map|{{vector|6 0 -5 2}} {{vector|-15 0 -2 7}}}}. This matches with the mapping provided {{vector|{{map|31 49 72 87}} {{map|0 1 0 0}}}}, i.e. it is its null-space. In [[canonical form]] this mapping and comma basis are {{vector|{{map|31 0 72 87}} {{map|0 1 0 0}}}} and {{map|{{vector|-72 0 31 0}} {{vector|-33 0 13 1}}}}, respectively. | ||
Elsewhere description claims that this temperament could be defined by tempering out the 31-5 and the 31-7 commas, were it not for torsion. I don't know what is "sad" about the torsion. Simply remove it by [[defactoring]], right? When these two commas are expressed as a comma | Elsewhere description claims that this temperament could be defined by tempering out the 31-5 and the 31-7 commas, were it not for torsion. I don't know what is "sad" about the torsion. Simply remove it by [[defactoring]], right? When these two commas are expressed as a comma basis for a temperament it looks like {{map|{{vector|-87 0 0 31}} {{vector|72 0 -31 0}}}}, and then if we put it in canonical form (which defactors it), we get the same thing {{map|{{vector|-72 0 31 0}} {{vector|-33 0 13 1}}}} as what's there. | ||
So can't we just remove the part where it says "but sadly, combining the two commas leads to torsion"? Otherwise, can we clarify what is sad? | So can't we just remove the part where it says "but sadly, combining the two commas leads to torsion"? Otherwise, can we clarify what is sad? | ||