Saturation, torsion, and contorsion: Difference between revisions
Cmloegcmluin (talk | contribs) add links to Tonalsoft |
Cmloegcmluin (talk | contribs) →History and terminology: remove not really correct statement; per the linked terminology proposal page, we suggest that torsion is not a good word for the periodicity block concept either |
||
| Line 29: | Line 29: | ||
The term ''torsion'' has been used since at least as early as 1932<ref>[https://scholar.google.com/scholar?q=%22torsion+group%22&hl=en&as_sdt=0%2C5&as_ylo=1900&as_yhi=1940 Google Scholar: Torsion group]</ref><ref>[https://math.stackexchange.com/questions/300586/where-does-the-word-torsion-in-algebra-come-from Stack Exchange | ''Where does the word "torsion" in algebra come from?'']</ref> and came to RTT from the mathematical field of group theory. Historically, a group-theory formalism was used to analyze comma bases with torsion, where the smallest comma displaying torsion was not made to vanish although a power of that comma was, which is musically impossible; using a linear algebra formalism as is preferred now, no such impossibility is suggested. The term ''contorsion'' was invented for RTT in 2002 by [[Paul Erlich]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2033.html#2456 Yahoo! Tuning Group | ''My top 5--for Paul'']</ref>, as a play on the word "co-torsion", being dual to the situation with "torsion" above. | The term ''torsion'' has been used since at least as early as 1932<ref>[https://scholar.google.com/scholar?q=%22torsion+group%22&hl=en&as_sdt=0%2C5&as_ylo=1900&as_yhi=1940 Google Scholar: Torsion group]</ref><ref>[https://math.stackexchange.com/questions/300586/where-does-the-word-torsion-in-algebra-come-from Stack Exchange | ''Where does the word "torsion" in algebra come from?'']</ref> and came to RTT from the mathematical field of group theory. Historically, a group-theory formalism was used to analyze comma bases with torsion, where the smallest comma displaying torsion was not made to vanish although a power of that comma was, which is musically impossible; using a linear algebra formalism as is preferred now, no such impossibility is suggested. The term ''contorsion'' was invented for RTT in 2002 by [[Paul Erlich]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2033.html#2456 Yahoo! Tuning Group | ''My top 5--for Paul'']</ref>, as a play on the word "co-torsion", being dual to the situation with "torsion" above. | ||
In the case of temperaments, [[Dave Keenan]] and [[Douglas Blumeyer]] have proposed and used '''defactoring''' as a replacement for ''saturation'' and '''enfactoring''' as a replacement for both ''torsion'' and ''contorsion''. So, a mapping or comma basis of a temperament is either defactored (saturated) or enfactored (unsaturated, having torsion/contorsion) | In the case of temperaments, [[Dave Keenan]] and [[Douglas Blumeyer]] have proposed<ref>See [[Defactoring terminology proposal]] for details.</ref> and used '''defactoring''' as a replacement for ''saturation'' and '''enfactoring''' as a replacement for both ''torsion'' and ''contorsion''. So, a mapping or comma basis of a temperament is either defactored (saturated) or enfactored (unsaturated, having torsion/contorsion). | ||
==See also== | ==See also== | ||