Lumma stability: Difference between revisions
Wikispaces>clumma **Imported revision 245800935 - Original comment: ** |
Wikispaces>clumma **Imported revision 245801077 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:clumma|clumma]] and made on <tt>2011-08-13 18: | : This revision was by author [[User:clumma|clumma]] and made on <tt>2011-08-13 18:46:22 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>245801077</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
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The IM for a scale is simply a list of all its intervals (dyads) grouped by the modes in which they appear. Scala will display it with "show/line intervals". Every fixed scale corresponds to one and only one IM. So if we assume that listeners will eventually perfect their picture of a scale's IM, we can infer things about the scale from its IM. | The IM for a scale is simply a list of all its intervals (dyads) grouped by the modes in which they appear. Scala will display it with "show/line intervals". Every fixed scale corresponds to one and only one IM. So if we assume that listeners will eventually perfect their picture of a scale's IM, we can infer things about the scale from its IM. | ||
Imagine a log-frequency ruler whose total length is the interval of equivalence of our periodic scale (e.g. 1200 cents). Mark off each interval in the IM on this ruler. Now we'll draw line segments on the ruler with colored pencil, using the marks as | Imagine a log-frequency ruler whose total length is the interval of equivalence of our periodic scale (e.g. 1200 cents). Mark off each interval in the IM on this ruler. Now we'll draw line segments on the ruler with colored pencil, using the marks as endpoints. We'll connect all marks belonging to the same interval class with a single line, using a different color for each interval class. Lumma stability is the portion of the ruler that has no pencil on it. The impropriety factor is the portion that's more than singly covered -- where different colors overlap. The idea being that when two interval classes overlap, listeners will not be able to distinguish them in all cases. Lumma stability measures how easily distinguishable the non-overlapping classes will be. | ||
Rothenberg stability is very similar, except it counts the number of overlaps, so it can't distinguish a gross overlap (in cents) from a small one, or detect when two interval classes are arbitrarily close to overlapping.</pre></div> | Rothenberg stability is very similar, except it counts the number of overlaps, so it can't distinguish a gross overlap (in cents) from a small one, or detect when two interval classes are arbitrarily close to overlapping.</pre></div> | ||
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The IM for a scale is simply a list of all its intervals (dyads) grouped by the modes in which they appear. Scala will display it with &quot;show/line intervals&quot;. Every fixed scale corresponds to one and only one IM. So if we assume that listeners will eventually perfect their picture of a scale's IM, we can infer things about the scale from its IM.<br /> | The IM for a scale is simply a list of all its intervals (dyads) grouped by the modes in which they appear. Scala will display it with &quot;show/line intervals&quot;. Every fixed scale corresponds to one and only one IM. So if we assume that listeners will eventually perfect their picture of a scale's IM, we can infer things about the scale from its IM.<br /> | ||
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Imagine a log-frequency ruler whose total length is the interval of equivalence of our periodic scale (e.g. 1200 cents). Mark off each interval in the IM on this ruler. Now we'll draw line segments on the ruler with colored pencil, using the marks as | Imagine a log-frequency ruler whose total length is the interval of equivalence of our periodic scale (e.g. 1200 cents). Mark off each interval in the IM on this ruler. Now we'll draw line segments on the ruler with colored pencil, using the marks as endpoints. We'll connect all marks belonging to the same interval class with a single line, using a different color for each interval class. Lumma stability is the portion of the ruler that has no pencil on it. The impropriety factor is the portion that's more than singly covered -- where different colors overlap. The idea being that when two interval classes overlap, listeners will not be able to distinguish them in all cases. Lumma stability measures how easily distinguishable the non-overlapping classes will be.<br /> | ||
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Rothenberg stability is very similar, except it counts the number of overlaps, so it can't distinguish a gross overlap (in cents) from a small one, or detect when two interval classes are arbitrarily close to overlapping.</body></html></pre></div> | Rothenberg stability is very similar, except it counts the number of overlaps, so it can't distinguish a gross overlap (in cents) from a small one, or detect when two interval classes are arbitrarily close to overlapping.</body></html></pre></div> | ||