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| = ARCHIVED WIKISPACES DISCUSSION BELOW =
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| '''All discussion below is archived from the Wikispaces export in its original unaltered form.'''
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| == Can we explain these things in English as well? ==
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| It would be a nice thing to not immediately assault the reader with PhD mathematical treatise-speak when they learn about scale classification....
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| Granted are two points:
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| 1) Much scale research goes on on the (various) Yahoo tuning lists. The research is valuable and discoveries are made, etc.
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| 2) Potentially, many of these discoveries are of musical value.
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| BUT---if we care/want musicians to even tinker with these concepts, we will scare them away with talks of "vals" and "monzos"...to the outsider, these are simply neologisms.
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| Just a thought. The xenwiki is setup as a resource, one would hope, for musicians, and not simply for PhD mathematicians.
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| Best,
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| AKJ
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| - '''akjmicro''' March 07, 2011, 01:01:50 PM UTC-0800
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| I agree with you. I tried to force a definition of val, monzo by adding links to (future) wiki pages, but this will not improve the readability.
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| As I've learned, some notations are very efficient, but some of them I cannot decode at all. Maybe some examples for these techniques will suffice for the non-mathematician of us.
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| Best regards,
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| Wolf
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| - '''xenwolf''' March 07, 2011, 11:53:22 PM UTC-0800
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| Here's an outline for how I think the page can be improved. Unfortunately the details will need to be filled in by Gene.
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| In 2001 it was discovered that [MOS] scales correspond to rank 2 regular temperamnts. For a regular temperament of arbitrary rank, there is a corroseponding hobbit scale (named for their relationship to [dwarf scales]). Examples may be found on the [Scalesmith] page.
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| *Definition*
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| Given a regular tempearment, we first find an equal temperament [val] v which supports it. Next, we define an [octave equivalent seminorm] for the temperament. This seminorm applies to monzos and sends any comma of the temperament, and also the octave, to zero. It measures the complexity of the octave-equivalent pitch class to which a monzo belongs. For example, in meantone temperament, the OE seminorm of 3/2 is <u>_ and of 3/1 is </u>_ and of 25/16 is ___. Roughly speaking, the hobbit is the scale consisting of the lowest OE complexity for each scale step mapped to the integer i by v (see [epimorphic] for details).
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| In the rank 2 case, the hobbit for v is identical to the MOS for v because...
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| *Examples*
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| Consider the 7-note hobbit for meantone temperament ... yields the familiar diatonic scale (MOS)...
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| Next, consider the 22-note hobbit for minerva temperament...
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| *Details*
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| Denoting the OE seminorm...
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| - '''clumma''' March 08, 2011, 10:16:42 PM UTC-0800
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| Wow, I cannot edit this. Useless.
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| - '''clumma''' March 08, 2011, 10:17:22 PM UTC-0800
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