User talk:Luqui

Nonchord tone

Quick explination:

The principle aspect of a nonchord tone is that it is not a part of a chord. Thus, in a seventh chord, a seventh is not a nonchord tone, it is a chord tone. Given a (seventh) chord with the four notes C-E-G-Bb, the Bb is a chord tone and not a nonchord tone.

How does one determine if a tone is a part of a chord if one does not already know? It depends, obviously, on context. A Bb played during a C major chord (CEG) does not necessarily turn that major chord into a seventh chord. A nonchord tone always resolves, while a chord tone does not (see nonchord tone).

Hopefully this explains somewhat. I have to go, but I will write more later. Please ask questions, and tell me to talk up or down if need be, on my talk page. Hyacinth 18:30, 9 Oct 2004 (UTC)

I am unable to determine what the chord you describe is. I would guess that C-Eb-Gb-B, despite the spelling, is not classified as a seventh chord, and maybe considered enharmonic spelling of another chord. Alternately, you could consider it a diminished chord with an added tone (the major seventh), see added tone chord. It may simply be a "nonharmonic" chord, which means not that its inharmonic, but that it is not analyzable using tonal theory. Hyacinth 22:16, 15 Oct 2004 (UTC)

My best guess right now is a major chord with an added (minor) ninth, B-D#-F#-C. Hyacinth 00:02, 6 Nov 2004 (UTC)

The chord C-Eb-Gb-B can be called a Cmi(ma7b5) chord in popular music. In common practice period theory it would be theoretically described as a "diminished-major chord," but because it uses thirds other than the M3 and m3, the chord is not found in the standard repertoire. --TobyRush 17:08, 10 Dec 2004 (UTC)

transitive closures

Is there an algorithm, that, given a transitive relation T, will return the smallest relation R such that the transitive closure of R is T? Is there such a smallest relation? I'm looking for such an algorithm, and this seems the most logical place to find a link to it. Luqui 10:55, July 19, 2005 (UTC)

Yes, and it's called transitive reduction, a concept that Wikipedia is not yet familiar with. Luqui 10:56, July 19, 2005 (UTC)

There is indeed a smallest one. To see that, consider that (1) the relation whereby every pair of members of the domain is related, is a transitive relation that is weaker than (i.e. that includes) T, and (2) the set of all such relations is closed under intersection, so the intersection of all such relations is another such relation; that intersection is therefore the smallest one. Michael Hardy 22:44, 19 July 2005 (UTC)

Wieman image

Hi, do you happen to know when Image:WiemanandCornell.jpg was taken? Thanks, AxelBoldt 16:52, 8 April 2006 (UTC)

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Unreferenced BLPs

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non-standard models of arithmetic

A while ago you added a comment on Goodstein's theorem at non-standard model of arithmetic. I find the comment confusing. Could you perhaps clarify it? Tkuvho (talk) 08:53, 24 October 2010 (UTC)

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