Talk:Diamond function/WikispacesArchive
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Arbitrary definition?
This definition of a diamond seems arbitrary to me. It assumes octave equivalence and does not include reciprocal ratios, except in the sense that they are reduced to within an octave (so 1/5 becomes 8/5).
A more sensible definition would be the one used by Partch, and the one hinted at by Woolhouse. Hence, diamond({1, 3, 5}) would be {1/1, 3/1, 5/1, 1/3, 1/5, 5/3, 3/5}.
- Sarzadoce October 22, 2012, 02:32:31 PM UTC-0700
It does include reciprocal ratios, and assumes octave equivalence. Of course it would be trivial to extend it to a function of the equivalence interval so that tritaves could be allowed to flourish, and then your proposal would be with the trivial interval of equivalence, 1.
You could also simply define another function, in my opinion a much less useful one, as the set of all ratios. Where does Partch do this, and what should it be called?
- genewardsmith October 23, 2012, 07:57:24 AM UTC-0700
But why is this function called "Diamond?" That is what I am asking. It doesn't resemble Partch's diamond, so I'm curious where that name came from in the first place.
- Sarzadoce October 23, 2012, 10:44:49 PM UTC-0700
It's what people have been calling the "q-limit diamond" for some time now, if you imput the odd integers up to q. And Wikipedia seems to think it's what Partch meant:
http://en.wikipedia.org/wiki/Tonality_diamond
- genewardsmith October 24, 2012, 02:12:32 PM UTC-0700
This is not at all what I recall from Genesis of a Music.
- Sarzadoce October 24, 2012, 11:22:07 PM UTC-0700
I don't see what the confusion is here. It seems like the only difference is octave equivalence, right? Partch had no problem with octave equivalence, so I think he'd be fine with this. No?
- keenanpepper October 26, 2012, 10:25:26 AM UTC-0700
Locking
We keep having trouble with this page, so I've locked it so that only organizers can mess with it. It may be that it needs to be made clearer to people who aren't getting the mathematical language.
- genewardsmith September 19, 2011, 09:39:14 AM UTC-0700
What does this mean?
"The diamond though can be based on melodic intervals as has been illustrated in its use with various All-Interval sets (13 & 31)." appears with no indication of what it means.
- genewardsmith May 28, 2011, 09:54:20 AM UTC-0700
I guess I'll remove it.
- genewardsmith June 28, 2011, 02:01:17 PM UTC-0700
I posted an invitation message to kraiggrady.
I guess, most users don't monitor changes and messages on the whole wiki, as I (and probably you) do.
--Peu
- xenwolf June 29, 2011, 12:24:17 AM UTC-0700
Why kreiggrady? http://xenharmonic.wikispaces.com/page/diff/Diamonds/175533319
(so let's wait a little while)
- xenwolf June 29, 2011, 12:28:21 AM UTC-0700
"has been illustrated" seems to refer to
http://anaphoria.com/31allintvl.PDF
- xenwolf June 29, 2011, 02:15:08 AM UTC-0700