[seqfan] Re: Need suggestions for test for compatible sequences for "voice leading"

[Alonso Del Arte]

I would suggest trying this out on a very basic level by taking a few
simple note-against-note cantus firmus and counterpoint exercises from
Fux's *Gradus ad Parnassus* (written in the form of a dialogue between
teacher and student), converting the cantus firmus and the counterpoint to
sequences of numbers of Z_12, and comparing the results against what the
teacher character evaluates the student character's work.

I predict that this would reveal a preference for sequences moving in
intervals of 1 or 2, with a preference to avoid the difference between two
voices being 6, the tritone or devil in music. Also a preference for the
first and last difference between two voices being 0 (corresponding to
either a unison or an octave).

Al

On Thu, Dec 3, 2015 at 3:58 PM, Neil Sloane <njasloane at gmail.com> wrote:

> I would expect that sequences which are cousins, such as A5, A203, A6520
> would work well together,
> where two unrelated sequences (Somos-4 = A6720) and Fib = A45, say, would
> not..
> In fact any two random sequences would be equally incompatible
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Thu, Dec 3, 2015 at 2:34 PM, Bob Selcoe <rselcoe at entouchonline.net>
> wrote:
>
> > Hi Jean-Paul, Neil and Seqfans,
> >
> > Jean-Paul - assuming this is essentially Neil's question, then it's still
> > not clear to me what needs to be avoided or accomplished.  Can you give
> two
> > brief two-sequence "chords", one that is and one that is not
> "compatible",
> > to illustrate the efficiency or parsimony you desire?  Others have
> > correctly pointed out some of the basic ambiguities with Neil's question
> as
> > posed; maybe some examples will clarify and get the ball rolling.
> >
> > Cheers,
> > Bob S
> >
> > --------------------------------------------------
> > From: "jean-paul allouche" <jean-paul.allouche at imj-prg.fr>
> > Sent: Thursday, December 03, 2015 12:52 PM
> > To: <seqfan at list.seqfan.eu>
> > Subject: [seqfan] Re: Need suggestions for test for compatible sequences
> > for "voice leading"
> >
> >
> > Dear all
> >>
> >> A related (or is it the same?) question would be, once two reasonably
> >> fitting sequences (or more) are found, to do voice leading, i.e., to
> >> combine these sequences to build new sequences giving the same
> >> "chords" but in a smoother manner (typically, e.g., to avoid crossing
> >> hands
> >> if playing the piano).
> >>
> >> best
> >> jean-paul
> >>
> >> Le 03/12/15 17:19, Neil Sloane a écrit :
> >>
> >>> Dear Seq Fans,
> >>>
> >>> In musical theory there is the concept of voice leading
> >>> (see
> >>> http://music.stackexchange.com/questions/14779/what-is-voice-leading )
> >>>
> >>> Question: suppose we made a series of two-note chords by combining two
> >>> sequences A and B. Can one formulate a test to see which pairs of
> >>> sequences
> >>> (A,B) are compatible, i.e. satisfy the rules for voice leading?
> >>>
> >>> Best regards
> >>> Neil
> >>>
> >>> Neil J. A. Sloane, President, OEIS Foundation.
> >>> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> >>> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway,
> NJ.
> >>> Phone: 732 828 6098; home page: http://NeilSloane.com
> >>> Email: njasloane at gmail.com
> >>>
> >>> _______________________________________________
> >>>
> >>> Seqfan Mailing list - http://list.seqfan.eu/
> >>>
> >>
> >>
> >> _______________________________________________
> >>
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> >>
> >>
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> >
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> >
>
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-- 
Alonso del Arte
Author at SmashWords.com
<https://www.smashwords.com/profile/view/AlonsoDelarte>
Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>