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

Ron Hardin rhhardin at att.net
Thu Dec 3 19:36:17 CET 2015

```I suppose (almost at random) the adagio of Faure op 89 is an examplehttps://www.youtube.com/watch?v=5-j6LLkpQYY
If you're not going to use actual frequencies but rather numbers as notes, the simple whole number ratio has to appear in exponentiation of them and you'd get preferred differences modulo 12, or whatever the key system is.
To get melodies you'd want the series to mostly stay in the same rank order, no swapping notes from soprano to bass parts.
You'd have to tighten the rules somehow to make it mathematically interesting.
rhhardin at mindspring.com rhhardin at att.net (either)

From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Sent: Thursday, December 3, 2015 1:09 PM
Subject: [seqfan] Re: Need suggestions for test for compatible sequences for "voice leading"

Ron, I guess one could ask, not just for a(n) to divide b(n), but
more generally that a(n) and b(n) contain the same set of primes in their
prime factorizations.

If we want to specify a key, then we would also require that a(n) and b(n),
for all n, belong to a specified set of residue classes mod 12, is that
right? What's a good Faure-ish example?

See https://oeis.org/wiki/Welcome#Compressed_Versions for "a *gzipped file*
<http://oeis.org/stripped.gz> containing just the sequences and their

Could you whip up a little program that would look at that data, and
use a pre-specified key, and suggest some pairs of sequences that would
sing nicely together?  (or triples, quadruples, .... as Alexei suggests)

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.
Email: njasloane at gmail.com

On Thu, Dec 3, 2015 at 12:28 PM, Ron Hardin <rhhardin at att.net> wrote:

> The two sequences are the melodies already. The question would be what
> constitutes acceptable chords.
> The literalized criterion would be simple whole number ratios.  You might
> want to add key, meaning both melodies stay within a certain subset of each
> octive.
> Faure violates that a little by using melody to suggest a new temporary
> key.
>  rhhardin at mindspring.com rhhardin at att.net (either)
>
>      From: Neil Sloane <njasloane at gmail.com>
>  To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
>  Sent: Thursday, December 3, 2015 11:19 AM
>  Subject: [seqfan] Need suggestions for test for compatible sequences for
>
> Dear Seq Fans,
>
> In musical theory there is the concept of 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.
> Email: njasloane at gmail.com
>
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