consonance of 13/8 vs. 11/8

greetings-

During a discussion with Paul Erlich awhile back, I mentioned that 13/8
sounded more consonant to me than 11/8. I attributed this to 11/8 falling in
the tritone "hump", while 13/8 sits between 5/3 and 8/5. After Paul gave us
David Canright's new web address I was reading his "Tour up the Harmonic
Series" (http://www.mbay.net/~anne/david/harmser/index.htm) and noticed that
he also hears 13/8 as more consonant than 11/8. So, I was wondering how
other distinguished ears in this forum might weigh in on this and what
implications it might have for theories of odd-limit (or prime limit, for
that matter) consonance indexing.

regards,

dante

Dante
i ran both intervals you mentioned through the HP frequency synth.
and i cannot comment on true consonance but i agree with you that the
13/8 at 208hz sounds more pleasant to me than the 11/8 at 176hz
I really think that the context-chord,progressionwould determine the use
but I have not used them both in a single scale actually I have not used 13/8
very much at all and 11/8 only in a 11ish scale
the 13/8 has a vacant neutral feel while I think the 11/8 is expecting something
to follow it.
Pat

Rosati wrote:

> From: "Rosati" <dante@pop.interport.net>
>
> greetings-
>
> During a discussion with Paul Erlich awhile back, I mentioned that 13/8
> sounded more consonant to me than 11/8. I attributed this to 11/8 falling in
> the tritone "hump", while 13/8 sits between 5/3 and 8/5. After Paul gave us
> David Canright's new web address I was reading his "Tour up the Harmonic
> Series" (http://www.mbay.net/~anne/david/harmser/index.htm) and noticed that
> he also hears 13/8 as more consonant than 11/8. So, I was wondering how
> other distinguished ears in this forum might weigh in on this and what
> implications it might have for theories of odd-limit (or prime limit, for
> that matter) consonance indexing.
>
> regards,
>
> dante
>
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[Rosati, TD 89:]
> During a discussion with Paul Erlich
> awhile back, I mentioned that 13/8
> sounded more consonant to me than 11/8.
> I attributed this to 11/8 falling in the
> tritone "hump", while 13/8 sits between
> 5/3 and 8/5. ...David Canright...also
> hears 13/8 as more consonant than 11/8.

Me too. I don't know if more consonant is
how I'd put it, but *like* 13/8 a lot more than
11/8, at least in the context of a chord or
chord progression. It can't be a matter of
prime/odd quality either, because I just posted
earlier that 11/6 is one of my favorite "major 7th"s.
But I've always liked the sound of 13/8 in
a chord.

I think you may be right about the significance
of the place of these intervals in terms of
their categorical perception. There's quite
a variety of both "tritones" and "6ths", and
you'll find them frequently used in "standard"
harmony (I'm thinking of jazz or other styles
that use lush chords) as "13th"s and "sharp 11"S,
the "13th"s perhaps more often than the "11th"s.

BTW, a *lot* of Jamaican rappers (I think the
term is "dance hall") use 11/8 in their vocals.

- Monzo
http://www.ixpres.com/interval/monzo/homepage.html

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Rosati wrote:

>
> During a discussion with Paul Erlich awhile back, I mentioned that 13/8
> sounded more consonant to me than 11/8. I attributed this to 11/8 falling in
> the tritone "hump", while 13/8 sits between 5/3 and 8/5. After Paul gave us
> David Canright's new web address I was reading his "Tour up the Harmonic
> Series" (http://www.mbay.net/~anne/david/harmser/index.htm) and noticed that
> he also hears 13/8 as more consonant than 11/8. So, I was wondering how
> other distinguished ears in this forum might weigh in on this and what
> implications it might have for theories of odd-limit (or prime limit, for
> that matter) consonance indexing.

I agree that 13/8 sounds more consonant than 11/8. But I have to remind myself
that those brought up around 12 et would have a harder time in incorporating
this interval as it lies outside it matrix. with 7,9,13,15,17,and 19, 23 (in
dominants) we can use them in 12 tone scale much easier
-- Kraig Grady
North American Embassy of Anaphoria Island
www.anaphoria.com

This post pretends to have a connection with sound, but is really purely
theoretical. Does Onelist have means of filtering out full-frontal
mathematics so that children need not be exposed to it?

I suppose the people who like 13/8 are sure they're not really listening to
18/11. The difference between these is quite a good 13-limit comma. (1 2 0
0 -1)H-(-3 0 0 0 0 1)H=(4 2 0 0 -1 -1)H or 144/143. A lack of 13-limit
commas was mentioned before. I reckon this is the best one. 13-limit
intervals are always going to be confused with 11-limit ones, so you may as
well make it official.

The "interesting" 13-limit intervals are 13/10 and 20/13 because they're the
only "large" ones distinct from 11-limit consonances in 31-equal. They're
also the wolves. I don't have any good chords that include them, though.

>I agree that 13/8 sounds more consonant than 11/8. But I have to remind
myself
>that those brought up around 12 et would have a harder time in
incorporating
>this interval as it lies outside it matrix. with 7,9,13,15,17,and 19, 23
(in
>dominants) we can use them in 12 tone scale much easier

Is this statement going to be clarified at any point? Has it been already?

While I'm at it, I have got some ideas on graphing 11-limit intervals. The
first is to recognise 11/9 as a neutral third, and so put it in the middle
of the fifth:

A----C/---E----G/---B----D/---F#---A/---C#
/ \ / \ / \ / \ /
/ \ Gb / \ Db / \ Ab / \ Eb /
/ D# \ / A# \ / E# \ / B# \ /
/ \ / \ / \ / \ /
F----A\---C----E\---G----B\---D----F/---A
\ / \ / \ / \ / \
\ D/ / \ A/ / \ E/ / \ B/ / \
\ / F# \ / C# \ / G# \ / D# \
\ / \ / \ / \ / \
Ab---C\---Eb---G\---Bb---D\---F----A\---C

This makes sense to me melodically, but harmony's a bit odd. A complete
11-limit chord looks like this:

5
/ \
/ \
/ 7 \
/ \
4---------6---------9----11

This is the easiest way of integrating the 13-limit as well. Call 13/8 the
neutral sixth. Assuming I got the diagram above right (which I wouldn't lay
money on) the complete chord should come out like this:

5
/ \
/ \
/ 7 \
/ \
13---4---------6---------9----11

The other 11-limit lattice gives a complete chord like this:

5
/ \
/ \
/ 11
/ 7 \
/ \
4-----------6-----------9

This works with the 11-limit comma 121/120 or (-3 -1 -1 0 2)H. If you
really want your 11-limit pure, obviously neither of these lattices will do.

Note that I use octave specific matrices above. So, for your determinantsm
make (4 2 0 0 -1 -1)H into (2 0 0 -1 -1)h and (-3 -1 -1 0 2)H into (-1 -1 0
2)h. The other 11-limit comma is where twice 11/9 is the same as 3/2, or
(-1 5 0 0 -2)H=0 or (5 0 0 -2)h=0. Note also that (-3 -1 -1 0 2)H + (-1 5 0
0 -2)H = (-4 4 -1 0 0)H which is the good old syntonic comma. So, in
meantone, one of these 11-limit commas implies the other. Hence they both
work in 31-equal. Or, putting it the other way round, if you want both the
11-limit commas to work you need to be in a meantone.

Graham Breed wrote,

>The "interesting" 13-limit intervals are 13/10 and 20/13 because
they're the
>only "large" ones distinct from 11-limit consonances in 31-equal.

I have a problem with defining 13-limit intervals in 31-equal beacuse
31-equal is only consistent through the 11-limit. This means that if you
try to construct a harmonic series through the 13th partial on a
31-equal instrument, you won't be able to use the best approximations of
all 13-limit intervals that are available in 31-equal.