Yahoo Tuning Groups Ultimate Backup tuning questions about 11 and 13 limit notes

Greetings. I've been trying to understand and deal
with higher limit notes, 11 & 13 really, and I have
some questions and observations that I'd like response
about.

First off, Jon Catler's music is how I'm most familiar
with 13-limit. I'm not too familiar with other uses
of 13, or with real world uses in traditional musics.
Jon says that because partials 8-16 are nature's first
full scale, that completely supports the use of 13
prime limit. From my understanding, that's an
erroneous rational. 13-limit may be fine but at least
to my ear it has nothing to do with partials 8-16
being any sort of more significant scale than many
other lower prime scales.

As for 11-limit, my ear tells me that 11/8 is
interesting but not really particularly consonant.
I'm not sure how I'd use it, at least not against 1/1.
11/6 seems a little more usable to my ear. And then
11/9 seems very consonant and usable. In fact, my ear
says 11/9 is noticeably more consonant than any other
neutral third.
So strangely enough, my ear says that 9:11 and then
6:11 are the most usable 11-limit harmonies, does that
make sense to you guys? what are the most common uses
of 11-limit?

Now, 13-limit I don't get as much. I hear it in Jon
Catler's recordings and it sound fine, but when I go
and listen carefully to different notes, I'm not sure
what to think of 13-limit notes.

Here's one main thing: I think I'd rather have 44/27
than 13/8 because they sound almost identical to me
when compared to 1/1, at least as far as what feeling
they portray. 44/27 is the 11/9 of 4/3 and I hear
much more difference between 13/8 and 44/27 when
paired with 4/3 than I do with 1/1. I haven't found
any place where 13 seems to give me a new feeling not
already defined by another note, and somehow 13
doesn't sound really any more in-tune to me either.
What am I missing?

-Aaron

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🔗Carl Lumma <ekin@lumma.org>

Hello Aaron,

>Jon says that because partials 8-16 are nature's first
>full scale, that completely supports the use of 13
>prime limit. From my understanding, that's an
>erroneous rational. 13-limit may be fine but at least
>to my ear it has nothing to do with partials 8-16
>being any sort of more significant scale than many
>other lower prime scales.

This seems like a correct evaluation.

>As for 11-limit, my ear tells me that 11/8 is
>interesting but not really particularly consonant.

11:4 is more consonant, as in a Partchian 4:5:6:7:9:11
hexad. But 11:8 sounds good to me, too.

Usually the higher-limit harmonies benefit from the
presence of supporting lower-limit harmonies.

>I'm not sure how I'd use it, at least not against 1/1.
>11/6 seems a little more usable to my ear.

11:6 approximates a diatonic major 7th, which may be
why you find it more palpable than 11:8, which is
very foreign to our ears, or may sound like a tritone,
which is a the greatest dissonance in diatonic music.

>And then 11/9 seems very consonant and usable. In
>fact, my ear says 11/9 is noticeably more consonant
>than any other neutral third.

Neutral thirds bother me, but 11:9 is definitely the
most consonant of them.

>what are the most common uses of 11-limit?

Very little use has been made of the 11-limit in
polyphonic music. Partch, and after him Denny
Genovese, and Prent Rodgers, found 11 in the
"tonality diamond".

David Doty may have touched on 11 in one or two
tracks of his album _Uncommon Practice_. Jules
Siegel made extensive use of it, and his music may
be available through the JI Network store.

You already know about Jon Catler.

>Here's one main thing: I think I'd rather have 44/27
>than 13/8 because they sound almost identical to me
>when compared to 1/1, at least as far as what feeling
>they portray. 44/27 is the 11/9 of 4/3 and I hear
>much more difference between 13/8 and 44/27 when
>paired with 4/3 than I do with 1/1. I haven't found
>any place where 13 seems to give me a new feeling not
>already defined by another note, and somehow 13
>doesn't sound really any more in-tune to me either.
>What am I missing?

13, of the higher harmonics, especially benefits from
the presence of lower harmonics. Try playing with
different voicings and inversions of the triads and
tetrads from the otonal Partch hexad, such as 4:5:13:15,
11:13:15, 9:13:14, etc.

As for your question about 44:27, the numbers in this
ratio are too high to give it 'identity' as a "just"
dyad. It's going to be heard as a mis- or re-tuning
of some lower-numbered ratio. For example, 13:11 sounds
pretty good, but not by virtue of it being a 13-limit
harmony -- it approximates a minor third. It may
sound smoother than other nearby irrational intervals,
but it won't have a fundamentally different sound from
a minor 3rd. So with 44:27, it may be approximating a
13:8, or an 18:11, or a 5:3, or who knows. As for why
you liked it better than 13:8... who knows?

-Carl

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Aaron Wolf <backfromthesilo@y...>
wrote:
> Greetings. I've been trying to understand and deal
> with higher limit notes, 11 & 13 really, and I have
> some questions and observations that I'd like response
> about.
>
> First off, Jon Catler's music is how I'm most familiar
> with 13-limit. I'm not too familiar with other uses
> of 13, or with real world uses in traditional musics.
> Jon says that because partials 8-16 are nature's first
> full scale, that completely supports the use of 13
> prime limit. From my understanding, that's an
> erroneous rational. 13-limit may be fine but at least
> to my ear it has nothing to do with partials 8-16
> being any sort of more significant scale than many
> other lower prime scales.

agreed. how about meantone scales or other tempered ones?

> As for 11-limit, my ear tells me that 11/8 is
> interesting but not really particularly consonant.
> I'm not sure how I'd use it, at least not against 1/1.
> 11/6 seems a little more usable to my ear. And then
> 11/9 seems very consonant and usable. In fact, my ear
> says 11/9 is noticeably more consonant than any other
> neutral third.
> So strangely enough, my ear says that 9:11 and then
> 6:11 are the most usable 11-limit harmonies, does that
> make sense to you guys? what are the most common uses
> of 11-limit?

all of those are typically (well, at least by partch) taken to be
about equally consonant, but this can depend greatly on context. over
on the harmonic entropy list, we were able to provide satisfactory
answers to these questions for different people working in different
contexts. 11:9 shows up mathematically as more consonant in certain
contexts because you are basically hearing it as a combination of 5:4
and 6:5 at the same time, while the other ratios of 11 are heard with
still more ambiguity. for example, look at

/tuning/files/perlich/stearns.jpg
/tuning/files/perlich/stearns2.jpg
/tuning/files/perlich/stearns3.jpg

so for the harmonic entropy model with parameters in this particular
range, your observations are confirmed -- 11:8 most dissonant, 11:6
in-between, 11:9 most consonant.

this one, though

/tuning/files/perlich/stearns3.jpg

puts 11:9 in-between (11:8 is hard to read, as it overlaps 10:9 in
this chart) in consonance.

i find a chord like 4:5:6:8:9:11 to be very satisfying, and of course
it contains all three of the intervals you mention, 11:8, 11:6, and
11:9. 11:4 might be more consonant than all three, though.

> Now, 13-limit I don't get as much. I hear it in Jon
> Catler's recordings and it sound fine, but when I go
> and listen carefully to different notes, I'm not sure
> what to think of 13-limit notes.
>
> Here's one main thing: I think I'd rather have 44/27
> than 13/8 because they sound almost identical to me
> when compared to 1/1, at least as far as what feeling
> they portray. 44/27 is the 11/9 of 4/3 and I hear
> much more difference between 13/8 and 44/27 when
> paired with 4/3 than I do with 1/1. I haven't found
> any place where 13 seems to give me a new feeling not
> already defined by another note, and somehow 13
> doesn't sound really any more in-tune to me either.
> What am I missing?
>
> -Aaron

i've only experienced 13-satisfaction in a few compositional moments,
and then only in chords of three or more notes. for dyads, once again
i can refer you to the harmonic entropy list. i guess you need to
move on from dyads to triads and larger chords if you hope to capture
that elusive 13-feeling with whatever musical means you're currently
engaged.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> 11:6 approximates a diatonic major 7th,

or minor 7th, just as well.

> or may sound like a tritone,
> which is a the greatest dissonance in diatonic music.

well, it's the most *characteristic* or *rare* dissonance in diatonic
music, i don't know about "greatest" . . .

> Very little use has been made of the 11-limit in
> polyphonic music.

i think some of my recent acoustic guitar improvisations count as 11-
limit third-species counterpoint, except no rules are followed.

> 13, of the higher harmonics, especially benefits from
> the presence of lower harmonics. Try playing with
> different voicings and inversions of the triads and
> tetrads from the otonal Partch hexad, such as 4:5:13:15,
> 11:13:15, 9:13:14, etc.

you mean the partch "octad" or "ogdoad"? the hexad, much like the amp
on spinal tap, only goes up to 11.

🔗Carl Lumma <ekin@lumma.org>

>> Very little use has been made of the 11-limit in
>> polyphonic music.
>
>i think some of my recent acoustic guitar improvisations count as 11-
>limit third-species counterpoint, except no rules are followed.

Recordings?

>> 13, of the higher harmonics, especially benefits from
>> the presence of lower harmonics. Try playing with
>> different voicings and inversions of the triads and
>> tetrads from the otonal Partch hexad, such as 4:5:13:15,
>> 11:13:15, 9:13:14, etc.
>
>you mean the partch "octad" or "ogdoad"? the hexad, much like the amp
>on spinal tap, only goes up to 11.

Ah, yes, thanks.

-Carl

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Afmmjr@aol.com

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗David Beardsley <db@biink.com>

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>

> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> > 11:6 approximates a diatonic major 7th,
>
> or minor 7th, just as well.

But it IS a neutral 7th. Not major, not minor - neutral.
I love it melodically, I haven't used it that much in a chord.

> > or may sound like a tritone,
> > which is a the greatest dissonance in diatonic music.
>
> well, it's the most *characteristic* or *rare* dissonance in diatonic
> music, i don't know about "greatest" . . .

I'd say a m2nd is more dissonant than a tritone. Lovely honk.

* David Beardsley
* microtonal guitar
* http://biink.com/db

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗backfromthesilo <backfromthesilo@yahoo.com>

Thanks guys for answering some of my questions.

As for chordal uses of 13 that makes a lot of sense. I've found
that the overtone chord, meaning the next highest note in the
chord being of a higher overtone, is very consonant even up to
very high limits. I was examining chords of exact overtones and
using octave compression but maintiaining the natural order (not
inverting any notes). I found that beyond 31-limit still sounded
consonant. In fact straight series of overtones is quite an
awesome sound. But I really have no idea how to use that in any
other musical context. It's almost so powerful an effect that it
denies any attempt to alter it when trying to progress on to other
musical ideas.

So, outside of the context of overtone chords, 13-limit seems not
to have much more value than 17 or 19-limit, except that with
11-limit already 13 can and should be added before 17 or 19
would be. In this context 13 just emphasizes and strengthens a
chord but does not change its feel.

On the other hand, as I've said 11-limit notes seem to give new
feelings and uses otherwise unavailable.

Also I don't agree that 11/6 is approximating anything. It sounds
awful when used simply to replace the context of a different 7th.
11/9 definitely has a distinct feeling from other thirds, though I
might agree with the argument that it contains some of each of
6/5 and 5/4...

I'm still interested in further thoughts on the issue, and again
thanks for the useful insights so far.

-Aaron

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗David Beardsley <db@biink.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗czhang23@aol.com

In a message dated 2003:06:09 01:30:47 PM, Johnny R. (Afmmjr@aol.com) writes:

>I have always preferred Harmonic13 tuning, wherein each of the scale tones
is made >up of a ratio consisting of a 13 or its multiple in the ratio.

Ah! Like the scale you used on _Raven_, right 0_o? Or what exactly?

---
Hanuman Zhang, the "Yves Klein Bleu Aardvark,"
musical mad scientist (no, I don't wanna take over the world, just the sound
spectrum...)

"What strange risk of hearing can bring sound to music - a hearing whose
obligation awakens a sensibility so new that it is forever a unique, new-born,
anti-death surprise, created now and now and now. .. a hearing whose moment
in time is always daybreak." - Lucia Dlugoszewski

"The wonderousness of the human mind is too great to be transferred into
music only by 7 or 12 elements of tone steps in one octave." - shakuhachi master
Masayuki Koga

"There's a rabbinical tradition that the music in heaven will be microtonal"
-annotative interpretation of Schottenstein Tehillim, 92:4, the verse being:
"Upon a ten-stringed * instrument and upon lyre, with singing accompanied by
harp." [* utilizing new tones]

NADA BRAHMA - Sanskrit, "sound [is the] Godhead"

"God utters me like a word containing a partial thought of himself." -Thomas
Merton

LILA - Sanskrit, "divine play/sport/whimsy" - "the universe is what happens
when God wants to play" - "joyous exercise of spontaneity involved in the art
of creation"

improvisation: "a process of liberation, a working around the assumptions
that define our civilization, and the results are open-ended." - John Berndt

🔗Afmmjr@aol.com

In a message dated 6/10/03 3:37:34 PM Eastern Daylight Time, czhang23@aol.com
writes:

> In a message dated 2003:06:09 01:30:47 PM, Johnny R. (Afmmjr@aol.com)
> writes:
>
> >I have always preferred Harmonic13 tuning, wherein each of the scale tones
> is made >up of a ratio consisting of a 13 or its multiple in the ratio.
>
> Ah! Like the scale you used on _Raven_, right 0_o? Or what exactly?
>
>

You can find the tuning on scala. I did use it for the Nevermore chords of
Raven, but that was a limited use. My ex-wife used it very effectively in
several pieces that I played on. (BTW, I have these available if anyone wants to
contact me off-List...she came in from Japan and handed me 15 for sale.)

I've used Harmonic13 in a new bassoon solo, yet unplayed...called Fire.
Also, I've used extensive Harmonic17 in my string quartet Trespass.

best, Johnny Reinhard

questions about 11 and 13 limit notes

🔗Aaron Wolf <backfromthesilo@yahoo.com>

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Afmmjr@aol.com

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗David Beardsley <db@biink.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗backfromthesilo <backfromthesilo@yahoo.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗David Beardsley <db@biink.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗czhang23@aol.com

🔗Afmmjr@aol.com