Yahoo Tuning Groups Ultimate Backup tuning the 'high 3rd'

I've been intrigued by the observation Jerry Eskelin
made that singers intuitively sing a 4:5 'major 3rd'
[= ~386 cents] with the 1/1 'root' [= 0 cents] alone,
but that when a 2:3 '5th' [= ~702 cents] is added to
this dyad to make a complete 'major triad', the 'major 3rd'
slides upward in pitch until it is larger than the
12-tET/12-EDO 'major 3rd' [= 2^(4/12) = 400 cents].

Several different possibilities have been suggested
for this 'high 3rd' in the ongoing discussion of it here
over the past few weeks, including 64:81 [= ~408 cents],
19:24 [= ~404 cents], and 7:9 [= ~435 cents]. The
7:9 has been pretty much rejected as not one that is
likely to be instinctively accepted as a smooth consonance.

I've made a MIDI file of some possibilities for this
'high 3rd', with some interesting results.
http://www.ixpres.com/interval/td/monzo/high3rd.mid

The chord is sequenced like the old Three Stooges
'hello hello hello' routine: in 4/4 time, the ratios
1/1 on the first beat, 5/4 on the third, and 3/2 on the
first beat of the second measure, with pitch-bend applied
continuously to the 5/4 between the first and second beats
of the second measure to create a glissando up to the target
'high 3rd'. Here are the possibilities I used:

1) m1-2 The 4:5 is held thru the entire chord.
I agree with Jerry that it doesn't sound like what
singers normally do.

2) m3-4 The 4:5 slides upward to 64:81.
This was the one that I thought would have sounded
the smoothest, based on the numerics of the ratios.
Not bad, but (surprisingly) to my ears not the best;
it sounds like it goes a little too sharp.

3) m5-6 The 4:5 slides upward to 2^(4/12).
To me, surprisingly, this was a close second-best.
Perhaps the role of cultural conditioning plays
a stronger part than we realize.

4) m7-8 The 4:5 slides upward to 19:24.
Most surprisingly of all, this possibility suggested
by Paul Erlich turned out to be the smoothest to my ears.

5) m9-10 The 4:5 slides upward to 11:14.
This one sounds pretty good to me, but a little too sharp.

6) m11-12 The 4:5 slides upward to 25:32.
This one definitely sounds too sharp to me,
which would certainly rule out 7:9.

I've asked John Starrett to make an mp3 of this,
so that if you have a lousy soundcard on your computer
(which makes the MIDI sound lousy) the mp3 will at
least sound as good as what I have. I use a Creative
Labs (i.e., Soundblaster) AWE64Value soundcard, and used
the General MIDI 'Choir Ahs' patch.

Feedback definitely wanted.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

________________________________________________________________
YOU'RE PAYING TOO MUCH FOR THE INTERNET!
Juno now offers FREE Internet Access!
Try it today - there's no risk! For your FREE software, visit:
http://dl.www.juno.com/get/tagj.

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

🔗John Link <johnlink@con2.com>

>From: Joe Monzo <monz@juno.com>
>
> The 7:9 has been pretty much rejected as not one that is
>likely to be instinctively accepted as a smooth consonance.

It sounded pretty good on my guitar, and when I played it over the phone
for Jerry he thought that I had found the third that he has been reporting.

>6) m11-12 The 4:5 slides upward to 25:32.
>This one definitely sounds too sharp to me,
>which would certainly rule out 7:9.

Not necessarily. Although 25:32 may sound too sharp, maybe it's not sharp
enough! Would it be possible for you to include the 7:9? I'd like to be
able to hear it side-by-side with the others.

Thanks for putting this together.

John Link

****************************************************************************

Watch for the CD "Live at Saint Peter's" by the JOHN LINK VOCAL QUINTET,
featuring original compositions as well as arrangements of instrumental
music by Brahe and Taylor, Chick Corea, Miles Davis, Claude Debussy, Bill
Evans, Ennio and Andrea Morricone, Modeste Mussorgsky, Erik Satie, and Earl
Zindars.

****************************************************************************

Check out WWW.DUESBERG.COM for information that could make the difference
between life and death for you or someone you know.

****************************************************************************

🔗Joe Monzo <monz@juno.com>

> [Paul Erlich, TD 493.14]
> Thanks for doing this Joe. However, I have to view your
> conclusions with suspicion since I heard a large amount
> of vibrato when I played this file. Did you listen to it
> with or without vibrato? Can you eliminate the vibrato
> in the file?

Hmmm... I specifically chose the General MIDI 'Choir Ahs'
patch because on my system it was the human voice sound
with the least vibrato. There has been no vibrato added
to the file, so I can't remove any. The vibrato you're
hearing must be built into your soundcard's sample.

Hopefully John Starrett will be able to make an mp3 of this
so you can hear it as I do.

>> [me, monz]
>> 2) m3-4 The 4:5 slides upward to 64:81.
>> This was the one that I thought would have sounded
>> the smoothest, based on the numerics of the ratios.
>
> Again, I beg you to reconsider your prime-oriented thinking.
> At least as far as "smoothness" is concerned, prime limit is
> _irrelevant_.

I wasn't thinking that 64:81 would be more consonant because
of any prime-oriented thinking; it was simply that I thought
there was more of a numerical 'lock' between 81/64 and 3/2
because they both have the same factors in their numerators
and denominators.

I've long since convinced myself that prime-limit is irrelevant
to 'consonance', altho I do still believe that it is important
with regard to 'affect' (or at least 'perceived affect', in
the case of intervals with *other* prime-limits that sound like
certain recognizable ones).

> [John Link, TD 493.15]
>> [me, monz]
>> The 7:9 has been pretty much rejected as not one that is
>>likely to be instinctively accepted as a smooth consonance.
>
> It sounded pretty good on my guitar, and when I played it
> over the phone for Jerry he thought that I had found the
> third that he has been reporting.
>
>> [me, monz]
>> 6) m11-12 The 4:5 slides upward to 25:32.
>> This one definitely sounds too sharp to me,
>> which would certainly rule out 7:9.
>
> Not necessarily. Although 25:32 may sound too sharp, maybe
> it's not sharp enough! Would it be possible for you to include
> the 7:9? I'd like to be able to hear it side-by-side with the
> others.

Yes, perhaps I had made a hasty decision, since I have no
idea what Jerry's 'high 3rd' sounds like.

I've added another rendition of the chord to the end of the
MIDI file, with a glissando from 4:5 to 7:9.

http://www.ixpres.com/interval/td/monzo/high3rd.mid

(John Starrett: if you're making an mp3 of this, use THIS one.)

-monz

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

Joe Monzo wrote,

>>I wasn't thinking that 64:81 would be more consonant because
>>of any prime-oriented thinking; it was simply that I thought
>>there was more of a numerical 'lock' between 81/64 and 3/2
>>because they both have the same factors in their numerators
>>and denominators.

I wrote,

>Of course you mean the same _prime_ factors; hence this _is_ prime-oriented
>thinking!

Now for something more constructive. The interval between 81/64 and 3/2 is
32:27. So how well do the two ratios lock? Well, (a) the 32nd harmonic of
one coincides with the 27th harmonic of the other. Not very convincing --
these harmonics are normally very weak. (b) they represent the 32nd and 27th
harmonics of a virtual fundamental created by the brain's central pitch
processor. Again, not very convincing, as a "best fit" virtual fundamental
treating these as the 6th and 5th harmonics, as well as one treating them as
the 19th and 16th harmonics, would be heard far more strongly.

Primarily, what matters is the size of the numbers 32 and 27. They are both
quite large. Hence, the "lock" between 3/2 and 81/64 is quite weak.

🔗Joe Monzo <monz@juno.com>

>> [me, monz, TD 493.13]
>> The 7:9 has been pretty much rejected as not one that is
>> likely to be instinctively accepted as a smooth consonance.

> [Jerry Eskelin, TD 496.5]
> Really??? I thought it sounded pretty good when John Link
> played "it"(?) on his guitar over the phone. Are we talking
> about the same interval? Perhaps John has a comment.

John has already responded to this:

> [John Link, TD 493.15]
> It sounded pretty good on my guitar, and when I played it
> over the phone for Jerry he thought that I had found the
> third that he has been reporting.

You should read that whole message; you'd be interested in it.

> [Jerry, TD 496.5]
> It's a little difficult to evaluate the target tunings since
> these sustain for only a short time. Would it be convenient
> to add a beat or two to each item to let the target tuning
> sustain a bit longer? Does your software allow
> for this without redoing the whole set up?
>
> Also, I agree with Paul that it would help "fine tune" the
> experiment if the vibrato could be eliminated. "Straight"
> tone is easier to tune (as well as evaluate for tuning).

That exactly the problem with using MIDI for audio examples
on the wwweb: what you hear on your end when you create the
file is likely to be radically different from what others
hear on their equipment.

I've prolonged each chord for an extra 4 beats, and
changed the patch to General MIDI 'English Horn'. It
still has vibrato, but less than any other appropriate
sound I could find (i.e., excluding organ patches,
which timbre would be totally inappropriate for this
experiment concerning human voices).
http://www.ixpres.com/interval/td/monzo/high3rd.mid

> The last two are so high they sound more like sus chords
> than major triads.

Yes, I agree with that. Of course context plays a role
here too. If the 1/1 - 32/25 - 3/2 chord were heard in
a different context, with the '3rd' right on 32/25 rather
than rising from the previous 5/4, it may sound more
like a 'major' triad.

> Certainly the 7:9 third, which sounds nothing like a
> perfect fourth, is not as high as these.

On the contrary, 7:9 [= ~435 cents] is noticeably higher
(in this context, speaking of intervals, one should really
say 'wider') than both 11:14 [= ~418 cents] and 25:32
[= ~427 cents].

> There are 7 items on your sound example and only 6 described here.
> What did I miss?

By the time you heard it, I had already updated it to
include 4:5 rising to 7:9, as requested by John Link
in TD 493.15.

>> [Paul Erlich, TD 493.22]
>> Even chords like 14:18:21 might take their place in a
>> new melodic/harmonic vocabulary that is divorced from the
>> familiar styles that have arisen over the last few hundred
>> years (for example, Margo Schulter has suggested using this
>> chord in a Xeno-Gothic context where the major third
>> (in this case tuned 7:9) typically resolves outward into
>> a perfect fifth).
>
> [Jerry Eskelin, TD 496.16]
> As in the chromatically adjusted Landini cadence, I presume?
> A historically unique form of "dominant"/tonic progression,
> to be sure. I can imagine the 7:9 third in this context with
> its "raised four" tugging anxiously toward the final chord
> fifth.

I think this is an excellent example of an historical usage
where 7:9 might be appropriate.

-monz

🔗Paul H. Erlich <PErlich@Acadian-Asset.com>

🔗Joe Monzo <monz@juno.com>

> [John Link, TD 500.2]
> I've been following the posts about the high third and
> unfortunately with my ancient equipment the samples that
> Joe put up play on my computer but they all sound the same,
> since there is no sliding up of the third! That's why I
> haven't put in my two cents about my impressions.

Unfortunately, as I've already noted several times, what
you hear in any MIDI-file is entirely dependent on how your
system is configured. (This is not the case with .mp3,
.wav, or Real-Audio, where you get what the creator of
the file actually recorded.)

It sounds to me like your particular problem is that your
pitch-bend settings are not having any effect.

There are a couple of places on the web where you can
download a very short MIDI-file that you can use to test
your pitch-bend settings. I think John deLaubenfels's site
is one, and IIRC Mark Nowitzky's is another. To play my
files correctly, you have to make sure that your pitch-bend
is set for 4096 pitch-bend units = 1 semitone.

> Based on what everybody else has reported, if the 9/7 is
> actually as high as Joe has it

A 9/7 is as high as it is - it has nothing to do with
what I do or don't do. It's slightly over 435 cents, period,
which makes it a larger interval than any of the other
'high 3rds' in my MIDI-file.

> then it is probably the case that my guitar experiment
> wasn't quite right, maybe due to old strings with inharmonic
> overtones. Tonight I did the guitar experiment again and
> used my tuning meter to measure the number of cents in the
> interval between 5/4 and 9/7 and between 9/7 and 4/3.
>
> Here are my results:
>
> 9/7 to 4/3 = 65 cents
>
> 4/5 to 9/7 = 50 cents
>
> According to my copy of Helmholtz the numbers should be
> 63 and 49.

Here's an accurate account:

(4/3) / (9/7)
= (4/3) * (7/9)
= 28/27
= ~62.96090365398 cents

In the second example, you meant '5/4 to 9/7'.

(9/7) / (5/4)
= (9/7) * (4/5)
= 36/35
= ~48.77038122719 cents

(Of course, the cents values are non-repeating irrational
decimal numbers, so even taken to 11 decimal places they're
still approximate, thus the ~ .)

I don't know if there are standard accepted names for these
septimal intervals, but they should both be referred to as
types of diesis, one large and one small (or 'major' and
'minor' if you prefer). They pop up all the time in
7-limit JI music.

> So I conclude that I have correctly tuned 9/7 on my guitar.

OK, I wasn't there when you played it, so I can't argue
with you about that. But 7:9 is *still* the widest '3rd'
in my experiment, and can be heard clearly as such on
my equipment and on that of others who have responded here.

> The triad that I formed including the 9/7 clearly does not
> sound like a suspended chord.

I also can't argue with that. Paul Erlich and I have both
noted in this thread that context has a lot to do with
*how* a chord or interval is perceived.

In this experiment, which I attempted to fashion exactly
the same way Jerry Eskelin explained his observations,
I start from the 4:5 in every case and glissando *up* to
the target 'high 3rd'. Under these conditions, I'm not
surprised that the 'high 3rds' that go beyond the 64:81
'Pythagorean 3rd' start sounding like suspended '4ths'.

As Paul noted, if the target pitch came after a *real*
'4th' (that is, the higher note first, then the lower),
it would very likely be perceived as a '3rd', even if
it is a very wide one like 7:9.

I suppose the only way to solve the puzzle once and for
all is for Jerry to have his singers perform the experiment,
and record each note on a separate track of a multi-track
recorder, so that a spectrogram analyzer can be used on
the track with the 'high 3rd'. Then we'll know *exactly*
what's going on mathematically.

-monz

🔗genewardsmith@juno.com

🔗Paul Erlich <paul@stretch-music.com>

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_7880.html#27354

> --- In tuning@y..., genewardsmith@j... wrote:
> > --- In tuning@y..., johnlink@c... (John Link) wrote:
> > > >From: Joe Monzo <monz@j...>
> >
> > > > The 7:9 has been pretty much rejected as not one that is
> > > >likely to be instinctively accepted as a smooth consonance.
> >
> > > It sounded pretty good on my guitar, and when I played it over
> the
> > phone
> > > for Jerry he thought that I had found the third that he has
been
> > reporting.
> >
> > What is and isn't smooth is a relative matter, but the supermajor
> > third is audible as a consonance of a kind.
>
> I agree, but how about in a major triad, which was the context of
> this (very old) discussion?

Now that we bring up this old chestnut again, I want to say that I
noted that in Brian McLaren's book, _Microtonality, Present, Past,
Future, To Eternity_ or whatever he modestly calls it, there is a
statement that researchers found that many subjects actually prefer a
major third wider than just...

Did you ever read this McLaren work?? (I can surely understand why
some people might not! :) )

______________ _____________
Joseph Pehrson

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> /tuning/topicId_7880.html#27354
>
> > --- In tuning@y..., genewardsmith@j... wrote:
> > > --- In tuning@y..., johnlink@c... (John Link) wrote:
> > > > >From: Joe Monzo <monz@j...>
> > >
> > > > > The 7:9 has been pretty much rejected as not one that is
> > > > >likely to be instinctively accepted as a smooth consonance.
> > >
> > > > It sounded pretty good on my guitar, and when I played it
over
> > the
> > > phone
> > > > for Jerry he thought that I had found the third that he has
> been
> > > reporting.
> > >
> > > What is and isn't smooth is a relative matter, but the
supermajor
> > > third is audible as a consonance of a kind.
> >
> > I agree, but how about in a major triad, which was the context of
> > this (very old) discussion?
>
>
> Now that we bring up this old chestnut again, I want to say that I
> noted that in Brian McLaren's book, _Microtonality, Present, Past,
> Future, To Eternity_ or whatever he modestly calls it, there is a
> statement that researchers found that many subjects actually prefer
a
> major third wider than just...

Yes, this is exactly what this "high 3rd" discussion was all about --
but the major third in question was about 404 cents, not anywhere
near the 435-cent value of the 9:7 interval.

Clearly the preference for this interval is the result of some
aesthetic shifts in our musical culture in the 18th century and
thereafter.

But "researchers" found many, many things -- depending on who
the "subjects" were and how "prefer" was defined . . . the "nutty
professor" likes to take 0.01% of the research and make it seem all-
important, even if it contradicts other research that he's cited in
arguments on different subjects. For example, are you familiar with
the Mathews and Roberts study on what "subjects" "prefer" with regard
to major triads?

🔗jpehrson@rcn.com

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_7880.html#27366

> --- In tuning@y..., jpehrson@r... wrote:
> > --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> >
> > /tuning/topicId_7880.html#27354
> >
> > > --- In tuning@y..., genewardsmith@j... wrote:
> > > > --- In tuning@y..., johnlink@c... (John Link) wrote:
> > > > > >From: Joe Monzo <monz@j...>
> > > >
> > > > > > The 7:9 has been pretty much rejected as not one that is
> > > > > >likely to be instinctively accepted as a smooth consonance.
> > > >
> > > > > It sounded pretty good on my guitar, and when I played it
> over
> > > the
> > > > phone
> > > > > for Jerry he thought that I had found the third that he has
> > been
> > > > reporting.
> > > >
> > > > What is and isn't smooth is a relative matter, but the
> supermajor
> > > > third is audible as a consonance of a kind.
> > >
> > > I agree, but how about in a major triad, which was the context
of
> > > this (very old) discussion?
> >
> >
> > Now that we bring up this old chestnut again, I want to say that
I
> > noted that in Brian McLaren's book, _Microtonality, Present,
Past,
> > Future, To Eternity_ or whatever he modestly calls it, there is a
> > statement that researchers found that many subjects actually
prefer
> a
> > major third wider than just...
>
> Yes, this is exactly what this "high 3rd" discussion was all about -
-
> but the major third in question was about 404 cents, not anywhere
> near the 435-cent value of the 9:7 interval.
>
> Clearly the preference for this interval is the result of some
> aesthetic shifts in our musical culture in the 18th century and
> thereafter.
>
> But "researchers" found many, many things -- depending on who
> the "subjects" were and how "prefer" was defined . . . the "nutty
> professor" likes to take 0.01% of the research and make it seem all-
> important, even if it contradicts other research that he's cited in
> arguments on different subjects. For example, are you familiar with
> the Mathews and Roberts study on what "subjects" "prefer" with
regard
> to major triads?

Well... was that the one where it ended up that there were two
different sets of listeners?? A "rich" set, or such like, that
prefered wider intervals and a "just" group that liked just ones??

__________ ________ ___________
Joseph Pehrson