Yahoo Tuning Groups Ultimate Backup tuning high third sound examples

As some of you have requested, I have compiled a series of sound files that
will (I hope) help you understand what I mean by "high third." These are all
mp3 files because they are only about a quarter the size of equivalent .wav
files. Each one is about 550k and downloads in about a minute with a 56k
modem. If anyone is interested in getting the .wav (or other) formats, I'll
be happy to email them directly (since these would put me way over my web
site limit).

In these examples, the root and/or fifth were played on my M-1 (using "solo
sax") and recorded in analog to Logic Audio on separate tracks. The thirds
are sung on an additional track while listening to the played pitches
through headphones. These individual tracks were then variously "mixed" to
create the aiff (is that right?) files that were then translated to mp3 for
posting.

Needless to say, please excuse my 65 year old diaphragm as it attempted to
hold the pitch as close to "steady" as possible. I started to edit out all
the blips, but it got a little crazy time-wise. I think it will serve to at
least give you the idea, and at best will provide enough data for those who
may wish to translate all of this to numbers. (I truly hope Paul will resist
calling it "a mess." :-)

The first file <http://home.earthlink.net/~stg3music/Rt-lo3.mp3> simply
demonstrates where I hear the 4:5 third in relation to a sounding root. When
I listened again later, it sounded a little sharp in spots, but I think its
pretty close. (I didn't measure this or any others objectively.)

The next file <http://home.earthlink.net/~stg3music/Rt-5th-lo.mp3> shows
where I think the 4:5 third would sound with both the root and fifth
sounding. To my ear, it sounds "mellow" and tends to activate a soft
"rumbling" of the common fundamental down low.

Next, the file <http://home.earthlink.net/~stg3music/Rt-5th-hi3.mp3>
demonstrates my concept of the "high third." This sounds much "cleaner" to
me than the previous example. It is also much "brighter" than the previous
example and seems easier to blend into a homogenous gestalt.

In the next file, <http://home.earthlink.net/~stg3music/Rt-ad5-adj3.mp3> I
have followed the format I used in the "college kids" item posted earlier.
It begins with the voice singing a 4:5 third above a sounding root, then
adds the fifth, causing(?) the third to move to a more "comfortable" "high
third" tuning.

The last item < http://home.earthlink.net/~stg3music/Adj3solo.mp3> provides
the "adjusting" sung third by itself in case anyone cares to measure the
amount of pitch change from the first few seconds to the last few seconds.

While these recordings are obviously done with a predetermined "result" in
mind, they do, I believe, represent what I have experienced in this regard
during my decades of working with vocal groups. This phenomenon has been
observed extensively in the tuning practices of others, many of whom who had
no knowledge of or expectation for of a "moving third."

I hope these recordings are helpful in bringing this thread to a reasonable
conclusion. Obviously, it would have been more efficient to have had these
recordings under my arm when I walked into the room; however, I explained
earlier why that didn't happen, so I won't go into it again here.

Needless to say, your reactions, perceptions and analyses are invited and
will be valuable to me in every case, no matter what your take on this may
be.

Jerry

🔗graham@microtonal.co.uk

In-Reply-To: <200003080051.QAA26494@harrier.prod.itd.earthlink.net>
Gerald Eskelin wrote

> Next, the file <http://home.earthlink.net/~stg3music/Rt-5th-hi3.mp3>
> demonstrates my concept of the "high third." This sounds much "cleaner"
> to
> me than the previous example. It is also much "brighter" than the
> previous
> example and seems easier to blend into a homogenous gestalt.

Well I never. The pitch ranges from 360 cents to around 9:7, relative to
the root.

With the lo3, the third also fluctuates up to 9:7, but dips lower to 270
cents. Yes, that's right, flat of a 6:5.

With the 5th-lo3, it's much the same, with fluctuations between 6:5 and
9:7. With both "low" thirds, the fluctuations are noticeable less then
with the "high" thirds.

Are my eyes or my Spectrogram deceiving me? The low third certainly
sounds consonant, and the high 3rd like 12-equal (not cleaner or
brighter). It seems that the human ear has a remarkable ability to
average out pitches.

Although the figures I'm giving aren't precise, they're as good as the
data. It's interesting that the extremes of vibration are close to
consonant intervals. Perhaps this could be exploited as a microtonal
effect.

The "high third" then seems to be the "low third" with the bottom end of
the vibrato cut out. Amazing that smaller fluctuations should sound less
blurred. I'd like some confirmation on this, because it's too weird to
believe.

Jerry, perhaps you should try singing live with Spectrogram running, like
I did. You might be surprised with what you see!

Graham
http://x31eq.com

🔗Gerald Eskelin <stg3music@earthlink.net>

Graham Breed wrote:
>
> Well I never. The pitch ranges from 360 cents to around 9:7, relative to
> the root.
>
> With the lo3, the third also fluctuates up to 9:7, but dips lower to 270
> cents. Yes, that's right, flat of a 6:5.
>
> With the 5th-lo3, it's much the same, with fluctuations between 6:5 and
> 9:7. With both "low" thirds, the fluctuations are noticeable less then
> with the "high" thirds.

Pretty wobbly, huh? Can't zero in on the "focus point"? Like "read my mind"?
LOL
>
> Are my eyes or my Spectrogram deceiving me? The low third certainly
> sounds consonant, and the high 3rd like 12-equal (not cleaner or
> brighter). It seems that the human ear has a remarkable ability to
> average out pitches.

Evidently so. It's also interesting to consider that the ear, while hearing
two related pitches whose wave patterns are not likely to physically line up
their common vibrations at exactly the same time, in effect "slides them
into focus" for comparison. Pretty impressive!!!
>
> Although the figures I'm giving aren't precise, they're as good as the
> data. It's interesting that the extremes of vibration are close to
> consonant intervals. Perhaps this could be exploited as a microtonal
> effect.
>
> The "high third" then seems to be the "low third" with the bottom end of
> the vibrato cut out.

It ain't vibrato, man, it just old age. :-) Seriously, vibrato would
fluctuate _much more than these fairly "straight" tones.

> Amazing that smaller fluctuations should sound less
> blurred. I'd like some confirmation on this, because it's too weird to
> believe.
>
> Jerry, perhaps you should try singing live with Spectrogram running, like
> I did. You might be surprised with what you see!

Coincidentally, I just downloaded a demo of the Spectrogram program
(Peabody-Digital) for mac. I haven't gotten into it yet and I have a
three-day convention coming up so it will likely be next week when I can do
what you suggest. But I certainly will. Thanks for the suggestion.

Thanks also, Graham, for taking the time to respond to the sound examples.

Jerry

🔗Gerald Eskelin <stg3music@earthlink.net>

🔗Carl Lumma <CLUMMA@NNI.COM>

🔗Gerald Eskelin <stg3music@earthlink.net>

> Paul Erlich wrote:
>
>> Graham, although it's true that Jerry's voice fluctuates quite a bit, it
>> does spend most of its time within a very narrow range. Is it possible
>> to
>> get some sort of histogram out of "Spectrogram"?

And Graham responded:
>
> For each frequency bin, you can get it to color according to the
> intensity. And with enough points in the transforms, you can see the
> peak. That means, as near as I can tell, the low third is at 6:5.
> There's still a few cents variation.

And an elephant is really a horse. Both of these intervals are clearly
recognizable as major thirds. The "low" major third here is miles away from
any similarity to a minor third (c.6:5). Respond, please.

> The high third example has a less clear peak.

More about "peak," please. (Perhaps I will be able to check that myself when
I get my Spectrogram up and running.)

> And when the pitch is
> relatively steady, it isn't always at the same point.

Can you clarify this? How can something be steady at different points? Do
you mean at different times? If so, at which times? If not, what?

> The variation is
> between 6:5 and the 400 cents from one such region to another. These are
> only quick calculations: it only ranges over two or three divisions.

Divisions?

I don't know, Graham. When my speedometer says 50 and I know I'm going about
80 I have the speedometer checked. There is no machine in the world that can
convince me I'm not singing variations of a major third here. Excuse me, but
I have to ask whether you are reading it correctly. If so, I suggest you
trash the program.

Your take, please.

Jerry

🔗Gerald Eskelin <stg3music@earthlink.net>

> Graham wrote,
>
>>For each frequency bin, you can get it to color according to the
>>intensity. And with enough points in the transforms, you can see the
>>peak. That means, as near as I can tell, the low third is at 6:5.
>>There's still a few cents variation.
>
>>The high third example has a less clear peak. And when the pitch is
>>relatively steady, it isn't always at the same point. The variation is
>>between 6:5 and the 400 cents from one such region to another.

And Paul Erlich responded:
>
> I sincerely hope you mean 5:4 and not 6:5 in the preceding two paragraphs.
> Otherwise, your spectrogram might need an encephalogram :)

Ha! I'll resist adding another "gram" to the list. I certainly hope to, too,
Paul. Otherwise Graham's input makes no sense.
>
> Thanks for doing the histogram, though!
>
> Anyway, it sure seems like you're saying Jerry was able to "lock" the low
> third much more accurately than he was the high third. A few cents variation
> around 5:4 is really the best you could hope for from a human vocalist.

I suspect the reason for the "security" on the low third was the " quiet
rumbling" of the fundamental assuring me that I was close. With the high
third, no such rumbling occurs, therefore there is likely more flexibility
as to the optimum placement.

In that regard, yesterday at the American Choral Directors Association
convention, I was able to hear about a half dozen of the best choirs in the
western states. Needless to say, I was taking a subjective tally of
distinctly low and high thirds in prominent locations (sustained chords,
particularly final tonic ones). Some groups used both in various contexts (I
didn't hear enough consistency to states _what contexts, although a
descending line landing on a sustained high third is a suspicious
candidate).

Not surprisingly, the most experienced group produced the most clearly high
thirds. However, a phenomenally fine children's choir of about 70 voices
often agreed on very high thirds. I doubt that the director would have
requested a particular tuning in different places. I would think the musical
context likely suggested the resulting tuning tacitly agreed upon
instinctively by the singers.

That was not the case with one excellent group of experienced singers,
however. A very fine and respected Southern California conductor, Donald
Brinegar, (whom I have watched grow from a pup) told me that he prefers the
low third and requests it from his singers. His choir specializes in
contemporary music and breathed life into every piece they sang.

I ran into Don when I first arrived and he "confessed" that he has been a
lurker on the Tuning List and has watched the "high third" discussion with
interest. He will be giving a workshop on tuning Saturday morning, so I have
to make a really hard decision as to whether I'll give up my regular golf
round and go see what he has to say. On the other hand, maybe I'll just buy
him lunch and find out later. :-)

After the afternoon set of concerts, I asked Don what he thought the ratio
of high thirds to low thirds was. He said two thirds high and one third low.
I tend to agree.

Jerry

🔗graham@microtonal.co.uk

Gerald Eskelin wrote:

> > For each frequency bin, you can get it to color according to the
> > intensity. And with enough points in the transforms, you can see
the
> > peak. That means, as near as I can tell, the low third is at 6:5.
> > There's still a few cents variation.
>
> And an elephant is really a horse. Both of these intervals are
clearly
> recognizable as major thirds. The "low" major third here is miles
away
> from
> any similarity to a minor third (c.6:5). Respond, please.

Yes, as has been guessed, 6:5 was a typo for 5:4.

> > The high third example has a less clear peak.
>
> More about "peak," please. (Perhaps I will be able to check that
myself
> when
> I get my Spectrogram up and running.)

As I said in the original message, there's a wide variation in pitch
over small periods of time. I think this is from 6:5 (definitely this
time) to 9:7. But, if you do the Fourier transform over a longer
period of time, you see a constant but blurred trace. The most
intense frequencies in that blur are colored differently, and fairly
consistently correspond to a 5:4. Which is what we would have
expected. Looks like the ear does a similar thing.

The "blurring" would presumably be interpreted by the ear similarly to
vibrato. However, it is qualitatively different. It looks like a
fractal trace, rather than a sine wave. I'd like to hotwire a synth
to emulate this. Maybe over the weekend. It must come from some
feature of the vocal chords, and is present, to greater or lesser
extent, in all the samples I've analysed that don't replace it with
gratuitous vibrato or portamento. Not that I have any kind of
statistically significant sample yet.

I don't think this is an artifact of the measuring process, as it
isn't present for synth generated sounds.

> > And when the pitch is
> > relatively steady, it isn't always at the same point.
>
> Can you clarify this? How can something be steady at different
points?
> Do
> you mean at different times? If so, at which times? If not, what?

Yes, at different times. What happens is that the trace is relatively
steady for a while, then wanders around a bit, and becomes steady
again. With the low third, it keeps hitting the same point when it's
steady. With the high third, I think there are three different steady
regions. Each is consistent, in that the average pitch is the same at
the beginning and end of the region, but the regions are not
consistent with each other. I think this is audible: I heard the
pitch rising, and the chord becoming more dissonant. I think the
computer showed the first region being 5:4, the middle around the 400
cents, and I forget for the last one. I don't have the trace open
here to check.

One interesting thing is that the blurring is actually greater for the
low third, only the peak is well defined. With the high third, the
pitch fluctuates over a smaller range, but without a clear center. At
least that's how I saw it. You can all check for yourselves.

> > The variation is
> > between 6:5 and the 400 cents from one such region to another.
These
> > are
> > only quick calculations: it only ranges over two or three
divisions.
>
> Divisions?

Should have been 5:4 again. I tend to be consistent with my errors:)
(Incidentally, I think it's far less likely that I would have called
a just major third a just minor third. Although still possible.)

Each time slice in the readout is a discrete Fourier transform at that
point. This is equivalent to a Fourier series about some low
fundamental. So you get equal divisions of frequency space. Each
point is colored to show the intensities of that range of frequencies.
Now, as I was measuring the fundamentals, the width of those
frequency ranges amounts to a few cents. So I can tell the difference
between a just and equal tempered major third, but can't tell whether
the high third is really 24:19.

🔗Gerald Eskelin <stg3music@earthlink.net>

Paul Erlich asked:
>
> So Jerry, what is your current theory as to what defines the "locking" or
> the "optimum placement" of the high third?

After the generous input from Tuning List members, and after two days of
hearing some of the best choirs in the world, I am considering the notion
that the "high third" is a very common phenomenon that results from musical
intuition and artistic preference.

-----------

> Are you giving up your notion that the high third (in
> the specific context of the major triad) is an interval of fixed size, like
> the low third which we all agree is 5:4?

Essentially, yes. Vicky McClure's extremely high third at the end of "Blue
In Green" shined a vivid light on that issue. The variety of "high thirds"
sung by various choirs at the ACDA conventions tended to settle the matter
for me.

This does not, however, answer the nagging question regarding the
"preference" of novice singers for the "high third" when the fifth is
introduced. I may simply learn to live with the mystery and go about
completing my existence in relative peace, knowing I exerted reasonable
effort to learn the "secret" of the high third. If my effort in this
regard has provoked the curiosity of someone younger who may be blessed with
keener insight, I will willingly and enthusiastically pass the baton.

Considerable thanks to all of the List members who have contributed to this
thread. Special thanks to John Link for getting me involved. Also, very much
appreciation to Paul Erlich who is at least as tenacious as I in following
up a "good story" and for not letting anyone "get away with anything." :-)

I'm also very interested in learning more about Graham's efforts in this
regard, as well as any other List members who have comments or questions. I
am still very much interested to know what the actual relative pitch was (or
pitches were) that I offered as my own "optimal" high third.

Jerry