Yahoo Tuning Groups Ultimate Backup tuning high third

Joe Monzo, responding to my earlier post, said:

> What I was trying to show
> you with the lattice was that, to an extent, even if you *do*
> hear the 'original root' (C 1/1) clearly, the relationships
> among the higher notes in the chord would make it easy for
> you to 'lock' onto the '2:3 fifth above the seventh partial',
> which would be F 21/16. Because 63/32 is present in the
> chord, you get the same 8:9:12 proportions between
> Bb 7/4 - C 63/32 - F 21/16 that you get between
> C 1/1 - D 9/8 - G 3/2.
>
An interesting observation and certainly helpful to fully understanding the
context. However, my delight was simply that the major triad that resulted
sounded quite like "my" high-third major triad (as you acknowledge below).
The fact that the fifth was easy to lock was additional to my main focus.

Monz continues:
>
> If you sang the F 21/16 correctly, which as I show above
> you probably did, because it's easy to hear, then you most
> certainly did hear the 14:18:21 'major triad with high 3rd'.

Later, responding to my quote:

>> Bottom line: If that was the 7:9 third, it sounds very close
>> to what I have been calling the "high third."

Monz said:
>
> OK. But if you're hearing 7:9 as the 'high 3rd' here, you
> should also be hearing it as the 'high 3rd' in my MIDI-file
> of your experiment, because it's exactly the same interval!
>
> I suggest that the context is playing tricks on you here.

Something is clearly playing tricks here, but I doubt very much that it has
anything to do with context. I would recognize the locked-in high-third
triad in a hurricane (don't hold me to that, please). I would think it has
more to do with the transmission and/or playing of the MIDI file. Although I
somewhat agree with your expressed preference for items 3 and 4 (if I
remember correctly), the later items (as played here) sound like something
from Mars. The pitches you identify as 7:9 in the last item on the MIDI file
sound (as played here) nothing like the 7:9 in the drone chord discussed
above--context considered.

Pending my getting some recordings posted, we could, if you like, let the
matter rest (unless, of course, a brilliant idea flashes).

Thanks,

Jerry

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

Gerald Eskelin wrote,

>Something is clearly playing tricks here, but I doubt very much that it has
>anything to do with context. I would recognize the locked-in high-third
>triad in a hurricane (don't hold me to that, please). I would think it has
>more to do with the transmission and/or playing of the MIDI file. Although
I
>somewhat agree with your expressed preference for items 3 and 4 (if I
>remember correctly), the later items (as played here) sound like something
>from Mars. The pitches you identify as 7:9 in the last item on the MIDI
file
>sound (as played here) nothing like the 7:9 in the drone chord discussed
>above--context considered.

Jerry --

While you are very convinced of the quality of your perceptions, when it
comes to how those perceptions translate into objective reality you are
clearly being fooled by several psychoacoustical illusions. There is nothing
that could make 7:9 come out right in one of Joe's MIDI files and not in
another. I've heard the files and had exactly the same reaction to them as
you. And yet I'm sure we're both hearing them correctly. That's because I've
played with these ratios extensively on my own. Yes, our ears do funny
things!

🔗Gerald Eskelin <stg3music@earthlink.net>

Paul Erlich admonished:

> Jerry --
>
> While you are very convinced of the quality of your perceptions, when it
> comes to how those perceptions translate into objective reality you are
> clearly being fooled by several psychoacoustical illusions. There is nothing
> that could make 7:9 come out right in one of Joe's MIDI files and not in
> another.

In which of Joe's files did the 7:9 come out right?

> I've heard the files and had exactly the same reaction to them as
> you. And yet I'm sure we're both hearing them correctly. That's because I've
> played with these ratios extensively on my own. Yes, our ears do funny
> things!

Okay, I agree that our ears often hear what they want to hear--particularly
when my wife is the source of the sounds. I must insist, however, that the
7:9 in the drone and the 7:9 in John's guitar chord sounded awfully fine.
Why didn't Joe's MIDI file?

I certainly respect your experience in hearing "these ratios" extensively.
Nevertheless, I learned a long time ago not to swallow something that
doesn't make sense to me--either perceptually or intellectually, or more
convincingly, both.

Okay? Ball in your court--(assuming you care to continue the game).

Jerry

🔗Gerald Eskelin <stg3music@earthlink.net>

From Paul Erlich:

> I have a suggestion that will help show that the 7:9 major third, which
> sounds like it's "from Mars" when the lower third in a major triad, sounds
> positively wonderful as the seventh and ninth of a dominant chord. I often
> perform this demonstration (or a close approximation) on my meantone piano
> and my 22-tET guitar. Hopefully, Joe Monzo or someone else will help create
> a MIDI file that will once and for all dispell all doubts that these
> intervals are really one and the same. I strongly encourage the rest of you
> to go over to your synth and try it yourself.

Okay. Lead on.

> Report back to us on what you
> hear.

Will do.

> Everyone's been strangely silent on this issue!

Silent????? Not everyone. :-)
>
> First, use 7:9 in a major triad, 7:9:10.5 (aka 14:18:21). Hold this for a
> while. Then drop out the upper voice, and introduce three lower voices,
> forming a 4:5:6:7:9 with the 7:9 held constant. Voila! The interval that was
> once so dissonant is now quite consonant.

But my synth won't play ratios--only cents. What now? Okay, I'll try it
anyway, to see if I can hear the effect you're talking about.

> What's going on here? Just another
> demonstration that context is everything. If the ear can understand the 7:9
> as the seventh and ninth partials of a clear fundamental, it is hearing
> something it is very familiar with. Almost every instrumental timbre has
> seventh and ninth partials -- though they normally go by unnoticed, they can
> be clearly heard if one focuses one's attention on them. However, in the
> triad 14:18:21, the numbers are too high to unambiguously represent familiar
> partials of a fundamental at 1, 2, 4, 8, or 16 (which would correspond to
> the _second_

the "second"? Can you use pitch names to help clarify?

> of this chord).

of what chord?

> The ear (actually the brain's central pitch
> processor) is confused -- it thinks it might be hearing a 4:5:6,

I believe I can tell the difference between a 4:5:6 and a "high third"
triad. However, I do remember the "illusion" I reported in regard to Joe's
MIDI experiment. Keep talking.

> or maybe
> 7:9:11,

which sounds roughly "augmented" to me. The 2:3 fifth is crucial to a
well-tuned major triad, I would think.

> or maybe 5:6:7;

No way! You are kidding, aren't you?

> 14:18:21 might even enter in as a weak contender

Weak????? I thought this was a high possibility in your early posts on this
subject? What changed your thinking? The Monzo MIDI file?

> if it's in a high enough register.

Why high? Midrange chords are easier to hear in tune.

> This confusion corresponds to a high degree
> of what I call "harmonic entropy", which is an important component of what
> we call dissonance.

Paul, I will do the experiment you describe (as best I can) because I
respect your opinion. But I do wonder why you have drifted from your
14:18:21 suggestion, which to me makes a great deal of sense--both
perceptually and intellectually.

Jerry

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

>> Jerry --
>>
>> While you are very convinced of the quality of your perceptions, when it
>> comes to how those perceptions translate into objective reality you are
>> clearly being fooled by several psychoacoustical illusions. There is
nothing
>> that could make 7:9 come out right in one of Joe's MIDI files and not in
>> another.

In which of Joe's files did the 7:9 come out right?

Your posts so far (and this one) seem to indicate that you thought the 7:9
sounded right in the "Young chord" file.

>I must insist, however, that the
>7:9 in the drone

Which was a MIDI file created by Joe?

>and the 7:9 in John's guitar chord sounded awfully fine.

The chord, 1/9:1/7:1/6 (aka 14:18:21), does sound fine -- I've mentioned how
sets of symaphetically resonating strings are great for utonal chords. And
how utonal chords must above all be played _quietly_. The acoustic guitar
over the phone probably fulfilled both conditions. Listening to Harry Partch
or David Canright at low levels often do too.

>Why didn't Joe's MIDI file?

The utonal chord has a beautiful configuration of overtones. But when trying
to figure out what the 1/9:1/7:1/6 chord is a set of overtones _of_, the ear
gets pretty confused -- it mainly wants to hear a 4:5:6 major triad, but the
5 (aka major third) is off by 3%. The brain's central pitch processor, which
is what provides a sensation of "pitch" at the fundamental of every overtone
series it encounters (even if the fundamental is physically absent), and
according to Parncutt provides a sensation of a "root" to chords, has an
accuracy of about 1%. So a 1% deviation from 4:5:6 (as in the 1/24:1/19:1/16
chord) is not a big threat to the clarity of the perception of a fundamental
1 below 4:5:6, while a 3% deviation threatens it greatly.

The 7:9 interval on its own is generally regarded as falling on the side of
dissonance, especially if not in a high register. The beating and roughness
of the fourth partial of the lower note against the third partial of the
upper note, and especially the fifth partial of the lower note against the
fourth partial of the upper note, tend to be excruciating. However, the
roughness seems to dissolve into a pleasant "periodicity buzz" when a 4:5:6
is placed beneath the 7:9, making for an extremely clear virtual pitch
sensation. In other words, the notes of the chord all blend into one big
note, two octaves below the 4, at 1. This latter effect is what I suggested
someone demonstrate in a MIDI file. Tones resembling Joe's oboe-like ones
would do nicely.

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

Jerry, I sense you misunderstood most of what I wrote in the post, and
perhaps a great deal of what I've written previously. Here goes.

>> First, use 7:9 in a major triad, 7:9:10.5 (aka 14:18:21). Hold this for a
>> while. Then drop out the upper voice, and introduce three lower voices,
>> forming a 4:5:6:7:9 with the 7:9 held constant. Voila! The interval that
was
>> once so dissonant is now quite consonant.

>But my synth won't play ratios--only cents. What now? Okay, I'll try it
>anyway, to see if I can hear the effect you're talking about.

Plus or minus a few cents is okay, as I'm sure Herman Miller will attest.

>> What's going on here? Just another
>> demonstration that context is everything. If the ear can understand the
7:9
>> as the seventh and ninth partials of a clear fundamental, it is hearing
>> something it is very familiar with. Almost every instrumental timbre has
>> seventh and ninth partials -- though they normally go by unnoticed, they
can
>> be clearly heard if one focuses one's attention on them. However, in the
>> triad 14:18:21, the numbers are too high to unambiguously represent
familiar
>> partials of a fundamental at 1, 2, 4, 8, or 16 (which would correspond to
>> the _second_

>the "second"? Can you use pitch names to help clarify?

If you construct 14:18:21 as a major triad on C, the fundamental would be at
around D. Remember how you tuned a C minor triad 6:7:9 and heard a
fundamental at F? Same idea.

>> The ear (actually the brain's central pitch
>> processor) is confused -- it thinks it might be hearing a 4:5:6,

>I believe I can tell the difference between a 4:5:6 and a "high third"
>triad.

Whether _you_ can tell the difference is not the issue. Of course you can
tell the difference. It's whether the central pitch processor (the brain
function responsible for giving you the sensation of that fundamental, even
if it's not really there) is the thing that's confused here.

>However, I do remember the "illusion" I reported in regard to Joe's
>MIDI experiment. Keep talking.

>> or maybe
>> 7:9:11,

>which sounds roughly "augmented" to me. The 2:3 fifth is crucial to a
>well-tuned major triad, I would think.

. . . talking about the central pitch processor . . .

>> or maybe 5:6:7;

>No way! You are kidding, aren't you?

. . . still talking about the central pitch processor . . .

>> 14:18:21 might even enter in as a weak contender

>Weak????? I thought this was a high possibility in your early posts on this
>subject? What changed your thinking? The Monzo MIDI file?

There are two misunderstandings going on here. First of all, what I'm
talking about as a "weak contender" is the ability of the central pitch
processor to hear an _actual_ 14:18:21 literally as the 14th, 18th, and 21st
partials of a missing fundamental.

Then, it seems you think I gave 14:18:21 as a likely contender for what the
major chord with high third is actually tuned like. I never did. I initially
said, and still maintain, that it is quite close to the equal-tempered major
chord.

>> if it's in a high enough register.

>Why high? Midrange chords are easier to hear in tune.

When you're including factor like eliminating beating of overtones, that is
true, but when you're just talking about the _central pitch processor_, the
optimum frequency range is high, 2-3 kHz if I recall correctly.

>But I do wonder why you have drifted from your
>14:18:21 suggestion, which to me makes a great deal of sense--both
>perceptually and intellectually.

So you did think that. No, I never did suggest that.

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

🔗Gerald Eskelin <stg3music@earthlink.net>

Paul Erlich offered:
>
> The utonal chord has a beautiful configuration of overtones. But when trying
> to figure out what the 1/9:1/7:1/6 chord is a set of overtones _of_, the ear
> gets pretty confused -- it mainly wants to hear a 4:5:6 major triad, but the
> 5 (aka major third) is off by 3%. The brain's central pitch processor, which
> is what provides a sensation of "pitch" at the fundamental of every overtone
> series it encounters (even if the fundamental is physically absent), and
> according to Parncutt provides a sensation of a "root" to chords, has an
> accuracy of about 1%. So a 1% deviation from 4:5:6 (as in the 1/24:1/19:1/16
> chord) is not a big threat to the clarity of the perception of a fundamental
> 1 below 4:5:6, while a 3% deviation threatens it greatly.

I understand the principle and have often had some fun with it by casually
playing minor third to my advanced class to which they unthinkingly respond
"major third." Clearly they are supplying the "phantom root" to the piano's
version of 5:6 and are imagining a "major triad."

I assume you are suggesting that this 3% error may explain why 7:9 is _not_
(I like this chat device. Thanks.) likely to be the "high third" we are
seeking. Right? Okay, I'm listening.
>
> The 7:9 interval on its own is generally regarded as falling on the side of
> dissonance, especially if not in a high register. The beating and roughness
> of the fourth partial of the lower note against the third partial of the
> upper note, and especially the fifth partial of the lower note against the
> fourth partial of the upper note, tend to be excruciating. However, the
> roughness seems to dissolve into a pleasant "periodicity buzz" when a 4:5:6
> is placed beneath the 7:9, making for an extremely clear virtual pitch
> sensation. In other words, the notes of the chord all blend into one big
> note, two octaves below the 4, at 1. This latter effect is what I suggested
> someone demonstrate in a MIDI file. Tones resembling Joe's oboe-like ones
> would do nicely.

I would try to tune such an interval with the synth, but I've experienced
such perceptual confusion with simple ratios like 2:3 that I doubt that I
can get anything close to a locked 7:9. Instead, I'll tune and record these
pitches vocally to a sounding (in headphones) root into my Emagic audio
program so I can hear them isolated. Perhaps that will put our conversation
on a more common ground.

Jerry

🔗Gerald Eskelin <stg3music@earthlink.net>

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

>I would try to tune such an interval with the synth, but I've experienced
>such perceptual confusion with simple ratios like 2:3 that I doubt that I
>can get anything close to a locked 7:9.

That seems bizarre to me. A 2:3 sounds perfectly fine to me up to 7 cents
flat or sharp, and even beyond that, I don't get perceptual confusion, just
roughness. I can get a 7:9 (which sounds "locked" when I use distortion to
help bring out the missing fundamental) anywhere on my 22-tone guitar -- the
fact that it's 1 cent sharp doesn't bother me in the least.

If I want to _totally_ eliminate beating, though, I would have to be within
a fraction of a cent of the just ratio. The 2:3 is 701.955� and a synth
playing a true 702� inteval is only off by .045�. To me, that indicates that
there's some other reason you're not satisfied with the synth. Even if the
synth is not really this accurate, can't you just pick the point at which
the relevant beating is slowest, and use that? You should be able to clearly
identify the cents value at which any particular beating is slowest, and so
determine, to within the accuracy of your synth, the intervals you're
looking for. No?

🔗Gerald Eskelin <stg3music@earthlink.net>

Christopher Chapman offered:

> I'd be willing to generate .WAV (or
> .AIFF, .MP3, or whatever) files of the chords in question using either
> pure sine waves or tones with harmonics that are simple sums of sine
> waves (just tell me how many harmonics you want and what decay). That
> way there should be no problem with vibrato on differing interpretations
> of General MIDI, etc.

You are an angel from heaven who has arrived at just the right dramatic
moment. (Are you the one who's on CBS Sunday nights around 8 o'clock? Guess
not. I don't think her name is Christopher. :-)
>
> If this would be of use, here's what I need to know:

Here's my opinion. I hope others will have suggestions as well.
>
> * what ratios (e.g., 4:5:6, 7:9:11, etc.)

4:5:6, at least for comparison, I would think. I don't see any need for
7:9:11, but 7:9:10.5 (14:18:21) is really important.

While we're at it, we might try finding a 6:7 (vicinity) third that "locks"
as a "minor seventh" to the 7:9:10.5 triad. There has been some reference to
needing a "high seventh" to go with the "high third."

> * pure sine vs. harmonics

Both would be nice, since Paul cited research with "sine" that may or may
not apply to "harmonics."

> * if harmonics, then how many and what decay
> (e.g. 8 harmonics, decay of 0.88 times previous amplitude)

Play with it. See what seems to facilitate "locking." Is decay going to be
helpful or distracting? I think constant loudness is better for this sort of
thing.

> * what format? (I know I can generate raw PCM, .WAV, .AIFF, and .MP3)

You're more likely than I to know what travels best and is more widely used
.
> * what base frequency? (A=440 Hz?, C=261.6 Hz?, what?)

Since our concerns are with relativity, I wouldn't think the base would
matter. Am I mistaken???
>
> [This message contained attachments]
>
I assume I didn't get them because I use the Digest form of the List?

Appreciate your offer, Christopher.

Jerry

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

🔗Gerald Eskelin <stg3music@earthlink.net>

To my post:
>
>>I would try to tune such an interval with the synth, but I've experienced
>>such perceptual confusion with simple ratios like 2:3 that I doubt that I
>>can get anything close to a locked 7:9.

Paul Erlich responded:
>
> That seems bizarre to me. A 2:3 sounds perfectly fine to me up to 7 cents
> flat or sharp, and even beyond that, I don't get perceptual confusion, just
> roughness.

I think we have a potential "moon landing" here. A 2:3 that is 7 cents off
is _not_ a 2:3. An interval within those parameters many be a "perfect
fifth" by concept, but not by a 2:3 by concept.

If the Harvard Dictionary article is correct that 2:3 is only 2-cents from
tempered and that we can't perceive such a small difference, then I'm likely
not listening to "cents" when I lock in an acoustic perfect fifth. What's
more, I can easily tell the difference between a piano fifth and a 2:3 fifth
(assuming that that's why it appears to lock). In short, if your ear seems
to tolerate a 7 cent deviation from an acoustically tuned 2:3 and it all
sounds "perfectly fine" you cannot be listening to the same 2:3 fifth I am.

When I sound a tempered fifth on the synth and then adjust the top pitch by
1-cent increments, there is no point at which I hear a locked acoustic
perfect fifth. I can, as you appear to be doing, recognize the interval as a
"perfect fifth" (in the "what is this interval" sense) as opposed to a minor
sixth or augmented fourth. (How different does a dog have to be to begin
resembling a bear? Of course, there is no perfect dog; but there is a
perfect [apparently]) fifth.

Play a simple-timbre low pitch and hum the fifth (better yet, the twelfth)
above, moving it slightly up and down until it finds "peace" (the very
bottom of Helmholtz"s "trough." There is very little (if any) room to be
moving around, particularly 7 cents worth.

I suspect that your "perfectly fine" is referring to recognition of a
"perfect fifth," not to a perceptually locked 2:3 consonance. Right? Wrong?
I'm all ears.

> I can get a 7:9 (which sounds "locked" when I use distortion to
> help bring out the missing fundamental) anywhere on my 22-tone guitar -- the
> fact that it's 1 cent sharp doesn't bother me in the least.

Perhaps you are experiencing the psychological correction you referred to
elsewhere in which the ear "improves" the tuning. In such a case, you would
"hear" the 7:9 "concept" just so long as the pitches are in that vicinity.
Your experience with 7:9 would then allow you to "hear" the implied root
even when the 7:9(?) tuning is slightly off.

I understand the principle that well-tuned intervals (apparently with
considerable deviation) will "suggest" an implied fundamental to an
experienced ear. However, such intervals can also lock acoustically (shall
we say) with the kind of precision I described above. For example, over a
sustained pitch hum a locked major third (4:5), then slide the hummed pitch
downward extremely slowly and listen to the lock points at 5:6 (implying the
third and fifth of a major triad), at 6:7 (implying the fifth and
flat-seventh of a dominant seventh chord), at 7:8 (implying the "blue"
seventh below a tonic), at 8:9 (implying tonic and supertonic).

Similarly, slide the well-tuned upper pitch of 4:5 slowly upward to lock in
a 7:9. There is a very precise spot at which it locks, just like the others.

Here is my reasoning. Please tell me (and I know by now that you will) if
this logic misfires in any way. Just as we can lock in the flat-3 when
sliding the third of a major third downward to transform the chord to minor,
I suspect that we can lock in a "high third" by sliding the 4:5 third of a
major chord upward to lock in what seems to be a 7:9 "third."

What remains of this "mystery," is to explain why singers move the 4:5 third
upward (above tempered) when the fifth is sounding. (It _always_works.)
>
> If I want to _totally_ eliminate beating, though, I would have to be within
> a fraction of a cent of the just ratio. The 2:3 is 701.955� and a synth
> playing a true 702� inteval is only off by .045�.

One can look at this to mean that "such a small difference could not
possible matter" or that "such a small difference apparently matters."

> To me, that indicates that
> there's some other reason you're not satisfied with the synth.

Let's explore that.

> Even if the
> synth is not really this accurate, can't you just pick the point at which
> the relevant beating is slowest, and use that? You should be able to clearly
> identify the cents value at which any particular beating is slowest, and so
> determine, to within the accuracy of your synth, the intervals you're
> looking for. No?

I will go directly to my synth (not bothering to pass GO) and play the game
again. Who knows? Perhaps your logical admonitions will inspire me to new
perceptions. All I ask is that you believe that I am being honest in my
reporting of what I have experienced on my own and what I have observed in
the performance and reports of others.

Later,

Jerry

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

Jerry, I did say:

>> If I want to _totally_ eliminate beating, though, I would have to be
within
>> a fraction of a cent of the just ratio.

So clearly I wasn't saying all fifths within 7� of a 2:3 sound the same to
me. I was just saying they all sound OK. If you don't like beating, then
clearly what I say above applies: you have to be within a fraction of a cent
of the just ratio.

>> 2:3 is 701.955� and a synth
>> playing a true 702� interval is only off by .045�.

>One can look at this to mean that "such a small difference could not
>possible matter" or that "such a small difference apparently matters."

>> To me, that indicates that
>> there's some other reason you're not satisfied with the synth.

>Let's explore that.

OK. Most synths that I am aware of have a true internal tuning table that
divides the octave into 512 or 768 equal parts. Cents values on the front
panel are rounded internally to one of those systems. So most likely, your
synth's "702� interval" is actually being "rounded" to 703.125� or
701.5625�. These values correspond to beat rates between the third partial
of A-440 and the second partial of the approximate E-660 of 0.9 Hz and 0.3
Hz respectively. You should be able to hear this beating clearly on your
synth (first, make sure you're using a tone with no chorus effects or
anything; then, play the chord and concentrate on hearing out the pitch of
the high E partial; then, count how many seconds it takes to beat -- about
once per second or once per three seconds?). An exact 702� would result in
two beats per minute -- not noticeable if you're only holding the interval
for 5 seconds.

>All I ask is that you believe that I am being honest in my
>reporting of what I have experienced on my own and what I have observed in
>the performance and reports of others.

Of that I have no doubt. So, have you listened to the .wav files Christopher
Chapman posted about an hour ago? What do you think?

>Here is my reasoning. Please tell me (and I know by now that you will) if
>this logic misfires in any way. Just as we can lock in the flat-3 when
>sliding the third of a major third downward to transform the chord to
minor,
>I suspect that we can lock in a "high third" by sliding the 4:5 third of a
>major chord upward to lock in what seems to be a 7:9 "third."

🔗Daniel Wolf <djwolf@snafu.de>

This touches on an important point. When an interval is sung or played on
instruments of variable pitch, there is a large amount of unsteadiness in
pitch levels. (Portamento, vibrato, chorus effects etc., whether intended or
accidental are almost inevitable). The target interval of the players is
often not really hit but passed through by the transient signals. My
impression is that in such situations, listeners, in effect, "sample" the
interval at the optimum, "locking", position.

In contrast, listeners respond to intervals played on instruments of fixed
pitch much less forgivingly because there is none of the gray area around
the intervals found with voices or variable-pitch instruments. (Personally,
if I'm going to use electronically generated sounds, I have to have the
accuracy of a Rayna or DSP, otherwise I'll stick with voices and acoustic
instruments).

Perhaps Mr. Eskelin would have much less trouble finding his desired
intervals if he were working with a pair of analog oscillators, where the
continuous frequency control would correspond more closely to his
experiences with voices.

Daniel Wolf
Frankfurt

> From: "Gerald Eskelin" <stg3music@earthlink.net>
>
> To my post:
> >
> >>I would try to tune such an interval with the synth, but I've
experienced
> >>such perceptual confusion with simple ratios like 2:3 that I doubt that
I
> >>can get anything close to a locked 7:9.

🔗David C Keenan <d.keenan@uq.net.au>

🔗Gerald Eskelin <stg3music@earthlink.net>

Paul Erlich clarified:
>
> So clearly I wasn't saying all fifths within 7� of a 2:3 sound the same to
> me. I was just saying they all sound OK. If you don't like beating, then
> clearly what I say above applies: you have to be within a fraction of a cent
> of the just ratio.

I guess I don't consider beating directly. I do understand (after reading
posts here) that to a microtonalist composer it is of considerable concern.
I guess, if you put it that way, I don't "like" beating in the sense that I
try to minimize it intuitively by seeking the most "agreeable" adjustment of
pitches under my control. But that is not to say that I don't enjoy the
delicious dissonances that result from the rub of "interestingly" (shall we
say) related pitches.

Paul, later:

>>> To me, that indicates that
>>> there's some other reason you're not satisfied with the synth.

Paul, continuing:

> Most synths that I am aware of have a true internal tuning table that
> divides the octave into 512 or 768 equal parts. Cents values on the front
> panel are rounded internally to one of those systems. So most likely, your
> synth's "702� interval" is actually being "rounded" to 703.125� or
> 701.5625�. These values correspond to beat rates between the third partial
> of A-440 and the second partial of the approximate E-660 of 0.9 Hz and 0.3
> Hz respectively. You should be able to hear this beating clearly on your
> synth (first, make sure you're using a tone with no chorus effects or
> anything; then, play the chord and concentrate on hearing out the pitch of
> the high E partial; then, count how many seconds it takes to beat -- about
> once per second or once per three seconds?). An exact 702� would result in
> two beats per minute -- not noticeable if you're only holding the interval
> for 5 seconds.

It would seem that such a fifth would certainly lock by my definition.
Therefore, I hereby solemnly swear that I will seek out this holy grail of
synthesized perfect fifths. (I hope my M-1 has read your paragraph and will
cooperate appropriately.

Paul, later:

> Have you listened to the .wav files Christopher
> Chapman posted about an hour ago? What do you think?

I have, but have not yet digested the implications. We had to leave shortly
thereafter to hear some of my singers who were performing at the "Cinegrill"
at the Hollywood Roosevelt Hotel on Hollywood Boulevard across from
Grauman's Chinese Theater (How's that for name dropping? :-) and so far
today I've done little more than grading a batch of Music Appreciation
exams. I'll try to get back to it tonight.

Jerry

🔗Gerald Eskelin <stg3music@earthlink.net>

Dave Keenan wrote:
>
> I'm glad you guys are having fun, but this thread looks like a lot of hot
> air to me.

Welcome, Dave. It's about time someone introduced some good old fashioned
honest pessimism here.

> Jerry, can you get it together to record a singer actually doing
> this, soon? And send the tape to someone who can analyse it.

Actually, Dave, I've been milking the hell out of sustaining dramatic
suspense. However, we have been dwelling too long on mere conflict. Your
contribution is most timely in that it provides a desperately needed element
of CRISIS.

The desperation was magnified last Wednesday when my recorder would not
release from automatic recording level, leaving more "fuzz" on the recording
than vocal tone. Unfortunately, I meet this group only twice a week. On
Monday I'll have to upgrade the equipment. I guess I'll unhook my Panasonic
3800 from my stack and go top-'o-the-line. At this point, I owe it to the
project.

Incidentally, the reason for waiting for the "new" choir is that they are
novice singers who have not been contaminated by "culture."

> Anyone who really thinks they are the singers are shifting from a 4:5 major
> third all the way to a 7:9 supermajor third has got to be kidding.

You have plenty of company here who share that point of view.

> My money
> is on that they are not making any significant shift when the fifth is
> introduced (say less than 2 cents), it just sounds that way.

Perhaps. We have considered that the effect may be a perceptual illusion.
Just in case, however, how much money did you have in mind?
>
> By the way, straight sawtooth waves (no envelope (organ), no filter, no
> reverb, no chorus, no vibrato) are a pretty useful standard for these kind
> of experiments. I think the amplitude of the nth harmonic is 1/n. This may
> be more realistic than 0.88^(n-1).

Many thanks, Dave, and I'm sure that others who's patience we have worn thin
will thank you as well.

Jerry

🔗David C Keenan <d.keenan@uq.net.au>

[Gerald Eskelin, TD 518.20]
>Welcome, Dave. It's about time someone introduced some good old fashioned
>honest pessimism here.
...
>Actually, Dave, I've been milking the hell out of sustaining dramatic
>suspense. However, we have been dwelling too long on mere conflict. Your
>contribution is most timely in that it provides a desperately needed element
>of CRISIS.

Hee hee! Thanks for a good chuckle, Jerry.

>> My money
>> is on that they are not making any significant shift when the fifth is
>> introduced (say less than 2 cents), it just sounds that way.
>
>Perhaps. We have considered that the effect may be a perceptual illusion.
>Just in case, however, how much money did you have in mind?

The conversion of such a small amount between Australian and US dollars would be a pain. But I promise to be real nice to you if I'm wrong. Like explain some microtonal mathematics of your choice, in detail with coloured diagrams. :-)

[Gerald Eskelin, TD 518.22]
>Wow! What a great contribution, Dave. I've been referring to the 6:7 third
>in my music theory classes as the "dinky third," and that really has no
>class at all. The term "subminor third" will allow me to regain my dignity
>as a very cool professor of music. Many thanks.

Wow! A chance to influence a real professor of music. Then you need the following list. It's essentially a translation and extension of the system of a Dutch guy named Adriaan D. Fokker who, by the way, also coauthored a paper on Relativity with Albert Einstein.

Ratio Name
----------------------------
11:12 narrow neutral second
10:11 neutral second
9:10 narrow major second
8:9 major second
7:8 supermajor second
6:7 subminor third
5:6 minor third
9:11 neutral third
4:5 major third
7:9 supermajor third
3:4 perfect fourth
8:11 super fourth
5:7 augmented fourth
7:10 diminished fifth
2:3 perfect fifth
7:11 subminor sixth
5:8 minor sixth
8:13 neutral sixth
3:5 major sixth
7:12 supermajor sixth
4:7 subminor seventh
5:9 wide minor seventh
6:11 neutral seventh
1:2 perfect octave
5:11 neutral ninth
4:9 major ninth
3:7 subminor tenth
5:12 minor tenth
2:5 major tenth
3:8 perfect eleventh
4:11 super eleventh

See http://dkeenan.com/Music/IntervalNaming.htm for more explanation (than you probably want).

Regards,

-- Dave Keenan
http://dkeenan.com

🔗Gerald Eskelin <stg3music@earthlink.net>

>> Dan Wolf suggested:
>> >
>> > Think of it this way: in pythagorean (orchestral strings are tuned in
>> > fifths) sharps are higher than flats;
>>
>> to which Jerry replied :
>>
>> In the interest of courtesy and thoroughness, I will give some more thought
>> to the idea of piled-up fifths influencing the tuning of thirds, however my
>> gut instinct is that the "solution" is more immediate than that. It seems a
>> real stretch to me to think that human ears hear in such terms.
>
and then Bob Valentine commented:

> But your own 'high third' appears AFTER a fifth is introduced. Somehow, the
> fifth influences the singers choice of third.

Bob, the topic was the _Pythagorean third, which requires that the third is
high because of the piling of four 2:3 fifths. My "demo" suggests that the
ear prefers the high third upon the sounding of _one third.

Incidentally, I mentioned recently that once conditioned to the high third a
performer can use it consistently whether or not the fifth is sounding. The
focus of my "research" here is to find out why experienced singers and
string players hear the high third as a "lock" and whether the "demo"
contains a clue in that novice ears consistently move the 4:5 third up to
the high position when the fifth is introduced.

Bob continues:
>
> Now for a few changes of subject.
>
> I'm very interested in how some of these issues
> are dealt with in the melody. For instance, singing in C, if the melody goes
> C-D-E, do you give any consideration to evening out the two 'tones?'

Everything is dependent on the prevailing harmony. If the C-D-E is sung by a
tuning-aware singer, it is the C and the E that is structural. The common
view of melody as simply "a series of pitches" is short sighted. In tonal
music, melody anchors to the prevailing harmony. I teach my students to be
aware of implied harmony as they sight read a tonal melody.

In the case you cite above, if the D is sung quickly as a passing tone, it
may or may not be treated as an 8:9, depending on the care and experience of
the singer. If the D is sustained for any appreciable duration, it is more
likely to be tuned to 8:9, I would think.

Regarding "evening out" the two steps, I have observed that beginning
students have far more trouble singing whole and half steps accurately than
singing thirds and fifths. I think the traditional method of "teaching"
scales before skips goes against the way we "naturally" perceive pitch
relationships--namely, by acoustic intervals. My beginning students have a
much easier time with 1-3-5 than with 1-2-3.

Incidentally, a tuning-aware singer can tune "acoustically" (largely by
memory and habit) when performing with a piano or guitar just so long as the
accompaniment stays off the melody line (a practice followed by any good
accompanist to allow the singer rhythmic freedom as well as tuning freedom).

> Does this
> contribut to arriving at a 'high third'?

I don't think "evening out" the steps would contribute to arriving at the
high third. I think the tuning of the E is anticipated by the singer even
before the D is sounded. However, the reverse may be true: that once the E
is imagined, the D is simply "plopped" in somewhere around the middle of the
major third.

> Similarly, in C, if the melody is
> going G-A-B, lets assume a V chord, are the 'tones' even and is the B a 'high
> third' to the G?

The same considerations would apply to the tuning of the dominant seventh
chord members.

> And how do you deal with punning? For instance, the end of the bridge to
> the song "All the Things you are" has a sustained G# which crosses from the
> key of E (where the bridge ended) to the #5 on a C7 chord and becomes an Ab
> on the F- chord which is the vi in the orginal key (Ab) that we've returned
> to. Would you interpret the "E" as Fb and the C7#5 is a C7b13???

In our (LA Jazz Choir singers) experience, pitches often "float" a bit when
chords are connected with distantly related roots. Assuming an a cappella
situation, I can imagine two scenarios. In the first, the melody's G#/Ab is
sung so forcefully that the other singers simply adjust to that pitch. Also,
a pitch-aware singer(s) might purposefully sing the the G# in a "low third"
tuning, remembering where the original key was, anticipating the Ab needed
for the return.

In the second scenario, the singers collectively compromise (including the
lead line), intuitively locking the modulatory chord (C7#5/C7b13) to the
destination tonality. In this case the G# might "float" into the Ab as the
ensemble moves back to the original key. Fortunately for them, singers and
string players don't have to make these decisions consciously, as
microtonalists clearly must. By some miracle they manage to end up in the
same key they started in. (Elsewhere, I described the 2.5 minutes of a
cappella "Midnight Sun," a highly chromatic song, that held tonic _every
time it was sung. I would love to post it but that much music would be a
very large file and I'm over my Earthlink limit.)

I hope this is helpful, Bob. Remember, it is simply my opinion based on
considerable experience and some knowledge of acoustics and music theory and
is not offered as "Truth."

Jerry

🔗Carl Lumma <CLUMMA@NNI.COM>

>>I saw a post on Usenet recently where somebody said that parallel major
>>thirds increase the tension.
>
>Parallel _major_ thirds would be a very non-diatonic phenomenon (q.v. _Close
>to the Edge_ by Yes) and increase tension due to its borrowing from distant
>keys.

Woohoo!

>In normal music, thirds are hidden away inside chords. For virtually all
>music written since the demise of meantone, this is true.

Uh? What about melodies harmonized in thirds? 6ths are maybe more common,
but....

>As I mentioned to some members off-List, I guess I had initially assumed
>that many here would have already experienced the "high third" phenomenon.
>It soon was clear that most of the members approach tuning from a
>historical/keyboard point of view and that this was not the case.

Jerry, I've sung in choirs for years, and I'm sure I've sung many thirds
sharper than any interval you'd care to name... but I can't say I have ever
noticed a "pull" for harmonic major thirds other than 5/4. If the
phenomenon is as common as you claim, a decent sound file, in wav format,
shouldn't be too hard to procure? As for the 24:19 theory, can anyone
create a sound file, with any combination of timbres and volumes, in which
this chord even remotely sounds "locked"? I doubt it.

-Carl

🔗Gerald Eskelin <stg3music@earthlink.net>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Carl wrote,

>As for the 24:19 theory, can anyone
>create a sound file, with any combination of timbres and volumes, in which
>this chord even remotely sounds "locked"? I doubt it.

Locking is a relative thing. If you're holding a fifth and moving the third
around, you will notice greater and lesser degrees of locking at different
intervals, as lower or higher harmonics become beatless. If you just play a
triad with a given third, it's hard to know whether it's locked or not,
since in addition to the beatless harmonics, there will be many beating
ones. I think it would be possible with some timbres, if one consciously
listens to the harmonic four octaves above the fifth, to tune a
1/24:1/19:1/16 triad by ear. When experimenting with dyads using sawtooth
waves, I recorded all intervals at which I heard a "lock" and the most
complex was 17:13. With triads, I suspect higher numbers (maybe as high as
24) could enter the picture. Ken Wauchope reported tuning ratios with
numbers up to 24 (those with numbers 19-24 he termed "difficult") in his
careful listening experiments.

If Jerry is right and singers produce locked triads with just fifths, but
major thirds significantly higher than 12-tET, then this seems like the best
candidate for an explanation. If the "locking" is illusory, but the
sharpness relative to 12-tET is real, then perhaps a Pythagorean explanation
based on some sort of extended reference via imagined tones is a possible
hypothesis that can be entertained. I'd be very skeptical, though.

🔗Gerald Eskelin <stg3music@earthlink.net>

To my comment:

>>As I mentioned to some members off-List, I guess I had initially assumed
>>that many here would have already experienced the "high third" phenomenon.
>>It soon was clear that most of the members approach tuning from a
>>historical/keyboard point of view and that this was not the case.

Carl Lumma responded:
>
> Jerry, I've sung in choirs for years, and I'm sure I've sung many thirds
> sharper than any interval you'd care to name... but I can't say I have ever
> noticed a "pull" for harmonic major thirds other than 5/4. If the
> phenomenon is as common as you claim, a decent sound file, in wav format,
> shouldn't be too hard to procure? As for the 24:19 theory, can anyone
> create a sound file, with any combination of timbres and volumes, in which
> this chord even remotely sounds "locked"? I doubt it.

I'm very much aware that not many choirs even attempt to sing anything but
key-board influenced tuning. Most singers and amateur choir directors don't
even know there is an alternative. That's _why I wrote "Lies My Music
Teacher Told Me." The main idea there is simply to inform singers to not
expect the keyboard to supply "best" vocal tunings.

The question of a "high third" would only arise in the context of
consciously seeking the "best" tuning for a major triad. With that in mind,
I will post some "home-made" demos next week in which I'll try to sing a
high third in what I hear as a locked position. We'll see what happens. At
this point, I really don't care what the outcome is. If this whole thing
turns out to be acoustic b---s---, I'll be just as happy (almost) as if we
discovered a mind-blowing mathematic explanation for this observable
phenomenon. At least, I can then confidently start looking in some other
place for an answer (if I still care enough to carry on the quest).

Incidentally, I'm not proposing that singers _should_ favor the high third
over a 5/4 third. I'm only reporting that many _do_ seem to favor it. I'm
just curious as to why. Paul seems to favor "cultural conditioning." Who
knows? I may join him. We'll see.

Thanks for your response,

Jerry

🔗Carl Lumma <CLUMMA@NNI.COM>

>I'm very much aware that not many choirs even attempt to sing anything but
>key-board influenced tuning. Most singers and amateur choir directors don't
>even know there is an alternative. That's _why I wrote "Lies My Music
>Teacher Told Me." The main idea there is simply to inform singers to not
>expect the keyboard to supply "best" vocal tunings.

That's a very important message to get across. Between my high school,
college, and barbershop experiences, however, I've never been asked to sing
along with a piano, in rehearsal or on stage. And I've never noticed
(although I haven't looked for it) a "high" harmonic major third.

>The question of a "high third" would only arise in the context of
>consciously seeking the "best" tuning for a major triad. With that in mind,
>I will post some "home-made" demos next week in which I'll try to sing a
>high third in what I hear as a locked position.

Cool!

>I'm just curious as to why. Paul seems to favor "cultural conditioning."
>Who knows? I may join him. We'll see.

I certainly don't think cultural conditioning is a factor. It is my strong
suspicion that there's a conditioning effect, but that it's only
short-acting, based on the music you've heard in the last hour or so. An
interesting experiment would be to record a famous work in both just and
tempered intonation, and then play it for different groups, and then ask
them to sing it back into a mic, subject it to pitch-tracking, and see what
attracts what. A control group could attempt to sing the song without
hearing it first.

I once met a pianist with absolute pitch who claimed to prefer 12-tet. But
when I played him something in meantone he didn't even notice! His sense
of absolute pitch was fantastic, however, at least at the piano (he could
"play" all kinds of noises, identify notes with his back turned, etc).

In general, if you listen to orchestras and choirs, they are no where near
12-tone. Orchestra intonation is usually terrible, even in the best
orchestras, but when it's good the results are fantastic.

-Carl

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Carl wrote,

>It is my strong
>suspicion that there's a conditioning effect, but that it's only
>short-acting, based on the music you've heard in the last hour or so.

Why don't you think long-term learning plays an equally strong role? The
mechanics of singing (or fingering on a string instrument) would certainly
be subject to long-term training phenomena. Pronunciation in speech is much
more dependent on long-term experience than on the last hour of exposure.
Why would intonation in singing be any different? I doubt many Western
singers could be trained to sing Arabic scales in one hour!

>I once met a pianist with absolute pitch who claimed to prefer 12-tet. But
>when I played him something in meantone he didn't even notice!

That's a pretty common reaction. A violinist roommate who I subjected to a
Mac playing Bach in various tunings thought the meantone (31-tET) sounded
in-tune but was disturbing due to _lacking_ a certain comfortable "noise"
associated with 12-tET (probably the off-key combination tones of 12-tET).
He thought Pythagorean and 19-tET versions were out-of-tune, and of course
12-tET was in-tune.

At least for Bach, bare fifths are so rare than 31-tET does not offend even
very sensitive ears.