Yahoo Tuning Groups Ultimate Backup tuning 7th harmonic in 45/32

--- In tuning@yahoogroups.com, Brad Lehman <bpl@...> wrote:

>
> Please go tune a real virginal that happens to be weak in any harmonics
> beyond the sixth, like the one I have right here in my office.

That's Our Boy Brad, again, showing his penchant for sweeping
generalizations and jumping to conclusions based upon his own purely
subjective experience. It's what endears him so to those of us who
have tried to get him to be a bit more scientific in the past, not
because we've got any ax to grind, but more so because Brad's
observations, which are often of value, would be so much more
compelling if they were free of this subjective mucking about.

I doubt Brad has ever actually done FFT analysis of a real harpsichord
to actually KNOW which harmonics are present or not, because if he
had, he wouldn't say such things. Harpsichords, like most closed box
instruments (violins, guitars, and the like), have pretty strong
formants which can color the sound significantly, meaning that, just
as with the voice, you can't speak of a spectrum which remains
constant from note to note. Instead you have fairly fixed resonance
peaks which filter the sound of each note differently, depending upon
how the frequencies of the partials line up with the instrument's
resonant frequencies. Thus sometimes the 7th is indeed absent, other
times it is very strong. So whether or not an interval which depends
upon higher harmonic congruence would beat or not depends on which
instrument you play it on and precisely where on the instrument. Other
things such as pitch level and even the weather can change things
subtly (a crowned or flat soundboard changes its response).

Anybody who wants to try it can mossy on over to the wonderful
resource run by some colleagues of mine here in Barcelona, the
Freesound audio bank:

http://freesound.iua.upf.edu/

Search for Harpsichord, and about halfway down the first page, the
samples begin with clav056, which is note 56, and descend by major
thirds until note 2. Granted, with the small number of notes available
here, you can't draw any real conclusions about the instrument
acoustical "fingerprint", but it's enough to see that there are areas
of resonance and damping which remain pretty constant within
registers. Run those through any good FFT/spectrogram software, and
see what you get.

Now, all that said, it IS true that even when upper partials are
lacking, you can get "strong" sounds which appear and disappear with
subtle tuning changes in intervals like a tritone. Haven't dug into it
enough to be able to describe exactly what is going on, nor do I want
to, 'cause I've got more pressing matters to attend to and I'll be my
bottom dollar that it simply has to do with summing and difference
tones. However, this "strongness" certainly will NOT be consistent
over the entire range of the instrument (as the spectral mix is
changing all the time), nor will it be consistent from instrument to
instrument. And in any case, it is most definitely not "pure" in the
normal sense of the word, as it has nothing whatsoever to do with the
absence of beating between congruent overtones which normally defines
a pure interval.

So I would say that Brad IS hearing something, he just doesn't know
what it is nor does he have a terminology to use for it (the one flows
from the other, logically, of course), so he grabbed the thing that
seemed best suited in the moment. Which may not have been the best
choice, since it makes him SEEM stupid, as though he doesn't know what
the acoustical basis for "purity" as it is normally understood is.

Ciao,

🔗Carl Lumma <carl@lumma.org>

> I doubt Brad has ever actually done FFT analysis of a real
> harpsichord to actually KNOW which harmonics are present or
> not, because if he had, he wouldn't say such things.
> Harpsichords, like most closed box instruments (violins,
> guitars, and the like), have pretty strong formants which
> can color the sound significantly, meaning that, just
> as with the voice, you can't speak of a spectrum which
> remains constant from note to note. Instead you have fairly
> fixed resonance peaks which filter the sound of each note
> differently, depending upon how the frequencies of the
> partials line up with the instrument's resonant frequencies.

Have any spectrograms to show? I doubt this is a very
significant effect with harpsichords.

> Thus sometimes the 7th is indeed absent,

Really? Have any evidence of this?

> So whether or not an interval which depends upon higher
> harmonic congruence would beat or not depends on which
> instrument you play it on and precisely where on the instrument.

45/32 has too many partials too close together for it to
be beatless on a harpsichord. Anyone who thinks I'm wrong
can have all the glory by posting a recording.

> Other
> things such as pitch level and even the weather can change things
> subtly (a crowned or flat soundboard changes its response).

But they can't make a 45/32 beatless.

> Anybody who wants to try it can mossy on over to the wonderful
> resource run by some colleagues of mine here in Barcelona, the
> Freesound audio bank:
>
> http://freesound.iua.upf.edu/
>
> Search for Harpsichord, and about halfway down the first page,
> the samples begin with clav056, which is note 56, and descend
> by major thirds until note 2. Granted, with the small number
> of notes available here, you can't draw any real conclusions
> about the instrument acoustical "fingerprint", but it's enough
> to see that there are areas of resonance and damping which
> remain pretty constant within registers. Run those through any
> good FFT/spectrogram software, and see what you get.

Sounds pretty mild...

-Carl

🔗Kraig Grady <kraiggrady@anaphoria.com>

I would like to point out that we can recognize people but can not often give a description to someone else to the point they could pick them out.
Sound can be quite elusive.
As far as empiricism in contrast to rationalism, music is probably one place i would expect music to be best described by the former.
The last century gave birth to allot of very rational music that was empirically utter nonsense.

albeit, i think Helmholtz serves as maybe the best model, as it react with range, as not all consonances are heard the same in all ranges.
nothing more than roughness is the guide.
perhaps there is a better model you prefer and then the parties might be best put on the table, it might clear things up.
I am not really taking sides and i don't have a harpsichord here so i nothing set in stone here.
But curious at what point does an interval become 'impure" say at what harmonic?
I will state again that 'pure' might not be the best term

Paul Poletti wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Brad > Lehman <bpl@...> wrote:
>
> >
> > Please go tune a real virginal that happens to be weak in any harmonics
> > beyond the sixth, like the one I have right here in my office.
>
> That's Our Boy Brad, again, showing his penchant for sweeping
> generalizations and jumping to conclusions based upon his own purely
> subjective experience. It's what endears him so to those of us who
> have tried to get him to be a bit more scientific in the past, not
> because we've got any ax to grind, but more so because Brad's
> observations, which are often of value, would be so much more
> compelling if they were free of this subjective mucking about.
>
> I doubt Brad has ever actually done FFT analysis of a real harpsichord
> to actually KNOW which harmonics are present or not, because if he
> had, he wouldn't say such things. Harpsichords, like most closed box
> instruments (violins, guitars, and the like), have pretty strong
> formants which can color the sound significantly, meaning that, just
> as with the voice, you can't speak of a spectrum which remains
> constant from note to note. Instead you have fairly fixed resonance
> peaks which filter the sound of each note differently, depending upon
> how the frequencies of the partials line up with the instrument's
> resonant frequencies. Thus sometimes the 7th is indeed absent, other
> times it is very strong. So whether or not an interval which depends
> upon higher harmonic congruence would beat or not depends on which
> instrument you play it on and precisely where on the instrument. Other
> things such as pitch level and even the weather can change things
> subtly (a crowned or flat soundboard changes its response).
>
> Anybody who wants to try it can mossy on over to the wonderful
> resource run by some colleagues of mine here in Barcelona, the
> Freesound audio bank:
>
> http://freesound.iua.upf.edu/ <http://freesound.iua.upf.edu/>
>
> Search for Harpsichord, and about halfway down the first page, the
> samples begin with clav056, which is note 56, and descend by major
> thirds until note 2. Granted, with the small number of notes available
> here, you can't draw any real conclusions about the instrument
> acoustical "fingerprint", but it's enough to see that there are areas
> of resonance and damping which remain pretty constant within
> registers. Run those through any good FFT/spectrogram software, and
> see what you get.
>
> Now, all that said, it IS true that even when upper partials are
> lacking, you can get "strong" sounds which appear and disappear with
> subtle tuning changes in intervals like a tritone. Haven't dug into it
> enough to be able to describe exactly what is going on, nor do I want
> to, 'cause I've got more pressing matters to attend to and I'll be my
> bottom dollar that it simply has to do with summing and difference
> tones. However, this "strongness" certainly will NOT be consistent
> over the entire range of the instrument (as the spectral mix is
> changing all the time), nor will it be consistent from instrument to
> instrument. And in any case, it is most definitely not "pure" in the
> normal sense of the word, as it has nothing whatsoever to do with the
> absence of beating between congruent overtones which normally defines
> a pure interval.
>
> So I would say that Brad IS hearing something, he just doesn't know
> what it is nor does he have a terminology to use for it (the one flows
> from the other, logically, of course), so he grabbed the thing that
> seemed best suited in the moment. Which may not have been the best
> choice, since it makes him SEEM stupid, as though he doesn't know what
> the acoustical basis for "purity" as it is normally understood is.
>
> Ciao,
>
> p
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Brad Lehman <bpl@umich.edu>

I wrote:
> Please go tune a real virginal that happens to be weak in any harmonics
> beyond the sixth, like the one I have right here in my office. There is
> no "regular and audible" beating in the 7th harmonic here, because it's
> drowned out by the lower ones. And the 45/32 rings out with a pure
> sound, no beating.
> > Harpsichords also lose most of those upper harmonics, and therefore
> also
> any "regular and audible" beating in the 45/32, when the lid is
> closed...or, for that matter, with the lid wide open but with the
> listener more than a few meters away from the instrument. Once again
> there is no "regular and audible" beating to disturb the effect of this
> interval.
> > I submit that practical issues such as these are more important (at
> least to me!) than any on-paper or on-computer-screen argumentation
> that
> the 7th harmonic doesn't line up.

And a bunch of people (rather predictably) complained about it. I shall try once more.

The effect is pure and obvious to me. I already mentioned that when one of these 1/6 comma tritones is played, my ear fills in the phantom 9:8 above the lower note, and I get a three-note chord. Well, it also fills in the phantom octave below that. The tritone gives me a four-note chord, all in simple pure ratios. The example was C-F#. I hear the intervening D, and the D an octave below. Counting up from the bottom, it's a pure 16:9 minor 7th, a pure 2:1 octave, and a pure 5:2 major 10th.

A spectrum analyzer is never going to hear this, or display it in numbers, because spectrum analyzers don't hear like specialists in 18th century harpsichord continuo. Spectrum analyzers, and by extension the engineers who trust them more than the hearing of functional harmony, don't fill in phantom notes...even when the phantom notes are obvious.

Regular 1/6 syntonic comma meantone puts the F# exactly one syntonic comma below the point (relative to C) where it would be in Pythagorean: C-G-D-A-E-B-F#, less one syntonic comma. That's why this is relevant. A naked tritone such as this, played on a regular 1/6 comma keyboard, gives that pure effect with pure and simple ratios...if one is able to hear these phantom notes completing the chord, thinking harmonically, with these notes being a right-hand continuo chord. This is MUCH stronger an effect than any listening for beats way up at the 7th harmonic of the lower note.

I'm no big fan of Kirnberger II, but it happens to have three of these chords exactly as I've been describing: C-Bb-E, G-F-B, and D-C-F#. The 7th is 16:9 and the 10th is 5:2. The pure sound of these is obvious. I hear the lower note of the tritone as the top of a 16:9, and the upper note as the top of a 5:2, both above the same (sometimes missing) bass note.

No, I'm not going to provide an illustrative recording of this. Anyone who wants to hear it is welcome to go set up a harpsichord and perceive it directly, which will make the point better anyway. Enough members here have already bitched about the unwelcome sound quality of my YouTube instructional videos, focusing on the impure listening experience from a mediocre microphone instead of on the pedagogical points in them. It ruins my motivation to make more of them with that camera. Anyway, they're here for anybody who is willing to do harpsichord tuning by ear:
http://www-personal.umich.edu/~bpl/larips/videos.html

And now I'm off for the rest of the day to go play a concert on a Flemish single with its bright overtones, and to make a recording on Tuesday on an Italian single that has stronger fundamentals. I would be using regular 1/6 for its fabulous sound, except that some of the repertoire in our gig uses too many D#, A#, E#, and B#...and there won't be time to retune during the show. So, I'm using a compromise that has only most of the naturals in 1/6, and the other notes tastefully moderated.

Brad Lehman

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

>
> Have any spectrograms to show? I doubt this is a very
> significant effect with harpsichords.

The formants of instruments like the harpsichord, fortepiano, and to a
much lessor extent, the modern piano (because it has no bottom, and
therefore no box, and also because -until recently- it was pretty much
voiced to remove upper partials) are complex and due to lots of
factors, among them box ressonances, soundboard response, and
plucking/striking points. Since none of these characteristics are
constants (not even strike point in modern pianos, regardless of what
the books will tell you), formants are largely localized, appearing,
disappearing, or shifting gradually as you move from one register to
another. It is these very formants which give the instruments
different registers, a quality which was valued in keyboard
instruments until the Romantic era, when the aesthetic turned upside
down and builders started trying to smooth everything out. It wasn't
just in keyboard instruments, mind you, but generally in everything.
During a lecture on the history of he klarinet some years back, Eric
Hoeprich told the story of the first truly chromatic instrument, with
keys that opened an ascending series of holes instead of merely
producing the forked fingerings need on natural instruments, which
cause marked tonal differences from note to note when you play a
chromatic scale. The inventor, sometime around 1820 as I recall, went
round demonstrating his instrument at the various conservatories of
Europe, and the juries comments from the Paris conservatory are
preserved, to wit: they found the invention most admirable, the only
fault being that the instrument failed to produce the pleasing variety
in the quality of the tones among the different tonalities.

Right, all that as means of introduction as to why modern musicians
may have trouble acknowledging something which most early music types
simply take for granted (including Brad, I'm sure): string keyboard
instruments - at least historic ones - have strong register
differences. Now, as to spectrograms, I've whipped up three for you,
using the samples I mentioned from FreeSound.

http://www.polettipiano.com/clave/AA->tenor_b.jpg

Blocks of repeated notes for the notes AA, D, F#, Bb, (tenor) d, g,
and b. You can easily see the regions of resonance and damping, which
generally remain more or less constant,rising slowly as pitch rises
though by no means keeping up with the rise in fundamental frequency.
The lowest anti-resonance, for example, starts at around 900 Hz and
pretty much stays there. The next is at 1,5 kHz, rises a bit and then
levels off at around 1,6 kHz. Above that there is another one at 2,4
kHz, which also rises a bit and then more or less levels off. Without
a note by note set of samples, it is hard to know exactly what is
going on, but yo get the general picture.

http://www.polettipiano.com/clave/d-g.jpg

http://www.polettipiano.com/clave/g-b.jpg

These other two spectrograms demonstrate how these formants change the
spectrum of individual notes over the range of the instrument. In
each case the left side of the screen shows repetitions of the first
note in the file name, the right side repetitions of the second note
in the file name. Just do some trace counting and you'll see that
harmonics which are weak, missing, altogether, or very strong on one
note may well be exactly the opposite on a note only a fourth or a
third away. In both cases, you can easily see how it is the formants
which are shaping the sound and not some aspect which retains the same
position relative to the fundamental frequency.

>
> > Thus sometimes the 7th is indeed absent,
>
> Really? Have any evidence of this?

Take a look at the spectrum of the note b. The 7th harmonic is almost
totally absent, appearing only as a component of the first burst of
sound right after the pluck, therefore of no value in tempering or
tuning pure an interval. While you're at it, take a look at the
spectrum for the g on the left. Note that the 5th harmonic is
completely gone, as are all of its multiples; have fun tuning or
tempering a major third with this note!

This is just the scientific proof for something that every
professional tuner knows, something that Brad is being a bit
disingenuous about; some intervals, even very simple ones like fifths,
fourths, and thirds, are just nigh to impossible to tune/temper in
some positions on every instrument. Try as you might, you just can't
hear the beats you need to do the job. That's precisely because
sometimes the harmonics which produce the beating just aren't there.
No harmonics, no beats, it's that simple.

>
> 45/32 has too many partials too close together for it to
> be beatless on a harpsichord. Anyone who thinks I'm wrong
> can have all the glory by posting a recording.

I agree with you completely. First of all, the chances that these
harmonics are even present at any perceivable level are about as much
as a snowball in hell, and even if they were there, as you say, the
neighboring harmonics are so close that the ear can't suss 'em out.
Generally speaking, anything above the 17th or 18th harmonic is too
crowded for tuning by ear. That is not to say that mathematically pure
intervals at higher ratios don't have unique sounds, only to say that
it is not the same (psycho)acoustic mechanism as the normal harmonic
congruence which gives simpler pure intervals there special character.
>
> > Other
> > things such as pitch level and even the weather can change things
> > subtly (a crowned or flat soundboard changes its response).
>
> But they can't make a 45/32 beatless.

On the contrary, if they suppress harmonics the harmonics that are
beating at 45/32, it will indeed make it beatless. You can even do
this with a major third. Take away 4 and 5 and all their multiples,
and you can detune it until hell freezes over and yo won't hear any beats.

In any event, as I've said, I doubt that 45 and 32 even exist in the
sound of acoustical string instruments. The inherent stiffness of most
stringing materials would dampen the minute vibrations of those modes
almost instantly - probably wouldn't allow them to develop in the
first place.
>
> > Anybody who wants to try it can mossy on over to the wonderful
> > resource run by some colleagues of mine here in Barcelona, the
> > Freesound audio bank:
> >
> > http://freesound.iua.upf.edu/
> >
> > Search for Harpsichord,
>
> Sounds pretty mild...

What does that mean? It's a harpsichord, man, a real one, and a
historically based one at that. Whad-ya want, some turbo-charged
overly bright synthesized fantasy harpsichord-like sound based on the
tinkle-tinkle of a Neupert or a Sperrhake?

;-)

Ciao,

🔗Paul Poletti <paul@polettipiano.com>

🔗Carl Lumma <carl@lumma.org>

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
> > Have any spectrograms to show? I doubt this is a very
> > significant effect with harpsichords.
>
> The formants of instruments like the harpsichord, fortepiano,
> and to a much lessor extent, the modern piano (because it
> has no bottom, and therefore no box, and also because
> -until recently- it was pretty much voiced to remove upper
> partials)

Where's the evidence that pianos were voiced to "remove
upper partials", and just how recently are you claiming it
changed? Are you by chance referring to the hard-hammer
Young Chang sound that became fashionable in the '90s?

> are complex and due to lots of
> factors, among them box ressonances, soundboard response,
> and plucking/striking points. Since none of these
> characteristics are constants (not even strike point in
> modern pianos, regardless of what the books will tell you),
> formants are largely localized, appearing, disappearing,
> or shifting gradually as you move from one register to
> another.

Changes in spectra due to pluck/strike point differences
aren't technically formants, but OK.

> It is these very formants which give the instruments
> different registers,

I think the cause of registers is primarily the transition
from wound to plain wire, and secondarily various
nonlinearities in the relationship between string
diameter/tension and playing force and hammer/plectrum
coupling.

But we're getting pretty distracted here.

//snip//

> Now, as to spectrograms, I've whipped up three for you,
> using the samples I mentioned from FreeSound.
>
> http://www.polettipiano.com/clave/AA->tenor_b.jpg
>
> Blocks of repeated notes for the notes AA, D, F#, Bb, (tenor)
> d, g, and b. You can easily see the regions of resonance and
> damping, which generally remain more or less constant, rising
> slowly as pitch rises though by no means keeping up with the
> rise in fundamental frequency. The lowest anti-resonance, for
> example, starts at around 900 Hz and pretty much stays there.
> The next is at 1,5 kHz, rises a bit and then levels off at
> around 1,6 kHz. Above that there is another one at 2,4
> kHz, which also rises a bit and then more or less levels off.
> Without a note by note set of samples, it is hard to know
> exactly what is going on, but yo get the general picture.

Though this isn't a very detailed spectrogram, I don't see
much evidence of prominent formants.

> http://www.polettipiano.com/clave/d-g.jpg
> http://www.polettipiano.com/clave/g-b.jpg
>
> These other two spectrograms demonstrate how these formants
> change the spectrum of individual notes over the range of
> the instrument. In each case the left side of the screen
> shows repetitions of the first note in the file name, the
> right side repetitions of the second note in the file name.
> Just do some trace counting and you'll see that harmonics
> which are weak, missing, altogether, or very strong on one
> note may well be exactly the opposite on a note only a fourth
> or a third away. In both cases, you can easily see how it is
> the formants which are shaping the sound and not some aspect
> which retains the same position relative to the fundamental
> frequency.

I'm not sure what we're seeing here, but it isn't going to
render a 45/32 beatless, that's for sure.

> > > Thus sometimes the 7th is indeed absent,
> >
> > Really? Have any evidence of this?
>
> Take a look at the spectrum of the note b. The 7th harmonic
> is almost totally absent, appearing only as a component of
> the first burst of sound right after the pluck,

Are we looking at the same images?

> While you're at it, take a look at the
> spectrum for the g on the left. Note that the 5th harmonic is
> completely gone, as are all of its multiples; have fun tuning
> or tempering a major third with this note!

That I can see.

> This is just the scientific proof for something that every
> professional tuner knows, something that Brad is being a bit
> disingenuous about; some intervals, even very simple ones like
> fifths, fourths, and thirds, are just nigh to impossible to
> tune/temper in some positions on every instrument.

I've only tuned 4 different harpsichords in my life, but I've
never had a problem. They're a cinch to tune in JI.

> > 45/32 has too many partials too close together for it to
> > be beatless on a harpsichord. Anyone who thinks I'm wrong
> > can have all the glory by posting a recording.
>
> I agree with you completely.

Whew.

> > > Other things such as pitch level and even the weather
> > > can change things subtly (a crowned or flat soundboard
> > > changes its response).
> >
> > But they can't make a 45/32 beatless.
>
> On the contrary, if they suppress harmonics the harmonics that are
> beating at 45/32, it will indeed make it beatless. You can even do
> this with a major third. Take away 4 and 5 and all their multiples,
> and you can detune it until hell freezes over and yo won't hear any
> beats.

The problem with 45/32 is that it no longer functions like a
just interval. You don't just remove the 45th and 32nd and
its multiples, because it's not just the 'unisons' that can beat.

> In any event, as I've said, I doubt that 45 and 32 even exist
> in the sound of acoustical

There's that word again. Isn't it just "acoustic"?

> > > Anybody who wants to try it can mossy on over to the wonderful
> > > resource run by some colleagues of mine here in Barcelona, the
> > > Freesound audio bank:
> > >
> > > http://freesound.iua.upf.edu/
> > >
> > > Search for Harpsichord,
> >
> > Sounds pretty mild...
>
> What does that mean? It's a harpsichord, man, a real one, and a
> historically based one at that. Whad-ya want, some turbo-charged
> overly bright synthesized fantasy harpsichord-like sound based
> on the tinkle-tinkle of a Neupert or a Sperrhake?
>
> ;-)

:) No, I just meant timbre changes from note to note sounded
pretty mild to me, compared to say, what you'll hear on most
pianos.

-Carl

🔗Brad Lehman <bpl@umich.edu>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > I'm no big fan of Kirnberger II, but it happens to have three
> > of these chords exactly as I've been describing: C-Bb-E, G-F-B,
> > and D-C-F#. The 7th is 16:9 and the 10th is 5:2. The pure
> > sound of these is obvious.
>
> For the record, are you talking about a bare 45/32 tritone
> sounding beatless, or are you talking about it sounding
> nice, or are you talking about these triads sounding nice?

For the record, I'm saying that all twelve of the tritones in regular
1/6 syntonic comma on a harpsichord are SO STRONG and so resonant that
they make me hear bass notes that are not even being played. The
harmonic events are that strong and that pure. The phantom bass note
is always (for me) at the major 3rd or 10th below one note (pure 5:4
or 5:2), and at the pure 16:9 below the other.

Examples: if it's Bb-E being played in that spacing, I hear the C a
7th below the Bb and a 10th below the E. If it's E-Bb in that other
inverted spacing, I hear the C a 3rd below the E and a 7th below the
Bb. Pure beatless 16:9 and 5:2 (or 5:4) here!

And even if the temperament's actual version of the missing bass note
is being played, somewhat off spot, the tritone inside the texture is
still so strong by itself that it locks the whole chord into a similar
effect.

Sure, I can go to each tritone in turn and stick my head inside the
instrument, right next to the strings and soundboard. There,
carefully, I can pick out beats of the upper harmonics for a short
time. But at any normal listening distance at least half a meter away
from the soundboard, all I hear is the purity of the tritone locking
in its harmony. I hear that even in five-note or six-note chords: if
there's a tritone in there anywhere, it makes incredible harmonic
gravity all by itself. And if it's a fully-diminished 7th chord, with
two tritones interlocked, that's a yet more powerful sound.

By contrast, trying any of this in equal or in various irregular
temperaments, it's just a muddled mess. No such clarity of focus that
I hear from regular 1/6. I don't get that from regular 1/4 comma,
either. Only 1/6.

>
> > No, I'm not going to provide an illustrative recording of this.
> > Anyone who wants to hear it is welcome to go set up a
> > harpsichord and perceive it directly,
>
> Not everyone has ready access to a harpsichord.

I understand, but not everyone has ready access to a retunable
synthesizer either (to get the other things being discussed by various
folks). Sorry, but I don't know of any way to illustrate my point
adequately except to have any curious person set up a complete regular
1/6 on a harpsichord. Then, spend a good solid 15 minutes improvising
through all sorts of chord progressions (simple and complex) to get a
feel of the way the thing moves, and resonates.

Now, off to the gig.

Brad Lehman

🔗Petr Parízek <p.parizek@chello.cz>

🔗Carl Lumma <carl@lumma.org>

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, Brad Lehman <bpl@...> wrote:
>
>
> The effect is pure and obvious to me. I already mentioned that when
one
> of these 1/6 comma tritones is played, my ear fills in the phantom 9:8
> above the lower note, and I get a three-note chord. Well, it also
fills
> in the phantom octave below that. The tritone gives me a four-note
> chord, all in simple pure ratios. The example was C-F#. I hear the
> intervening D, and the D an octave below. Counting up from the bottom,
> it's a pure 16:9 minor 7th, a pure 2:1 octave, and a pure 5:2 major
10th.

What just a gosh darn minute, here! Brad started all this by saying:

"The diminished 7th chords are spectacular in regular 1/6 comma, since
they're built of two pure tritones interlocked."

Evidently, whatever Brad meant then and still means by his peculiar
use of the word "pure", the effect was so compelling that he even
posited that:

"Maybe that strong sound contributed to the heavy use of diminished 7th
chords by 18th century composers; or vice versa, their use of those is
some evidence (perhaps weak, but there nonetheless) of a regular 1/6
layout or something near it?"

Now he wants us to believe that most compelling aspect of this
mysterious "purity" which eludes us all, both conceptually and
aurally, despite being an effect which is "pure and obvious" to him
(not quite sure what THAT means - is "pure" the same as "compelling"?
Or does it sound to Brad like what the rest of us call "pure"? Or is
it an effect which is "purely" personal, i.e. "to him"? We can but
wonder...), THE strongest argument for the 45/32 aug.4 being something
of exceptional musical quality, is that by playing but two notes of
any aug.4 in 1/6 mean, you get a double "buy one get the second one
free" deal in that it automatically fills in the two notes which make
the octave of the root of a dominant 7th chord which is a step (a pure
step, mind you, 9/8, and not a mere Lehman "pure" step, but a PURE
pure step, which is pure to everyone, effectively speaking,
obviously... at least to me). This leaves Brad with several
interesting dilemmas:

(1) Since the "phantom" note which gets filled in above the lower note
of the +4 is in fact a pure whole tone (9/8), it must be a bitter pill
to swallow indeed whenever one is actually required by the score to
let these notes sound not by the conjuring-up of phantoms but rather
by the mundane process of the mere depression of keys, beings as the
interval which is actually produced by an instrument tuned in 1/6 mean
ain't nuthin' 'tall like that which dwelleth in the ears of Brad,
being pure as it is.

(2) Going back to Brad's original message, pity the poor musician who
hears like Brad and must play one of these "spectacular" dim7 chords;
since they are indeed composed of "two [Lehman-]pure tritones
interlocked", and since he has established twice now that these "pure"
tritones automatically imply the roots of dominant 7 chords, he must
hear TWO superimposed dominant 7 chords. For example, if he were to
play my example of F#-A-C-Eb, he would not only hear, as he himself
has stated, the two D's which are phantom accomplices to the C-F#, but
logically there would be no way to avoid hearing two F's, generated
not by any process known to acoustical science but rather
ectoplasmically by the spectacularly pure 45/32 aug4 Eb-A.

Brad DOES state that ectoplasmic voice leading only manifests when the
+4ths appear "nakedly", which begins to give the whole thing the kinky
feel of one of those 1950's grade C made-for-the-drive-in-movies
"creature features", involving supernatural entities,
extraterestrials, or mutant humanoids inevitably carrying-off
scantly-clad beauties. The question is, if these "pure" intervals are
sooooo compelling when "naked", how do they loose this quality when
they are intimately intertwined with yet another compellingly-naked
+4? My mind boggles! I would think the effect could not but be doubled
thereby, perhaps even quadrupled!!

Now, for those who want to hear what this might sound like, I've
whipped up a little audio file, dutifully following Brad's
instructions to use a sound which has no harmonics above 6, 45/32 aug
4ths, and 9/8 seconds above the lower tone with an octave below that:

www.polettipiano.com/faith_based_acoustics/purecluster.mp3

Doesn't exactly remind me of anything I'd expect from "specialists in
18th century harpsichord continuo"... more like Messian, actually.

Additionally, for those who want to try accompany Brad through his
looking glass and into the alternative space-time continuo-um of the
18th century specialist, a magical world where the Evil Wicked Dr.
Science with his monstrous Spectrum-o-thons is kept safely at bay,
I've posted another audio file of just (purely speaking) the 45/32 +4
alone, sustained for a spell, and then followed by the mystical
appearance of Our Lady of the Phantom Octave:

www.polettipiano.com/faith_based_acoustics/indoctrinate_me.mp3

Listen to it over and over again until you begin to hear the octave
BEFORE it is actually played. It may take some time, but with enough
exposure, sooner or later, you will be assimilated. Sleep deprivation
and waterboarding helps speed the process.

Happy Trails!

🔗Petr Parízek <p.parizek@chello.cz>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

LOL!

I actually imagine to hear E-C-E-F#, not D-C-D-F# as Brad does. My
experience is just not "acoustical" though, more likely psychological. It
must be the mental effect due to my prolonged exposure to the ludicrous
arguments against the supposed non-existence (hasha) of Allah Almighty by
the natural selection prophet Richard Dawkin.

LOL once more!

Oz.

----- Original Message -----
From: "Paul Poletti" <paul@polettipiano.com>
To: <tuning@yahoogroups.com>
Sent: 17 ï¿½ubat 2008 Pazar 22:31
Subject: [tuning] Re: 7th harmonic in 45/32

> --- In tuning@yahoogroups.com, Brad Lehman <bpl@...> wrote:
> >
> >
> > The effect is pure and obvious to me. I already mentioned that when
> one
> > of these 1/6 comma tritones is played, my ear fills in the phantom 9:8
> > above the lower note, and I get a three-note chord. Well, it also
> fills
> > in the phantom octave below that. The tritone gives me a four-note
> > chord, all in simple pure ratios. The example was C-F#. I hear the
> > intervening D, and the D an octave below. Counting up from the bottom,
> > it's a pure 16:9 minor 7th, a pure 2:1 octave, and a pure 5:2 major
> 10th.
>
> What just a gosh darn minute, here! Brad started all this by saying:
>
> "The diminished 7th chords are spectacular in regular 1/6 comma, since
> they're built of two pure tritones interlocked."
>
> Evidently, whatever Brad meant then and still means by his peculiar
> use of the word "pure", the effect was so compelling that he even
> posited that:
>
> "Maybe that strong sound contributed to the heavy use of diminished 7th
> chords by 18th century composers; or vice versa, their use of those is
> some evidence (perhaps weak, but there nonetheless) of a regular 1/6
> layout or something near it?"
>
> Now he wants us to believe that most compelling aspect of this
> mysterious "purity" which eludes us all, both conceptually and
> aurally, despite being an effect which is "pure and obvious" to him
> (not quite sure what THAT means - is "pure" the same as "compelling"?
> Or does it sound to Brad like what the rest of us call "pure"? Or is
> it an effect which is "purely" personal, i.e. "to him"? We can but
> wonder...), THE strongest argument for the 45/32 aug.4 being something
> of exceptional musical quality, is that by playing but two notes of
> any aug.4 in 1/6 mean, you get a double "buy one get the second one
> free" deal in that it automatically fills in the two notes which make
> the octave of the root of a dominant 7th chord which is a step (a pure
> step, mind you, 9/8, and not a mere Lehman "pure" step, but a PURE
> pure step, which is pure to everyone, effectively speaking,
> obviously... at least to me). This leaves Brad with several
> interesting dilemmas:
>
> (1) Since the "phantom" note which gets filled in above the lower note
> of the +4 is in fact a pure whole tone (9/8), it must be a bitter pill
> to swallow indeed whenever one is actually required by the score to
> let these notes sound not by the conjuring-up of phantoms but rather
> by the mundane process of the mere depression of keys, beings as the
> interval which is actually produced by an instrument tuned in 1/6 mean
> ain't nuthin' 'tall like that which dwelleth in the ears of Brad,
> being pure as it is.
>
> (2) Going back to Brad's original message, pity the poor musician who
> hears like Brad and must play one of these "spectacular" dim7 chords;
> since they are indeed composed of "two [Lehman-]pure tritones
> interlocked", and since he has established twice now that these "pure"
> tritones automatically imply the roots of dominant 7 chords, he must
> hear TWO superimposed dominant 7 chords. For example, if he were to
> play my example of F#-A-C-Eb, he would not only hear, as he himself
> has stated, the two D's which are phantom accomplices to the C-F#, but
> logically there would be no way to avoid hearing two F's, generated
> not by any process known to acoustical science but rather
> ectoplasmically by the spectacularly pure 45/32 aug4 Eb-A.
>
> Brad DOES state that ectoplasmic voice leading only manifests when the
> +4ths appear "nakedly", which begins to give the whole thing the kinky
> feel of one of those 1950's grade C made-for-the-drive-in-movies
> "creature features", involving supernatural entities,
> extraterestrials, or mutant humanoids inevitably carrying-off
> scantly-clad beauties. The question is, if these "pure" intervals are
> sooooo compelling when "naked", how do they loose this quality when
> they are intimately intertwined with yet another compellingly-naked
> +4? My mind boggles! I would think the effect could not but be doubled
> thereby, perhaps even quadrupled!!
>
> Now, for those who want to hear what this might sound like, I've
> whipped up a little audio file, dutifully following Brad's
> instructions to use a sound which has no harmonics above 6, 45/32 aug
> 4ths, and 9/8 seconds above the lower tone with an octave below that:
>
> www.polettipiano.com/faith_based_acoustics/purecluster.mp3
>
> Doesn't exactly remind me of anything I'd expect from "specialists in
> 18th century harpsichord continuo"... more like Messian, actually.
>
> Additionally, for those who want to try accompany Brad through his
> looking glass and into the alternative space-time continuo-um of the
> 18th century specialist, a magical world where the Evil Wicked Dr.
> Science with his monstrous Spectrum-o-thons is kept safely at bay,
> I've posted another audio file of just (purely speaking) the 45/32 +4
> alone, sustained for a spell, and then followed by the mystical
> appearance of Our Lady of the Phantom Octave:
>
> www.polettipiano.com/faith_based_acoustics/indoctrinate_me.mp3
>
> Listen to it over and over again until you begin to hear the octave
> BEFORE it is actually played. It may take some time, but with enough
> exposure, sooner or later, you will be assimilated. Sleep deprivation
> and waterboarding helps speed the process.
>
> Happy Trails!
>
> P
>

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Paul Poletti" <paul@> wrote:
> > > Have any spectrograms to show? I doubt this is a very
> > > significant effect with harpsichords.
> >
> > The formants of instruments like the harpsichord, fortepiano,
> > and to a much lessor extent, the modern piano (because it
> > has no bottom, and therefore no box, and also because
> > -until recently- it was pretty much voiced to remove upper
> > partials)
>
> Where's the evidence that pianos were voiced to "remove
> upper partials",

I'm talking about the great shift in aesthetic that ocured between
about 1800 and 1840, which first involved a move from either no
leather (yes, bare wood) or one or two very thin layers of leather on
the hammers to huge stacks of up to 13 layers or so and then
eventually to felt.

> and just how recently are you claiming it
> changed? Are you by chance referring to the hard-hammer
> Young Chang sound that became fashionable in the '90s?

I don't know when it changed because I don't like modern pianos and
tend to stay away from them as much as possible. I do know that almost
every recent piano I have met sounds harsh and nasty compared to the
c.1900 instrument I am more comfortable with. Friends who are modern
piano techs tell me this harsh sound has been growing in popularity
for a decade or two, so that agrees with your date.
>
> > are complex and due to lots of
> > factors, among them box ressonances, soundboard response,
> > and plucking/striking points. Since none of these
> > characteristics are constants (not even strike point in
> > modern pianos, regardless of what the books will tell you),
> > formants are largely localized, appearing, disappearing,
> > or shifting gradually as you move from one register to
> > another.
>
> Changes in spectra due to pluck/strike point differences
> aren't technically formants, but OK.

Well, the use of the word formant for describing things which affect
the sound of musical instruments other than the voice is not entirely
correct. Acousticians have borrowed the term from phonetics to
describe those resonances of instruments which are relatively fixed
and act as filters, much as real formants do. What I meant is that
irregularities in pluck/strike point can interact with formants (be
they air resonances or structural resonances) to create registers.
>
> > It is these very formants which give the instruments
> > different registers,
>
> I think the cause of registers is primarily the transition
> from wound to plain wire, and secondarily various
> nonlinearities in the relationship between string
> diameter/tension and playing force and hammer/plectrum
> coupling.

The overwhelming majority of instruments I am talking about have NO
wound strings, so there is no transition. The also have but one
bridge, so there is no transition from bass to treble bridge, another
favorite of those who only know the modern piano. The standard
literature, which makes much of out of string tension inconsistencies,
is written by people who have no experience with the vast differences
in stringing and scaling one encounters building and restoring
harpsichords and early pianos, everything from exceedingly
foreshortened scales all the way up to scales which remain Pythagorean
for almost the entire instrument. This experience teaches one that
most of what you read is largely much ado about nothing, and that the
sort of realistic tension changes which can be accomplished are
insufficient to produce any marked tonal differences. That said, gross
aberrations, such as the current fad for exceptionally low tension
among certain builders, can produce noticable tonal differences.
>
> But we're getting pretty distracted here.

Yes and no. The spectrum of a musical tone has a vast influence upon
the sound of different tunings, as Bill Sethares has so aptly
demonstrated.

>
> Though this isn't a very detailed spectrogram, I don't see
> much evidence of prominent formants.

I'm sure you see the black swaths of no or weak harmonics. The areas
in between are obviously formants

>
> I'm not sure what we're seeing here, but it isn't going to
> render a 45/32 beatless, that's for sure.

These particular examples, no. I just wanted to demonstrate that any
given harmonic can be totally absent from the mix, which is what you
wondered about. It could just as well be the 7th, in which case any
near-miss to a septimal pure interval will in fact be beatless. As I
said, take out the 4 and 5th harmonics and their multiples, and even a
Pythagorean major third is beatless.
>
> > > > Thus sometimes the 7th is indeed absent,
> > >
> > > Really? Have any evidence of this?
> >
> > Take a look at the spectrum of the note b. The 7th harmonic
> > is almost totally absent, appearing only as a component of
> > the first burst of sound right after the pluck,
>
> Are we looking at the same images?

The correct image is g-b.jpg. The right side shows repeated plucks of
the note b. In other word, the right half of the screen shows 11
rapidly consecutive plucks of the note b, each about 3/4 of a second
after the previous. Counting up from the bottom trace, which is the
fundamental, the 4th harmonic is almost absent, being only the ghost
of a trace. The 5th harmonic is rather strong aai, and the 6th is
about as weak as the 4th. The 7th is very weak, appearing only very
briefly at each moment of pluck, represented by a dashed trace. The
9th harmonic is similar, though it last a fraction of a second longer.
The 10th is also weak and dies quickly, though last longer than the
9th. The 11th is relatively strong and constant again. 12 is weak and
momentary. 13 is quite strong but dies rather fast, not quit lasting
the 3/4 of a second or so of each sample. 14, 15, 16, and 17 are for
all intents and purpose gone, though the can be faintly seen. Get it now?
>
> > While you're at it, take a look at the
> > spectrum for the g on the left. Note that the 5th harmonic is
> > completely gone, as are all of its multiples; have fun tuning
> > or tempering a major third with this note!
>
> That I can see.
>
> > This is just the scientific proof for something that every
> > professional tuner knows, something that Brad is being a bit
> > disingenuous about; some intervals, even very simple ones like
> > fifths, fourths, and thirds, are just nigh to impossible to
> > tune/temper in some positions on every instrument.
>
> I've only tuned 4 different harpsichords in my life, but I've
> never had a problem. They're a cinch to tune in JI.

I'm talking about real tuning, no JI! Try tempering 1/6th mean by ear
on a variety of Italians. Or setting the various Neidhardts, where the
majority of intervals o must set are tempered. That will yo make aware
of all sort of funkiness.
>
> The problem with 45/32 is that it no longer functions like a
> just interval. You don't just remove the 45th and 32nd and
> its multiples, because it's not just the 'unisons' that can beat.

Agreed completely. I think Brad is just completely out to lunch, as
should be obvious by now. He lives and breathes and hears on the
Planet of Brad.

>
> > In any event, as I've said, I doubt that 45 and 32 even exist
> > in the sound of acoustical
>
> There's that word again. Isn't it just "acoustic"?

According to Merriam Webster, acoustical is a variant of acoustic.
What do I know? After 16 years of either using other's people's
languages or using simplified English, mine has gone all to hell.

> >
> > What does that mean? It's a harpsichord, man, a real one, and a
> > historically based one at that. Whad-ya want, some turbo-charged
> > overly bright synthesized fantasy harpsichord-like sound based
> > on the tinkle-tinkle of a Neupert or a Sperrhake?
> >
> > ;-)
>
> :) No, I just meant timbre changes from note to note sounded
> pretty mild to me, compared to say, what you'll hear on most
> pianos.

Yeah, that's one of the interesting things about acoustic(al)
instruments. Given a set of samples like that, you think, it's all the
same, more or less. But if you take any one sample and stuff it into a
sampling synthesizer and play an octave of notes, you instantly
recognize that it is fake precisely because it IS all the same. Then
if you look at the spectrums of individual notes, you see how
different they are, and you wonder why we accept it as even. It's just
the same as how we recognize vowel as that particular vowel even
though the spectrum is drastically different when spoken by different
people, or even by the same person at different pitches.

Interesting, that, and how it all feeds back onto tuning, since tuning
by nature depends upon and assumes constant spectrum, something which
never happens in the real world.

Ciao,

🔗Petr Parízek <p.parizek@chello.cz>

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

a 45/32 produces a difference tone of 13 which would be a bit low of the tone of your scale, but wight imitate that function enough

Brad Lehman wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Carl > Lumma" <carl@...> wrote:
> >
> > > I'm no big fan of Kirnberger II, but it happens to have three
> > > of these chords exactly as I've been describing: C-Bb-E, G-F-B,
> > > and D-C-F#. The 7th is 16:9 and the 10th is 5:2. The pure
> > > sound of these is obvious.
> >
> > For the record, are you talking about a bare 45/32 tritone
> > sounding beatless, or are you talking about it sounding
> > nice, or are you talking about these triads sounding nice?
>
> For the record, I'm saying that all twelve of the tritones in regular
> 1/6 syntonic comma on a harpsichord are SO STRONG and so resonant that
> they make me hear bass notes that are not even being played. The
> harmonic events are that strong and that pure. The phantom bass note
> is always (for me) at the major 3rd or 10th below one note (pure 5:4
> or 5:2), and at the pure 16:9 below the other.
>
> Examples: if it's Bb-E being played in that spacing, I hear the C a
> 7th below the Bb and a 10th below the E. If it's E-Bb in that other
> inverted spacing, I hear the C a 3rd below the E and a 7th below the
> Bb. Pure beatless 16:9 and 5:2 (or 5:4) here!
>
> And even if the temperament's actual version of the missing bass note
> is being played, somewhat off spot, the tritone inside the texture is
> still so strong by itself that it locks the whole chord into a similar
> effect.
>
> Sure, I can go to each tritone in turn and stick my head inside the
> instrument, right next to the strings and soundboard. There,
> carefully, I can pick out beats of the upper harmonics for a short
> time. But at any normal listening distance at least half a meter away
> from the soundboard, all I hear is the purity of the tritone locking
> in its harmony. I hear that even in five-note or six-note chords: if
> there's a tritone in there anywhere, it makes incredible harmonic
> gravity all by itself. And if it's a fully-diminished 7th chord, with
> two tritones interlocked, that's a yet more powerful sound.
>
> By contrast, trying any of this in equal or in various irregular
> temperaments, it's just a muddled mess. No such clarity of focus that
> I hear from regular 1/6. I don't get that from regular 1/4 comma,
> either. Only 1/6.
>
> >
> > > No, I'm not going to provide an illustrative recording of this.
> > > Anyone who wants to hear it is welcome to go set up a
> > > harpsichord and perceive it directly,
> >
> > Not everyone has ready access to a harpsichord.
>
> I understand, but not everyone has ready access to a retunable
> synthesizer either (to get the other things being discussed by various
> folks). Sorry, but I don't know of any way to illustrate my point
> adequately except to have any curious person set up a complete regular
> 1/6 on a harpsichord. Then, spend a good solid 15 minutes improvising
> through all sorts of chord progressions (simple and complex) to get a
> feel of the way the thing moves, and resonates.
>
> Now, off to the gig.
>
> Brad Lehman
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Carl Lumma <carl@lumma.org>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Petr Parízek <p.parizek@chello.cz>

🔗Carl Lumma <carl@lumma.org>

> > --- In tuning@yahoogroups.com, "Paul Poletti" <paul@> wrote:
> > Where's the evidence that pianos were voiced to "remove
> > upper partials",
>
> I'm talking about the great shift in aesthetic that ocurred
> between about 1800 and 1840, which first involved a move from
> either no leather (yes, bare wood) or one or two very thin
> layers of leather on the hammers to huge stacks of up to
> 13 layers or so and then eventually to felt.

So 1840 is "recent", and bare wood or leather hammers remove
upper partials?

> > Though this isn't a very detailed spectrogram, I don't see
> > much evidence of prominent formants.
>
> I'm sure you see the black swaths of no or weak harmonics.
> The areas in between are obviously formants

If you want to call them that. Since they seem to change
from note to note, I probably wouldn't.

> > > This is just the scientific proof for something that every
> > > professional tuner knows, something that Brad is being a bit
> > > disingenuous about; some intervals, even very simple ones like
> > > fifths, fourths, and thirds, are just nigh to impossible to
> > > tune/temper in some positions on every instrument.
> >
> > I've only tuned 4 different harpsichords in my life, but I've
> > never had a problem. They're a cinch to tune in JI.
>
> I'm talking about real tuning, no JI!

JI's not a real tuning?

> > > In any event, as I've said, I doubt that 45 and 32 even exist
> > > in the sound of acoustical
> >
> > There's that word again. Isn't it just "acoustic"?
>
> According to Merriam Webster, acoustical is a variant of acoustic.
> What do I know? After 16 years of either using other's people's
> languages or using simplified English, mine has gone all to hell.

I stand corrected.

> > > What does that mean? It's a harpsichord, man, a real one, and a
> > > historically based one at that. Whad-ya want, some turbo-charged
> > > overly bright synthesized fantasy harpsichord-like sound based
> > > on the tinkle-tinkle of a Neupert or a Sperrhake?
> > >
> > > ;-)
> >
> > :) No, I just meant timbre changes from note to note sounded
> > pretty mild to me, compared to say, what you'll hear on most
> > pianos.
>
> Yeah, that's one of the interesting things about acoustic(al)
> instruments. Given a set of samples like that, you think, it's
> all the same, more or less. But if you take any one sample and
> stuff it into a sampling synthesizer and play an octave of
> notes, you instantly recognize that it is fake precisely because
> it IS all the same.

There are a lot of reasons incomplete keyboard samples can
sound fake.

-Carl

🔗Carl Lumma <carl@lumma.org>

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > --- In tuning@yahoogroups.com, "Paul Poletti" <paul@> wrote:
> > > Where's the evidence that pianos were voiced to "remove
> > > upper partials",
> >
> > I'm talking about the great shift in aesthetic that ocurred
> > between about 1800 and 1840, which first involved a move from
> > either no leather (yes, bare wood) or one or two very thin
> > layers of leather on the hammers to huge stacks of up to
> > 13 layers or so and then eventually to felt.
>
> So 1840 is "recent", and bare wood or leather hammers remove
> upper partials?

No. 1800-1840 is when they started voicing instruments dull, by piling
up the leather or using felt. "Recent" is the past 20 or 30 years,
when harsh modern pianos seem to have started becoming the fad.
>
> > > Though this isn't a very detailed spectrogram, I don't see
> > > much evidence of prominent formants.
> >
> > I'm sure you see the black swaths of no or weak harmonics.
> > The areas in between are obviously formants
>
> If you want to call them that. Since they seem to change
> from note to note, I probably wouldn't.

They change about as much as the formants of vowels change in the
lower octave of a soprano range as she sings progressively higher.
Vocal formants are essential constant, though not absolutely constant.
But yes, in general, as I said, because instrument formants are due
primarily to structural and internal resonances, which are somewhat
localized, and since soundboard excitation is also localized, the two
combine to produce slowly changing formants. If we had every note, we
could see them changing continuously.

> > >
> > > I've only tuned 4 different harpsichords in my life, but I've
> > > never had a problem. They're a cinch to tune in JI.
> >
> > I'm talking about real tuning, no JI!
>
> JI's not a real tuning?
>
By "tuning", I meant the process of adjusting the notes on an
instrument, not a system of interval proportions. If you are a
professional tuner catering to the early music crowd, nobody ever asks
you to set JI. That's what I meant by it's not a real tuning.

>
> There are a lot of reasons incomplete keyboard samples can
> sound fake.

Couldn't agree more, but register is one of the biggies. The converse
is also true, BTW. I know some builders who project a 20th century
aesthetic on the early piano and do it so well that the instrument
sounds fake to me, as though it were electronic, since it has no
register changes.

Ciao,

🔗Paul Poletti <paul@polettipiano.com>

🔗Petr Parízek <p.parizek@chello.cz>

🔗Carl Lumma <carl@lumma.org>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Tom Dent <stringph@gmail.com>

Monz doesn't have a Tonalsoft entry on 'pure' intervals. But one can
learn a lot from the JI entry:

http://tonalsoft.com/enc/j/just.aspx

"The beatless tuning of an interval, one that brings it into agreement
with some analogous interval in the harmonic series. Such intervals
are considered to be acoustically pure. They are expressed by ratios
containing the smallest possible integers corresponding to the lowest
analogous partials of the harmonic series."

It's perfectly clear. Now as often encountered here, we have the
'paradox' of JI: the sum or difference of two pure intervals remains
JI, but need not be pure in any acoustically meaningful sense. (Some
authors use 'pure' to denote some 5-limit JI intervals regardless of
their consonance or beating: such a purely formal/mathematical usage
is acoustically meaningless.)

Thus 25/24, 32/27, 36/25, 81/64 and a whole host of other 5-limit
intervals are in no way 'pure', despite being composed of just ratios.
These intervals are close enough to 1/1, 6/5, 7/5, 5/4 that their
beating is clearly audible (with minimal and reasonable assumptions
about instrumental timbre).

So what I did last night was start (on the 'Flemish' model
harpsichord) with tenor d, tune pure M3 to f#, pure fifth to c#' and
fourth to g#'. This creates a JI 45/32 between d and g#. And what
happens? It beats. It is not pure. To me it just sounded like any old
tempered tritone. I was able to put the tritone into pure tuning by
ear, by eliminating the beats: the result is 7/5. (Recording to follow
soon.)

It remains a mystery what Brad's definition of 'pure' could be, such
that obviously beating intervals can satisfy it.

It might also be useful to check some historical writers' definitions
of 'pure' intervals. So far as I know there is no acoustically
meaningful definition that does not require the elimination of beats.

There are authors with 'sloppy' definitions, such that 'pure' just
means 'not unpleasantly out of tune' - e.g. CPE Bach's statement that
all keys should sound equally 'pure' ... clearly not a request for JI!
Since it is a matter of taste how much tempering one can put into an
interval before it stops being 'pure' in this sense, such statements
are always vague and unquantifiable.

~~~T~~~

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
> --- In tuning@yahoogroups.com, Petr Parízek <p.parizek@> wrote:
> >
> > Kraig wrote:
> >
> >
> >
> > > a 45/32 produces a difference tone of 13 which would be a bit low
> of the
> > > tone of your scale, but wight imitate that function enough
> >
> >
> >
> > I don't understand. If 32 is C4 and 45 is F#4, then 13 is about 40
> cents higher than Ab2 but not D2 or D3 which Brad was talking about.
>
> You're quite right. If you actually play C-F# quite high on a keyboard
> tuned in 1/6 mean, you can easily hear the Ab/A. Just did it.
> >
> > I don't understand.
>
> Neither do I...
> >
> > Petr
> Paul
>

🔗Brad Lehman <bpl@umich.edu>

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:

>
> So what I did last night was start (on the 'Flemish' model
> harpsichord) with tenor d, tune pure M3 to f#, pure fifth to c#' and
> fourth to g#'. This creates a JI 45/32 between d and g#.

Actually, what you (and Brad) are doing is defining the limits of the
basic framework of 1/6 comma meantone. Setting the pure major third
simultaneously establishes the Syntonic comma and spreads it over a
range spanning 4 adjacent fifths, even though the individual fifths
are not yet established. Adding two more pure fifths (going clockwise
around the circle) merely expands the territory to 6 fifths, which is
the very defintion of 1/6 comma meantone: the Syntonic comma
distributed over 6 fifths. The only thing left to do is temper the 6
fifths between the extremes by the same amount. The same trick works
with 1/5 comma by adding one fifth on top of the third, or 2/7 by
taking one pure fifth AWAY from TWO stacked pure major thirds (thus,
two Syntonic commas spanning 7 fifths), or 2/9 by adding one more
fifth tow two stacked pure major thirds. In all cases, you are doing
exactly what the name says. No need for that tedious inaccurate
mucking about with "tune a pure major third and then expand it a
little". Just do it right from the get-go.

> And whath
> happens? It beats. It is not pure. To me it just sounded like any old
> tempered tritone. I was able to put the tritone into pure tuning by
> ear, by eliminating the beats: the result is 7/5. (Recording to follow
> soon.)

Of course you're right, though I would say that it is not entirely
corect to speak of a "pure" tritone, since it is a contradiction in
terms. A "tritone" is by definition three tones, and three pure tones
(9/8 cubed) makes an interval which is anything but "pure". Better
perhaps to say that 7/5 is a septimal augmented 4th.

>
> It remains a mystery what Brad's definition of 'pure' could be, such
> that obviously beating intervals can satisfy it.

Your main problem, Thomas, is that you're not following the lesson
closely enough. Brad specifically said that it has to be done on an
instrument which has little harmonic development above the 6th
partial. Originally it seemed to be only the case with the spinet in
his office, but now it appears to be a deficiency which afflicts ALL
his instruments.

In any event, you must find a similarly harmonically-crippled
instrument to perform the experiment. Alternatively, you can adapt a
normal instrument by installing a set of Lehman String Purifiers (Pat.
Pending), also available in many music shops under the brand name
Sept-Away Mini-Mutes. Put one on each string in the position indicated
in the instructions, and that nasty, bothersome beating will
disappear, leaving only the pure, strong, and obvious ringing of the
45/32 tritone.

>
> It might also be useful to check some historical writers' definitions
> of 'pure' intervals. So far as I know there is no acoustically
> meaningful definition that does not require the elimination of beats.
>
Like the very vivid and precise descriptions of Praetorius and
Werckmeister, for example. But then, alas, neither of them were
experts in 18th century continuo realization.

Ciao,

🔗Petr Parízek <p.parizek@chello.cz>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Tom Dent <stringph@gmail.com>

It depends *which* higher harmonics. If you could be a bit clearer
about what Henk Badings actually did, I could tell what I thought
about him. Perhaps you should not leap to conclusions about what my
definition is.

My working definition is that any single interval, for which someone
can reliably hear beating when it is tempered (given some instrumental
timbre consisting of the harmonic series), and which one can tune by
ear through elimination of beats, can be meaningfully called pure.

Since I believe I have been able to tune a 19/15 on an 'Italian'
harpsichord, due to the peculiar structure of its partials, it seems
not unreasonable that certain intervals whose numerator and
denominator go up to 15-20 could be done by ear in favourable
circumstances.

However, I don't believe that anyone can tune 32/27 by eliminating
beats between the 27th and 32nd partials. Nor can anything like a
semitone be tuned by ear by eliminating beats. It is not simply the
largeness of the numbers, it is the proximity of simpler intervals, as
people know very well. Eg I don't think 13/12 can be done directly by ear.

Whether 16/9 can be called 'pure' is highly debatable. Can one hear
beats in a slightly tempered 16/9 ?

There is a very interesting paper somewhere about some brass players
who investigated exactly this question: exactly what intervals can be
recognized and tuned beatless by ear?

~~~T~~~

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> So in your definition Hank Badings' use of higher harmonics is not
using
> pure intervals. I would disagree.
>
>
>
> Tom Dent wrote:
> >
> > Thus 25/24, 32/27, 36/25, 81/64 and a whole host of other 5-limit
> > intervals are in no way 'pure', despite being composed of just ratios.
> > These intervals are close enough to 1/1, 6/5, 7/5, 5/4 that their
> > beating is clearly audible (with minimal and reasonable assumptions
> > about instrumental timbre).
> >
> >

🔗Petr Parízek <p.parizek@chello.cz>

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>

> > Whether 16/9 can be called 'pure' is highly debatable. Can one hear
> > beats in a slightly tempered 16/9 ?
>
>
>
> Yes, as long as the overtones are loud enough. Just tried it with a
periodic sawtooth and it worked perfectly.
>
I definitely support Petr's assertion. About 3 years ago, I sat down,
put on my reasonably good headphones and most definitely did NOT turn
them up all the way precisely to avoid harmonic distortion, and mixed
myself a nice bright tone quality with strong harmonics up to the
64th, and then started with a unison and slowly raised the pitch of
one of the notes, simply listening and stopping at every incidence of
beating which I could hear and then tune "pure" merely be ear. I then
looked at the proportion from the Abysnth tuning window and figured
out what pair of overtones was causing the beating I was hearing.
Here's a chart of everything I could do BY EAR, graphed against lines
for 12-EDO:

http://www.polettipiano.com/Beatable_odds.jpg

Granted, in real life, timbres this bright are few and far between.

The only possible occurrence of a possible example of listening this
high i can suggest is a recording i have of sarangi and shanai, in
which both players repeatedly produce a narrow leading tone of 81
cents. They do it time and time again and spot on every time, together
and separately. Now 81 cents shy of an octave just happens to be
21/11. Whether or not they actually hear that particular overtone
congruence between their own instrument and the tampura or are just
locked into the sound of that particular interval is anybody's guess.

But in regards to Brad's supposed 45/32 interval, all of this is moot
because he stated that the tone color must be poor in upper partials.
Otherwise the 7 would be wailing away against 5 or 10, why is exactly
why none of us can understand what he's on about.

Ciao,

🔗Ozan Yarman <ozanyarman@ozanyarman.com>

A wonderful demonstration regarding the validity of simple-integer ratios in
interval tuning. Are all the ratios 19-limit?

Oz.

----- Original Message -----
From: "Paul Poletti" <paul@polettipiano.com>
To: <tuning@yahoogroups.com>
Sent: 19 ï¿½ubat 2008 Salï¿½ 1:29
Subject: [tuning] Re: 7th harmonic in 45/32

--- In tuning@yahoogroups.com, Petr Parï¿½zek <p.parizek@...> wrote:
>

http://www.polettipiano.com/Beatable_odds.jpg

Granted, in real life, timbres this bright are few and far between.

Ciao,

🔗Kraig Grady <kraiggrady@anaphoria.com>

I did not jump to a conclusion a conclusion what you meant by pure, i asked, repeatedly. I am not on Brad's side, i am as i said, am curious, well was.

Tom Dent wrote:
>
>
> It depends *which* higher harmonics. If you could be a bit clearer
> about what Henk Badings actually did, I could tell what I thought
> about him. Perhaps you should not leap to conclusions about what my
> definition is.
>
> My working definition is that any single interval, for which someone
> can reliably hear beating when it is tempered (given some instrumental
> timbre consisting of the harmonic series), and which one can tune by
> ear through elimination of beats, can be meaningfully called pure.
>
> Since I believe I have been able to tune a 19/15 on an 'Italian'
> harpsichord, due to the peculiar structure of its partials, it seems
> not unreasonable that certain intervals whose numerator and
> denominator go up to 15-20 could be done by ear in favourable
> circumstances.
>
> However, I don't believe that anyone can tune 32/27 by eliminating
> beats between the 27th and 32nd partials. Nor can anything like a
> semitone be tuned by ear by eliminating beats. It is not simply the
> largeness of the numbers, it is the proximity of simpler intervals, as
> people know very well. Eg I don't think 13/12 can be done directly by ear.
>
> Whether 16/9 can be called 'pure' is highly debatable. Can one hear
> beats in a slightly tempered 16/9 ?
>
> There is a very interesting paper somewhere about some brass players
> who investigated exactly this question: exactly what intervals can be
> recognized and tuned beatless by ear?
>
> ~~~T~~~
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > So in your definition Hank Badings' use of higher harmonics is not
> using
> > pure intervals. I would disagree.
> >
> >
> >
> > Tom Dent wrote:
> > >
> > > Thus 25/24, 32/27, 36/25, 81/64 and a whole host of other 5-limit
> > > intervals are in no way 'pure', despite being composed of just ratios.
> > > These intervals are close enough to 1/1, 6/5, 7/5, 5/4 that their
> > > beating is clearly audible (with minimal and reasonable assumptions
> > > about instrumental timbre).
> > >
> > >
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Graham Breed <gbreed@gmail.com>

🔗Tom Dent <stringph@gmail.com>

🔗Graham Breed <gbreed@gmail.com>

🔗Brad Lehman <bpl@umich.edu>

> > Must be the decidedly
> > non-harpsichordistic timbre, then.
> > Actually, the timbre is quite similar to a lot of harpsichords I've
> examined: 2nd partial slightly stronger than the fundamental, and then
> a slight roll-off, but as per your instructions, nothing at all above
> the 6th partial. It's not exactly like any given instrument, but to
> say that it is "decidedly non-harpsichordistic" is simply not true.

What if you'd manufacture something that has a diminuendo and a bloom like real harpsichord tone, instead of the flatlined sustained sound (your "indoctrinate_me" file) that changes the experiment? Even if you've sampled or simulated a waveform from a single vibrating harpsichord string (what material? iron? brass? oder?), as soon as you sustain it you've altered its character profoundly.

And play the tritone's two notes together, or nearly so, instead of staggered by a second or more. The two notes have to have a similar intensity, similar voicing, and similar bloom/decay pattern for this to sound anything like a harpsichord.

Better yet, what if you'd make top-quality recordings of real harpsichord sound at various distances from the strings and soundboard, such as 10cm / 50cm / 2m / 10m / 30m in the direction where the player/tuner sits, and similar distances in other directions too?

Furthermore, listeners to ordinary 18th century harpsichord music have to make their assessment of intervallic quality almost immediately as the notes are played...not after 15-30 seconds of contemplation of a single artificially sustained sound.

When I'm tuning here, I usually know in the first half second or so if I've got the 45/32 tritone spot-on with one syntonic comma of shift between the two notes. It's pure. If it were necessary, which it isn't, I can temporarily tune a bass note under it giving the simultaneous 16:9 and the 5:2 or 5:4 against both notes.

And far more time and energy is being wasted here explaining this to (mostly) non-harpsichord-tuners than simply doing it. It's just not that hard to do, and it doesn't need rationalized explanations either. I know that Paul, Tom, and some others here DO tune harpsichords with more than adequate by-ear experience, and I remain startled that either they honestly don't hear what I do, or that they're too proud or self-certain or whatever to admit experiencing the (to me, obvious) purity of 45/32 on real harpsichords. Synthesized simulations aren't the same.

Brad Lehman

🔗Petr Parízek <p.parizek@chello.cz>

🔗Tom Dent <stringph@gmail.com>

🔗Petr Parízek <p.parizek@chello.cz>

🔗Carl Lumma <carl@lumma.org>

🔗Petr Parízek <p.parizek@chello.cz>

🔗Carl Lumma <carl@lumma.org>

Hi Petr,

> > I know of nothing about epimorics that makes them
> > easier to tune by ear than other rations of comparable
> > complexity.
>
> I'm pretty surprised that you who can hear perhaps every
> single cent deviation can say something like this.

I make no claims to superior hearing. I can tune pianos,
and I can tune my 15-limit slide guitar and that's about it.

> Small whole number ratios make the common fundamental well
> audible.

Yes, but how does this aid tuning? In the demo you posted,
we listened for the disappearance of beats, not the appearance
of the virtual fundamental.

> In case of epimoric ratios, the actual difference tone is
> equal to the fundamental, which makes it even clearer.

I think combination tones are of very limited use in tuning.
There may be specialized cases where they are useful, but
not in general.

> As to my own experience, I could always hear epimoric
> intervals much clearer than any others.

Can you hear 6/5 clearer than 5/3?

> > So much for the 'reed organ timbre too thick' hypothesis.
> > How far can you go, Petr? I tend to doubt even 14/13 would
> > work, but I'm curious to see.
>
> He asked if it was possible to tune 16/9 or 13/12 by
> eliminating beats and didn't say anything about the actual
> timbres. That's why I responded that it was, as long as the
> overtones were loud enough.

I was referring to my previous message regarding the Sabat
paper, where I speculated that they couldn't tune higher than
8/7 due to the thickness of the reed organ timbre. Obviously,
that's not a good explanation.

> The same is true for the 16/15 which I spoke about in my
> last answer.

I think it'd be a great exercise if you made files for the
epimores from 8/7 through 25/24 (if you were so inclined).
Ideally the sweep would go from the mediant below to the
mediant above the target ratio in the series of epimores,
i.e. from 19/17 to 17/15 for 9/8, with the target ratio in
the middle of the file.

> And if they are not, then there's always the
> possibility to begin the tuning in higher octaves where you
> can hear difference tones which can also help you an awful
> lot -- at least as far as I can hear them.

Where has this technique been helpful for you? I've
never tuned by listening to difference tones.

-Carl

🔗Petr Parízek <p.parizek@chello.cz>

Carl wrote:

> Yes, but how does this aid tuning?

Simply. If the interval is getting close to epimoric, the difference tones (which there are more of them audible if the sounding tones are rather high) get close to regular harmonic series, which proves the general synchronicity of the periods quite nicely -- i.e. the common fundamental. If it was a "semi-epimoric" factor (if I can use a term like that) like 9/7 or 7/5, the actual difference tone would be an octave higher than the fundamental and the surrounding difference tones would resemble odd harmonic series.

> I think combination tones are of very limited use in tuning.
> There may be specialized cases where they are useful, but
> not in general.

I don't think so. Again, when I hear JI intervals in higher octaves (meaning just diads without any third tone), I can often (let's say X for the lower frequency and Y for the higher one) hear Y-X and 2X-Y, sometimes also 3X-2Y, and rarely even 2Y-X. If the sound is richer in overtones, even more difference tones become audible. About four hours ago, I tried to play various JI intervals with a harmonium sample on my keyboard. When I got to 9/7, I was actually able to hear an additional 3:4:5 in the background. When I reached 14/11, I could eventually hear a non-existent 5:6:8 there. What's my explanation? For 9/7, the actual difference tone is 2 and the surrounding difference tones are 3, 5, and 11. For 14/11, they are 3, 5, 8, 17, respectively. Because the harmonium sample I used has its 2nd harmonic quite loud, the actual difference tones of the upper octaves also played a part, which is 4 in the first case and 6 in the second one.

> Can you hear 6/5 clearer than 5/3?

Yes, usually it sounds to me like that.

> I think it'd be a great exercise if you made files for the
> epimores from 8/7 through 25/24 (if you were so inclined).
> Ideally the sweep would go from the mediant below to the
> mediant above the target ratio in the series of epimores,
> i.e. from 19/17 to 17/15 for 9/8, with the target ratio in
> the middle of the file.

Sounds like a nice challenge. Do you have any preferences about absolute pitches or about the loudnesses of the overtones?

> Where has this technique been helpful for you? I've
> never tuned by listening to difference tones.

More than once, actually. One of the events, for example, was in 2004 when I was (not by sending SysEx dumps but instead by listening and retuning a sampler by ear) tuning a 17-limit meantone scale starting unexpectedly with Eb-G# of 17/13. See "parizek_17lqmt.scl" in Manuel's archive for more details.

Petr

🔗Petr Parízek <p.parizek@chello.cz>

🔗Paul Poletti <paul@polettipiano.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

actually your accusations is this thread have not at all been scientific. you guess that brad relates to a foreigner who just moved here, smoking something. pure fancy my dear boy.
and the lowest form of dialog i might add. What if Brad hears something you and tom can't?

now that you have concluded that only simple ratios can be tuned by ear let me point out that their are far more cultures on the globe that tune by ear that don't use simple ratios.
perhaps i could say that you are more interested in defending some false rationalization of reality, but i am not going to match my metaphysical assumptions with your own.

maybe we could have learned something , maybe social conditioning of Brad's past that feeds back into his perception, (perception is 90% feedback you know) but i guess the path chosen that there is nothing to learn is lazier way to deal with the issue.

Paul Poletti wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Brad > Lehman <bpl@...> wrote:
> >
> > > > Must be the decidedly
> > > > non-harpsichordistic timbre, then.
> > >
> > > Actually, the timbre is quite similar to a lot of harpsichords
> I've
> > > examined: 2nd partial slightly stronger than the fundamental,
> and then
> > > a slight roll-off, but as per your instructions, nothing at
> all above
> > > the 6th partial. It's not exactly like any given instrument,
> but to
> > > say that it is "decidedly non-harpsichordistic" is simply not
> true.
> >
> > What if you'd manufacture something that has a diminuendo and a bloom
> > like real harpsichord tone, [snip]
>
> What if you created a whole bunch of Red Herrings and dragged them
> across the trail, inventing a bunch of pseudo scientific nonsense that
> has nothing whatsoever to do with whether or not an augmented fourth
> can somehow create phantom tones that turn it into a V7 chord? What if
> you went on and on with such claptrap for an entire posting, hoping to
> entrap gullible readers who know even less than you about acoustics?
> What if nobody bought it?
>
> Ciao,
>
> P
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Aaron Krister Johnson <aaron@akjmusic.com>

Hey, this thread is really interesting.....

It's easily solvable...one could simply do a listening test, as we've
done in the past. If Brad can hear something special about 45/32,
there ought to be an aural test that would decide the matter.

Anyway, it's a shame that people get real nasty and competitive around
here to begin with. There's plenty of subtle things going on with
tuning, and it's easy to be misled, and to self-mislead. I think I've
proven this amply with my listening tests more than once. I'll never
forget how surprised I was by how easy most well-temps can pass for
each other, and how many people get attached to one of them or
another, and yet cannot recognize them in front of their ears. And
then there was that test a while ago, where six tones that ranged in 6
cents were played as a tone row, and the task was to find their order.
No one passed. No one. in spite of many bold claims to the contrary.

Kraig's point about perception is true, and I would add that we often
perceive by suggestion...I've even enjoyed the qualities of meantone
tuning while not listening to meantone, but thinking I've set my
keyboard tuning tables to it, when in fact it was set to something
else closer to 12-equal. Funny thing, perception.

Anyway, let's not try to pounce on each other like vultures--if Brad
as it turns out made a bold claim that wasn't back-upable, who among
us hasn't from time to time.

If those kinds of things never happen to you, congrats on being a
superior human being in every way.

-AKJ

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> actually your accusations is this thread have not at all been
> scientific. you guess that brad relates to a foreigner who just moved
> here, smoking something. pure fancy my dear boy.
> and the lowest form of dialog i might add. What if Brad hears something
> you and tom can't?
>
> now that you have concluded that only simple ratios can be tuned by ear
> let me point out that their are far more cultures on the globe that
tune
> by ear that don't use simple ratios.
> perhaps i could say that you are more interested in defending some
false
> rationalization of reality, but i am not going to match my metaphysical
> assumptions with your own.
>
> maybe we could have learned something , maybe social conditioning of
> Brad's past that feeds back into his perception, (perception is 90%
> feedback you know) but i guess the path chosen that there is nothing to
> learn is lazier way to deal with the issue.
>
> Paul Poletti wrote:
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Brad
> > Lehman <bpl@> wrote:
> > >
> > > > > Must be the decidedly
> > > > > non-harpsichordistic timbre, then.
> > > >
> > > > Actually, the timbre is quite similar to a lot of harpsichords
> > I've
> > > > examined: 2nd partial slightly stronger than the fundamental,
> > and then
> > > > a slight roll-off, but as per your instructions, nothing at
> > all above
> > > > the 6th partial. It's not exactly like any given instrument,
> > but to
> > > > say that it is "decidedly non-harpsichordistic" is simply not
> > true.
> > >
> > > What if you'd manufacture something that has a diminuendo and a
bloom
> > > like real harpsichord tone, [snip]
> >
> > What if you created a whole bunch of Red Herrings and dragged them
> > across the trail, inventing a bunch of pseudo scientific nonsense that
> > has nothing whatsoever to do with whether or not an augmented fourth
> > can somehow create phantom tones that turn it into a V7 chord? What if
> > you went on and on with such claptrap for an entire posting, hoping to
> > entrap gullible readers who know even less than you about acoustics?
> > What if nobody bought it?
> >
> > Ciao,
> >
> > P
> >
> >
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island
<http://anaphoria.com/index.html>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles
>

🔗Carl Lumma <carl@lumma.org>

Petr wrote...
> > I think combination tones are of very limited use in tuning.
> > There may be specialized cases where they are useful, but
> > not in general.
>
> I don't think so. Again, when I hear JI intervals in higher
> octaves (meaning just diads without any third tone), I can often
> (let's say X for the lower frequency and Y for the higher one)
> hear Y-X and 2X-Y, sometimes also 3X-2Y, and rarely even 2Y-X.
> If the sound is richer in overtones, even more difference tones
> become audible. About four hours ago, I tried to play various
> JI intervals with a harmonium sample on my keyboard. When I got
> to 9/7, I was actually able to hear an additional 3:4:5 in the
> background. When I reached 14/11, I could eventually hear a
> non-existent 5:6:8 there. What's my explanation? For 9/7, the
> actual difference tone is 2 and the surrounding difference tones
> are 3, 5, and 11. For 14/11, they are 3, 5, 8, 17, respectively.
> Because the harmonium sample I used has its 2nd harmonic quite
> loud, the actual difference tones of the upper octaves also
> played a part, which is 4 in the first case and 6 in the second
> one.

Sure you can hear these things, but do they help you
accurately tune the main interval?

> > Can you hear 6/5 clearer than 5/3?
>
> Yes, usually it sounds to me like that.

For me the 'locked' region around 6/5 is not as well
defined as around 5/3.

> > I think it'd be a great exercise if you made files for the
> > epimores from 8/7 through 25/24 (if you were so inclined).
> > Ideally the sweep would go from the mediant below to the
> > mediant above the target ratio in the series of epimores,
> > i.e. from 19/17 to 17/15 for 9/8, with the target ratio in
> > the middle of the file.
>
> Sounds like a nice challenge. Do you have any preferences
> about absolute pitches or about the loudnesses of the overtones?

I would start each file on different pitch between
middle C and the A below it. Else, pitch memory
could be used to find the targets.
As for the overtones, whatever you think would be best.
Perhaps a good idea not to go too far to the sawtooth
end of things, as such timbres can fatigue the ear with
repeated listening.

> > Where has this technique been helpful for you? I've
> > never tuned by listening to difference tones.
>
> More than once, actually. One of the events, for example,
> was in 2004 when I was (not by sending SysEx dumps but
> instead by listening and retuning a sampler by ear) tuning
> a 17-limit meantone scale starting unexpectedly with Eb-G#
> of 17/13. See "parizek_17lqmt.scl" in Manuel's archive for
> more details.

OK, I'll look it up.

-Carl

🔗Carl Lumma <carl@lumma.org>

🔗Robert walker <robertwalker@robertinventor.com>

Hi Aaron,

Actually, I think there are things that those tests can easily miss out on. I think also that when musicians take those tests and find that they can't pass them, they may unnecessarily tell themselves that they can't hear something when in fact they can - just not in the sense that was tested by the tests. Reason being that there are many ways of hearing, which may not always involve intellectually identifying pitches as e..g higher or lower.

For instance when notes are very close together in pitch, sometimes one may hear that there is a difference, but not be sure which is the highest in pitch of the two. Not even able to tell which was played first. Just that it seems to be two different pitches rather than a single pitch. I remember that used to happen to me quite a lot a few years ago though not often now. Some people can distinguish notes a tone or a semitone apart but can't tell which of the two is higher - as is mentioned in Shepard's original paper.

That then needs a subtler test than just to get someone to put the pitches in order, or to say which is the higher.

You could still test it. One idea is to have pairs of pitches. Some of the pairs are identical notes, and some are non identical. Then ask the listener to identify whether the two notes they hear are the same pitch or differ in pitch, without asking them to identify which they think is the highest in pitch.

But you can get more subtle than that too. You can be influenced by things that you can't actually distinguish intellectually, because you haven't yet learnt to identify them in words. But maybe your body responds in subtly different ways, e.g. different piano touch or something. Like using a dowsing rod to detect the presence of water, putting aside whether that actually works or not but same principle. That if you set up a delicate balance in your body then it may be influenced by things you can't actually intellectually hear. So one may perhaps play in a subtly different way in a tuning that you can't actually distinguish by ear in an intellectual fashion.

That could be quite hard to test, but real nevertheless. You probably could still test it if you did a delicate enough kind of experiment to pick up on the thing you are testing for. I.e.. the test has to match the effect you are looking for and it's not always that obvious what is a suitable test, it seems, in this area.

Just a few ideas to throw out :-)..

Robert

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
> Brad Lehman wrote:
>
>
>
> > Better yet, what if you'd make top-quality recordings of real
> > harpsichord sound at various distances from the strings and
soundboard,
> > such as 10cm / 50cm / 2m / 10m / 30m in the direction where the
> > player/tuner sits, and similar distances in other directions too?
>
>
>
> If there's something which most people don't find pure, they
>probably won't find it pure even on a real harpsichord.

Amen to that!

>I've tried lots of samples yesterday, no matter if those were
>decaying or sustained sounds, no matter if their timbres had a
>"bloom" or not,

Couldn't have said it better myself.

> no matter if their overtones were loud or soft, whatever I tried to
>play D-G# C#-A in 1/6-comma meantone, I always heard two "fictitious"
>slightly mistuned bass fifths of Bb-F and A-E, which can be explained
>by the difference tones. Having this very clear and easily
>understandable experience with sound samples which were so much
>different from each other, I would probably not begin hearing
>something completely new on the harpsichord you talk about.

Exactly! I've been tuning harpsichords and historic pianos for about
35 years now. I can't begin to estimate how many different instruments
I've tuned in this time, good, bad, and downright butt ugly. I started
tuning by ear, but in the early 1980's, after many attempts to build a
good visual indicator (a combination of strobe and oscilliscope), I
realized that it was stupid to use your eyes for something your ears
are far better at. So I designed and produced the "Poletti Box", a
tone generator programmed with about 40 temperaments which could be
shifted in pitch from A=1 Hz to about 490 Hz in 0,1 Hz steps. Ever
since then, I've tuned by setting the twelve unisons of the tenor
octave to the 12 tones provided by some sort of electronic device.

Now this doesn't mean that I don't check the quality of intervals
after finishing, and one of the things that is really interesting
about the whole process is how real instruments can differ slightly
from electronic precision. One of my main points has always been
accuracy, never accepting anything less than at least 0,01 Hz (not
cents) in terms of frequency production, which keeps any beating error
to a tolerable minimum. It's quite interesting how on some
instruments, even though the unisons can sound absolutely perfect
against the electronic sound, certain intervals such as fifths or
thirds don't beat correctly and require some minor tweaking. It all
comes down to localized funkiness, of course, inharmonicity caused by
a false string, localized aberrations in soundboard impedance, and the
like.

All that said, my overwhelming conclusion is that it is only more
difficult to hear anything on a real instrument than on an electronic
instrument, provided of course that the electronic is both precise and
reasonable rich in overtone content. It is not for nothing that
Werckmeister said the student of tuning who has trouble with a
harpsichord should practice using a regal. Why? Precisely because the
tone is (a) sustained and (b) rich in harmonics. Brad's implied
assertion that somehow his phantom tones are suddenly going to appear
if we impose all the handicaps and DISadvantages of the sound of a
real harpsichord is just plain nonsense. And remember, his whole point
initially was that this effect was so overwhelming and powerful that
it might have compelled several generations of composers to use
certain chord structures. Now he would have use believe that it only
exists under carefully controlled conditions, with only a certain type
of string materials, at certain precise distance to "the strings"
(which any Acoustics 1a student can tell you are NOT the point of
sound radiation source in ANY string instrument), with only certain
envelopes (the proper term for Brad's "diminuendo" and "bloom"), etc.
etc. etc.

Brad simply doesn't want to accept that his perception is subjective,
so he keeps changing his story and tossing out one pointless argument
after another. I would posit that since it is HIS assertion that he
hears it on HIS harpsichords tuned by HIM, the responsibility of
providing any proof rests upon him. So he should stop dreaming up
excuses, get himself down to Radio Shack and shell out 15 bucks or so
for a decent microphone and then make a recording at whatever distance
he wants, though I would posit that since HE hears it when he is
tuning, the most logical point to place the mic would be next to his
head as he is seated at the instrument (how many people listen to the
instrument at a distance of 5cm from the strings?). That should end
the matter once and for all. Either we will hear or we won't, punkt
schluß!

Ciao,

🔗Tom Dent <stringph@gmail.com>

--- In tuning@yahoogroups.com, Petr Parízek <p.parizek@...> wrote:
>
>
> "Sound files would be very welcome! Particularly tuning 13/12 by
elimination of beats..."
>
> Okay, here is a recording of two sawtooth periods with relative
frequencies of 13 and 12. The 13 is slightly higher at the beginning
and it's getting closer and closer to the actual 13 until the beats
disappear: http://download.yousendit.com/BF6B043C16DC85A3
>
> Petr

Thanks - for me, this file more or less proves my point. The beats you
listen out for and eliminate are barely audible behind a permanent,
huge, hairy slew of much louder beats from the interference of lower
harmonics. These lower harmonics tell me (unreconstructed tonalist
that I am) that it's a simply a dissonance or a mistuned unison. I
hadn't realized to what extent one might tune dissonances exactly by
listening to beats behind beats...

Even harder for me, and I suspect others, would be to identify 14/13
vs. 13/12 vs. 12/11 etc. without external help. (I.e. listen to one
such interval and identify it immediately.)

This makes me tweak, or rather complete, my definition: not only
should 'pure' intervals be tunable beatless precisely by ear, they
should be immediately recognizable and consonant.

Yes, this is another subjective and fuzzy criterion, but it is
semantically and acoustically as clear as it can be, and has
historical backing.

7/6 may be recognized as a consonance (at least since Huyghens), while
25/24 is a dissonance. Somewhere between the two, possibly depending
on timbre, absolute pitch etc., there must be a (fuzzy) boundary.

By the way, has there been any study on the variability of difference
tone perception? Since it is apparently due to nonlinearities in the
ear and auditory nervous system I would expect it to differ
significantly among the population.
~~~T~~~

🔗Tom Dent <stringph@gmail.com>

--- In tuning@yahoogroups.com, "Aaron Krister Johnson" <aaron@...> wrote:
>
> Hey, this thread is really interesting.....
>
> It's easily solvable...one could simply do a listening test, as we've
> done in the past.

So listen to my harpsichord recording already! That's a start, at least.

> If Brad can hear something special about 45/32,
> there ought to be an aural test that would decide the matter.

Ah, you mean feed him intervals which are nearly but not exactly
45/32, with timbres missing the 7th harmonic, and see if he can pick
out the 'purest' one.
Good idea, but there are too many get-out clauses... 'Not
harpsichordistic enough!' 'No bloom!' 'Beats appearing where they
shouldn't be!' 'Wrongly synthesized!'

But this is not really the reason why we are arguing. What Brad hears
is a personal experience that (by definition) no-one else can have
access to.

The point is that, in his capacity as Historical Temperament Scholar,
he has used this (apparently unreproducible) personal experience of
'pure 45/32' to try and make broad deductions about what people 250 or
300 years ago were hearing and tuning.

Before doing this, one ought to try and find out if other people do
have a similar experience of hearing. I tend to believe that the basic
acoustics of human hearing haven't changed that much over the last 300
years.
If almost no-one today hears intervals like you think you do, it's a
fairly good bet that no-one in 1730 did either. (Unless you have the
unique luck to have inherited a set of genuine early 18th century ears!)

> Kraig's point about perception is true

Well... I would hope that almost everyone could agree, in many cases,
whether a simple interval is beating or not. Not everything in
acoustics is subjective.

> if Brad as it turns out made a bold claim that wasn't back-upable,
> who among us hasn't from time to time.

Not just 'made a bold claim', but based a whole superstructure of
speculation upon it, and written about that as if it were historical
fact. History can never be quite objective, but an effort towards it
should be made.
~~~T~~~

🔗Paul Poletti <paul@polettipiano.com>

🔗Petr Parízek <p.parizek@chello.cz>

🔗Carl Lumma <carl@lumma.org>

🔗Brad Lehman <bpl@umich.edu>

Posted by: "Kraig Grady" kraiggrady@anaphoria.com (apparently directed to Paul P):

> actually your accusations is this thread have not at all been
> scientific. you guess that brad relates to a foreigner who just moved
> here, smoking something. pure fancy my dear boy.
> and the lowest form of dialog i might add. What if Brad hears something
> you and tom can't?
> > now that you have concluded that only simple ratios can be tuned by ear
> let me point out that their are far more cultures on the globe that
> tune
> by ear that don't use simple ratios.
> perhaps i could say that you are more interested in defending some
> false
> rationalization of reality, but i am not going to match my metaphysical
> assumptions with your own.
> > maybe we could have learned something , maybe social conditioning of
> Brad's past that feeds back into his perception, (perception is 90%
> feedback you know) but i guess the path chosen that there is nothing to
> learn is lazier way to deal with the issue.

Thanks Kraig!

In my case it's all very simple, and obvious (to me). For lack of a clearer term this morning, I hear geometrically. In 25 years of tuning harpsichords by ear, I have messed around with plenty of JI scales. It's as easy as doing straightedge-and-compass constructions on paper. It builds shapes and relationships. I don't see or hear numbers, or think in any numbers. It's not about beats, either, other than the obvious zeroing of beats from each tuning step/relationship to the next.

When I hear a 45/32 tritone, an augmented fourth, I recognize that instantly as "pure" because both members belong to an easy JI scale in relationship with one another...and my ear automatically fills in more members of the same scale, the most obvious first new note being (as I said) a 9/8 second above or a 16/9 minor seventh below. It makes a triangle of the three notes, all in simple ratios. The main members of that JI scale snap into place (in my ear) even if some of them aren't being played; it's enough to hear that two of them are being played, especially with an interval as strongly directional as a tritone. Play me a 45/32 tritone and I instantly recognize the shape "pure dominant 7th: root-M3-m7 in JI"...even when the root isn't being played.

That same 45/32 tritone happens to be present in regular 1/6 syntonic comma, because there's an offset of exactly one syntonic comma to get from one to the other. In the old superscript notation used by Murray Barbour et al, the first tuning book I really dove into (hands on at harpsichords) before I was 20, it's for example a D 0 and a G# -1.

I've been hearing in this way for more than half my life, when dealing with whole-number offsets of syntonic commas, and it's just an instantaneous (right-brained?) process in my perception. Maybe some would classify this and dismiss this as merely a subjective thing, and therefore not real TO THEM, but it's obviously an objective and measurable reality that I'm hearing: the offset of exactly one syntonic comma defining geometric marker points, and laying out other elements of simple scales. When I hear a tritone within regular 1/6, it's huge; and when I hear two of them interlocked as a diminished-7th, it's even more huge. It's pure. It makes the harpsichord more powerful when it's a 45/32 than when it is off-spot. It's so startling when it comes up that I can't NOT hear it, even though I spend most of my time playing in other temperaments where things ARE deliberately off-spot by a little bit. (And maybe, because of that, it's more of a special treat whenever I return to regular 1/6 syntonic or fool around with more JI, hands on. Simplicity and complexity both have their virtues, and they do different things to or in the brain.)

I'm sorry that my descriptions of this don't convince people who weren't already hearing it.

Brad Lehman

🔗Kraig Grady <kraiggrady@anaphoria.com>

No reason to qualify your perception as subjective. There is no such thing as objective perception. It seems that some are using the term "pure" to mean acoustical and it seems you are using it in the sense of pure "functionally". This is the way people tune around the world and why a 14 Vietnamese girl can tune her string instrument to intervals that are impossible for us, she understands the function ( thought of often as an emotional quality) of how an interval "works" in a scale.

Brad Lehman wrote:
>
> Posted by: "Kraig Grady" kraiggrady@anaphoria.com > <mailto:kraiggrady%40anaphoria.com> (apparently directed
> to Paul P):
>
> > actually your accusations is this thread have not at all been
> > scientific. you guess that brad relates to a foreigner who just moved
> > here, smoking something. pure fancy my dear boy.
> > and the lowest form of dialog i might add. What if Brad hears something
> > you and tom can't?
> >
> > now that you have concluded that only simple ratios can be tuned by ear
> > let me point out that their are far more cultures on the globe that
> > tune
> > by ear that don't use simple ratios.
> > perhaps i could say that you are more interested in defending some
> > false
> > rationalization of reality, but i am not going to match my metaphysical
> > assumptions with your own.
> >
> > maybe we could have learned something , maybe social conditioning of
> > Brad's past that feeds back into his perception, (perception is 90%
> > feedback you know) but i guess the path chosen that there is nothing to
> > learn is lazier way to deal with the issue.
>
> Thanks Kraig!
>
> In my case it's all very simple, and obvious (to me). For lack of a
> clearer term this morning, I hear geometrically. In 25 years of tuning
> harpsichords by ear, I have messed around with plenty of JI scales.
> It's as easy as doing straightedge-and-compass constructions on paper.
> It builds shapes and relationships. I don't see or hear numbers, or
> think in any numbers. It's not about beats, either, other than the
> obvious zeroing of beats from each tuning step/relationship to the next.
>
> When I hear a 45/32 tritone, an augmented fourth, I recognize that
> instantly as "pure" because both members belong to an easy JI scale in
> relationship with one another...and my ear automatically fills in more
> members of the same scale, the most obvious first new note being (as I
> said) a 9/8 second above or a 16/9 minor seventh below. It makes a
> triangle of the three notes, all in simple ratios. The main members of
> that JI scale snap into place (in my ear) even if some of them aren't
> being played; it's enough to hear that two of them are being played,
> especially with an interval as strongly directional as a tritone. Play
> me a 45/32 tritone and I instantly recognize the shape "pure dominant
> 7th: root-M3-m7 in JI"...even when the root isn't being played.
>
> That same 45/32 tritone happens to be present in regular 1/6 syntonic
> comma, because there's an offset of exactly one syntonic comma to get
> from one to the other. In the old superscript notation used by Murray
> Barbour et al, the first tuning book I really dove into (hands on at
> harpsichords) before I was 20, it's for example a D 0 and a G# -1.
>
> I've been hearing in this way for more than half my life, when dealing
> with whole-number offsets of syntonic commas, and it's just an
> instantaneous (right-brained?) process in my perception. Maybe some
> would classify this and dismiss this as merely a subjective thing, and
> therefore not real TO THEM, but it's obviously an objective and
> measurable reality that I'm hearing: the offset of exactly one syntonic
> comma defining geometric marker points, and laying out other elements of
> simple scales. When I hear a tritone within regular 1/6, it's huge; and
> when I hear two of them interlocked as a diminished-7th, it's even more
> huge. It's pure. It makes the harpsichord more powerful when it's a
> 45/32 than when it is off-spot. It's so startling when it comes up that
> I can't NOT hear it, even though I spend most of my time playing in
> other temperaments where things ARE deliberately off-spot by a little
> bit. (And maybe, because of that, it's more of a special treat whenever
> I return to regular 1/6 syntonic or fool around with more JI, hands on.
> Simplicity and complexity both have their virtues, and they do
> different things to or in the brain.)
>
> I'm sorry that my descriptions of this don't convince people who weren't
> already hearing it.
>
> Brad Lehman
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, Brad Lehman <bpl@...> wrote:

Thanks to Brad for finally (!) at least attempting to provide us with
an explanation of what is going on inside his head. Now let's take a
good hard objective look at it.
>
> In my case it's all very simple, and obvious (to me). For lack of a
> clearer term this morning, I hear geometrically. In 25 years of tuning
> harpsichords by ear, I have messed around with plenty of JI scales.
> It's as easy as doing straightedge-and-compass constructions on paper.
> It builds shapes and relationships. I don't see or hear numbers, or
> think in any numbers. It's not about beats, either, other than the
> obvious zeroing of beats from each tuning step/relationship to the next.

Right. It seems as though Brad is saying that his mental processing of
musical tones seeks relationships which can be explained with extended
JI relationships, a sort of virtual reduction of an extended JI
fractalization. Ok, let's go with that idea and see where it takes us.
>
> When I hear a 45/32 tritone, an augmented fourth, I recognize that
> instantly as "pure" because both members belong to an easy JI scale in
> relationship with one another...and my ear automatically fills in more
> members of the same scale, the most obvious first new note being (as I
> said) a 9/8 second above or a 16/9 minor seventh below. It makes a
> triangle of the three notes, all in simple ratios. The main members of
> that JI scale snap into place (in my ear) even if some of them aren't
> being played; it's enough to hear that two of them are being played,
> especially with an interval as strongly directional as a tritone.

Right. So the salient points are:

(1) any two notes which "both ... belong to an easy JI scale in
relationship with one another" are perceived by Brad as being pure,
precisely because they fit into some sort of extended JI scheme. We're
not quite sure what the word "easy" means, but we might assume it
means "simple", as in fairly simple ratios, or perhaps JI
relationships which don't require too many leap-frog jumps on Brad's
internal sonic checkerboard; shall we say, a minimum of JI
fractalization?

(2) that other tones which are not physically sounding appear in
Brad's perceptual tonescape because they fit into some solution to the
internal search process which fits a relatively simple set of JI
ratios, again requiring a minimum of fractalization, in order to fill
in the gaps and produce a larger, more complex harmonic structure
which is nonetheless composed of simple ratios.

I think it is fair to say that's an accurate analysis of his logic,
but someone correct me please if I am missing something or overstating
something else.

Now, the logic in application:

> Play
> me a 45/32 tritone and I instantly recognize the shape "pure dominant
> 7th: root-M3-m7 in JI"...even when the root isn't being played.

Right. Understood, at lest I think so. Now the obvious elephant in
Brad's intellectual workshop, which outh to be pretty easy for anybody
on this list to see, might be phrased thusly; "So Brad, what happens
when you hear a tritone in 1/3 comma meantone?"

Why? Because the tritone in 1/3 mean has the ratio of 25/18, which is
not only an even simpler version of a "pure" augmented fourth, using
the standard terminology of pure (i.e. an incidence of harmonic
congruence which is lower in the series of both tones rather than
higher), but it also would seem by Brad's logic to create an even more
compelling series of "easy" JI relationships. Assuming the upper note
makes a pure major third above some note, we would get the following
series of 4 notes from top down:

25
20
18
10

25/20 = 5/4
20/18 = 10/9 or the minor whole tone, a simple and readily
recognizable interval
18/10 = 9/5 which is the second most simple "natural 7th", being
almost as "pure" (again by normal definition) as THE natural 7th, 7/4,
and certainly far more simple than Brad's "easy" 16/9 minor 7th.

So, if we tally it all up, we have:

(a) two intervals which are markedly simpler than Brad's 1/6 comma
version, the augmented 4th and the minor 7th

(b) one interval which is ever so slightly more complex (the minor
whole tone as opposed to the major)

So by Brad's logic, the augmented 4th in 1/3 comma meantone should be
even purer yet, since it fits into what would appear to be an even
"easier JI scale". At the very least, I would think it would be
equally "Brad-pure" (maybe we should call it Brure?... after we figure
out exactly what IT is, that is!).

Hmmmm....

>
> Maybe some
> would classify this and dismiss this as merely a subjective thing, and
> therefore not real TO THEM, but it's obviously an objective and
> measurable reality that I'm hearing: the offset of exactly one syntonic
> comma defining geometric marker points, and laying out other
elements of
> simple scales.

This is where Brad gets into trouble, and having had lots of these
disagreements with Brad over the years, it seems to be a recurring
breakdown point in his arguments: he looses track of what is truly
objective and measurable and what is a subjective conclusion drawn
from a series of objective conditions. It's rather like me saying that
if I stand on the street in front the entrance to my building, I can
see the supermarket 30 meters around the corner, because I can see the
bank and restaurant and the flower shop on the other three corners,
and after years of going there I know that the supermarket is just 30
meters to the left of that triangle of reference points. All true
enough, and the relationships between those observable objects and the
supermarket are all objective and verifiable by anyone; yet the fact
remains that just because I can see three points from which one can
indeed see the supermarket, I cannot actually SEE the supermarket from
where I am now, no matter how vivid it is in my imagination, nor can
anyone else, and therefore, "seeing" the supermarket is not an
objective reality.

> When I hear a tritone within regular 1/6, it's huge; and
> when I hear two of them interlocked as a diminished-7th, it's even more
> huge. It's pure.

Umm, now it seems as though width is also a factor of Brure. OK, we'll
just have to accept that and throw it into the mix. A work in progress...

> It makes the harpsichord more powerful when it's a
> 45/32 than when it is off-spot. It's so startling when it comes up
that
> I can't NOT hear it, even though I spend most of my time playing in
> other temperaments where things ARE deliberately off-spot by a little
> bit.

Right. So I think the only logical interpretation of this statement is
that Brad likes the particular sound of this interval, and so when he
hears it, it stands out to him. That it actually increase the acoustic
output of the harpsichord is highly unlikely, but that could easily be
verified objectively. Let's leave it in the bin labeled "unverifiable
assertion" for the moment, which bin is definitely on the subjective
side of our intellectual workbench.

> Simplicity and complexity both have their virtues, and they do
> different things to or in the brain.)

Couldn't agree more. It's just not clear exactly how they are
operative in the set of conditions you have laid out for us, and/or
how one situation compares to similar conditions of simplicity and
complexity.
>
> I'm sorry that my descriptions of this don't convince people who
weren't
> already hearing it.

Well, unless I missed a post, the only person who was "already"
hearing it, and the only person who still is "already" hearing it, is
you. So it's kind of a funny sentence, which would seem to imply that
there are more people in Brad's camp than just Brad himself.

Once again, I think the only way to understand this is that Brad has a
series of subjective expectations which so strongly influence his
perception that he has difficulty separating that which is actually
occurring from that which he imagines. Not intended as a putdown, and
I will say that the capability of compelling imagination is very
important for good musicianship, or at least for allowing someone to
make interesting music. One should be aware of it, though, and not
assume that others are automatically on your wavelength, and also not
imply that their problem is that they aren't "experts" in the
interpretation of 18th continuo, which would mean a simple lack of
knowledge. This doesn't seem to be the case. It's just that they
aren't Brad.

Ciao,

🔗Tom Dent <stringph@gmail.com>

I think if you set up 1/4-comma meantone on a harpsichord and ask a
hundred harpsichordists whether middle c-e is pure or whether c-g is
beating, you will get the answer 'Yes' 100 times. That is perception
but it is not subjective...

If we can read 300-year old books and still understand, to some
extent, what they said about tuning, there must be some objective
elements in acoustic perception. It is precisely these elements - 'if
you do this, you will hear that' - that let us get anywhere at all
with history. (This has led to an overvaluing of mathematically
precise source material, but that's another story.)

I don't object at all to Brad's hearing 'geometrically'. But I would
object if he or anyone else were to say or imply he has a special or
better or deeper insight into historic tunings because of it.

And what is Kraig doing saying (previous message) that I 'can't' hear
whatever it is? What I can't do is things like play the
'Hammerklavier' sonata or run a 4-minute mile. So is my hearing not
good or practised or geometric enough for the magic tritone? ... 'Can'
and 'can't' are pretty judgemental. I simply *don't* hear it.

Anyway, 'functional purity' is still mysterious to me. Does the 45/32
tritone have a special, irreplaceable musical function within a scale
that other tritones that are also somewhat sharper than 7/5 definitely
don't? Seems to me that many intervals in the Western chromatic scale
can fulfil their functions pretty well within a largish range of
intonation - maybe up to a comma.

How far can Brad adjust the interval such that the magic feeling is
still there? What is the wiggle-room? How precise is his aural
geometry? This would be a good time for some self-testing, tuning
hammer in hand...

~~~T~~~

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> No reason to qualify your perception as subjective. There is no such
> thing as objective perception. It seems that some are using the term
> "pure" to mean acoustical and it seems you are using it in the sense of
> pure "functionally". This is the way people tune around the world and
> why a 14 Vietnamese girl can tune her string instrument to intervals
> that are impossible for us, she understands the function ( thought of
> often as an emotional quality) of how an interval "works" in a scale.
>
>

🔗Paul Poletti <paul@polettipiano.com>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> No reason to qualify your perception as subjective. There is no such
> thing as objective perception.

Yes and No. Ultimately, existence is an illusion, yet we persist in
giving form and shape to our illusion by inventing concepts such as
dark/light, hot/cold, up/down, here/there, now/then. It is all just
more of that sweet/sour fruit of the Tree of the Knowledge of Good and
Bad, which is there reason we are barred from entering the Garden.

Generally, it helps your journey through the illusion if you don't
start redefining the form and shape that fellow travelers have already
given to certain basic aspects. If for example, you think right really
ought to be called left, or up really should be called down, there are
certain functions in the Grand Shared Dream you shouldn't consider
fulfilling, like air traffic controller to name one. This
subjective/objective dichotomy is a favorite whipping boy for those
who like to play with these concepts, but ultimately such denial of
any difference between the two generates a lot more heat than light,
at least compared to cold and dark. Basically, it comes down to this:
if you go about using terms in ways which are basically in
contradiction with how most people understand them, your communication
skills will be limited. Unless you are a poet, in which case they
would be enhanced.

> It seems that some are using the term
> "pure" to mean acoustical and it seems you are using it in the sense of
> pure "functionally". This is the way people tune around the world and
> why a 14 Vietnamese girl can tune her string instrument to intervals
> that are impossible for us, she understands the function ( thought of
> often as an emotional quality) of how an interval "works" in a scale.

Interesting proposition, that Brad is thinking in melodic
relationships rather than harmonically. But I don't think Brad means
this. I think he actually hears imaginary harmonic chord structures,
and when he talks about the compelling nature of the sound, he means
harmonically.

By the way, there is nothing mystical about 14 year old girls tuning
intervals which sound foreign to us. Millions of musicians every day
quite accurately produce ET major and minor thirds, which are
completely arbitrary intervals, and they sound quite foreign (and
ugly) to me. I really don't think I could sing or tune one anymore,
except by laying down an equal temperament on a keyboard. But just
Bam! lay my finge in the right space on an unfretted string? No way!
But the fact that so many people CAN do it is nothing more mysteious
than Indoctrination. It is a powerful force, which requires no further
explanation, functional, emotional, or otherwise. It's just salivation
upon hearing ringing bells, that's all.
>
> Brad Lehman wrote:
> >
> > Posted by: "Kraig Grady" kraiggrady@...
> > <mailto:kraiggrady%40anaphoria.com> (apparently directed
> > to Paul P):
> >
> > > actually your [snip snip snip SNIP]

BTW, am I wrong, or do a lot of people here not seem to care that they
are uselessly filling up list archival space with endless repetitions
of entire postings attached to the end of their reply? On other groups
I contribute to, this is considered to be very bad form. And I don't
think it is an empty worry. Has anybody else noticed lately how
incredibly slow YahooGroups has become? Takes forever for it to
search, to load pages, to bring up lists, etc. Storage is NOT
infinite, you know, and they can't go on forever providing it for
free, especially not when people make it a habit of just tearing-off
the wrappers and tossing them on the virtual ground over and over again.

Ciao,

🔗Brad Lehman <bpl@umich.edu>

🔗Kraig Grady <kraiggrady@anaphoria.com>

You continue to misunderstand every single post of mine, even humorous ones. Frankly i tried to contact you off list to deal with a rather minor misunderstanding, but you refused to discuss it.
but i will try once more.
I don't remember brad saying it was beatless, he said it had a pure quality to his ear. Pure is subjective to the culture, for example, as i showed an example.
By functional i am referring the to a dominant chord. As we know a 7/5 does not work in dominant chord so i assume Brad is applying the term in reference to that.
It seemed by his response that he confirmed that at least in part.
The whole argument, as far as i can see, is one and only one of terminology.
As you might know i am an promoter of JI over other systems so i will use 7s when ever the opportunity allows me too. I am not going to use Brad's tuning i do not think. But like those that use ETs i will accept what people tell me what they hear to some extent. Scriabin saw colors, and yet i can take a 100 people and none of them will see what he saw. I don't see what this proves except the rarity of his perception. and likewise that i would not assume some defect of those who don't since those words were being put into my mouth.

Tom Dent wrote:
>
>
> I think if you set up 1/4-comma meantone on a harpsichord and ask a
> hundred harpsichordists whether middle c-e is pure or whether c-g is
> beating, you will get the answer 'Yes' 100 times. That is perception
> but it is not subjective...
>
> If we can read 300-year old books and still understand, to some
> extent, what they said about tuning, there must be some objective
> elements in acoustic perception. It is precisely these elements - 'if
> you do this, you will hear that' - that let us get anywhere at all
> with history. (This has led to an overvaluing of mathematically
> precise source material, but that's another story.)
>
> I don't object at all to Brad's hearing 'geometrically'. But I would
> object if he or anyone else were to say or imply he has a special or
> better or deeper insight into historic tunings because of it.
>
> And what is Kraig doing saying (previous message) that I 'can't' hear
> whatever it is? What I can't do is things like play the
> 'Hammerklavier' sonata or run a 4-minute mile. So is my hearing not
> good or practised or geometric enough for the magic tritone? ... 'Can'
> and 'can't' are pretty judgemental. I simply *don't* hear it.
>
> Anyway, 'functional purity' is still mysterious to me. Does the 45/32
> tritone have a special, irreplaceable musical function within a scale
> that other tritones that are also somewhat sharper than 7/5 definitely
> don't? Seems to me that many intervals in the Western chromatic scale
> can fulfil their functions pretty well within a largish range of
> intonation - maybe up to a comma.
>
> How far can Brad adjust the interval such that the magic feeling is
> still there? What is the wiggle-room? How precise is his aural
> geometry? This would be a good time for some self-testing, tuning
> hammer in hand...
>
> ~~~T~~~
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > No reason to qualify your perception as subjective. There is no such
> > thing as objective perception. It seems that some are using the term
> > "pure" to mean acoustical and it seems you are using it in the sense of
> > pure "functionally". This is the way people tune around the world and
> > why a 14 Vietnamese girl can tune her string instrument to intervals
> > that are impossible for us, she understands the function ( thought of
> > often as an emotional quality) of how an interval "works" in a scale.
> >
> >
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Kraig Grady <kraiggrady@anaphoria.com>

Brad response seem to confirm what i said.
As far as the meaning of words that everyone uses, there is disagreement even among those that are on your side, so i state, there is not one completely define meaning. LA Monte Young would say all his intervals are pure and he is in the range of over 200. not that he is right or you are wrong, just that it means different things to different people. That people think and hear differently is a cause to celebration, cause in the end, it creates greater diversity in the music we can enjoy.
I cannot tune ET intervals at all and i always found them confusing which is how ended up working in different tunings so early.

Paul Poletti wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > No reason to qualify your perception as subjective. There is no such
> > thing as objective perception.
>
> Yes and No. Ultimately, existence is an illusion, yet we persist in
> giving form and shape to our illusion by inventing concepts such as
> dark/light, hot/cold, up/down, here/there, now/then. It is all just
> more of that sweet/sour fruit of the Tree of the Knowledge of Good and
> Bad, which is there reason we are barred from entering the Garden.
>
> Generally, it helps your journey through the illusion if you don't
> start redefining the form and shape that fellow travelers have already
> given to certain basic aspects. If for example, you think right really
> ought to be called left, or up really should be called down, there are
> certain functions in the Grand Shared Dream you shouldn't consider
> fulfilling, like air traffic controller to name one. This
> subjective/objective dichotomy is a favorite whipping boy for those
> who like to play with these concepts, but ultimately such denial of
> any difference between the two generates a lot more heat than light,
> at least compared to cold and dark. Basically, it comes down to this:
> if you go about using terms in ways which are basically in
> contradiction with how most people understand them, your communication
> skills will be limited. Unless you are a poet, in which case they
> would be enhanced.
>
> > It seems that some are using the term
> > "pure" to mean acoustical and it seems you are using it in the sense of
> > pure "functionally". This is the way people tune around the world and
> > why a 14 Vietnamese girl can tune her string instrument to intervals
> > that are impossible for us, she understands the function ( thought of
> > often as an emotional quality) of how an interval "works" in a scale.
>
> Interesting proposition, that Brad is thinking in melodic
> relationships rather than harmonically. But I don't think Brad means
> this. I think he actually hears imaginary harmonic chord structures,
> and when he talks about the compelling nature of the sound, he means
> harmonically.
>
> By the way, there is nothing mystical about 14 year old girls tuning
> intervals which sound foreign to us. Millions of musicians every day
> quite accurately produce ET major and minor thirds, which are
> completely arbitrary intervals, and they sound quite foreign (and
> ugly) to me. I really don't think I could sing or tune one anymore,
> except by laying down an equal temperament on a keyboard. But just
> Bam! lay my finge in the right space on an unfretted string? No way!
> But the fact that so many people CAN do it is nothing more mysteious
> than Indoctrination. It is a powerful force, which requires no further
> explanation, functional, emotional, or otherwise. It's just salivation
> upon hearing ringing bells, that's all.
> >
> > Brad Lehman wrote:
> > >
> > > Posted by: "Kraig Grady" kraiggrady@...
> > > <mailto:kraiggrady%40anaphoria.com> (apparently directed
> > > to Paul P):
> > >
> > > > actually your [snip snip snip SNIP]
>
> BTW, am I wrong, or do a lot of people here not seem to care that they
> are uselessly filling up list archival space with endless repetitions
> of entire postings attached to the end of their reply? On other groups
> I contribute to, this is considered to be very bad form. And I don't
> think it is an empty worry. Has anybody else noticed lately how
> incredibly slow YahooGroups has become? Takes forever for it to
> search, to load pages, to bring up lists, etc. Storage is NOT
> infinite, you know, and they can't go on forever providing it for
> free, especially not when people make it a habit of just tearing-off
> the wrappers and tossing them on the virtual ground over and over again.
>
> Ciao,
>
> P
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Carl Lumma <carl@lumma.org>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Paul Poletti <paul@polettipiano.com>

🔗Aaron Krister Johnson <aaron@akjmusic.com>

Kraig, I like your points AND Carl's points here.

The term "Just Intonation" has always bothered me, and I find rational
intonation more accurate. JI can and often does, beat like crazy.

But still, like Carl says, the 'kernel intervals' let us call them, of
JI, are meant to not beat--of course we can play '2nd generation
intervals' which beat like mad, but the main reason for being of JI is
the stasis and stability of beatless intervals as reference points.

So, anyway, Brad *should* answer whether he hears those intervals as
beatless.

-AKJ.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> Pure is a bad word maybe in all cases.
> It implies everything else is dirty and/or impure,
> hence is loaded with value judgments.
> Kyle Gann's music is nothing but JI,
> but anything but beatless.
> so not good to associate these terms either.
> separately is fine!
>
> Carl Lumma wrote:
> >
> > Brad wrote...
> > > Of course I hear 25/18 (and its inversion, 36/25) as pure, in 1/3
> > > comma mean.
> >
> > Brad- "pure" is a common synonym for "beatless". Are you claiming
> > these intervals are beatless? Yes or no will suffice.
> >
> > To those of us using "pure" to mean beatless, maybe we shouldn't.
> > Maybe we should say beatless.
> >
> > To those of us using "pure" to mean something else, maybe they
> > shouldn't, either. Maybe they should be a little more creative
> > and pick words that don't have a semi-standard meaning in
> > psychoacoustics.
> >
> > "Just" is also sometimes used as a synonym for beatless, but
> > not as often as "pure" is I think, and anyway it probably
> > shouldn't be. But still it may serve those interested in
> > describing their perceptions to avoid loaded terms like these.
> >
> > -Carl
> >
> >
>
> --
> Kraig Grady
> North American Embassy of Anaphoria Island
<http://anaphoria.com/index.html>
> The Wandering Medicine Show
> KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles
>

🔗Carl Lumma <carl@lumma.org>

🔗Kraig Grady <kraiggrady@anaphoria.com>

I tend to think of beatless not as a definition but a common, but not always, quality. The rationality came first and the empirical quality was noticed afterwards. Rational Intonation i could be convinced of after all this blood on the floor.
I agree and always have that the quality of 7/5 should be different than 45/32. or some other unknown factor is involved.
I would be satisfied to hear what Brad hears in the 7/5, beatless or any quality would be educational.

Aaron Krister Johnson wrote:
>
> Kraig, I like your points AND Carl's points here.
>
> The term "Just Intonation" has always bothered me, and I find rational
> intonation more accurate. JI can and often does, beat like crazy.
>
> But still, like Carl says, the 'kernel intervals' let us call them, of
> JI, are meant to not beat--of course we can play '2nd generation
> intervals' which beat like mad, but the main reason for being of JI is
> the stasis and stability of beatless intervals as reference points.
>
> So, anyway, Brad *should* answer whether he hears those intervals as
> beatless.
>
> -AKJ.
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > Pure is a bad word maybe in all cases.
> > It implies everything else is dirty and/or impure,
> > hence is loaded with value judgments.
> > Kyle Gann's music is nothing but JI,
> > but anything but beatless.
> > so not good to associate these terms either.
> > separately is fine!
> >
> > Carl Lumma wrote:
> > >
> > > Brad wrote...
> > > > Of course I hear 25/18 (and its inversion, 36/25) as pure, in 1/3
> > > > comma mean.
> > >
> > > Brad- "pure" is a common synonym for "beatless". Are you claiming
> > > these intervals are beatless? Yes or no will suffice.
> > >
> > > To those of us using "pure" to mean beatless, maybe we shouldn't.
> > > Maybe we should say beatless.
> > >
> > > To those of us using "pure" to mean something else, maybe they
> > > shouldn't, either. Maybe they should be a little more creative
> > > and pick words that don't have a semi-standard meaning in
> > > psychoacoustics.
> > >
> > > "Just" is also sometimes used as a synonym for beatless, but
> > > not as often as "pure" is I think, and anyway it probably
> > > shouldn't be. But still it may serve those interested in
> > > describing their perceptions to avoid loaded terms like these.
> > >
> > > -Carl
> > >
> > >
> >
> > --
> > Kraig Grady
> > North American Embassy of Anaphoria Island
> <http://anaphoria.com/index.html <http://anaphoria.com/index.html>>
> > The Wandering Medicine Show
> > KXLU <http://www.kxlu.com/main/index.asp > <http://www.kxlu.com/main/index.asp>> 88.9 FM Wed 8-9 pm Los Angeles
> >
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗Magnus Jonsson <magnus@smartelectronix.com>

🔗Tom Dent <stringph@gmail.com>

Well, that cri de coeur was quite revealing.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:

> I don't remember brad saying it was beatless, he said it had a pure
> quality to his ear.

OK, that means that his idea is *different* from that of many German
Baroque sources, which present quite clearly the idea of eliminating
beats in consonances. It looks to me as if Brad's idea is more
appropriate to 20th century JI than to German Baroque keyboard tuning.

> Pure is subjective to the culture, for example, as i
> showed an example.

I'm not sure what you showed. If some Vietnamese musician produces
intervals that we find alien, that doesn't necessarily show that
Vietnamese musical culture has some idea of 'purity' of intonation. Do
Vietnamese musicians actually talk about 'pure' intervals anyway?

Actually I'd be quite happy to discard the term, as it seems to be
rather acoustically fuzzy in modern usage. Except that, as I said, it
is fairly important to me to try and understand historical sources
that use it.

> By functional i am referring to a dominant chord.
> As we know a 7/5 does not work in dominant chord

What? 'We' don't know this. You are saying so, but I can't see why.

Why in Huyghens' name should a dominant 7th not include 7/5 (or rather
10/7)?
What's wrong with 1 - 3/2 - 25/28 - 5/2 ?
Did you listen to my harpsichord recordings with functional 7/5 tritones?

> Scriabin saw colors,
> and yet i can take a 100 people and none of them will see what he
saw. I
> don't see what this proves except the rarity of his perception.

Fine. Now imagine you are writing instructions to tune a harpsichord
by ear. Will you guide your reader by referring to perceptions that
are common to almost all the population - or will you choose to talk
about things that only very few people perceive.

> i would not assume some defect of those who don't since
> those words were being put into my mouth.

You did actually write 'What if Brad hears something that [Paul] or
Tom can't'. In most contexts this implies that the first person has
better hearing than the other two. But I don't want to be too picky.
~~~T~~~