Survey: Your favorite sizes for thirds?

Hello, everyone, and this is a quick survey on what sizes of regular
thirds people most frequently use.

An interesting question is how one's preferences for sizes of major
and minor thirds can affect one's choices of tuning systems -- or vice
versa.

An advantage of this survey is that you are definitely encouraged to
write your own customized answer, with the responses suggested below
only a possible starting point, and with multiple answers quite likely
if you favor a variety of tuning systems and styles.

QUESTION 1. In your favorite tuning systems, or the ones you most
commonly use, are regular major and minor thirds at or near:

(a) 5:4 and 6:5 (386.31/315.64 cents);

(b) 400 and 300 cents (as in 12n-EDO);

(c) 81:64 and 32:27 (Pythagorean, 407.82/294.13 cents);

(c) 14:11 and 13:11 (417.51/289.21 cents);

(d) 9:7 and 7:6 (435.08/266.87 cents); or

(e) other (e.g. irregular temperament or JI system)?

QUESTION 2. What sizes for major and minor thirds do you commonly take
as your musical norm -- possibly, but not necessarily, the same as
your answer(s) to Question 1:

(a) 5:4 and 6:5 (386.31/315.64 cents);

(b) 400 and 300 cents (as in 12n-EDO);

(c) 81:64 and 32:27 (Pythagorean, 407.82/294.13 cents);

(c) 14:11 and 13:11 (417.51/289.21 cents);

(d) 9:7 and 7:6 (435.08/266.87 cents); or

(e) other (e.g. irregular temperament or JI system)?

Part of the fun is that answers could be simple or intricate.

For example, someone who strongly prefers 1/4-comma meantone and uses
it in mainly in a 16th-century European fashion could answer (a) to
both questions: 5:4 and 6:5 (the first pure, the second slightly
impure) are the regular third sizes in this tuning, and the usual or
"normally preferred" ones stylistically.

Similarly, somone who prefers 22-EDO as a regular tuning, and uses it
as a temperament with the regular thirds of around 9:7 and 7:6 setting
the musical norm, could answer (d) for both questions.

However, for example, someone who favors Paul Erlich's decatonic and
tetradic harmony in 22-EDO (approximate 4:5:6:7) is relying in a
consonant tetrad both on the regular near-6:7 minor third (4/22
octave) and on the non-regular thirds near 5:4 and 6:5 (7/22 and 6/22
octave).

Again, freeform responses, or questions if any of this is unclear, are
warmly invited.

Most appreciatively,

Margo Schulter
mschulter@value.net

In a message dated 10/15/02 3:03:49 PM Central Daylight Time,
MSCHULTER@VALUE.NET writes:

> QUESTION 1. In your favorite tuning systems, or the ones you most
> commonly use, are regular major and minor thirds at or near:
>
> (a) 5:4 and 6:5 (386.31/315.64 cents);
> (d) 9:7 and 7:6 (435.08/266.87 cents);

Margo,

My organ provides both the above. The latter is used in the harmonic 9th
chord and
> in septimal minor keys.

> QUESTION 2. What sizes for major and minor thirds do you commonly take
> as your musical norm -- possibly, but not necessarily, the same as
> your answer(s) to Question 1:
>
> (a) 5:4 and 6:5 (386.31/315.64 cents);
> (d) 9:7 and 7:6 (435.08/266.87 cents); or

The above is normal for my organ. But (a) are tempered 1-2 cents to merge
some #s and bs, and to keep the intervals notes from being in phase, a
musical No No. One reason an orchestra sounds so nice is because the
instruments don't play in phase.

(d) 9/7 is tempered three cents since D is 200 cents.

Those who seek to have their just intonation 100% perfect theoretically,
create something unnatural, as it's not found in nature for harmonic-partials
aboee the 3rd one.

My organ has perfect octaves, except between the left and right keyboard
halves, which are split at Middle C. As octaves in phase in the midrange make
the higher note sound very-much louder (4 x, as I recall) than it should, and
thus distort chords it is in. The diminished harmonic 7th chord in my organ
is worth 884 cents, a perfect 6th, which in that case sounds OK.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:

> Those who seek to have their just intonation 100% perfect
theoretically,
> create something unnatural, as it's not found in nature for
harmonic-partials
> aboee the 3rd one.

i don't know what you mean by that, nor what's special about the 3rd
one.

this page is one of the few that lays things out correctly (speaking
as a physicist):

http://www.phys.unsw.edu.au/~jw/harmonics.html

bowed strings:

"The inharmonicity disappears when the strings are bowed, but is more
noticeable when they are plucked or struck. Because the bow's stick-
slip action is periodic, it drives all of the resonances of the
string at exactly harmonic ratios, even if it has to drive them
slightly off their natural frequency"

real pipes:

"For any one note, however, the lip or the reed performs the same
(strongly non-linear) role as the bow: the lip or reed undergoes
periodic vibration and so produces a harmonic spectrum."

therefore, in most circumstances, violins, 'cellos, brasses, and
reeds will all produce 100% perfect "just intonation" overtone
series, subject of course to the classical uncertaintly principle:

"* "steady" here means over a very long time. Measurements of
frequency are ultimately limited by the Uncertainty Principle. If you
play a note for m seconds, the frequency of its harmonics cannot be
measured with an accuracy greater than about 1/m Hz. If your spectrum
analyser measures over only k seconds, it cannot measure more
accurately than about 1/k Hz."

of course this limitation can be "overcome" if you have some way of
knowing *a priori* the characteristics of the signal -- then you can
use wave-counting, for example.

In a message dated 10/15/02 5:49:27 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> therefore, in most circumstances, violins, 'cellos, brasses, and
> reeds will all produce 100% perfect "just intonation" overtone
> series, subject of course to the classical uncertaintly principle:
>
> "* "steady" here means over a very long time. Measurements of
> frequency are ultimately limited by the Uncertainty Principle.

And an organ stop book I had listed many uncertainties organ pipes are
subject to which prevents their harmonic spectrum from bein perfectly in tune
for any length of time, if at all.

Pauline

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

/tuning/topicId_39612.html#39612
>
> QUESTION 1. In your favorite tuning systems, or the ones you most
> commonly use, are regular major and minor thirds at or near:
>
> (a) 5:4 and 6:5 (386.31/315.64 cents);
>
> (b) 400 and 300 cents (as in 12n-EDO);
>

***Hello Margo! I'm afraid my response to your poll is not going to
be all the "profound" but it *is* what I have been doing. Naturally,
my background, like that of many composers is in 12-tET, so I've used
"b" all my life. However, I've taken a liking to "a" through my
appreciation of the "compromises" that we've had to endure with 12-
equal.

So, the just thirds would really be *optimal* for me in my music
right now, if I can get a way to practically implement them!

I'd like to think that in my current use of 72tET, I can have *both*
of the above... altering by 1/12 of a tone as I please, and yet
remaining in a practical system that musicians conversant with 12-tET
can play. The other sizes you cite I haven't really used, but I'm
sure you'll get other commentary on those by the group...

Joe Pehrson

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/15/02 5:49:27 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > therefore, in most circumstances, violins, 'cellos, brasses, and
> > reeds will all produce 100% perfect "just intonation" overtone
> > series, subject of course to the classical uncertaintly principle:
> >
> > "* "steady" here means over a very long time. Measurements of
> > frequency are ultimately limited by the Uncertainty Principle.
>
> And an organ stop book I had listed many uncertainties organ pipes
are
> subject to which prevents their harmonic spectrum from bein
perfectly in tune
> for any length of time, if at all.
>
> Pauline

pauline, please read the link again. yes, strings and pipes *do* have
their spectra of resonant frequencies *systematically deviating* from
true just relationships. the details of the construction of these
bodies will have a great bearing on the amount of deviation, with
irregularities in construction tending to exacerbate the deviations.
HOWEVER, the means of producing a steady tone in these media, by
their very nature of involving nonlinear, pull the spectrum all the
way to a harmonic one (due to the phenomenon of *phase-locking* which
you should read about) by the time the initial attack transient of
the note is over. i suspect your book, like most on the subject,
considers the first point but neglects the latter. but i won't be
closed-minded. if you ever recover this book, i'd be happy to
consider any arguments it makes.

to be honest, and if you look over my postings on the subject over
the last 6+ years you'll see, i was never quite sure about flutes and
organ pipes -- since they seem like they might be driven by multi-
element systems -- but for reeds, brass, bowed strings, and the human
voice, the situation is clear: no systematic deviation from integer
harmonic ("just") overtone series. if the amplitude is held steady,
and this fact is known a priori, there is no limit to how *short* the
time window can be made with this condition still holding (according
to wave-counting or similar "hypercertain" methods).

In a message dated 10/16/02 6:03:51 AM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> HOWEVER, the means of producing a steady tone in these media, by
> their very nature of involving nonlinear, pull the spectrum all the
> way to a harmonic one (due to the phenomenon of *phase-locking* which
> you should read about) by the time the initial attack transient of
> the note is over.

OK. Even if one accepts your postion on this concerning the harmonic spectrum
in a given tone, that's a far cry musically from deliberately having notes in
a played interval or chord locked in phase. As I know without question this
doens't occur naturally in acoustic muisc, certainly not in pipe organs.

My own ears tell me orchestral instruments don't play in phase. One can even
see this fact in the string section, as the players don't bow at the same
instant, nor the same length. Even their bow lengths and style vary between
instruments.

I once had a top-octave tone generator from Paia Electronics in OK that
produced an chromatic octave of JI notes locked in phase. And it sounded very
unnatural! The major 3rds had a reedy tone besides, unwanted in msot music.

> i was never quite sure about flutes and
> organ pipes -- since they seem like they might be driven by multi-
> element systems

Yes, there are several activities at work in pruducing tone from an organ
pipe. And open pipes sound both from the mouth and top. All pipes sound
through the pipe walls also. One reason why analog electronic organs usually
failed to sound like pipe organs, becasue they failed to reproduce the
pipe-wall harmonics and enharmonics. That is, they cut off the harmonic train
at the point suggested in harmonic charts. Whereas the actual train is much
longer, very weak, yet audible. A metal organ pipe has a certain metallic
sound.

When ET organs have their pipes set C one one one side and C# on the other
side, so the major 3rds are closer together, they try to sound as near just
intonation as possible! They don't quite make it, but the sound is better
than ET.

Pauline

In a message dated 10/16/02 7:28:58 AM Central Daylight Time,
billarnoldfla@yahoo.com writes:

> Would you mind elaborating about your comment, "One reason an orchestra
> sounds so nice is because the instruments don't play in phase."

My own ears tell me orchestral instruments don't play in phase. One can even
see this fact in the string section, as the players don't bow at the same
instant, nor the same length. Even their bow lengths and style vary between
instruments.

> I understand "cycles" behave this way and wonder WHY an "orchestra
> sounds so nice" because of it?

I once had a top-octave tone generator from Paia Electronics in OK that
produced an chromatic octave of JI notes locked in phase. And it sounded very
unnatural! The major 3rds had a reedy tone besides, unwanted in most music.

> Can you also elaborate on WHY "As octaves in phase in the midrange make
> the higher note sound very-much louder"?

Unfortunately, I no longr have Steven Irwin's book on electroic organ stops
that discussed this issue. But I can hear it with my ears. That's one reason
I split the keyboards at Middle C. Also to have more stop-use flexibility.

Low-end and high-end in-phase octaves likewise make the higher note sound
much louder theoretically. But our ears are less sensitve to it than in the
midrange. But having all octaves out of phase sound better. That's one
argument kit-organ builders had for having each octave as separate tone
generators. They even had each note within an octave separate for the
ultimate in pipe-organ realism.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/16/02 6:03:51 AM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > HOWEVER, the means of producing a steady tone in these media, by
> > their very nature of involving nonlinear, pull the spectrum all
the
> > way to a harmonic one (due to the phenomenon of *phase-locking*
which
> > you should read about) by the time the initial attack transient
of
> > the note is over.
>
> OK. Even if one accepts your postion on this concerning the
harmonic spectrum
> in a given tone, that's a far cry musically from deliberately
having notes in
> a played interval or chord locked in phase. As I know without
question this
> doens't occur naturally in acoustic muisc, certainly not in pipe
organs.
>
> My own ears tell me orchestral instruments don't play in phase. One
can even
> see this fact in the string section, as the players don't bow at
the same
> instant, nor the same length. Even their bow lengths and style vary
between
> instruments.
>
> I once had a top-octave tone generator from Paia Electronics in OK
that
> produced an chromatic octave of JI notes locked in phase. And it
sounded very
> unnatural! The major 3rds had a reedy tone besides, unwanted in
msot music.

i will not argue with you on thesee additional points. however, it is
good to know that there are those out there (and around here) who
have come to appreciate, and make musical use of, artificially
generated harmonies in exact, phase-locked, just intonation. it's not
conventional western music, certainly, but it's certainly a valid
avenue of avant-garde musical experimentation.

> When ET organs have their pipes set C one one one side and C# on
the other
> side, so the major 3rds are closer together, they try to sound as
near just
> intonation as possible! They don't quite make it, but the sound is
better
> than ET.

can you elaborate on this? i'm not clear on exactly what you're
discussing here.

In a message dated 10/16/02 1:12:55 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> > When ET organs have their pipes set C one one one side and C# on
> the other
> > side, so the major 3rds are closer together, they try to sound as
> near just
> > intonation as possible! They don't quite make it, but the sound is
> better
> > than ET.
>
> can you elaborate on this? i'm not clear on exactly what you're
> discussing here.
>
In some pipe-organ installations the Great Principal 8' stop, the most
imposrtant one in the whole organ, when commonly a facade, has the rank
divised in two. The Cs are on side and the C# on the other, and the other
notes likewsie. Thus in a trial C and E are on the left side and G on the
right.

That is, C, D, E, F#, G#, A# are on the left, and C#, D#, F, G,A, B on the
right. This places C and E two pipes closer than they otherwise woudl be,
close enough for them to affect each other tonally. When sounded together, C
and E by nature via their harmonic spectrums try to speak in perfect tune
with each other.

However the 14 cents difference beteween JI and ET prevents them from
speaking in real JI, but several cents closer than they would if further
apart. In other words, any pipe rank arranged thus tuned to ET doesn't speak
major thirds in ET. However, normally only the facade Principal pipes are
thus arranged. Thus a certain celeste or chorus is created when the stop is
played with other stops laid out in pitch order from Bass to Treble.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/16/02 1:12:55 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > > When ET organs have their pipes set C one one one side and C#
on
> > the other
> > > side, so the major 3rds are closer together, they try to sound
as
> > near just
> > > intonation as possible! They don't quite make it, but the sound
is
> > better
> > > than ET.
> >
> > can you elaborate on this? i'm not clear on exactly what you're
> > discussing here.
> >
> In some pipe-organ installations the Great Principal 8' stop, the
most
> imposrtant one in the whole organ, when commonly a facade, has the
rank
> divised in two. The Cs are on side and the C# on the other, and the
other
> notes likewsie. Thus in a trial C and E are on the left side and G
on the
> right.
>
> That is, C, D, E, F#, G#, A# are on the left, and C#, D#, F, G,A,
B on the
> right. This places C and E two pipes closer than they otherwise
woudl be,
> close enough for them to affect each other tonally. When sounded
together, C
> and E by nature via their harmonic spectrums try to speak in
perfect tune
> with each other.
>
> However the 14 cents difference beteween JI and ET prevents them
from
> speaking in real JI, but several cents closer than they would if
further
> apart. In other words, any pipe rank arranged thus tuned to ET
doesn't speak
> major thirds in ET.

interesting. a couple of months ago someone (was it ed foote?)
mentioned a similar phenomenon in which organ pipes tuned within
perhaps a cent or two of a simple JI ratio, if physically close or
connected, can pull each other into true, phase-locked JI harmony --
reminding me much of how pendulums mounted on the same wall end up
swinging exactly in phase with one another. a name was even given to
this (former -- organ-pipe) phenomenon, but when i asked for more
information, i was greeted with silence.

i take it you'd be skeptical that such a phenomenon actually occurs :)

In a message dated 10/16/02 2:30:19 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> a couple of months ago someone (was it ed foote?)
> mentioned a similar phenomenon in which organ pipes tuned within
> perhaps a cent or two of a simple JI ratio, if physically close or
> connected, can pull each other into true, phase-locked JI harmony --
>
> i take it you'd be skeptical that such a phenomenon actually occurs :)
>
They could be in JT. But their differences in physical size and pitch would
prevent them from be 100% in phase, which is a good thing musically. I've
studied and read several music physics books. And I've read negative remarks
about musical tone being in phase, and how unmusical and unnatural that
really is. I myself don't want it.Those who do can have it!

Pauline

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
>
> QUESTION 1. In your favorite tuning systems, or the ones you most
> commonly use, are regular major and minor thirds at or near:
>
> (a) 5:4 and 6:5 (386.31/315.64 cents);
> (b) 400 and 300 cents (as in 12n-EDO);
> (c) 81:64 and 32:27 (Pythagorean, 407.82/294.13 cents);
> (c) 14:11 and 13:11 (417.51/289.21 cents);
> (d) 9:7 and 7:6 (435.08/266.87 cents); or
> (e) other (e.g. irregular temperament or JI system)?

If I had to narrow my favorite tunings down to three, they would be:

1) 31-ET -- near (a)

2) my 19+3 temperament -- near (a)

3) my 29-tone high-tolerance temperament (a 15-limit microtemperament
I designed in 1975, but have not yet presented on this list) -- very
near (a) -- (4:5 is exact; 5:6 is wide, ~1.6 cents in the best keys)

> QUESTION 2. What sizes for major and minor thirds do you commonly
take
> as your musical norm -- possibly, but not necessarily, the same as
> your answer(s) to Question 1:
>
> (a) 5:4 and 6:5 (386.31/315.64 cents);
> (b) 400 and 300 cents (as in 12n-EDO);
> (c) 81:64 and 32:27 (Pythagorean, 407.82/294.13 cents);
> (c) 14:11 and 13:11 (417.51/289.21 cents);
> (d) 9:7 and 7:6 (435.08/266.87 cents); or
> (e) other (e.g. irregular temperament or JI system)?

I prefer a tonal system that has two sizes of major thirds (and thus
two sizes of minor thirds): one close to 4:5 to favor harmony; and
the other somewhat wider than Pythagorean and somewhat narrower than
7:9 to create a leading tone that is effective both melodically and
harmonically (effective harmonically because its dissonance is
effective once it is resolved to a more consonant chord.)

Two of the above three tunings have the required thirds:

In 31-ET:
a harmonic third ~0.7 cents wide
a melodic third ~426 cents
In 29-HTT:
a harmonic third an exact 4:5 available in 6 keys
a melodic third ~414 cents (close to 11:14) available in 15 keys
both of the above thirds available in 4 keys

--George

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/16/02 2:30:19 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > a couple of months ago someone (was it ed foote?)
> > mentioned a similar phenomenon in which organ pipes tuned within
> > perhaps a cent or two of a simple JI ratio, if physically close
or
> > connected, can pull each other into true, phase-locked JI
harmony --
> >
> > i take it you'd be skeptical that such a phenomenon actually
occurs :)
> >
> They could be in JT. But their differences in physical size and
pitch would
> prevent them from be 100% in phase,

why is that? pendulums which are slightly different in size, and
frequency (when isolated from one another), come to swing perfectly
in phase with one another when mounted on the same wall. why
shouldn't something similar be true for organ pipes?

> which is a good thing musically. I've
> studied and read several music physics books. And I've read
negative remarks
> about musical tone being in phase, and how unmusical and unnatural
that
> really is. I myself don't want it.Those who do can have it!

if the two sources are in phase-locked ji but separated in space,
then you can change the relative phase by just moving your head
around! this might have something to do with what goes on at lamonte
young's dreamhouse . . .

In a message dated 10/16/02 3:23:22 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> why is that? pendulums which are slightly different in size, and
> frequency (when isolated from one another), come to swing perfectly
> in phase with one another when mounted on the same wall. why
> shouldn't something similar be true for organ pipes?
>
Pendulums can be cast very accurately. Organ pipes are essentially made by
hand. No two are exactly alike, not even in the same rank made by the same
person. Thankfully, there's enough variation deliberate or not to keep the
pipes sounding out of phase. I've played several pipe organs, and listened to
many. And I've never dedected any sounding intervals or chords perfectly in
phase.

Pauline

For me it is like choosing between one's children. I would not consider
playing favorites.

best, Johnny Reinhard

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/16/02 3:23:22 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > why is that? pendulums which are slightly different in size, and
> > frequency (when isolated from one another), come to swing
perfectly
> > in phase with one another when mounted on the same wall. why
> > shouldn't something similar be true for organ pipes?
> >
> Pendulums can be cast very accurately.

they need not be for this to work!!!

> Organ pipes are essentially made by
> hand. No two are exactly alike, not even in the same rank made by
the same
> person.

ditto.

> Thankfully, there's enough variation deliberate or not to keep the
> pipes sounding out of phase. I've played several pipe organs, and
listened to
> many. And I've never dedected any sounding intervals or chords
perfectly in
> phase.

did you ever *try* physically connecting (say through *very* close
proximity, so air vibrations effectively connect) two organ pipes
which, separately, were tuned to within a cent or so of a simple just
ratio? i guess not, as the result which we're arguing about is not
one you would have wanted anyway.

also, a pendantic note about "in phase" and "out of phase" -- both
situations decribe phase-locked just intonation (especially 1/1s),
it's just that in the former you have constructive interference and
in the latter, destructive interference. both are probably equally
undesirable to you -- what you seem to be after is (very slow)
beating.

which of course is what you get even if you play a "JI" electric
guitar (plucked strings are slightly inharmonic), especially one with
frets placed in integer ratio positions relative to the nut (i.e.,
not compensated for the slight deflection involved in pushing the
string down to the fingerboard).

17/13

http://www.screwmusicforever.com/SHREESWIFT/Silica

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_39612.html#39690

>
> why is that? pendulums which are slightly different in size, and
> frequency (when isolated from one another), come to swing perfectly
> in phase with one another when mounted on the same wall. why
> shouldn't something similar be true for organ pipes?
>

***You know, that's pretty amazing... I'd like to see that. Why is
that happening, are they "shaking the wall" or what???

JP

In a message dated 10/16/02 6:14:55 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> did you ever *try* physically connecting (say through *very* close
> proximity, so air vibrations effectively connect) two organ pipes
> which, separately, were tuned to within a cent or so of a simple just
> ratio? i guess not, as the result which we're arguing about is not
> one you would have wanted anyway.
>
When organ pipes are too close together, they prevent each other from
speaking right. Thus sometimes a pipe may be turned at an angle, or even
backwards in the hole to correct the problem.

Pauline

Pauline,

Thank you for the thoughtful response.

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
-------------------------------------------------------------------
"There is magic in the web" Shakespeare (Othello, Act 3, Scene 4)
-------------------------------------------------------------------

--- prophecyspirit@aol.com wrote:
> In a message dated 10/16/02 7:28:58 AM Central Daylight Time,
> billarnoldfla@yahoo.com writes:
>
>
> > Would you mind elaborating about your comment, "One reason an orchestra
> > sounds so nice is because the instruments don't play in phase."
>
> My own ears tell me orchestral instruments don't play in phase. One can even
> see this fact in the string section, as the players don't bow at the same
> instant, nor the same length. Even their bow lengths and style vary between
> instruments.
>
>
> > I understand "cycles" behave this way and wonder WHY an "orchestra
> > sounds so nice" because of it?
>
> I once had a top-octave tone generator from Paia Electronics in OK that
> produced an chromatic octave of JI notes locked in phase. And it sounded very
> unnatural! The major 3rds had a reedy tone besides, unwanted in most music.
>
> > Can you also elaborate on WHY "As octaves in phase in the midrange make
> > the higher note sound very-much louder"?
>
>
> Unfortunately, I no longr have Steven Irwin's book on electroic organ stops
> that discussed this issue. But I can hear it with my ears. That's one reason
> I split the keyboards at Middle C. Also to have more stop-use flexibility.
>
> Low-end and high-end in-phase octaves likewise make the higher note sound
> much louder theoretically. But our ears are less sensitve to it than in the
> midrange. But having all octaves out of phase sound better. That's one
> argument kit-organ builders had for having each octave as separate tone
> generators. They even had each note within an octave separate for the
> ultimate in pipe-organ realism.
>
> Pauline
>

__________________________________________________
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--- prophecyspirit@aol.com wrote:
> In some pipe-organ installations the Great Principal 8' stop, the most
> imposrtant one in the whole organ, when commonly a facade, has the rank
> divised in two. The Cs are on side and the C# on the other, and the other
> notes likewsie. Thus in a trial C and E are on the left side and G on the
> right.
>
> That is, C, D, E, F#, G#, A# are on the left, and C#, D#, F, G,A, B on the
> right. This places C and E two pipes closer than they otherwise woudl be,
> close enough for them to affect each other tonally. When sounded together, C
> and E by nature via their harmonic spectrums try to speak in perfect tune
> with each other.
>
> Sincerely,
> Pauline W. Phillips,

Pauline, can you explain why C and F# are on the left,
while C# and F are on the right?

What would happen if C and F were on the left,
while C# and F# were on the right?

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
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In a message dated 10/17/02 9:53:01 AM Central Daylight Time,
billarnoldfla@yahoo.com writes:

> Pauline, can you explain why C and F# are on the left,
> while C# and F are on the right?
>
> What would happen if C and F were on the left,
> while C# and F# were on the right?
>
The C and C# arrangemeent is partly for looks. That way either the high or
low pitches can be in the middle. Otherise the 8' rank would be tall ont he
left side and very short on the right. A facade 8' rank doesn't look good
that way. Ranks inside the organ loft are normally arranged according to
their pitch, as no one but the organ tuner, repairman or organist sees them.

Wendy

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/17/02 9:53:01 AM Central Daylight Time,
> billarnoldfla@y... writes:
>
>
> > Pauline, can you explain why C and F# are on the left,
> > while C# and F are on the right?

> The C and C# arrangemeent is partly for looks. That way either the
> high or low pitches can be in the middle.

And isn't it even simpler than that: they just alternate the pipes from side to side, going up chromatically, so that they are (visually) balanced in size?

Cheers,
Jon

In a message dated 10/17/02 11:18:30 AM Central Daylight Time,
JSZANTO@ADNC.COM writes:

> they just alternate the pipes from side to side, going up chromatically, so
> that they are (visually) balanced in size?
>
> Jon
>
Right. There's either a mountain peak in the middle or a deep valley. But the
arrangement does affect how major 3rds sound. But I doubt that was the
original raeson for it. As Meantone and Werckmeister have even better major
3rds than the C and C# arrangement provides. This arrangement also spreads
the sound out better.

My church just bought a three-manual Johannus digital-sampled organ. The
voicer made the Swell and Great Principal 8' stops the C/C# way. There's two
organ lofts with an empty space between. So in a minor 7th chord C-E-Bb comes
from the left side and G from the right.

The Positif (Choir) Principal 8' all comes from the right side. Probably on
the theory a Positif was a small portable organ set at a 90-degree angle to
the main organ, playable with the right hand. Or becasue the Ruckpositif was
behind the organist's back on a rail.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:

/tuning/topicId_39612.html#39739

> In a message dated 10/17/02 11:18:30 AM Central Daylight Time,
> JSZANTO@A... writes:
>
>
> > they just alternate the pipes from side to side, going up
chromatically, so
> > that they are (visually) balanced in size?
> >
> > Jon
> >
> Right. There's either a mountain peak in the middle or a deep
valley. But the
> arrangement does affect how major 3rds sound. But I doubt that was
the
> original raeson for it. As Meantone and Werckmeister have even
better major
> 3rds than the C and C# arrangement provides. This arrangement also
spreads
> the sound out better.
>
> My church just bought a three-manual Johannus digital-sampled
organ. The
> voicer made the Swell and Great Principal 8' stops the C/C# way.
There's two
> organ lofts with an empty space between. So in a minor 7th chord C-
E-Bb comes
> from the left side and G from the right.
>
> The Positif (Choir) Principal 8' all comes from the right side.
Probably on
> the theory a Positif was a small portable organ set at a 90-degree
angle to
> the main organ, playable with the right hand. Or becasue the
Ruckpositif was
> behind the organist's back on a rail.
>
> Pauline

***I love writing for organ, but recently I was *shocked* to find
that the organ has virtually *no* possibility for crescendo and
diminuendo other than *adding overtones* by bigger mixes in the
stops! I asked the organist if it weren't possible to change the
dynamics somewhat with a pedal for the Swell rank. (I remembered
that from my rather abbreviated organ lessons..) He said, yes, but
only on *that* particular rank... and even that was not so effective.

So, basically *all dynamics* are involved with this adding of
partials, which is why this is such a significant topic. And even
then, everything is *latticed*; there is really no smooth crescendo
or diminuendo, everything is "on or off!" And having more than one
dynamic in different manuals in a piece going on simultaneously *is*
possible, but can be rather involved to accomplish, and again
*latticed.*

So the way these *mixtures* are put together are absolutely crucial
to the final sound. Sounds to me as though Pauline really *likes*
some of the inconsistencies of slight mistuning. More like the "real
world..." It's fascinating to think about the clash or contrast
between the *natural* overtones of the pipes and the inherent tuning,
be it 12-equal, Werckmeister, or whatever...

J. Pehrson

hello,

Pauline:
> When ET organs have their pipes set C one one one side and C# on the
> other side, so the major 3rds are closer together, they try to sound
> as near just intonation as possible! They don't quite make it, but
> the sound is better than ET.

That means that if you play C, then E, then release C, the E goes up
to the pipe natural frequency!!

The idea that near-just pipe organ pair can enter lock phase mode to
play in JI is more than interresting! It is downright fascinating.
This means that the organ can not be considered as a fixed tuning
instrument, but, to a certain extend as an adaptative one. So there
could be a pitch drift between a pipe sounding alone and a pipe
sounding at a near just interval. Is it possible to provide an sound
example of this phenomena?

> Those who seek to have their just intonation 100% perfect
> theoretically, create something unnatural, as it's not found in
> nature for harmonic-partials aboee the 3rd one.

The perfection is not measurable, but with enough time to settle (and
enough skill from the performers) a capella ensemble can sign nearly
perfect triads, i.e. as perfect as can be measured (with the crude
means I have at hand), let say within one or two cents, and it
certainly not sound unnatural.
I suspect that reed wind ensemble can do even better that.

> And an organ stop book I had listed many uncertainties organ pipes
are
> subject to which prevents their harmonic spectrum from bein
perfectly
> in tune for any length of time, if at all.

I have been involved in some harsh "uncertainty principle" discussion
on this NG as an advocate of intrincics limitation of pitch
measurement. Nevertheless,the incertainty on measurement does not
involve AT ALL incertainty on the process under mesurement. I think
that after the air flow settle in the pipes, the tone should be fairly
stable, as should be any resonant system. What make you think that the
tone of many pipes singning together is not stable?

The explanation of why organ tuning systematically deviate from just
has perhaps to do with the "warmth" given by the beat of upper
frequencie that gives a vibrato-like quality that make them more like
human voice.

I am not sure if your acceptance of the term "in phase" is in phase
:-) with the common (physical) acceptance of the term, so I am not
sure to understand what your are talking about. Let say that we have N
sources providing pure sine:

S1 = A * sin (( omega * t ) + PHI1)
S2 = A * sin (( omega * t ) + PHI2)
.....
SN = A * sin (( omega * t ) + PHIN)

They are in phase if PHI1 = PHI2 ....= PHIN. If all sources are
in phase the overall amplitude goes as N while if the phases are
random, the overall amplitude goes (statistically) as square root of
N. So, as you stated, if many pipes in unison are in phase, yes they
sound louder.

It worth to be noted that the notion of "being in phase" makes sense
only if the sources separation is much smaller than the wavelenth. So
this may makes sense for organ pipes that are near to each other (as
your organ building/tuning hand-on experience demonstrates).
This does not make sense for violins in an orchestra because their
distance to each other is of the order of magnitude of wavelength or
bigger. Further any violin is so much different from any other violin
in term of tone and phase, that even if they where stacked, there
would probably be no such thing as significant acoustical coupling.
The warmth of string ensemble is due to the clustering of instrument
with slighlty different tones and slighly different pitch due to
different vibrato speed, width and phase.

I think that your understanding of "phase" is much broader than the
physics acceptance and include pitch and tone. Am I correct?

In fact when talking about "physical" phase, the human ear is
(nearly) totally insensitive to phase on stable signal. Phase is
percepually important in the attack an decay of sound, but not on
stable part.

When there are multiple similar sources, we may be sensitives to some
effects of the phase, but not to the phase by itself.

yours truly

François Laferrière

In a message dated 10/17/02 11:16:26 PM Central Daylight Time,
jpehrson@rcn.com writes:

> but recently I was *shocked* to find
> that the organ has virtually *no* possibility for crescendo and
> diminuendo other than *adding overtones* by bigger mixes in the
> stops!

The crescendo pedal adds whole stops, not just their overtones. And nowadays
the CP is programable by the organist, so the gradation in tone is to his/her
liking for a given composition. On the other hand, trained organists don't
use the CP all that much.

I asked the organist if it weren't possible to change the
> dynamics somewhat with a pedal for the Swell rank. He said, yes, but
> only on *that* particular rank... and even that was not so effective.

That depends on the organ. Some organs have the Great division expresionless.
Others have only the facade stops thus. Others a small swellbox for certain
stops. Still others have the whole organ under expression.

The way most organ flue pipe are constructed (like a recorder) it's not
possible to alter their loudness via the air sent them without at the same
time changing their pitch significently. To maintain the right pitch they'd
need to be constructed like the orchestral flute instrument or stop is
constructed. That woud greatly add to the cost. And there'd be less variation
in stop quality possible.

So the Spanish and British invented the swellbox with swell shutters similar
to venetian blinds. The resulting sound isn't like what can be doen with
dynamics in an orchestra or band, nor on the piano. But trained organists
today don't use the swell pedals all that much either. Pumping the swells was
a theater-organ practice.

> Sounds to me as though Pauline really *likes*
> some of the inconsistencies of slight mistuning. More like the "real
> world..."

The so-called mistuning used in my Phillips Just-Temperament Scale is so
slight the combinational tones are maintained at virtual full strength. So
there's no audible loss in JI tone quality.

Pauline

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> ***I love writing for organ, but recently I was *shocked* to find
> that the organ has virtually *no* possibility for crescendo and
> diminuendo other than *adding overtones* by bigger mixes in the
> stops! I asked the organist if it weren't possible to change the
> dynamics somewhat with a pedal for the Swell rank. (I remembered
> that from my rather abbreviated organ lessons..) He said, yes, but
> only on *that* particular rank... and even that was not so
effective.

First, let's get the terminology straight. A "rank" is a set of
pipes (one assigned to each key of one of the "manuals" or keyboards)
having a single timbre; each rank generally has its own on/off
controller, called a "stop." A "division" (e.g., swell, great, and
pedal divisions) consists of one or (usually) more ranks of pipes
placed on a wind chest and assigned to be controlled (or played) from
a specific manual (having the same name as the division) or the
pedals.

The swell division gets its name from the fact that its pipes are in
an enclosure have a set of shutters (something on the order of
vertical blinds) in front that are controlled by a "swell pedal" to
reduce the volume of sound by partial or complete closing. Most
organs built in the 20th century also have the great, pedal, and
additional divisions similarly enclosed separately from the swell
division and operated by a second expression pedal. There is also
usually a "crescendo pedal" that can control the volume of all of the
divisions simultaneously by adding stops one at a time in a fixed
order.

However, this is not the whole story. What I have described above is
characteristic of a "romantic organ", one designed and built
primarily for the requirements of 19th-century organ music. More
suitable for the works of J. S. Bach and earlier composers is the
classic-voiced organ which, in addition to lacking any sort of swell-
box with shutters, has the pipes voiced so that the tone has a more
abrupt (almost percussive) attack (or "chiff"), which makes the
attack of the romantic organ sound mushy by comparison.

The classic and romantic organs therefore have distinctly different
sounds, so you would almost have to consider them different
instruments, as different as, say, an acoustic and an electric guitar.

--George

In a message dated 10/18/02 11:46:40 AM Central Daylight Time,
gdsecor@yahoo.com writes:

> The classic and romantic organs therefore have distinctly different
> sounds, so you would almost have to consider them different
> instruments, as different as, say, an acoustic and an electric guitar.
>
> --George
>
Thanks, George. You gave a good explanation of basic "organology," to borrow
a medical term.

Pauline

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

/tuning/topicId_39612.html#39752

> The classic and romantic organs therefore have distinctly different
> sounds, so you would almost have to consider them different
> instruments, as different as, say, an acoustic and an electric
guitar.
>
> --George

***Thank you George and Pauline for the organ corrections/updates!

Joseph Pehrson

--- In tuning@y..., "Pat PAgano" <ppagano@b...> wrote:
> 17/13

That's ~464 cents -- you've got to be kidding!

--George

In a message dated 10/18/02 10:47:58 AM Central Daylight Time,
francois.laferriere@oxymel.com writes:

> That means that if you play C, then E, then release C, the E goes up
> to the pipe natural frequency!!

François ,

Right. Organ pipes as well rise somewhat in pitch as the pipe speaks, as the
air pressure rises.

> The idea that near-just pipe organ pair can enter lock phase mode to
> play in JI is more than interresting! It is downright fascinating.
> Is it possible to provide an sound
> example of this phenomena?

The natural pitch the pipe rises to when played alone referred to was ET. not
JI. I don't have access to a pipe organ right now. And no mike for my
recorder either.

>
> The perfection is not measurable, but with enough time to settle a capella
> ensemble can sign nearly
> perfect triads, i.e. as perfect as can be measured , let say within one or
> two cents, and it certainly not sound unnatural.
>
My JT scale I posted here is +/- 1-2 cents off the theoretical value. When I
refer to 100%, I mean exactly that as produced electronically. It does sound
unnatural!

One of the complaints pipe organists have had with analog electronic organs
was their locked-in-phase notes. As pipe-organ pipes don't speak in phase
with other notes except randomly and momnetarily.

> I think
> that after the air flow settle in the pipes, the tone should be fairly
> stable, as should be any resonant system. What make you think that the
> tone of many pipes singning together is not stable?

They are ssas stable as wind instruments. Whose players don't play every note
perfectly. Every time a Principal note or chord is repeated in succession, it
soundis different each time. As the attack, decay and harmonic structure
varies.

> The explanation of why organ tuning systematically deviate from just
> has perhaps to do with the "warmth" given by the beat of upper
> frequencie that gives a vibrato-like quality that make them more like
> human voice.

Some harmonics, perhaps better called enharmonics, in some stops like
strings or reeds beat with each other and with the harmonic partials. This
may become very noticeable in the very low Pedal pitches.

>
> I am not sure if your acceptance of the term "in phase" is in phase
> :-) with the common (physical) acceptance of the term,

By in phase I mean hwhen all possible harmonics and their fundamental tones
sound perfectly together beatless when produced electronically. Musical tone
produced acoustically aren't that accurate.

So, as you stated, if many pipes in unison are in phase, yes they>
> sound louder.

I didn't say any notes, but octaves. and on analog electronic organs, not
pipe organs.. The higher note in such octaves in midrange do sound louder.
Organ books say so, and ia can hear it myself. That's one reason why I
split my keyboard tone generators between Tenor B and Middle C.

> The warmth of string ensemble is due to the clustering of instrument
> with slighlty different tones and slighly different pitch due to
> different vibrato speed, width and phase.

That's essentially what I've been saying. Vioolinists don't play in phase, as
their bows aren't in exact moving order. I think my use to the term "in
phase" is what musical people and music physicists mean. Electroniclly
produced sound in phase sounds much differenen from the same sound produced
acoustically not in perfect phase. I can hear the difference myself.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:

> I think my use to the term "in
> phase" is what musical people and music physicists mean.

i'm afraid i must disagree. "out of phase" is perfectly beatless,
just like "in phase" -- it's just that out of phase is *much* quieter
than "in phase". this is well-known to anyone who has ever hooked up
a pair of stereo speakers :), or worked at any length with pure-ji
electronic tone generators.

moreover, two phase-locked sound sources, *separated* in space, will
produce a standing pattern of "in phase" and "out of phase" regions
in space. as you move through the space, you will experience
oscillating intensities as you pass, successively, through regions of
reinforcement and cancellation.

let me suggest this high school tutorial to everyone (even PhDs!):

http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l3a.html

http://www.ndt-
ed.org/EducationResources/HighSchool/Sound/interference.htm

http://www.daidan.co.jp/english/english/technology/establish/est_2_2.h
tml

http://library.thinkquest.org/19537/Physics5.html?
tqskip1=1&tqtime=1018

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/interf.html

http://sgra.jpl.nasa.gov/us-space-
vlbi/outreach/sound_wave_interference.pdf

>let me suggest this high school tutorial to everyone (even PhDs!):
>http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l3a.html

Really?

'The human ear cannot hear beating faster than 7Hz.'
'The flute approximates a pure tone'

And the page repeats the story that I had in High School and that
I repeated here not long ago, which you smacked down to a lack of
basic knowledge of acoustics, that beating happens 'in the air'.

-Carl

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> >let me suggest this high school tutorial to everyone (even PhDs!):
> >http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/u11l3a.html
>
> Really?
>
> 'The human ear cannot hear beating faster than 7Hz.'

where did you find that quote? i only see:

"The human ear is capable of detecting beats with frequencies of 7 Hz
and below."

which is true. however, this question asserts something so false it's
ridiculous:

"Why don't we hear beats when different keys on the piano are played
at the same time?

> 'The flute approximates a pure tone'

better than any other instrument . . .

> And the page repeats the story that I had in High School and that
> I repeated here not long ago, which you smacked down to a lack of
> basic knowledge of acoustics, that beating happens 'in the air'.

where do you read that? i don't see that story anywhere on this page.
the interference discussed does happen in air/space, but that is for
two *identical* pitches, and hence is not beating.

and anyway, my objection (not long ago) was mainly intended to point
out that beating is a function of our limited hearing resolution --
two notes 1 Hz apart might be resolved as separate pitches, without
any perception of beating, by an organism from another planet
(probably a large, slow-moving being).

>> 'The human ear cannot hear beating faster than 7Hz.'
>
> where did you find that quote? i only see:
>
>"The human ear is capable of detecting beats with frequencies
>of 7 Hz and below."

That's the quote (notice the single quotes on my text). It isn't
correct.

> which is true.

Oh yeah?

>> 'The flute approximates a pure tone'
>
> better than any other instrument . . .

Among orchestral instruments, perhaps. But still not even close
to true.

>>And the page repeats the story that I had in High School and that
>>I repeated here not long ago, which you smacked down to a lack of
>>basic knowledge of acoustics, that beating happens 'in the air'.
>
>where do you read that? i don't see that story anywhere on this
>page. the interference discussed does happen in air/space, but
>that is for two *identical* pitches, and hence is not beating.

They discuss constructive and destruct. reinforcement in the
air, sound as a longitudinal wave, etc. A framework which
permits beating 'in the air' for a pair of nearly-tuned pure
tones. No?

> and anyway, my objection (not long ago) was mainly intended to
> point out that beating is a function of our limited hearing
> resolution -- two notes 1 Hz apart might be resolved as separate
> pitches, without any perception of beating, by an organism from
> another planet (probably a large, slow-moving being).

Huh.

-Carl

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> >> 'The human ear cannot hear beating faster than 7Hz.'
> >
> > where did you find that quote? i only see:
> >
> >"The human ear is capable of detecting beats with frequencies
> >of 7 Hz and below."
>
> That's the quote (notice the single quotes on my text). It isn't
> correct.
>
> > which is true.
>
> Oh yeah?

yes, the human ear *is* capable of detecting beats with frequencies
of 7 Hz and below. it's also capable of detecting som faster beats,
but this statement didn't rule that out.

> >>And the page repeats the story that I had in High School and that
> >>I repeated here not long ago, which you smacked down to a lack of
> >>basic knowledge of acoustics, that beating happens 'in the air'.
> >
> >where do you read that? i don't see that story anywhere on this
> >page. the interference discussed does happen in air/space, but
> >that is for two *identical* pitches, and hence is not beating.
>
> They discuss constructive and destruct. reinforcement in the
> air, sound as a longitudinal wave, etc.

yes, interference! not beating.

> A framework which
> permits beating 'in the air' for a pair of nearly-tuned pure
> tones. No?

where do you make that jump?

> > and anyway, my objection (not long ago) was mainly intended to
> > point out that beating is a function of our limited hearing
> > resolution -- two notes 1 Hz apart might be resolved as separate
> > pitches, without any perception of beating, by an organism from
> > another planet (probably a large, slow-moving being).
>
> Huh.

waves are a tricky subject until you've gone through fourier's
theorem in depth. quantum mechanics is a great route, particularly
the proof that the gaussian probability profile maximizes the
uncertainty (it gets you that "equals sign" in the heisenberg
principle). the classical case is exactly analogous, of course . . .

>>>"The human ear is capable of detecting beats with frequencies
>>>of 7 Hz and below."
>>
>> That's the quote (notice the single quotes on my text). It isn't
>> correct.
>>
>>> which is true.
>>
>> Oh yeah?
>
>yes, the human ear *is* capable of detecting beats with frequencies
>of 7 Hz and below. it's also capable of detecting som faster beats,
>but this statement didn't rule that out.

It seemed to me to rule it out. Maybe my bad.

>>They discuss constructive and destruct. reinforcement in the
>>air, sound as a longitudinal wave, etc.
>
>yes, interference! not beating.
>
>>A framework which permits beating 'in the air' for a pair of
>>nearly-tuned pure tones. No?
>
>where do you make that jump?

Like this:
http://surendranath.tripod.com/Beats/Beats.html

Assuming that the values on the y axis represent longitudinal
air pressure, and red and green sources are very near, isn't
this correct? And doesn't it explain what we hear?

-Carl

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:

/tuning/topicId_39612.html#39906

> >>>"The human ear is capable of detecting beats with frequencies
> >>>of 7 Hz and below."
> >>
> >> That's the quote (notice the single quotes on my text). It isn't
> >> correct.
> >>
> >>> which is true.
> >>
> >> Oh yeah?
> >
> >yes, the human ear *is* capable of detecting beats with
frequencies
> >of 7 Hz and below. it's also capable of detecting som faster
beats,
> >but this statement didn't rule that out.
>
> It seemed to me to rule it out. Maybe my bad.
>
> >>They discuss constructive and destruct. reinforcement in the
> >>air, sound as a longitudinal wave, etc.
> >
> >yes, interference! not beating.
> >
> >>A framework which permits beating 'in the air' for a pair of
> >>nearly-tuned pure tones. No?
> >
> >where do you make that jump?
>
> Like this:
> http://surendranath.tripod.com/Beats/Beats.html
>
> Assuming that the values on the y axis represent longitudinal
> air pressure, and red and green sources are very near, isn't
> this correct? And doesn't it explain what we hear?
>
> -Carl

***This is a pretty cool little java applet here! Too bad it doesn't
make a sound, too, but I guess one can't have everything...

J. Pehrson

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:

> Like this:
> http://surendranath.tripod.com/Beats/Beats.html
>
> Assuming that the values on the y axis represent longitudinal
> air pressure, and red and green sources are very near, isn't
> this correct? And doesn't it explain what we hear?
>
> -Carl

carl, if the two waves were in a 5:6 frequency ratio, you'd still see
the same kind of pattern, but you wouldn't hear any beating! what you
see is not always what you hear. the point at which the sensation of
two separate tones gives way to the sensation of one tone with
variable amplitude is a function of physiology, not "air".

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
>
> > Like this:
> > http://surendranath.tripod.com/Beats/Beats.html
> >
> > Assuming that the values on the y axis represent longitudinal
> > air pressure, and red and green sources are very near, isn't
> > this correct? And doesn't it explain what we hear?
> >
> > -Carl
>
> carl, if the two waves were in a 5:6 frequency ratio,

you can actually arrange this on the applet -- try 10 Hz and 12 Hz,
or 15Hz and 18Hz.

> you'd still see
> the same kind of pattern, but you wouldn't hear any beating! what
you
> see is not always what you hear. the point at which the sensation
of
> two separate tones gives way to the sensation of one tone with
> variable amplitude is a function of physiology, not "air".

>carl, if the two waves were in a 5:6 frequency ratio, you'd
>still see the same kind of pattern, but you wouldn't hear any
>beating! what you see is not always what you hear. the point
>at which the sensation of two separate tones gives way to the
>sensation of one tone with variable amplitude is a function
>of physiology, not "air".

Okay, I see what you're saying now, and that it must be right.
Thanks.

-Carl