[Ian Iveson]

My supermarket is selling eggs in boxes of 5 and 10. This European
decimalisation thing has obviously overstepped the mark. The boxes
don't work properly. There is cubic close packing, and hexagonal close
packing. 5 and 10 are really bad numbers.

We don't even have 10 fingers. It's a dreadful historical mistake.
Octal would have been fine.

Dozens are the best sharing numbers by far, obviously.

In a recent discussion with Iain I probably made the mistake of
thinking numbers were slightly different when the most likely cause
was rounding error.

Can anyone confirm that, for an even-tempered scale of n intervals per
octave, the mth harmonic of any note will be itself be a note in the
same scale if n/m is an integer, or if m is a power of 2? Sorry for
the clumsiness of expression.

Hence 12 intervals in the most common scale, and the aural
assimilation of 2,3,4,6,8 and 12H.

I guess ppl argue, somewhere still, about whether the development of
our taste for modern harmony has shaped our senses, or whether the
history of music was bound to end up this way because of how our ears
work. I'm inclined to think there is a dynamic relationship between
the two. Action and reaction are equal and opposite. Music theory and
psychoacoustics are opposites in some ways, and equal in others. But
music is the action. Music comes first.

I still have a picture on my wall of the first release of the Yamaha
R1 motorcycle, which to my eyes was a revolution in style. After years
of copying and then surpassing European and US engineering, the R1
quite suddenly, but nonetheless subtly, subsumed western style into
something totally Japanese. No longer at our cutting edge, they became
their own. The R1 has Japanese eyes.

They also appear, in this process of redefinition, to have lost
immediate view of their own history. My son brought a girl from Japan
and, desperate for some point of intercultural commonality but
depending for my knowledge of her country upon what I have gleaned
from playing "Samurai, Total War", I quizzed her on the subject of sea
shanties. I played her "Sailor song", sung by Sandy Denny with
Fairport Convention, being the only approximation to the genre in my
collection, whilst Tom attempted to translate the story.

She explained that most Japanese people are more concerned about
earthquakes. Sea shanties are not part of popular consciousness.
Further the origin of fish troubles them no more than current affairs,
to which they seem oblivious. I suspect continuity of tradition is
maintained only through the feudal clan system, now a preserve of the
great and good. They must be the people who buy the astronomically
priced super-high-end Japanese audio stuff.

Hopefully China won't make the same mistake. Traditionally they use
fewer notes than us, but still within the same structure. There is
less history of the complications arising from many instruments
playing different notes simultaneously, so although their scale is
like ours it is more pure...closer to the ideal even temper, I am
told.

A popular, caring culture of simplicity and purity should suit valve
audio perfectly. I wonder how long we might wait for an amplifier with
a Chinese soul?

Anyway, I read that intermodulation distortion is bad because it is
not harmonic. So what...why isn't harmonic distortion bad because it
is not intermodular? What would a scale built around sums and
differences, rather than multiples, sound like?

Just as some harmonic distortion has a musical effect within the
common western scale, is there some kind of music within which IM
would be transparent?

In the absence of progress in the history of music, it won't be long
before these Europeans decimalise it. Time will be next. Dancing won't
be much fun. It's a while since I have done any dancing. It's not
sausages and chips that's making us fat. We've stopped dancing.

Ian

[bassett[_2_]]

"Ian Iveson" wrote in message
. ..
My supermarket is selling eggs in boxes of 5 and 10. This European
decimalisation thing has obviously overstepped the mark. The boxes don't
work properly. There is cubic close packing, and hexagonal close packing.
5 and 10 are really bad numbers.


The answer is quite simple buy five and one is a double yolker, buy
ten and two have double Yolk's.

next thing you'll be reporting a 10 hour CLOCK


bassett

[David R Brooks]

Ian Iveson wrote:
My supermarket is selling eggs in boxes of 5 and 10. This European
decimalisation thing has obviously overstepped the mark. The boxes
don't work properly. There is cubic close packing, and hexagonal close
packing. 5 and 10 are really bad numbers.

No doubt sold at the same price as 6 & 12 were before?

[Arny Krueger]

"Ian Iveson" wrote in
message

Anyway, I read that intermodulation distortion is bad
because it is not harmonic. So what...why isn't harmonic
distortion bad because it is not intermodular?

I think you are missing a critical piece of knowlege - audio equipment does
not have harmonic or intermodulation distortion. Those are just abstractions
and mesruement techniuqes that we use to characterize a certain class of
imperfections in audio gear.

The general class of imperfection in audio gear that leads to the
abstractions we call harmonic and intermodulation distortion, is called
curvature of the input-output curve. An ideal piece of high fidelity gear
will have a straight-line input-output curve. IOW, if you put in 1.000...
volt and get out 2.000... volts, then if you put in 2.000... volts you will
get 4.000... volts. If the input-output curve is nonlinear, if you put in
1.000... volt and get out 2.000... volts, then if you put in 2.000... volts
you might get 5 volts, or 4.1 volts or 3.9998 volts, but not 4.000... volts.

As a general rule, any piece of audio gear that produces spurious harmonic
signals while amplifying music, will concurrently generate spurious
intermodulation signals. So, trying to separate the two can be a big waste
of time, and lead to all sorts of thoughts that are not productive.

[thomas]

On Apr 11, 11:54 pm, "Ian Iveson"
wrote:

I guess ppl argue, somewhere still, about whether the development of
our taste for modern harmony has shaped our senses, or whether the
history of music was bound to end up this way because of how our ears
work. I'm inclined to think there is a dynamic relationship between
the two. Action and reaction are equal and opposite. Music theory and
psychoacoustics are opposites in some ways, and equal in others. But
music is the action. Music comes first.

Just as some harmonic distortion has a musical effect within the
common western scale, is there some kind of music within which IM
would be transparent?

One issue that you haven't raised is the problem of Equal Temperament.
This modern tuning system is already a distortion of the natural
harmonic set of overtones.

I don't have enough electronics knowledge to answer your question, but
I am certain that tuning systems would have to be taken into account
as part of the answer.

[Eeyore]

Ian Iveson wrote:

Can anyone confirm that, for an even-tempered scale of n intervals per
octave, the mth harmonic of any note will be itself be a note in the
same scale if n/m is an integer, or if m is a power of 2? Sorry for
the clumsiness of expression.

Uh ?

Graham

[Iain Churches]

Ian Iveson wrote:

Can anyone confirm that, for an even-tempered scale of n intervals per
octave, the mth harmonic of any note will be itself be a note in the
same scale if n/m is an integer, or if m is a power of 2? Sorry for
the clumsiness of expression.


It may well be. I fear that transposition to the sopranino
Sarusaphone and the counter-clockwise ukulele may
prove to be the exceptions to the rule.

Iain

[coffeedj]

The discussion of harmonics with respect to instruments is quite
fascinating, and a bit a diversion for those interested.

Tuned string instruments use a 'just' or diatonic tuning--that uses perfect
fifths or fourths between the strings. This results in harmonics that
create natural resonance from string to string. Every good string player
knows if the instrument is out of tune by playing just one string--the
harmonics give it away.

Percussion instrumnets, like the piano, use a tempered [close to, but not
the exactly the same as Pythagorean, which is based on the 12th root of 2]
tuning which flats the fifths (or sharps the fourths) ever so slightly.
This is not percieved as out of tune (for most people) becuase the three
strings per note in the upper register muddy the out-of-tuneness of the
sound. In the bottom register where there is just one string per note--our
sense of pitch is not as accurate. Harmonics are totally different on
piano--and have much less impact. However, I know piano tuners who use
special high-tension strings for the bass just to create extra sympathetic
harmonic resonance in the upper registers. They also tune the piano
slightly different as well, but I'm not sure what the algorithm is.

A harspsichord is a string instrument because the strings are plucked-not
struck with a hammer. It can be tuned either 'tempered' or 'just', but it
sounds out of tune if a tempered tuning is used. When I was the concert
master of the college symphony and on tour, it was my job to tune the
harpsichord for each concert. Since it was used only for one piece in the
first half and one in the second half (most of the time) I would retune the
harpsichord for each specific performance so that it was diatonically tuned
to the correct key for that performance. If one piece was in Emaj and the
second in Cmin, that meant a lot of work--as almost every note had to
change. Going from Amin to Dmaj on the other hand was just a quick touch up
since D is the dominant in the key A.

An interesting side note is that on a 'just' tuned instrument--there can be
problems when playing unaccompianed. For example: in the E minor Partita,
first movement, for the unaccompianed violin (piece every one is familiar
with in these days of ring tones) there is a modulation from E minor to B
major to F# , back to E minor. The key of F# minor uses no open strings, so
the violinist by ear will naturally tune F# to be a perfect fith to B major.
Unfortunately, if you do that, when you transition back to E minor--the open
E string is now out of tune with respect to the F# key you were just
playing. Thus the violinist has to slightly flat the transition to F# from
B in order to keep the following modulation back to E in tune. On a piano
of course, this problem would not exist.

On other interesting side note is that genetically there are people who
sense of accuracy of pitch is so acute that they can not stand to listen to
music. Everything sounds out of tune to them. These are usually the
children of two classical concert musicians.

At the other end of the scale is a rock concert. The volume in the bass is
usually turned up until the distortion is so high the center of the note
cannot even be found.

Can anyone confirm that, for an even-tempered scale of n intervals per
octave, the mth harmonic of any note will be itself be a note in the same
scale if n/m is an integer, or if m is a power of 2? Sorry for the
clumsiness of expression.

Hence 12 intervals in the most common scale, and the aural assimilation of
2,3,4,6,8 and 12H.

I guess ppl argue, somewhere still, about whether the development of our
taste for modern harmony has shaped our senses, or whether the history of
music was bound to end up this way because of how our ears work. I'm
inclined to think there is a dynamic relationship between the two. Action
and reaction are equal and opposite. Music theory and psychoacoustics are
opposites in some ways, and equal in others. But music is the action.
Music comes first.

I still have a picture on my wall of the first release of the Yamaha R1
motorcycle, which to my eyes was a revolution in style. After years of
copying and then surpassing European and US engineering, the R1 quite
suddenly, but nonetheless subtly, subsumed western style into something
totally Japanese. No longer at our cutting edge, they became their own.
The R1 has Japanese eyes.

They also appear, in this process of redefinition, to have lost immediate
view of their own history. My son brought a girl from Japan and, desperate
for some point of intercultural commonality but depending for my knowledge
of her country upon what I have gleaned from playing "Samurai, Total War",
I quizzed her on the subject of sea shanties. I played her "Sailor song",
sung by Sandy Denny with Fairport Convention, being the only approximation
to the genre in my collection, whilst Tom attempted to translate the
story.

She explained that most Japanese people are more concerned about
earthquakes. Sea shanties are not part of popular consciousness. Further
the origin of fish troubles them no more than current affairs, to which
they seem oblivious. I suspect continuity of tradition is maintained only
through the feudal clan system, now a preserve of the great and good. They
must be the people who buy the astronomically priced super-high-end
Japanese audio stuff.

Hopefully China won't make the same mistake. Traditionally they use fewer
notes than us, but still within the same structure. There is less history
of the complications arising from many instruments playing different notes
simultaneously, so although their scale is like ours it is more
pure...closer to the ideal even temper, I am told.

A popular, caring culture of simplicity and purity should suit valve audio
perfectly. I wonder how long we might wait for an amplifier with a Chinese
soul?

Anyway, I read that intermodulation distortion is bad because it is not
harmonic. So what...why isn't harmonic distortion bad because it is not
intermodular? What would a scale built around sums and differences, rather
than multiples, sound like?

Just as some harmonic distortion has a musical effect within the common
western scale, is there some kind of music within which IM would be
transparent?

In the absence of progress in the history of music, it won't be long
before these Europeans decimalise it. Time will be next. Dancing won't be
much fun. It's a while since I have done any dancing. It's not sausages
and chips that's making us fat. We've stopped dancing.

Ian

[Ian Iveson]

Arny said:

Anyway, I read that intermodulation distortion is bad
because it is not harmonic. So what...why isn't harmonic
distortion bad because it is not intermodular?

I think you are missing a critical piece of knowledge - audio
equipment does not have harmonic or intermodulation distortion.
Those are just abstractions and measurement techniques that we use
to characterize a certain class of imperfections in audio gear.

The general class of imperfection in audio gear that leads to the
abstractions we call harmonic and intermodulation distortion, is
called curvature of the input-output curve. An ideal piece of high
fidelity gear will have a straight-line input-output curve. IOW, if
you put in 1.000... volt and get out 2.000... volts, then if you put
in 2.000... volts you will get 4.000... volts. If the input-output
curve is nonlinear, if you put in 1.000... volt and get out 2.000...
volts, then if you put in 2.000... volts you might get 5 volts, or
4.1 volts or 3.9998 volts, but not 4.000... volts.

As a general rule, any piece of audio gear that produces spurious
harmonic signals while amplifying music, will concurrently generate
spurious intermodulation signals. So, trying to separate the two can
be a big waste of time, and lead to all sorts of thoughts that are
not productive.

I am hoping someone else might query your first paragraph, Arny, which
I wouldn't have expected from you. I'm shocked

As an act of devotion, I passed it through my American spellchecker.

I'll give it another day or so, if you don't mind, save to say that
*all* thoughts are potentially productive, and to agree with your
implied definition of a non-linear system, from which it follows that,
in the output of such a system, the IMD and HD it produces are
interrelated (dammit).

Thanks, Ian

[Ian Iveson]

Eeyore grunted

Can anyone confirm that, for an even-tempered scale of n intervals
per
octave, the mth harmonic of any note will be itself be a note in
the
same scale if n/m is an integer, or if m is a power of 2? Sorry for
the clumsiness of expression.

Uh ?

I'm a prophet, not a dictionary.

Ian

[Ian Iveson]

coffeedj wrote

The discussion of harmonics with respect to instruments is quite
fascinating, and a bit a diversion for those interested.

Tuned string instruments use a 'just' or diatonic tuning--that uses
perfect fifths or fourths between the strings. This results in
harmonics that create natural resonance from string to string.
Every good string player knows if the instrument is out of tune by
playing just one string--the harmonics give it away.

Percussion instrumnets, like the piano, use a tempered [close to,
but not the exactly the same as Pythagorean, which is based on the
12th root of 2] tuning which flats the fifths (or sharps the
fourths) ever so slightly. This is not percieved as out of tune (for
most people) becuase the three strings per note in the upper
register muddy the out-of-tuneness of the sound. In the bottom
register where there is just one string per note--our sense of pitch
is not as accurate. Harmonics are totally different on piano--and
have much less impact. However, I know piano tuners who use special
high-tension strings for the bass just to create extra sympathetic
harmonic resonance in the upper registers. They also tune the piano
slightly different as well, but I'm not sure what the algorithm is.

A harspsichord is a string instrument because the strings are
plucked-not struck with a hammer. It can be tuned either 'tempered'
or 'just', but it sounds out of tune if a tempered tuning is used.
When I was the concert master of the college symphony and on tour,
it was my job to tune the harpsichord for each concert. Since it
was used only for one piece in the first half and one in the second
half (most of the time) I would retune the harpsichord for each
specific performance so that it was diatonically tuned to the
correct key for that performance. If one piece was in Emaj and the
second in Cmin, that meant a lot of work--as almost every note had
to change. Going from Amin to Dmaj on the other hand was just a
quick touch up since D is the dominant in the key A.

An interesting side note is that on a 'just' tuned instrument--there
can be problems when playing unaccompianed. For example: in the E
minor Partita, first movement, for the unaccompianed violin (piece
every one is familiar with in these days of ring tones) there is a
modulation from E minor to B major to F# , back to E minor. The key
of F# minor uses no open strings, so the violinist by ear will
naturally tune F# to be a perfect fith to B major. Unfortunately, if
you do that, when you transition back to E minor--the open E string
is now out of tune with respect to the F# key you were just playing.
Thus the violinist has to slightly flat the transition to F# from B
in order to keep the following modulation back to E in tune. On a
piano of course, this problem would not exist.

On other interesting side note is that genetically there are people
who sense of accuracy of pitch is so acute that they can not stand
to listen to music. Everything sounds out of tune to them. These
are usually the children of two classical concert musicians.

At the other end of the scale is a rock concert. The volume in the
bass is usually turned up until the distortion is so high the center
of the note cannot even be found.


Thanks, in my library of real-world intelligence.

It seemed to me I should find out something about what I'm trying to
amplify.

cheers, Ian

[Ian Iveson]

Arny said

Anyway, I read that intermodulation distortion is bad
because it is not harmonic. So what...why isn't harmonic
distortion bad because it is not intermodular?

I think you are missing a critical piece of knowlege - audio
equipment does not have harmonic or intermodulation distortion.
Those are just abstractions and mesruement techniuqes that we use to
characterize a certain class of imperfections in audio gear.

I'm still surprised you said this, and still hoping someone else might
respond. Last time I tried to make the distinction there was clamour
from the defenders of the faith.

The general class of imperfection in audio gear that leads to the
abstractions we call harmonic and intermodulation distortion, is
called curvature of the input-output curve.

Urgh. That's an awkward and ugly expression! Never come across it
before, thankfully.

An ideal piece of high fidelity gear will have a straight-line
input-output curve. IOW, if you put in 1.000... volt and get out
2.000... volts, then if you put in 2.000... volts you will get
4.000... volts. If the input-output curve is nonlinear, if you put
in 1.000... volt and get out 2.000... volts, then if you put in
2.000... volts you might get 5 volts, or 4.1 volts or 3.9998 volts,
but not 4.000... volts.

Good. Close to a textbook definition of "non-linear".

As a general rule, any piece of audio gear that produces spurious
harmonic signals while amplifying music, will concurrently generate
spurious intermodulation signals. So, trying to separate the two can
be a big waste of time, and lead to all sorts of thoughts that are
not productive.

A reduction to absurdity was implicit, I hoped. So in my scale, based
on intermodulation rather than harmonic intervals, the IM distortion
may be assimilated, but the attendant and inescapable harmonics all
sound unmusical. Damn, and I've just about finished working out the
fret spacing. Back to the drawing board.

Incidentally, is a "spurious harmonic signal" the same thing as "just
an abstraction"?

cheers, Ian

[Arny Krueger]

"Ian Iveson" wrote in
message
. uk
Arny said

As a general rule, any piece of audio gear that produces
spurious harmonic signals while amplifying music, will
concurrently generate spurious intermodulation signals.
So, trying to separate the two can be a big waste of
time, and lead to all sorts of thoughts that are not
productive.

A reduction to absurdity was implicit, I hoped. So in my
scale, based on intermodulation rather than harmonic
intervals, the IM distortion may be assimilated, but the
attendant and inescapable harmonics all sound unmusical.

More like the reverse. The harmonics may be assimilated, but the attendant
and inescapable IM is very likely to sound unmusical.

The harmonics may be assimilated because they occur at the same frequencies
as the harmonics that are part of the musical input signal. A musical
instrument may also generate some intermodulation products, but they are
generally smaller than the harmonics. The low-order harmonics in some
musical signals may exceed the amplitude of the fundamentals.

Incidentally, is a "spurious harmonic signal" the same
thing as "just an abstraction"?

The spurious harmonic signal is a real signal, just like the spurious
intermodulation signal. Nothing abstract about either of them.

[Ian Iveson]

Arny Krueger wrote

...So in my
scale, based on intermodulation rather than harmonic
intervals, the IM distortion may be assimilated, but the
attendant and inescapable harmonics all sound unmusical.

More like the reverse. The harmonics may be assimilated, but the
attendant and inescapable IM is very likely to sound unmusical.

Sorry Arny, but I don't think you are quite following my argument.
That's OK, though, I was only musing and as you said, more or less,
not all thoughts are useful or interesting to everybody. With respect
to a scale based on intermodulation, rather than harmony, IM would be
assimilated, and harmonics would stick out like sore thumbs.

I am interested in opposites per se, but I must admit it is a minority
pursuit.

So I find it remarkable that, to define a harmonic scale, the
difference between the top and bottom notes is a given, and the only
basic decision that needs to made is how many intervals should divide
it. Twelve turns out to be the optimum number, as far as history has
so far decided, but other numbers are feasible. For a scale based on
intermodulation, in contrast, the intervals choose themselves, and the
only decision that needs to be made is the difference between the top
and bottom notes.

Now I am just beginning to wonder to what extent the intermodulation
products arising from harmonic intervals are themselves harmonious.

I know I'm barking. It may not even be the right tree. Oh well, ho
hum, etc. As you were...

The harmonics may be assimilated because they occur at the same
frequencies as the harmonics that are part of the musical input
signal. A musical instrument may also generate some intermodulation
products, but they are generally smaller than the harmonics. The
low-order harmonics in some musical signals may exceed the amplitude
of the fundamentals.

This seems much the same as what I wrote in the first place, that you
seemed to disagree with.

Incidentally, is a "spurious harmonic signal" the same
thing as "just an abstraction"?

The spurious harmonic signal is a real signal, just like the
spurious intermodulation signal. Nothing abstract about either of
them.

But I don't see how you square this with the rest of what you wrote,
e.g.

"I think you are missing a critical piece of knowlege - audio
equipment does
not have harmonic or intermodulation distortion. Those are just
abstractions
and mesruement techniuqes that we use to characterize a certain class
of
imperfections in audio gear.

"The general class of imperfection in audio gear that leads to the
abstractions we call harmonic and intermodulation distortion..."

I tried some time ago to discuss the difference between identity and
equivalence, particularly with respect to Fourier. That went quite
badly I recall.

cheers, Ian