Why is a train whistle a minor 7th chord?

I'm sure you've noticed that a four-note train whistle is
approximately a minor seventh chord (something like e3-g3-b3-d4.
Please don't ask me how it's tuned! ... though I believe the shreeking
of it does bend the pitches...) I wonder how they ended up with that
chord? Could this chord be one of the most consonant chords (= no
octave doublings) you can get with four notes? (Maybe c4-e4-g4-b4 is
more consonant?) I imagine for power and denseness they would want a
closed position chord.

How about train whistles in other countries? Same chord?

On Sun, 05 Mar 2006, "traktus5" wrote:
>
> I'm sure you've noticed that a four-note train whistle is
> approximately a minor seventh chord (something like e3-g3-b3-d4.
> Please don't ask me how it's tuned! ... though I believe the shreeking
> of it does bend the pitches...) I wonder how they ended up with that
> chord? Could this chord be one of the most consonant chords (= no
> octave doublings) you can get with four notes? (Maybe c4-e4-g4-b4 is
> more consonant?) I imagine for power and denseness they would want a
> closed position chord.
>
> How about train whistles in other countries? Same chord?

Hi Kelly,

Here in Australia, I've only ever heard a one- or two-note
whistle; the second note arising by Doppler Shift when the
train passes you. Whilst living in Malaysia, I was rarely ever
on or near a train, and frankly don't remember anything
remarkable. (It WAS almost 30 years ago!)

Where can I hear a recording of the kinds of whistle you're
talking about?

Regards,
Yahya

PS Does this topic really belong in this HE forum? YA

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Hi Yahya - I guess this is a bit off topic. (Do you know a good site
for misc. acoustics, not so centered on tuning? ...though I think
there is some relevence to the question: "... Could this chord be one
of the most consonant chords (= no > > octave doublings) you can get
with four notes? (Maybe c4-e4-g4-b4 is > > more consonant?) I
imagine for power and denseness they would want a > > closed position
chord....)

Since Paul's not around, do you have any interest in discussing
whether the interval 6:3 is of any relavance in the chord 5:6:9 (ie,
the ratio of the numerators of the intervals 6/5 and 3/2, as discussed
towards the end of message #978?)

thanks, Kelly

Hi Kelly,

I don't think this theory is a good predictor of consonance in general - consider when two same ratios are stacked on top of each other. This is generally dissonant for any ratio with prime limit >= 5. The ratio between the numerators (and the denominators too) is simply 1:1, but the sound is dissonant.

Best regards
Magnus

On Tue, 7 Mar 2006, traktus5 wrote:

> whether the interval 6:3 is of any relavance in the chord 5:6:9 (ie,
> the ratio of the numerators of the intervals 6/5 and 3/2, as discussed
> towards the end of message #978?)
>
> thanks, Kelly

On Tue, 7 Mar 2006, Magnus Jonsson wrote:
>
> Hi Kelly,
>
> I don't think this theory is a good predictor of consonance in general -
> consider when two same ratios are stacked on top of each other. This is
> generally dissonant for any ratio with prime limit >= 5. The ratio between
> the numerators (and the denominators too) is simply 1:1, but the sound is
> dissonant.
>
> Best regards
> Magnus
>
> On Tue, 7 Mar 2006, traktus5 wrote:
>
> > whether the interval 6:3 is of any relavance in the chord 5:6:9 (ie,
> > the ratio of the numerators of the intervals 6/5 and 3/2, as discussed
> > towards the end of message #978?)
> >
> > thanks, Kelly

Hi Kelly,

I have to agree with Magnus. In the chord 5:6:9,
you have -

1. The first-order ratios 5:6, 5:9 and 2:3 (=6:9),
arising from the three fundamentals.

2. The second- and higher-order ratios, arising
from the strong overtone partials of the timbres
of those three fundamental notes.

For example, if all three are played on an
instrument with only odd partials,
the 5 gives rise to 15, 25, 35, 45, 55, 65 ...
the 6 gives rise to 18, 30, 42, 54, 66 ...
the 9 gives rise to 27, 45, 63 ...

3. The ratios of the difference tones of the
fundamentals (1, 3, and 4) to each other, to
the overtones and to the fundamentals.

4. The ratios of the difference tones of the
overtones (2, 6, 8, ...) to each other, to the
overtones and to the fundamentals.

Which ones of these actually contribute to the
final sound is pretty much a question of timbre,
by which I mean the relative strengths of the
partials, and of amplitude, since soft sounds may
have inaudible interactions. For synthetic
instruments, the result may also depend on phase,
but that's not usually so for acoustic instruments.

With all these different numbers in play, all of
which arise from purely physical considerations
there's no need to involve a *hypothetical*
interval 6:3. You really need to relate ALL the
sounds of the chord to a common number, their
GCD (Greatest Common Divisor). For 5:6:9, this
is 1. Then relating this to a notional frequency,
eg A 110 Hz, your chord is 550, 660, 990 Hz.
These notes have overtones at integer multiples
of those three frequencies, and difference tones
at integer multiples of the GCD note, 110 Hz.
(I'm assuming harmonic timbres.)

However you realise your chord, it must be
expressed as specific frequencies. If you stick
to exact integer ratios, those frequencies have a
GCD which may well be in the audible range, as in
my example using 110 Hz. For higher integer limit
chords, the GCD may be subsonic. But even then,
all of the components of the sound you hear will
be integer multiples of that number. You will only
hear those ones which exceed the sensitivity of
your ears. Even then, you may not be aware of
all those frequencies which your ears detect!

As I understand Paul's theory of HE, it has two
interesting consequences: smaller integer ratios
are more consonant, and small deviations from
exact ratios do not destroy consonance. At least,
that's how I read the graph ...

So what I said above about exact ratios also applies
largely to ratios that are as exact as fallible humans
can make them.

Regards,
Yahya

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Hello. Thanks for your comments, Magnus and Yahya. I have a
partial response/question:

> 2. The second- and higher-order ratios, arising
> from the strong overtone partials of the timbres
> of those three fundamental notes.

> For example, if all three are played on an
> instrument with only odd partials,
> the 5 gives rise to 15, 25, 35, 45, 55, 65 ...
> the 6 gives rise to 18, 30, 42, 54, 66 ...
> the 9 gives rise to 27, 45, 63 ...

To have "only odd partials," why not just 'build' a harmonic series,
with odd numbers only, on each primary chord note, like with the
chord e3-g3-d4, as follows: e3-b4-g#5...;g3-d5-b5; and d4-a5-
F#6...)? I'm not familiar with your manner of calculation.

ARe you reckoning the partials as arising from each primary chord
note, or from the implied shared fundamental (ie, in may example,
C1).

I'm weak in mathematics, so I think we have a disconnect.

I will respond to the rest in a bit! I have a hunch there are
other "components", as well, to the sound, but need to study this.
thanks

Hi...

> > I don't think this theory is a good predictor of consonance in
general > consider when two same ratios are stacked on top of each
other. This is> > generally dissonant for any ratio with prime limit
>= 5. The ratio between> > the numerators (and the denominators too)
is simply 1:1, but the sound is> > dissonant.
> >
> > Magnus

> > On Tue, 7 Mar 2006, traktus5 wrote:> > > whether the interval
6:3 is of any relavance in the chord 5:6:9 (ie,> > > the ratio of
the numerators of the intervals 6/5 and 3/2, as discussed
> > > towards the end of message #978?)

Did I say *consonance*? There are two other aspects of my thinking
on this:

One, that the 6:3 ratio of the numerators of 5:6:9 'speaks to', in a
sense, the harmonic series, in a 'displaced' fashion, as follows.
The G in 4:5:6 (c4-e4-g4) is represented by 6 (from 6/5) and 3 (from
3/2). So, with 4:5:9, the 3:2 'slides up' to a new postion (9:6).
That's why I see the 6:3 of 4:5:9 as expressing, in a 'recombinant'
kind of way (like genes jumping around in a chromosone!), the
harmonic series as represented by 4:5:6, and find it useful to
compare how the the 3/2 interval 'interacts' differently with it's
sister intervals in different chords.

2) Also, is it possible that having multiple 'representations' of
three in the same chord (put that way, 'cause I still don't
understand the difference between powers, logs, and doubling
series!) could have an acoustical effect? You have 3, 3x2, and 3x3,
in the numerators of 5:6:9's intervals (6/5, 3/2, 9/5). I know this
could be facile numerology, but have you listened to the chord e4-g4-
f#5 (20:24:45) lately*? (Let's suppose we're hearing the same
chord, regardless of tuning.) Aside from it's very open but rough
quality, I fancy that the 9 (of 9/4) and the 6 (of 6/5), 'resonate
in some manner', probably because of the 3/2 ratio (of 9/6).

I know I'm out on a limb, but do you really believe that the unique
qualities which certain chord types possess (such as triads, seventh
chords, and their inversions), is fully described by tonalness,
difference tones, beats, partials, and roughness?

(*By the way, the musical intro to the movie Citizen Kane, by
Bernard Hermann, has a great minor ninth chord, in the scene with
the monkeys and statues. The exact cue is the Statue of the Cat in
the mist, if you're interested.)

(I still need to respond to Yahya's comments below.)

Thanks ...

Kelly

>
> I have to agree with Magnus. In the chord 5:6:9,
> you have -
>
> 1. The first-order ratios 5:6, 5:9 and 2:3 (=6:9),
> arising from the three fundamentals.
>
> 2. The second- and higher-order ratios, arising
> from the strong overtone partials of the timbres
> of those three fundamental notes.
>
> For example, if all three are played on an
> instrument with only odd partials,
> the 5 gives rise to 15, 25, 35, 45, 55, 65 ...
> the 6 gives rise to 18, 30, 42, 54, 66 ...
> the 9 gives rise to 27, 45, 63 ...
>
> 3. The ratios of the difference tones of the
> fundamentals (1, 3, and 4) to each other, to
> the overtones and to the fundamentals.
>
> 4. The ratios of the difference tones of the
> overtones (2, 6, 8, ...) to each other, to the
> overtones and to the fundamentals.
>
> Which ones of these actually contribute to the
> final sound is pretty much a question of timbre,
> by which I mean the relative strengths of the
> partials, and of amplitude, since soft sounds may
> have inaudible interactions. For synthetic
> instruments, the result may also depend on phase,
> but that's not usually so for acoustic instruments.
>
> With all these different numbers in play, all of
> which arise from purely physical considerations
> there's no need to involve a *hypothetical*
> interval 6:3. You really need to relate ALL the
> sounds of the chord to a common number, their
> GCD (Greatest Common Divisor). For 5:6:9, this
> is 1. Then relating this to a notional frequency,
> eg A 110 Hz, your chord is 550, 660, 990 Hz.
> These notes have overtones at integer multiples
> of those three frequencies, and difference tones
> at integer multiples of the GCD note, 110 Hz.
> (I'm assuming harmonic timbres.)
>
> However you realise your chord, it must be
> expressed as specific frequencies. If you stick
> to exact integer ratios, those frequencies have a
> GCD which may well be in the audible range, as in
> my example using 110 Hz. For higher integer limit
> chords, the GCD may be subsonic. But even then,
> all of the components of the sound you hear will
> be integer multiples of that number. You will only
> hear those ones which exceed the sensitivity of
> your ears. Even then, you may not be aware of
> all those frequencies which your ears detect!
>
> As I understand Paul's theory of HE, it has two
> interesting consequences: smaller integer ratios
> are more consonant, and small deviations from
> exact ratios do not destroy consonance. At least,
> that's how I read the graph ...
>
> So what I said above about exact ratios also applies
> largely to ratios that are as exact as fallible humans
> can make them.
>
> Regards,
> Yahya
>
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> No virus found in this outgoing message.
> Checked by AVG Free Edition.
> Version: 7.1.375 / Virus Database: 268.2.1/277 - Release Date:
8/3/06
>

Hi Kelly,

On Fri, 10 Mar 2006, "traktus5" wrote:
>
> Hello. Thanks for your comments, Magnus and Yahya. I have a
> partial response/question:
>
> > 2. The second- and higher-order ratios, arising
> > from the strong overtone partials of the timbres
> > of those three fundamental notes.
>
> > For example, if all three are played on an
> > instrument with only odd partials,
> > the 5 gives rise to 15, 25, 35, 45, 55, 65 ...
> > the 6 gives rise to 18, 30, 42, 54, 66 ...
> > the 9 gives rise to 27, 45, 63 ...
>
> To have "only odd partials," why not just 'build' a harmonic series,
> with odd numbers only, on each primary chord note, like with the
> chord e3-g3-d4, as follows: e3-b4-g#5...;g3-d5-b5; and d4-a5-
> F#6...)? ...

No need. I'm talking of an _instrument_ that
produces only the first, third, fifth, seventh, etc
multiples of the fundamental tone as overtones
(all even multiples being unavailable because of
the instrument's construction.)

However, if you were using pure sine tones, you
could synthesis _something like_ this timbre by
stacking the same multiples in a chord. The only
real difference would be in the relative strength
of each "partial".

> ... I'm not familiar with your manner of calculation.

Just multiplied each base factor (5, 6 or 9) in
turn by the odd numbers (1,) 3, 5, 7, 9, ...

> ARe you reckoning the partials as arising from each primary chord
> note, ...

Yes.

> ... or from the implied shared fundamental (ie, in may example,
> C1).

Definitely not!

> I'm weak in mathematics, so I think we have a disconnect.

Is the arithmetic clearer now?

> I will respond to the rest in a bit! I have a hunch there are
> other "components", as well, to the sound, but need to study this.
> thanks

Pleasure!

Regards,
Yahya

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