question on a set of harmonics/numbers

I've been working a lot lately with prime-numbered harmonics (following La Monte Young's lead), and want to start playing with something different. It occurred to me that the set of odd numbers that aren't prime might be interesting.

I'm not a deep math guy, though I can handle a certain, so I'm asking here instead of tuning-math (where it's mostly over my head): does anyone know if there is a name for this set of numbers, and if so, can they point me to some resources? Has anyone used this set in a musical context before?

- Dave

--
Dave Seidel
[blog] http://superluminal.com/dave/weblog
[music] http://mysterybear.net

hi Dave,

--- In tuning@yahoogroups.com, Dave Seidel <dave@s...> wrote:

> I've been working a lot lately with prime-numbered
> harmonics (following La Monte Young's lead), and want to
> start playing with something different. It occurred to
> me that the set of odd numbers that aren't prime might
> be interesting.
>
> I'm not a deep math guy, though I can handle a certain,
> so I'm asking here instead of tuning-math (where it's
> mostly over my head): does anyone know if there is a
> name for this set of numbers, and if so, can they point
> me to some resources? Has anyone used this set in a
> musical context before?

numbers which are not prime are called "composite".
this includes all non-prime odd numbers as well as
all even numbers larger than 2.

i've never heard of anyone using specifically the
odd composites as a basis for harmony. however, note
that combining various notes tuned this way is going
to result in intervals which have the usual prime ratios.

i.e., say you combine a 9 with a 15 -- that results in
a 5:3 ratio. etc.

it's easy to see what results you get if you represent
the ratios as monzos and do the vector addition:

(click "reply" to view properly in the Yahoo web interface)

[0 1, 1> = 15
- [0 2, 0> = 9
-----------
[0 -1, 1> = 5/3

note that the monzos for all of your numbers will have
a zero for the exponent of 2, because they're all odd.

-monz

On Mon, 2005-02-28 at 16:07, Dave Seidel wrote:
> It occurred to me that the set of odd numbers that aren't
> prime might be interesting.
>
> Has anyone used this set in a musical context before?

There has been some publication by the Richter Herf-Institute
(www.moz.ac.at/user/herf/index_gb.html) which discusses the construction
and sound quality of chords whose frequency ratios form arithmetic
series. This certainly includes the odd numbers.

If memory serves me right, the mentioned publication is the following
(in German):

Maedel, Rolf: Mikrotöne - Aufbau, Klangwert, Beziehungen. Innsbruck:
Edition Helbling 1983.

Best,
Torsten

--
Torsten Anders
Sonic Arts Research Centre
Queen's University Belfast
Tel: +44 28 9097 4761 (office)
+44 28 9066 7439 (private)
www.torsten-anders.de

Thanks, monz, I knew there have to be a phrase that described the set. I also need to read up more on your site about monzos, that's a pretty elegant notation. I see what you're saying about the intervals made by combining the values.

I've been looking at it from a slightly different perspective, noticing that each odd composite that, when considered as a ratio, cannot be further reduced, makes a different unique interval in relation to 1/1.

For example, I took all odd composites within the first 128 harmonics, reduced them to ratios, put them into a Scala, added 1/1 and 2/1, and got this "scale":

65/64
33/32
69/64
35/32
9/8
75/64
77/64
39/32
81/64
21/16
85/64
87/64
45/32
91/64
93/64
95/64
49/32
99/64
25/16
51/32
27/16
55/32
111/64
57/32
115/64
117/64
119/64
15/8
121/64
123/64
125/64
63/32
2/1

Not sure what to do with this yet, just playing around so far.

- Dave

monz wrote:
> > hi Dave,
> > numbers which are not prime are called "composite".
> this includes all non-prime odd numbers as well as
> all even numbers larger than 2.
> > i've never heard of anyone using specifically the
> odd composites as a basis for harmony. however, note
> that combining various notes tuned this way is going
> to result in intervals which have the usual prime ratios.
> > i.e., say you combine a 9 with a 15 -- that results in
> a 5:3 ratio. etc.
> > it's easy to see what results you get if you represent
> the ratios as monzos and do the vector addition:
> > (click "reply" to view properly in the Yahoo web interface)
> > [0 1, 1> = 15
> - [0 2, 0> = 9
> -----------
> [0 -1, 1> = 5/3
> > note that the monzos for all of your numbers will have
> a zero for the exponent of 2, because they're all odd.
> > > -monz

Thanks Torsten, I will look into these resources (although unfortunately I don't read German.)

By the way, I downloaded "With Shifting Joints" a few days ago and found it very interesting. I look forward to listening to more of your work.

- Dave

Torsten Anders wrote:
> On Mon, 2005-02-28 at 16:07, Dave Seidel wrote:
> >>It occurred to me that the set of odd numbers that aren't >>prime might be interesting.
>>
>>Has anyone used this set in a musical context before?
> > > There has been some publication by the Richter Herf-Institute
> (www.moz.ac.at/user/herf/index_gb.html) which discusses the construction
> and sound quality of chords whose frequency ratios form arithmetic
> series. This certainly includes the odd numbers.
> > If memory serves me right, the mentioned publication is the following
> (in German):
> > Maedel, Rolf: Mikrotöne - Aufbau, Klangwert, Beziehungen. Innsbruck:
> Edition Helbling 1983.
> > Best,
> Torsten
>

On Mon, 2005-02-28 at 19:55, Dave Seidel wrote:
> By the way, I downloaded "With Shifting Joints" a few days ago and found
> it very interesting. I look forward to listening to more of your work.

Thanks for your interest. Actually, the stereo version is like a
black-and-white picture of the real thing. In case you are interested, I
may make the 8-chan version accessible for you (a few 100MB download or
send as data CD by snail-mail).

I just checked out your site and had a listen to The Gemini Nebula. I
like your somewhat puristic approach -- I had a look at your Csound file
to see how little there really is.. I am really impressed what you can
do with so few sine waves alone ;-)

BTW, you mentioned La Monte Young: are you aware of any CDs one could
buy? So far I could only find sold out records... Perhaps even the Well
Tuned Piano somewhere?

Best,
Torsten

--
Torsten Anders
Sonic Arts Research Centre
Queen's University Belfast
Tel: +44 28 9097 4761 (office)
+44 28 9066 7439 (private)
www.torsten-anders.de

Thanks, Torsten, I'd love to hear the 8-channel version. A download that size would be difficult for me, so a CD would be preferable. I appreciate the offer, so let me know if I should send you my snail mail address privately.

Glad you like the Gemini Nebula piece. I'm just finishing up a third piece in what has become a three-part series based on Young's sine-wave installations, and I hope to have it up in the next few days. (The first one is called "Symmetrical Melodic Variation on the Romantic Symmetry", also on my site.) I'm enjoying using simple means; partly because the LMY work that inspired me uses only sines, but frankly also because I'm a new partitioner when it comes to electronic music (and Csound in particular), so it makes sense for me to take small steps. The new piece is a little more layered and varied in texture.

There are very few LMY CDs available, and none of the big sine-wave pieces have been recorded (nor would they really. I'm fortunate to have a copy of the out-of-print Well Tuned Piano CD set, which I've had for a number of years, and I have a copy of "The Melodic Version of The Second Dream of The High-Tension Line Stepdown Transformer from The Four Dreams of China" CD, which is also out of print. There is a newer (1987) performance of the WTP available on DVD that I want to check out (as a DVD, it also includes Marian Zazeela's visual contribution), but it's pretty expensive. You can see what's available at www.lamonteyoung.com. Otherwise, I can only recommend taking a look on eBay once in a while. Too many of his pieces have never been released in any form, although his famous "Trio for Strings" is due to be performed this fall and recorded for release next year (in a just intonation version).

My guide in working with the ideas in his sine-wave installations is a great article by Kyle Gann that was published in a book called "Sound and Light", which is devoted to Young's and Zazeela's work. It's still in print, ISBN 0-8387-5346-9.

- Dave

Torsten Anders wrote:
> Thanks for your interest. Actually, the stereo version is like a
> black-and-white picture of the real thing. In case you are interested, I
> may make the 8-chan version accessible for you (a few 100MB download or
> send as data CD by snail-mail).
> > I just checked out your site and had a listen to The Gemini Nebula. I
> like your somewhat puristic approach -- I had a look at your Csound file
> to see how little there really is.. I am really impressed what you can
> do with so few sine waves alone ;-) > > BTW, you mentioned La Monte Young: are you aware of any CDs one could
> buy? So far I could only find sold out records... Perhaps even the Well
> Tuned Piano somewhere?
> > Best,
> Torsten
>

on 1/3/05 12:49, Dave Seidel at dave@superluminal.com wrote:

>
> Thanks, Torsten, I'd love to hear the 8-channel version. A download
> that size would be difficult for me, so a CD would be preferable. I
> appreciate the offer, so let me know if I should send you my snail mail
> address privately.
>
> Glad you like the Gemini Nebula piece. I'm just finishing up a third
> piece in what has become a three-part series based on Young's sine-wave
> installations, and I hope to have it up in the next few days. (The
> first one is called "Symmetrical Melodic Variation on the Romantic
> Symmetry", also on my site.) I'm enjoying using simple means; partly
> because the LMY work that inspired me uses only sines, but frankly also
> because I'm a new partitioner when it comes to electronic music (and
> Csound in particular), so it makes sense for me to take small steps.
> The new piece is a little more layered and varied in texture.
>
> There are very few LMY CDs available, and none of the big sine-wave
> pieces have been recorded (nor would they really. I'm fortunate to have
> a copy of the out-of-print Well Tuned Piano CD set, which I've had for a
> number of years, and I have a copy of "The Melodic Version of The Second
> Dream of The High-Tension Line Stepdown Transformer from The Four Dreams
> of China" CD, which is also out of print. There is a newer (1987)
> performance of the WTP available on DVD that I want to check out (as a
> DVD, it also includes Marian Zazeela's visual contribution), but it's
> pretty expensive. You can see what's available at www.lamonteyoung.com.
> Otherwise, I can only recommend taking a look on eBay once in a while.
> Too many of his pieces have never been released in any form, although
> his famous "Trio for Strings" is due to be performed this fall and
> recorded for release next year (in a just intonation version).
>
> My guide in working with the ideas in his sine-wave installations is a
> great article by Kyle Gann that was published in a book called "Sound
> and Light", which is devoted to Young's and Zazeela's work. It's still
> in print, ISBN 0-8387-5346-9.
>
> - Dave
>
>

I haven't been following this thread from the beginning but it's too
coincidental not to comment. You might be interested in news of a
forthcoming premiere of an 8 channel work in Just Intonation. The piece, to
be played at Aberdeen University, Scotland, on March 17, is 56 minutes long
and uses the 1.3.5.7.9.11 Eikosany. It began life as a composition for 8
voices and/or instruments, hence the 8 channels.

I was tempted to use pure waves and might do in the future but I decided
against it for this version because a) it's been done and I don't like
copying other artists if I can help it, and b) I like the idea and the sound
of synthesising my own timbres (using a combination of FM, subtractive and
additive synthesis). Nonetheless I am a great admirer of LMY and have
allowed the boldness and spirit of his work to influence me greatly.

The piece will be presented as an immersive installation with 8 Genelecs
driven by 8 portable CD players, all switched on at the same time by 8
members of the audience. I'll have the graphic score and some of the
Eikosany's geometric structures taped out on the floor space enclosed by the
speakers so that listeners can walk through the modulations. Very arty.

The only thing I would say is that the sound of long sustained slowly moving
Justly Intoned harmonies coming at you from all directions with contrasting
passages of noise and glitch is a powerful listening experience. There is no
"sweet spot" as you have in a static listening environment. Different
combination tones arise in different locations. The slightest movement of
the head can reveal new combinations. LMY was on to this in the Dream House.
In the true spirit of acousmatics I have refrained from gratuitously bolting
on some video.

I'll be mixing it to ADAT for various calls and to various surround formats
once I "procure" the necessary software.

One point that I wonder about. Do we really hear sine waves over speakers? I
thought that all speakers, no matter how refined, introduced some measure of
harmonic distortion. Just a thought.

mopani

Wow, this sounds great! I wish I could be there to experience it. I'm planning on a trip down to NYC in the next month or so to visit the Dream House.

I think it's great to use different timbres. I wouldn't be surprised if speakers do tend to introduce some distortion, but I don't really know. In the piece I'm preparing to publish now, I use a few pure sines, but also some additive ones. It's very easy in Csound (and I'm sure in other systems as well) to build a composite waveform with complete control over the choice of partials, and the relative strength and phase of each partial. So in some cases I'll use a waveform that only uses multiples of the fundamental (e.g., partials 1, 2, 4, and 8) to get a more full sound without muddying the tuning.

- Dave

mopani@tiscali.co.uk wrote:
> I haven't been following this thread from the beginning but it's too
> coincidental not to comment. You might be interested in news of a
> forthcoming premiere of an 8 channel work in Just Intonation. The piece, to
> be played at Aberdeen University, Scotland, on March 17, is 56 minutes long
> and uses the 1.3.5.7.9.11 Eikosany. It began life as a composition for 8
> voices and/or instruments, hence the 8 channels.
> > I was tempted to use pure waves and might do in the future but I decided
> against it for this version because a) it's been done and I don't like
> copying other artists if I can help it, and b) I like the idea and the sound
> of synthesising my own timbres (using a combination of FM, subtractive and
> additive synthesis). Nonetheless I am a great admirer of LMY and have
> allowed the boldness and spirit of his work to influence me greatly.
> > The piece will be presented as an immersive installation with 8 Genelecs
> driven by 8 portable CD players, all switched on at the same time by 8
> members of the audience. I'll have the graphic score and some of the
> Eikosany's geometric structures taped out on the floor space enclosed by the
> speakers so that listeners can walk through the modulations. Very arty.
> > The only thing I would say is that the sound of long sustained slowly moving
> Justly Intoned harmonies coming at you from all directions with contrasting
> passages of noise and glitch is a powerful listening experience. There is no
> "sweet spot" as you have in a static listening environment. Different
> combination tones arise in different locations. The slightest movement of
> the head can reveal new combinations. LMY was on to this in the Dream House.
> In the true spirit of acousmatics I have refrained from gratuitously bolting
> on some video. > > I'll be mixing it to ADAT for various calls and to various surround formats
> once I "procure" the necessary software.
> > One point that I wonder about. Do we really hear sine waves over speakers? I
> thought that all speakers, no matter how refined, introduced some measure of
> harmonic distortion. Just a thought.
> > mopani
> > > > > > > You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
> > > > > > > >

on 1/3/05 13:54, Dave Seidel at dave@superluminal.com wrote:

>
> Wow, this sounds great! I wish I could be there to experience it. I'm
> planning on a trip down to NYC in the next month or so to visit the
> Dream House.
>
> I think it's great to use different timbres. I wouldn't be surprised if
> speakers do tend to introduce some distortion, but I don't really know.
> In the piece I'm preparing to publish now, I use a few pure sines, but
> also some additive ones. It's very easy in Csound (and I'm sure in
> other systems as well) to build a composite waveform with complete
> control over the choice of partials, and the relative strength and phase
> of each partial. So in some cases I'll use a waveform that only uses
> multiples of the fundamental (e.g., partials 1, 2, 4, and 8) to get a
> more full sound without muddying the tuning.
>
> - Dave
>

Another interesting phenomenon is that pure (or as near as) sine waves sound
strangely out of tune, especially in the low register and in combination
with more complex timbres. I don't see this as a problem as I like to work
with perception. In fact I've sketched out a whole sound art piece based on
this little bit of info. Good luck with your work Dave.

best
mopani

Too bad I didn't get the CD version. My cassete version of the Well-Tuned
Piano by La Monte Young has degraded and is unlistenable. Johnny Reinhard

--- In tuning@yahoogroups.com, <mopani@t...> wrote:

> One point that I wonder about. Do we really hear sine waves over
speakers? I
> thought that all speakers, no matter how refined, introduced some
measure of
> harmonic distortion. Just a thought.
>
> mopani

Even if one managed to create a refined enough set of speakers,
Alison, there would still be the harmonic distortion introduced by
the middle ear and other parts of the human auditory system. The
ear's distortion is responsible for the difference tones and other
combinational tones (including subjective harmonics) that are often
inaudible but become overwhelming at loud aural volumes of the given
sound. The higher-order combinational tone 2*f1-f2 is audible even at
low volumes and is hence thought to arise as a result of higher-level
processing in the brain.

Maybe this answer wasn't really relevant to you . . . can you talk
more about the acoustic effects you're going for? Maybe it's the
spacial intereference patterns you're interested in. In order to get
total constructive and total destructive interference (your ears
can't produce combinational tones from silence!) in various parts of
the room, you need two different speakers to produce sound waves
which, when a half-cycle phase shift is applied, cancel themselves
out. Therefore, odd harmonics introduced by the speakers shouldn't be
a problem at all -- it's just the even harmonics which threaten to
spoil the effect. I don't know if it's easier to make speakers
produce only odd-order distortion products than to produce none
whatsoever, but it's worth looking into, if this is the effect you're
concerned with. I know this odd- vs. even-order distortion product
question does come up a lot in the sound reproduction field, so I
think you should be able to find some answers without too much
trouble.

--- In tuning@yahoogroups.com, Dave Seidel <dave@s...> wrote:
> Wow, this sounds great! I wish I could be there to experience it.
I'm
> planning on a trip down to NYC in the next month or so to visit the
> Dream House.
>
> I think it's great to use different timbres. I wouldn't be
surprised if
> speakers do tend to introduce some distortion, but I don't really
know.
> In the piece I'm preparing to publish now, I use a few pure
sines, but
> also some additive ones. It's very easy in Csound (and I'm sure in
> other systems as well) to build a composite waveform with complete
> control over the choice of partials, and the relative strength and
phase
> of each partial. So in some cases I'll use a waveform that only
uses
> multiples of the fundamental (e.g., partials 1, 2, 4, and 8) to get
a
> more full sound without muddying the tuning.

1) I think harmonic partials make the tuning more clear, rather than
muddying it. In fact, as Aaron mentioned to me over the phone, almost
any of the 12-note circulating tunings produce pretty much the same
effect when sine-wave timbres are used, while rich harmonic timbres
make the differences between the different tunings crystal clear. And
in the case of JI tunings, harmonic partials are even more
appropriate. The human auditory system is designed to extract the
pitch of notes from the first few partials (often partials #3-6), and
the stronger and more harmonic these partials are, the clearer and
less muddy the perception of the tuning of the pitch.

2) As I wrote to Alison, you might want to try using only odd
partials, if your intention is to get the same strong bands of
constructive and destructive interference in the room (as a result of
different relative distances from your head to each of the two
speakers depending on where you are in the room) that you would get
with sine waves.

--- In tuning@yahoogroups.com, <mopani@t...> wrote:

> Another interesting phenomenon is that pure (or as near as) sine
waves sound
> strangely out of tune, especially in the low register and in
combination
> with more complex timbres.

What do you mean by out of tune? Certainly it's true that sine waves
a pure octave (2:1) apart sound like they're closer than an octave to
one another, particularly in the lowest and highest registers. In
many cases you need an interval of, say, 1209 cents, rather than 1200
cents, to get two sine waves to sound like they're producing the same
pitch (up to octave-equivalence). Harmonic partials greatly mitigate
this effect, as you might expect due to all the pure octaves in the
harmonic series.

Maybe this is what you meant by "out of tune". Or maybe it's the
inherent "muddiness" of sine waves. The human voice and many natural
sounds often have exactly harmonic partials, so it's not surprising
that the human auditory system gets confused when presented with
isolated pure tones (sine waves).

> I don't see this as a problem as I like to work
> with perception. In fact I've sketched out a whole sound art piece
based on
> this little bit of info.

I'd love to hear more about this, Alison!

On Tue, 2005-03-01 at 11:49, Dave Seidel wrote:
> Thanks, Torsten, I'd love to hear the 8-channel version. A download
> that size would be difficult for me, so a CD would be preferable. I
> appreciate the offer, so let me know if I should send you my snail mail
> address privately.

Just send me your address and don't expect the CD to arrive the next day
;-)

> Glad you like the Gemini Nebula piece. I'm just finishing up a third
> piece in what has become a three-part series based on Young's sine-wave
> installations, and I hope to have it up in the next few days. (The
> first one is called "Symmetrical Melodic Variation on the Romantic
> Symmetry", also on my site.) I'm enjoying using simple means; partly
> because the LMY work that inspired me uses only sines, but frankly also
> because I'm a new partitioner when it comes to electronic music (and
> Csound in particular), so it makes sense for me to take small steps.
> The new piece is a little more layered and varied in texture.

I meanwhile listend to 'Symmetrical Melodic Variation..'. However, to be
honest I definitely prefer 'Gemini Nebula'. The 'Variation' sounds much
more 'flat' to me, I could hardly perceive any spatialisation. I figure,
the 'spatial beating' was one of the things I liked most in Gemini
Nebula. I daresay, in electro-acoustic music spatialisation tends to be
even more important than tuning ;-)

Best,
Torsten

--
Torsten Anders
Sonic Arts Research Centre
Queen's University Belfast
Tel: +44 28 9097 4761 (office)
+44 28 9066 7439 (private)
www.torsten-anders.de

No problem, I appreciate your comments. I've been considering going back and revising that one anyway, not only for spatialization, but for timbre as well.

- Dave

Torsten Anders wrote:
> I meanwhile listend to 'Symmetrical Melodic Variation..'. However, to be
> honest I definitely prefer 'Gemini Nebula'. The 'Variation' sounds much
> more 'flat' to me, I could hardly perceive any spatialisation. I figure,
> the 'spatial beating' was one of the things I liked most in Gemini
> Nebula. I daresay, in electro-acoustic music spatialisation tends to be
> even more important than tuning ;-)

>I'd love to hear more about this, Alison!

I think that's James, not Alison.

-Carl

on 1/3/05 20:22, wallyesterpaulrus at wallyesterpaulrus@yahoo.com wrote:

>
>
> --- In tuning@yahoogroups.com, <mopani@t...> wrote:
>
>> Another interesting phenomenon is that pure (or as near as) sine
> waves sound
>> strangely out of tune, especially in the low register and in
> combination
>> with more complex timbres.
>
> What do you mean by out of tune? Certainly it's true that sine waves
> a pure octave (2:1) apart sound like they're closer than an octave to
> one another, particularly in the lowest and highest registers. In
> many cases you need an interval of, say, 1209 cents, rather than 1200
> cents, to get two sine waves to sound like they're producing the same
> pitch (up to octave-equivalence). Harmonic partials greatly mitigate
> this effect, as you might expect due to all the pure octaves in the
> harmonic series.

I'm referring here to Pierre Schaeffer's observation in "Solfege de l'objet
sonore" where he demonstrates descending octaves using the piano, sine waves
and the bassoon. The three points he makes are that the pure tones are
almost inaudible in low registers, they often sound an octave lower than
notes of the same pitch with a rich spectrum and they sometimes sound out of
tune. To my ears he's right and you have explained here and elsewhere why
this is so. My take on this is that it's interesting to listen to and could
become the basis of a work of sound art if presented in the right context.
Op art comes to mind as an example from the plastic arts.
>
> Maybe this is what you meant by "out of tune". Or maybe it's the
> inherent "muddiness" of sine waves. The human voice and many natural
> sounds often have exactly harmonic partials, so it's not surprising
> that the human auditory system gets confused when presented with
> isolated pure tones (sine waves).
>
>> I don't see this as a problem as I like to work
>> with perception. In fact I've sketched out a whole sound art piece
> based on
>> this little bit of info.
>
> I'd love to hear more about this, Alison!
>

I'll post details as they arise.

mopani

on 1/3/05 20:10, wallyesterpaulrus at wallyesterpaulrus@yahoo.com wrote:

>
>
> --- In tuning@yahoogroups.com, <mopani@t...> wrote:
>
>> One point that I wonder about. Do we really hear sine waves over
> speakers? I
>> thought that all speakers, no matter how refined, introduced some
> measure of
>> harmonic distortion. Just a thought.
>>
>> mopani
>
> Even if one managed to create a refined enough set of speakers,
> Alison, there would still be the harmonic distortion introduced by
> the middle ear and other parts of the human auditory system. The
> ear's distortion is responsible for the difference tones and other
> combinational tones (including subjective harmonics) that are often
> inaudible but become overwhelming at loud aural volumes of the given
> sound. The higher-order combinational tone 2*f1-f2 is audible even at
> low volumes and is hence thought to arise as a result of higher-level
> processing in the brain.
>
> Maybe this answer wasn't really relevant to you . . . can you talk
> more about the acoustic effects you're going for? Maybe it's the
> spacial intereference patterns you're interested in. In order to get
> total constructive and total destructive interference (your ears
> can't produce combinational tones from silence!) in various parts of
> the room, you need two different speakers to produce sound waves
> which, when a half-cycle phase shift is applied, cancel themselves
> out. Therefore, odd harmonics introduced by the speakers shouldn't be
> a problem at all -- it's just the even harmonics which threaten to
> spoil the effect. I don't know if it's easier to make speakers
> produce only odd-order distortion products than to produce none
> whatsoever, but it's worth looking into, if this is the effect you're
> concerned with. I know this odd- vs. even-order distortion product
> question does come up a lot in the sound reproduction field, so I
> think you should be able to find some answers without too much
> trouble.

Thes are helpful points. I've made notes on the the phase shift and odd
harmonic phenomena in the past. The next step is to find interesting ways of
presenting the sounds. Although I'm fascinated by the physics I'm looking
at all this in terms of how I can make successful pieces. I have a friend
who uses a DJ's double CD deck to spin two similar timbres (usually fairly
pure). He then wiggles the pitch of one tone to eke out the combination
tones, which as you say, are overwhelming at loud volumes. He also muddies
the timbres using another part of his set-up. Now this can be very subtle to
the point that you feel your head flutter in slightly different ways as you
shift your ears even a few millimetres towards or away from one or other of
a stereo pair of speakers.

I understand most about how this comes about. But with eight speakers and
multiple timbres, some very complex FM timbres and some consisting of
reasonably simple sine and square, the parameters multiply to such an extent
that I wouldn't even attempt to explain what's going on. I simply wallow in
the sound, observing as I go and moving the pitches around the
multi-dimensional space in as artful a manner as possible. I (along with
most of the practitioners in this field) am very much at the experimental
stage. I do notice interesting changes in perception (remember in the
present installation some of the chords sustain for over a minute) as you
approach fields of two or three speakers at a time. This must be a function
of the relative amplitude of certain tones and the effect this has on
beating. I would reckon, though correct me if I'm wrong, that having your
back to some speakers whilst facing others will 'shift' the sound due to the
head absorbing certain frequencies as explained by Benade.

If anything the radical aspect of this is the context. You get to move
around the sound field 'feeling' the piece in a sculptural sense instead of
being stuck in row 42b with heartburn and an itchy arse whilst looking up
the cellist's nose. That has to be progress.

mopani

--- In tuning@yahoogroups.com, <mopani@t...> wrote:

> I do notice interesting changes in perception (remember in the
> present installation some of the chords sustain for over a minute)
as you
> approach fields of two or three speakers at a time. This must be a
function
> of the relative amplitude of certain tones and the effect this has
on
> beating.

Are you speaking of the static, spatial patterns of constructive and
destructive interference that I was referring to before? When that
occurs, moving your head around causes beating, which can be
understood either in terms of the Doppler shift of the frequencies
coming out of the speakers, or in terms of simply "surfing" the
static interference patterns in the room.

> If anything the radical aspect of this is the context. You get to
move
> around the sound field 'feeling' the piece in a sculptural sense
instead of
> being stuck in row 42b with heartburn and an itchy arse whilst
looking up
> the cellist's nose. That has to be progress.

Sounds great, Alison -- here's to progress!

on 2/3/05 20:51, wallyesterpaulrus at wallyesterpaulrus@yahoo.com wrote:

>
>
> --- In tuning@yahoogroups.com, <mopani@t...> wrote:
>
>> I do notice interesting changes in perception (remember in the
>> present installation some of the chords sustain for over a minute)
> as you
>> approach fields of two or three speakers at a time. This must be a
> function
>> of the relative amplitude of certain tones and the effect this has
> on
>> beating.
>
> Are you speaking of the static, spatial patterns of constructive and
> destructive interference that I was referring to before? When that
> occurs, moving your head around causes beating, which can be
> understood either in terms of the Doppler shift of the frequencies
> coming out of the speakers, or in terms of simply "surfing" the
> static interference patterns in the room.

That would seem to explain what I'm experiencing very well.
>
>> If anything the radical aspect of this is the context. You get to
> move
>> around the sound field 'feeling' the piece in a sculptural sense
> instead of
>> being stuck in row 42b with heartburn and an itchy arse whilst
> looking up
>> the cellist's nose. That has to be progress.
>
> Sounds great, Alison -- here's to progress!

Thanks

mopani

Dave Seidel wrote (about La Monte's several out of print works):

"...The Melodic Version of The Second Dream of The High-Tension Line
Stepdown Transformer from The Four Dreams of China" CD..."

...I have a copy of this that I'm willing to part with if anybody
here is interested. Please contact me off-list: jimcole "at"
spectralvoices "dot" com

BTW Dave, I'm listening to "The Gemini Nebula" now and it's
entrancing - nice work!

~jim (a sporadic lurker)

http://www.spectralvoices.com

--- In tuning@yahoogroups.com, Dave Seidel <dave@s...> wrote:

> I'm not a deep math guy, though I can handle a certain, so I'm asking
> here instead of tuning-math (where it's mostly over my head): does
> anyone know if there is a name for this set of numbers, and if so, can
> they point me to some resources? Has anyone used this set in a musical
> context before?

Number theorists call such numbers "odd composite numbers"; this
factoid is probably useless to your purpose. The first two odd
composite numbers are 9 and 15, and from this we immediately find 15/9
= 5/3, so at least we have major sixths/minor thirds in this system.
The intervals derived from just 2, 9 and 15 form a mathematical group,
and include not only 6/5, but 2048/2025, 16/15, and 9/8.

--- In tuning@yahoogroups.com, "Jim Cole" <thejimcole@y...> wrote:
>
>
> Dave Seidel wrote (about La Monte's several out of print works):
>
> "...The Melodic Version of The Second Dream of The High-Tension
Line
> Stepdown Transformer from The Four Dreams of China" CD..."
>
> ...I have a copy of this that I'm willing to part with if anybody
> here is interested. Please contact me off-list: jimcole "at"
> spectralvoices "dot" com
>
> BTW Dave, I'm listening to "The Gemini Nebula" now and it's
> entrancing - nice work!
>
> ~jim (a sporadic lurker)
>
> http://www.spectralvoices.com

Hi Jim, I notice that you'll be performing in my neighborhood
(Somerville, MA) on March 12th. Do you want to give us any details on
the performance?

Thanks, Jim!

- Dave

Jim Cole wrote:
> > BTW Dave, I'm listening to "The Gemini Nebula" now and it's > entrancing - nice work!

Paul wrote:
> Hi Jim, I notice that you'll be performing in my neighborhood
> (Somerville, MA) on March 12th. Do you want to give us any details
on the performance?

Thank you very much for asking Paul and allowing me the chance to
tell a bit about it here on the list.

I'll be performing sections of my latest solo work "The Way Beyond"
of immersive, multilayered overtone singing (using a "virtual water
tower" set up of deep reverb and Echoplex looping). The program will
also feature direct unamplified overtone singing "songs" with
acoustic guitar. It'll be an intimate home concert setting that my
friend Andy Wood is hosting (reservations at 617-776-7974)

Thanks again for the interest,

~jim
http://www.spectralvoices.com

--- In tuning@yahoogroups.com, "Jim Cole" <thejimcole@y...> wrote:
>
>
> Paul wrote:
> > Hi Jim, I notice that you'll be performing in my neighborhood
> > (Somerville, MA) on March 12th. Do you want to give us any
details
> on the performance?
>
> Thank you very much for asking Paul and allowing me the chance to
> tell a bit about it here on the list.
>
> I'll be performing sections of my latest solo work "The Way
Beyond"
> of immersive, multilayered overtone singing (using a "virtual
water
> tower" set up of deep reverb and Echoplex looping).

Wow!

> The program will
> also feature direct unamplified overtone singing "songs" with
> acoustic guitar. It'll be an intimate home concert setting that
my
> friend Andy Wood is hosting (reservations at 617-776-7974)

I met Andy's roommate the other day!

> Thanks again for the interest,
>
> ~jim
> http://www.spectralvoices.com

Hi Jim --

It seems we have some musician friends in common. Bonnie Rovics
(who's played flute with me at a number of gigs and countless
parties) says she knows you. Remember her?

Jim, I hope we get to do some throat singing and guitar playing
together when you're in town. Perhaps after the gig? Hopefully,
Bonnie will be there too . . .

Anyway, we were talking about the Boston radio situation in e-mail,
so I thought I'd post this (from my violinist friend/collaborator
Katt Hernandez):

*********************************************************************
Right-ist christian fundamentalists are
gettign ready to shut down two of our college stations- WZBC and
WMFO. I'm
nto joking. if you care about local music and teh freedom to
broadcast it,
please write a letter and send it off as soon as possible.

Letters must be sent to FCC by Friday.
Link for info:
http://www.democracies.com/

NEWS
A chain of 400 radio stations is grabbing non-commercial stations
around
Boston and the nation to expand their syndicated satellite-fed
signal. The
evangelical CSN International has over 200 applications filed with
the
FCC for FM radio, not to mention their TV and AM holdings. Their
would-be
90.5 FM WSMA with 20,000 Watts would spread its signal across
Boston,
Quincy, Hingham, Weymouth, Taunton and to the northwest. They plan
to
locate the transmitter in Scituate, MA. Normally, non-commercial
stations
are required to operate a human-staffed "main studio" in their city
of
license. Non-commercial stations are supposed to have a local
character
with local production about local affairs, and not be overrun by a
chain's canned programming. But in February CSN International moved
to
eliminate that requirement for WSMA would-be 90.5 FM in Scituate.
That
is, CSN has asked the FCC to waive the normal requirement for
a "main
studio." They will succeed, unless a concerted opposition is
mounted. As
you probably know, many evangelical Christian broadcast chains
enjoyed a
spree of buying small non-commercial radio stations across the
country in
recent years, often taking community and college frequencies that
weren't
organized to defend against it. This national issue is featured in
the
Feb. 25 "Media Minutes" update by Free Press.

Listeners affected include those to:

WZBC 90.3 FM, Newton MA
Serving the surrounding community with 1,000 Watts live-DJ
programming
(Boston College).

WMFO 91.5 FM, Medford, MA
Serving the surrounding community with 125 Watts live-DJ programming
(Tufts University).
http://www.democracies.com/
*********************************************************************

N.P. Harry Partch on my iPod (he just said "I was a bum once
myself", just like on the t-shirt Jon kindly sent me!)

Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" >
> Right-ist christian fundamentalists are
> gettign ready to shut down two of our college stations- WZBC and
> WMFO. I'm
> nto joking. if you care about local music and teh freedom to
> broadcast it,
> please write a letter and send it off as soon as possible.
>
> Letters must be sent to FCC by Friday.
> Link for info:
> http://www.democracies.com/

I'll send in a letter. I really am getting annoyed with this s**t!

> N.P. Harry Partch on my iPod (he just said "I was a bum once
> myself", just like on the t-shirt Jon kindly sent me!)

Heh. If I had to list my most humbling moments, right at the top would
be one of my role's in the 1976 production of "U.S. Highball", where
(as a young man in his early 20's) I had to play/sing the part of the
old man who crawls out of a piano box to utter that line. Yeah, right!

Cheers,
Jon (who remembers that Kraig Grady was in the audience back then...)