Tune Smithy => Projects => Topic started by: brian on July 29, 2008, 04:58:29 AM

Forum for Tune Smithy, Bounce Metronome and other software from Robert Inventor

Title: musical chords
Post by: brian on July 29, 2008, 04:58:29 AM
Hi All

I am currently examining the nature of chords on a western scale keyboard.  I find that the way in which we hear even simple chords of just 2 notes (sometimes called a diad - is this a real word?) is not described by the conventional summation of 2 sine waves - pure tones.  for example C + G  has a periodic repetition of an Octave below C' and the chord does indeed deepen to the extent that you cant hear the original middle C tone. 

I can send examples of this to interested parties.

My limited maths also shows that the general explanation of sounds via audio spectrum analysis is not correct either.  Either I am wrong or the audio industry has been using audio analysis tools that do not represent the response of the human ear to chordal sounds

Any correpsondance on this would be most gratefully received

PS, I only discovered this anomaly via Roberts Tunesmithy prog which I have been fiddling with for some years - a quite unique research tool in its own right


Title: Re: musical chords
Post by: Robert Walker on July 29, 2008, 07:10:33 AM
I'd answer that you are right, and it is correct to say that the "audio industry has been using audio analysis tools that do not represent the response of the human ear to chordal sounds", because they aren't designed to do that.

Maybe it will help to think over why that would be a problem. Why should it matter that they use audio analysis tools that do a frequency analysis of the sounds rather than a human ear response analysis?

Compare the photographic industry - photos do a colour frequency analysis of the pictures in terms of R, G and B components. When we look at photos we may see things that can't be detected in any kind of RGB analysis, e.g. the green dot in this optical illusion:

Lots and Lots and Lots of Illusions (
- Scroll down a bit. Then try the experiment where you look at the black spot in the middle of the swirling green dots.

An analysis of the light you see will only find green light. But any human eye will see a pink dot.

Yet whenever you process photos, e.g. add effects, vary the colours etc, you work with the RGB not what the human eye sees. It doesn't seem to matter that the software is working with a subtly different view on the photo from the human eye.

Similarly the audio tools are designed to split a sound into its component frequencies, which when added together again should reconstruct the original sound. This lets you process the sound e.g. by removing low hum or a high hiss, and when you put the frequencies back together again you get the original recording.

If they tried to reproduce human hearing, then you could no longer do this sort of thing. E.g. if you did a human hearing response analysis of the C + G chord, then put the result back together again, the low C would increase in volume, so it would no longer sound like the original. Every time you do it then the low C would increase in volume compared with the other sounds.

Usually this isn't what you want to happen, so it is better to use the frequency analysis rather than to try to model human hearing exactly.

With the C + G chord, there is indeed a repeating pattern at that frequency. But the pattern that repeats is a complex one which the frequency analysis splits up into higher frequency component sine waves. So a sine wave type analysis doesn't find it. An analysis looking for repeating similar waves of any shape, with no restrictions on the shape, will find it (but then it won't find the higher frequency components).

It is an interesting question, whether there is any way to analyse the sound to duplicate what a human ear can hear. I don't know the answer - does anyone else?

Sometimes it might matter - with mp3s then things that can't be heard by the human ear are ignored when the audio is compressed. To do that sort of thing, you would need a model of human hearing.

That's something I don't know anything about and may be interesting to follow up, and such a model could be very useful in some situations.

But I don't think it indicates a problem with the audio tools. They are fine, and you are right too, that would be what I'd say :-).

Perhaps it could help to describe some particular situations that interest you where you need a model of human hearing rather than a frequency analysis. That could help focus the discussion on some particular situation where there is a real world problem needing a solution.

Does this help?




Title: Re: musical chords
Post by: brian on July 31, 2008, 03:42:24 AM
Hi Robert

I made an interesting discovery, which I noted below

Ive found a way to play symbolic sounds like sin(2 PI() f t)  and sin(2 PI()1.5ft) and store them separately on the left and right hand stereo channels. 

A self evident point is that a chord is composed of two or more physically separate sound sources in real life instruments - I cant off hand think of any instrument breaks this rule?

Amazingly, when C and G are played as separate channels (they were generated separately) then they sound more like the real real life experience

Please check enclosed sample

When I mix these samples down to form a combined two tone sound, lo and behold you get this phenomena of the chord sounding an octave below ie at the beat frequency in this case of fc/2 namely 128 hz.  The difference is very distinct  and clearly shows and error in the way we combine sounds on a PC

If I am right then no synthesised chord will sound right on a PC

please check second sample

What do you make of that?

Ive tried the major triad, and with the miracle of my 5.1 SB sound card I am able to play each tone on a separate speaker via sound forge 9 (which now support surround sound), which gives the expected result
sadly I cant supply an example as the average player like winamp mixes the sample down to normal stero 2 channel with an ugly result.

I think I would probably have to record the sound from the speakers via a microphone to get the correct timbre, rather than the ugly one

Can TS3 handle this problem?

Title: Re: musical chords
Post by: Robert Walker on July 31, 2008, 05:50:35 AM
Hi Brian,

Thanks for the clips, that's interesting. I listened to them over headphones. The low C did sound much louder in the mix down to me as well. With the two tones in separate channels I hear the C to left, G to right and the low C in the middle. Maybe it is something to do with the spatial separation of the tones that makes the C sound as if it is quieter?

One idea - the C because it is dead centre feels as if it is closer to me than the ones sounding to left and right. So perhaps one automatically compensates for that, and treats it as a quieter sound??

I've never been asked this before, but perhaps FTS may be able to handle quad sound recordings if you record in the temp recording window, window 71. The record to file window definitely can't handle it.

I don't have the hardware here to test it at present to see if it can be done. It would probably be better to use a dedicated sound recording program like Goldwave. It is something I can look into for the future, low priority though as it's not a major component of FTS, and other programs would handle recording better.

If you want a counter example, and instrument that plays chords that aren't physically separated, well multi-phonics on wind instruments are like that, e.g. you can play multi-phonics on recorder on some notes. With keyboard like piano, it depends where you sit - if you sit directly in front of a grand piano then the notes would be all in the same direction, though from player's point of view they are spread out spatially.

But - is that the original motivation for your question, to find out why recorded mixes of sin waves have stronger difference tones than instrument ensembles?

Maybe that is something to do with it. I wonder also if perhaps when you play with another player then you might hear the difference tones more strongly than someone else would who listens to the two of you playing, if it is something to do with the spatial position of the difference tone.



Title: Re: musical chords
Post by: Robert Walker on July 31, 2008, 12:42:08 PM
No that can't be it - if it was to do with the apparent distance of the sound, a closer sound would be perceived as louder at the same heard volume, rather than quieter.

I wonder why the difference tone sounds quieter when the other tones are to left and right and the difference tone is in the centre. Anyone got any ideas?

Title: Re: musical chords
Post by: brian on July 31, 2008, 11:57:24 PM
Hi robert

Well for me the two tones played as left and right stereo  sound much more natural than the mixed tones.  Its even worse with the major triad, where the mix sound sound is atrocious not all pleasant , and thats from pure tones

I will try and arrange to record the C and G sound via a microphone and look at the waveform.  there must be something radically different?  The mystery plot thickens

Title: Re: musical chords
Post by: Robert Walker on October 10, 2008, 01:27:36 AM
Hi Brian,

There's an interesting thread in the tuning list right now about "dichotic listening" used to reduce the percieved harshness of chords:

"Creative use of stereo in tuning"

Also, linked from that discussion:

I wonder if perception of binaural difference tones can vary simiarly?


Title: Re: musical chords
Post by: brian on October 10, 2008, 08:31:34 PM
Hi Robert

Sorry Ive been absent fopr a while, lots of domestic issues got in the way together with a catastrophic crash of XP due to a rogue rootkit virus, really nasty.  I had to do a complete reformat and re-install all my apps, 2 weeks wasted time

The last time I looked at trojans etc was 2 years ago and I thought I was pretty well covered with AVG, but it failed to point out that you must schedule routine disc scans which do an in depth scan rather than the on-the-fly virus protection available during run time

I thought that trojans would be relatively harmless even if present as I am not connected to the net, but I was very mis informed, they are now very malicious.  A whole new breed out there to trash your computer. :D

will try an get back on track soon but not for another monthe I suspect.

please keep me informed and thanks very much for the tip I will go and digest the subject at leisure - very interesting, never heard of it before, obviously a whole new plethora of phenomena out there to be discovered.

PS  coming back to an earlier topic, is there any easy way to produce a very much cut down version of your work suitable of school kids and instruction on musical scales and chords and rhythm.  As you realise the present package is far far too complex for elementary users

I can make suggestions as to the core features which basically centre around the simple 12 TET keyboard
The package must be user friendly and assume little prior knowledgeand all the features must be virtually self evident (to the teacher at least) so little need for a user manual (apart from setup issues)

one might argue, why not use a convention electronic keyboard

well one argument is that to use the keyboard one need to be able to play it
secondly it is very limited in terms of exploring musical theory in general

A cut down version of yours could contain lots of tutorial examples and infinite variety for experimentation

for example, try explaining ASDR - ye you can use a lot of words but some simple well crafted examples and the ability to overlay an ASDR setting on all the notes of a well known tune would be very entertaining

anyway just some thoughts by way of teaching young minds ;D

Title: Re: musical chords
Post by: Robert Walker on October 19, 2008, 06:55:04 AM
Hi Brian,

Sorry to hear about your trojan. I've found one very useful additional tool is the free McAffee site advisor because it shows a red warning flag in Google search listings against any recognised dubious web sites. If you visit a dubious web site through a link, it shows a red warning flag in the browser status bar.

Surprisingly many sites high in the search results are infected these days. For instance if you search for a screensaver in google, then the very first site (at present) is reported by McAffee as spyware infected - as shown in their scan results for the downloads on the site - and with many adverse comments from users. Quite a few of the other sites in the first ten listing are spyware or adware infected.  It is a free plug in for your internet browser - you don't need to be a McAffee user to install it.

Another thing one can do is to use Virtual PC which is free nowadays, to run a virtual PC on your desktop, and install any programs you are unsure about within that first, or any programs you downloaded just to test - helps to keep the registry clear as well. Virus researchers use them to deliberately infect the virtual PC with any number of virus and trojan programs without affecting the  host computer at all.

Yes I'd like to make the program suitable for children to use. It is easiest to start with something that is already close to what is needed. I wonder which task is most suitable for children of the existing ones?

Perhaps the metronome and polyrhythms task? Other ideas might be the fractal tune player too, maybe the chord player, or the Lambdoma task? One of the issues is that it has to fit within some part of the teaching syllabus, unless meant for children's leisure activities - with that teaching clock program, my sister said that the part to do with making your own custom chimes, though fun, would be something you couldn't teach as such, because not something they are required to learn - except for something for them to play around with at idle moments. So it seems one needs to know what the syllabus is and design the program around that. There must be an element of rhythm teaching anyway so I think that task is a likely one to be useful in schools at least. Also the chord player surely could be of some interest to teachers?

Do you have any thoughts about that?

 At the moment I'm focussing on getting FTS into shape as it required more post release bug fixing and improvements than I expected. But once that is all done, I could be interested in working on a cut down version of one of the tasks, as an experiment to see if it works, and start with one that seems easy to convert. If that worked, with positive feedback from teachers, and if I got some sales for it, I could then go on to do the same with other tasks. Since it's a new departure for me, then I'd want to start with something easy to adapt for the first attempt, if possible.



Title: Re: musical chords
Post by: brian on October 20, 2008, 12:04:34 AM
Hi Robert

Thanks for the tip about siteadvisor, have installed it right away.  will also look at virtual pc.  I wonder if it can really protect against viruses migrating to any other part of the hard disk?

As for the school project, yes agreed it must fit in with the school curriculum.  So the basic keyboard player should be the starting point together with a musical notation display. Then move on through the various aspects, such as

note length
basic musical time
2/3 4/4  3/4 6/8

scales  ET 12t
C maj scale
rotation by 5ths8 tone scales with example tunes  dorian, phrygian etc

quads and upwards

modulating between scales (advanced students)
complex rhythms

but thats off the top of my head and could provide enough material from junior thru to high school

Im afraid I cant see the benefit of fractAL or lambdoma stuff for ordinary school work.  its basically random pleasing sounds like wind chimes

need something that allows ready practice supporting lessons with examples and the opportunity to look further by experimentation

As for complex rhythms, we are basically limited to 64x3 =192 tics in conventional western music

I always wanted to be able to compose rhythms using an excel style spread sheet approach

there are drum kit synthesiser that offer a lattice notation but they are usually limited to 16 24, or32 cells (but I may be out of date here)

I have always foiund rhythm problematical

anyway just a few thoughtws

Title: Re: musical chords
Post by: Robert Walker on October 21, 2008, 02:32:03 AM
Hi Brian,

Glad you installed site advisor.

I'll answer first about Virtual PC then in another e-mail about the rest.

You are certainly a lot safer running unknown programs within the virtual machine. But whether technically it is completely impossible for viruses and trojans to cross over to the host machine I don't know. It must be pretty hard or they wouldn't use them for virus research but whether technically impossible I don't know. 

Also there are one or two possible routes to look out for, which you need to be careful about.

You need to install the virtual machine additions in order to get files too / from the machine. You can then move those files using drag and drop, click on a file within the virtual machine and drag it out of the machine to where you want it to go.

So the virus would have to infect a file that you drag out of the machine. You can also let the virtual machine see folders on the host computer, or your DVD drive - if the DVD drive is writable, or if you share folders obviously that's a way it can connect. Or if there were any vulnerability in the Virtual Machine Additions themselves which a virus could be written to exploit.

It connects to the internet usually via shared networking. It doesn't appear on the network places in the host machine, so there is no obvious way for viruses to get to the host via the network:
A virtual machine that is configured to use shared networking behaves like a computer behind a Network Address Translation (NAT) router. Shared networking does not support inbound port mapping. External computers cannot access a server that is running in the virtual machine or any ports on the virtual machine. Shared networking also does not support networking between virtual machines or from the host operating system to the virtual machine."

So it would seem to be pretty safe, but whether that means it is techincially impossible for any virus to exploit any vulnerability, I don't know.

I always install AV and firewall on the virtual PC as well, and if you download lots of programs, install anti-spyware and anti adware such as Spybot Search and Destroy, Windows Defender and AdAware.

So, you should treat it just like any other computer connected to the internet in that way. Then, as well as helping to stop it get infected, the firewall would also help prevent it infecting anything else.

Then be careful about use of shared folders and shared DVD drives and which files you drag / drop to the host.

BTW another nice thing about a virtual machine is that it is very easy to back up - just back up two files, the virtual machine and its hard disk, and you can even carrry the virtual machine about with you on a USB stick and run it on any machine with Virtual PC.

Title: Re: musical chords
Post by: Robert Walker on October 21, 2008, 02:50:08 AM
Hi Brian,

Well, I think FTS could potentially help with some parts of the curriculum as you outlined it. With the rhythm, have you tried out Tune Smithy's Metronome for Rhythms and Multi-Beat Polyrhythms: (

I've done a fair bit more on it in the last week in fact, particularly working on the ways of making it easy to adjust individual times and volumes within the bar. With extra material by way of tutorials about how to use it and set it up, perhaps it may go quite a bit towards what one would need for rhythm teaching? I wonder if you'd be interested to take a look at it and see what you make of it?

The chord work could perhaps use the chord player: (

With the fractal music, what I thought the fractal composition tasks in FTS might be of interest for is as a way to explore instrumentation. You can try out the effect of unsual combinations of instruments for instance, and children could use it to explore instrumentation long before they could expect to write compositions themselves for an orchestra or for many instruments playing at once.

Something along the lines of this part of the new fractal tunes tutorial: (

With the Lambdoma, the interesting thing there is that it lets you explore intervals in the harmonic series, including unusual ones like 7/8 etc, which are harmonious but not normally "allowed" in western music. So I think it could be of interest to children, and help with thinking "outside the box" but whether it can fit in the curriculum I don't know.

So anyway my first thoughts would be that the most promising would be the chord player and the polyrhythm metronome, possibly the fractal tunes too for learning about some aspects of instrumentation and orchestration.

The midi keyboard retuning could be of interest, but I feel I need to do work on making it easier to use than it is now, before one could start to think about it in this context. Making software easy to use is in some ways the most challenging part of software development I find.

The PC keyboard player for that matter could also be of interest in the same way. I'll be working a bit on the midi keyboard retuning in the near future, it's my next thing to work on after the fractal tunes and metronome tasks, which is what I'm working on now.

What do you think?