Linear music - a slight terminological issue

Hi again.

In late 2002, I've made some stuff which I was privately calling "Linear music". Recently, I've discovered that many people were using the term "linear music" for something completely different. However, from what I could find it seems to me that the usage of the term is not very explicit as some people called it "horizontal music", which I personally would find much more logical for this, and the thing which I dubbed "linear music" (for my personal use so far) didn't seem to be discussed anywhere.

What I used to call "linear music" in 2002 is music based on modes whose transposition is made, in most cases, in a linear way rather than exponential -- i.e. if one voice plays a 5-tone melody using relative frequencies of "18, 16, 15, 13.5, 12" and another voice plays the theme 6 units lower, then its relative frequencies are "12, 10, 9, 7.5, 6" (which means the ratios between the two get successively larger but the differences remain constant). My idea was that you could, if desired, eventually mix more than two voices so that another may play, for example, 3 units lower than the second one, and yet another may play, let's say, 3 units higher than the first one (should we make the harmonies a bit more "unconventional") or that sort of stuff. This means that scales may be transposed this way as well, which in turn excludes the option of general periods for scales (like octaves, for example). To a certain extent, this might be accomplished using an algorithm or device capable of linear frequency shifting, as long as the overtones are soft enough or have fast decay. The most "straight-forward" application is probably found in amplitude modulation (i.e. parallel multiplication) if one of the two signals is a periodic sine wave.

So my questions are two.

#1. Does anyone of you think the term "linear music" is indeed qualified to mean something else?

#2. If all the terms like "linear tunings" or "linear scales" are in use for something else, do you think there might be another word which would more or less describe what I was describing here?

Thanks.

Petr

--- In tuning@yahoogroups.com, Petr Pařízek <petrparizek2000@...> wrote:

> #2. If all the terms like "linear tunings" or "linear scales" are in use for
> something else, do you think there might be another word which would more or
> less describe what I was describing here?

I used to think of adding a constant term to each frequency as "arithmetic transposition". It can produce some interesting effects.

On Tue, Mar 1, 2011 at 3:37 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Petr Pařízek <petrparizek2000@...> wrote:
>
> > #2. If all the terms like "linear tunings" or "linear scales" are in use for
> > something else, do you think there might be another word which would more or
> > less describe what I was describing here?
>
> I used to think of adding a constant term to each frequency as "arithmetic transposition". It can produce some interesting effects.

I've been calling it "heterodyning," from here:

http://en.wikipedia.org/wiki/Heterodyne

This is kind of inaccurate, as heterodyning involves the nonlinear
creation of sum and difference tones, whereas we're now just talking
about the nonlinear creation of sum tones. I guess the real term is
SSAM, Single Sideband Amplitude Modulation, but damn, that's a
mouthful.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > I used to think of adding a constant term to each frequency as "arithmetic transposition". It can produce some interesting effects.
>
> I've been calling it "heterodyning," from here:
>
> http://en.wikipedia.org/wiki/Heterodyne
>
> This is kind of inaccurate, as heterodyning involves the nonlinear
> creation of sum and difference tones, whereas we're now just talking
> about the nonlinear creation of sum tones.

I included negative numbers. Adding a negative term can be pretty extreme in its results.

On Tue, Mar 1, 2011 at 4:02 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > I used to think of adding a constant term to each frequency as "arithmetic transposition". It can produce some interesting effects.
> >
> > I've been calling it "heterodyning," from here:
> >
> > http://en.wikipedia.org/wiki/Heterodyne
> >
> > This is kind of inaccurate, as heterodyning involves the nonlinear
> > creation of sum and difference tones, whereas we're now just talking
> > about the nonlinear creation of sum tones.
>
> I included negative numbers. Adding a negative term can be pretty extreme in its results.

Well, more specifically, it refers to the number of sidebands
produced. Heterodyning means that you multiply the signal by
sin(2*pi*f*t), and every frequency a, b, c in the original signal then
gets split into a+f and a-f, b+f and b-f, c+f and c-f, etc. This is a
double sideband amplitude modulation technique.

We're describing taking every frequency a, b, c in the original signal
and then getting a+f, b+f, c+f, etc out of the operation, whether f is
positive or negative, so we're just looking for single sideband
amplitude modulation.

-Mike

--- In tuning@yahoogroups.com, Petr Pařízek <petrparizek2000@...> wrote:
>
> Hi again.
>
> In late 2002, I've made some stuff which I was privately
> calling "Linear music". Recently, I've discovered that many people
> were using the term "linear music" for something completely
> different. However, from what I could find it seems to me that the
> usage of the term is not very explicit as some people called
> it "horizontal music", which I personally would find much more
> logical for this, and the thing which I dubbed "linear music" (for
> my personal use so far) didn't seem to be discussed anywhere.
>
> What I used to call "linear music" in 2002 is music based on modes
> whose transposition is made, in most cases, in a linear way rather
> than exponential -- i.e. if one voice plays a 5-tone melody using
> relative frequencies of "18, 16, 15, 13.5, 12" and another voice
> plays the theme 6 units lower, then its relative frequencies
> are "12, 10, 9, 7.5, 6" (which means the ratios between the two get
> successively larger but the differences remain constant).
>

When I hear the term "linear music" without knowing anything about the context, I associate it with "lines", which associates to "melodic lines" and, indeed, to what generally is called "horizontal music" (more focused on melodic lines) as opposed to "vertical music structures" (focused on chords), terms that, e.g., are used to make the distinction between modal jazz and "traditional" jazz.

Hence I would say the term "linear music" for what you describe above is not a good choice, a misleading one in any case. I would also, like Gene, suggest "arithmetic transpositions", or maybe "arithmetic tuning".
--
Hans Straub

Did anyone tried the "Shift" function of the "Spectral Transform"
Plug-in from GRM Tools ?
I assisted to a demonstration years ago and this is exactly what it
does for any piece of audio : adding or substracting all frequencies
by one fixed frequency value.
Another "Spectral Transform" tool (Warp) reverts the spectrum upside
down of any piece of music, keeping the same intervals (like the
"invert" function of Scala) etc.
They propose a free download trial during 15 days :
http://www.inagrm.com/accueil/outils/grm-tools/spectral-transform
http://www.inagrm.com/accueil/outils/grm-tools/télécharger
Unfortunately I wasn't able to find an english page about it...

Gene's suggestion "Arithmetic transposition" is a term I would thinkappropriate,
with possible variants like "Arithmetic translation" or "Arithmetic
modulation", or just... "Frequency shift".
- - - - - - -
Jacques

Petr wrote :
> What I used to call "linear music" in 2002 is music based on modes
> whose
> transposition is made, in most cases, in a linear way rather than
> exponential -- i.e. if one voice plays a 5-tone melody using relative
> frequencies of "18, 16, 15, 13.5, 12" and another voice plays the
> theme 6
> units lower, then its relative frequencies are "12, 10, 9, 7.5,
> 6" (which
> means the ratios between the two get successively larger but the
> differences
> remain constant). My idea was that you could, if desired,
> eventually mix
> more than two voices so that another may play, for example, 3 units
> lower
> than the second one, and yet another may play, let's say, 3 units
> higher
> than the first one (should we make the harmonies a bit more
> "unconventional") or that sort of stuff. This means that scales may be
> transposed this way as well, which in turn excludes the option of
> general
> periods for scales (like octaves, for example). To a certain
> extent, this
> might be accomplished using an algorithm or device capable of linear
> frequency shifting, as long as the overtones are soft enough or
> have fast
> decay. The most "straight-forward" application is probably found in
> amplitude modulation (i.e. parallel multiplication) if one of the two
> signals is a periodic sine wave.
>
> So my questions are two.
>
> #1. Does anyone of you think the term "linear music" is indeed
> qualified to
> mean something else?
>
> #2. If all the terms like "linear tunings" or "linear scales" are
> in use for
> something else, do you think there might be another word which
> would more or
> less describe what I was describing here?
>
> Thanks.
>
> Petr

Jacques wrote:

> Another "Spectral Transform" tool (Warp) reverts the spectrum upside down > of any piece of music, keeping
> the same intervals (like the "invert" function of Scala) etc.

Wait a minute. Does it mean that if I input a sharp periodic waveform, it "rewards me" with a subharmonic series? This would mean that if I loaded it with a minor triad played with anything else than sine waves, I would get multiple major triads in steps of a subharmonic series.

This seems to be exactly the thing one of my friends was asking me about -- man, he was raising that question over 10 years ago! :-D

What strikes me most about this, however, is the fact that a linear frequency shift can be done easily without FFT but I think you'll definitely need some FFT to do the exponential inversion you're describing. And once you get into FFT, you get into framing the sound. And once you start framing, you have to overlap the frames to prevent crackles and pops. And once you start overlapping the frames, ... Well, FFT bubbles. 8-)

Petr

--- In tuning@yahoogroups.com, Petr Parízek <petrparizek2000@...> wrote:
>
> Jacques wrote:
>
> > Another "Spectral Transform" tool (Warp) reverts the spectrum upside down
> > of any piece of music, keeping
> > the same intervals (like the "invert" function of Scala) etc.
>
> Wait a minute. Does it mean that if I input a sharp periodic waveform, it
> "rewards me" with a subharmonic series? This would mean that if I loaded it
> with a minor triad played with anything else than sine waves, I would get
> multiple major triads in steps of a subharmonic series.
>
> This seems to be exactly the thing one of my friends was asking me about --
> man, he was raising that question over 10 years ago! :-D
>
> What strikes me most about this, however, is the fact that a linear
> frequency shift can be done easily without FFT but I think you'll definitely
> need some FFT to do the exponential inversion you're describing. And once
> you get into FFT, you get into framing the sound. And once you start
> framing, you have to overlap the frames to prevent crackles and pops. And
> once you start overlapping the frames, ... Well, FFT bubbles. 8-)
>
> Petr

Good questions. That was many years ago and I don't remember precisely, but in the demo I heard what I recall was a instrumental polyphony that got inverted, the bass playing the inverted melody in the high register etc. I don't know what would happen with strong harmonic sounds. I downloaded the french manual of the RTAS version (real time plug-in for ProTools) and it shows several parameters you can play with such as :
gain, mix, smooth, band, scale, interpolation, quality, freq in and freq out (= respective zero positions of transfers) ...
Worse than that, it offers you to draw a vectorial curve of your own that controls the transfers between input frequencies in x and output frequencies in y... Obviously, and as the name "FreqWarp" indicates, it is not exactly meant for microtonal purposes but rather for sound effects...

About the "Shift" plug-in, they say "this transforms a harmonic sound into an inharmonic one"...
Some of us could see other applications - but apparently no one tried it on this list. (?)
- - - - -
Jacques