Yahoo Tuning Groups Ultimate Backup tuning Sound test: conclusion

***For #1 AKA "A"****
http://www.geocities.com/djtrancendance/PHI/7notesperoctave1.wav

In general
"B is annoying...(cut)...if music were to be changed for the better, the extreme weird/annoying sounds should be left out. " -Tony Danaza

"In terms of this specific example set, the first one is easier to
listen to because something about the detuning of the second one does
indeed throw me off" -Mike Battaglia

On 'tonal color'
"I had a slight preference for the first one,
which has a nice shimmering quality compared with the drone-like sound
of the second example." -Herman

"The first one is colorful and rainbow-ish....at the moment, I prefer colorful rainbow-ish things, so I'll say the first one."
-Mike B

******For #2 AKA "B"***********
http://www.geocities.com/djtrancendance/PHI/7notesperoctave2.wav

In general:
"B sounds significantly more pleasant for two reasons. First, I hate those terribly stretched octaves. And then, I love harmonic synchronicity." -Petr (for the record, the octave is indeed stretched to 2.03/1 instead of 2/1)

"I like B better too." -Marcel
"For me, B sounded much better." -Kalle

On 'relaxation'

"This time the tranquil quality of the second
example sounded better than the agitated quality of the first example." -Herman Miller

******For neither*************
"The first sounds like a "sound" like a synth voice/sample. The second is clearly a note cluster.
so... how can I decide?" -Chris
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----------------------------------------------------------------------
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So (drum roll), here are what the scale #1 and #2 actually were

A) (AKA #1): A seven note subset of my PHI scale played as a chord
B) (AKA #2): The harmonic series harmonics 7 to 14 (7/7,8/7,9/7,10/7,11/7,12/7,13/7,14/7) played as a chord!

-----------------------
Judging by the results, it seems A) has a fairly clear advantage for tonal color. Comments ranged from "Rainbow-ish" -Mike B to "shimmering" -Herman Miller.
---
Meanwhile, far as which one won with respect to "relaxation/emotional-consonance", it seems relatively mixed.

For example, Herman thought B) sounded "tranquil" while Tony thought B) was "annoying" and "extremely weird".
-------------------------------------------

As a side-note, since B) actually contains the same overtone patterns instruments have, it struck me that Chris actually found A) as sounding more like an instrument sample (the exact opposite of what it "should" be in most written theory!)
It all seems to beg the question "are the harmonics which occur in nature not necessarily the most natural sounding"?

-------------------------------------------
Thanks to general statements like "I like B better too" -Marcel and similar statements by Kalle and Petr...I think it's clear B won by something like 60% to 40%.

However (at least to me) A) tipped the scales on tonal color and, for some, also actually came off as much more relaxing than B).

So I wonder, after reading this...does this bring up any issues/possibilities with the idea of the harmonic series' not having a monopoly over relaxed/colorful music and/or open any psycho-acoustic questions/possibilities for you (not just for my scale specifically, but any scale or even timbre not based on JI)?

🔗Mike Battaglia <battaglia01@...>

I said the first one sounded "colorful and rainbowish" and the second
one sounded like a "burning light." If the second one hadn't had that
beating, I might well have said I preferred that one. There are plenty
of times I prefer the sound of the naked overtone series to a
pandiatonic major scale or what have you. The one I chose was mainly a
matter of mood, although I will say the stretching in the first
example sounded really good.

> Judging by the results, it seems A) has a fairly clear advantage for tonal
> color. Comments ranged from "Rainbow-ish" -Mike B to "shimmering" -Herman
> Miller.

Nobody ever claimed that the overtone series had a monopoly on
pleasant sounding music. As for the examples you posted, I like the
sound of the harmonic series, but you had either detuned the series or
used a timbre that was so inharmonic that I could hear a significant
amount of beating. Go ahead and post the same examples without
detuning the overtone series or stretching any octave or using
inharmonic timbres or doing whatever you did that caused the beating
and let's run the test again.

> ---
> Meanwhile, far as which one won with respect to
> "relaxation/emotional-consonance", it seems relatively mixed.

Chords don't have a fixed emotional content that is constant in every
situation. If you play C minor and then E minor, that E minor will
have a completely different emotional delivery than if you play B
major and then E minor.

Note that the order in which the two examples were played likely had
an impact, and the aforementioned detuning of the harmonic series (or
the timbre) is what killed it for me.

> It all seems to beg the question "are the harmonics which occur in nature
> not necessarily the most natural sounding"?

Intervals that aren't harmonics in nature can be perfectly natural
sounding. JI harmonics can sound perfectly natural as well. Both of
these are "natural" and can lead into other musical events
"naturally." Go look up some of the recent discussion about metastable
ratios that maximally avoid being near small-number JI ratios on
purpose for another foray into this area (or "gray tones" as I liked
to call them, although the name never caught on).

I would imagine the statement that the first one sounded more like an
instrument was true because the second one blended into the sound of a
low subtone with significant beating on top, and the first one
exhibited no such blending. Thus the second one didn't quite fuse into
a timbre, but the first one sounded like one timbre playing a lot of
different notes.

> So I wonder, after reading this...does this bring up any
> issues/possibilities with the idea of the harmonic series' not having a
> monopoly over relaxed/colorful music and/or open any psycho-acoustic
> questions/possibilities for you (not just for my scale specifically, but any
> scale or even timbre not based on JI)?

I don't think many people around here would say it did. But for the
record, your first example sounded like a C major scale that was
significantly stretched. I heard a stretched C major, an F major, and
a G major being played simultaneously, along with the relationships of
all of the other dyads in the scale. That -still- implies harmonic
relationships between the notes - how could I hear a "major" sound
without some concept of a "major chord" - which is an otonal triad
itself - being in there somewhere? However, in this instance, the
scale's stretch - its deviation from the overtone series - also
carried a quite pleasant sound in and of itself.

The fact that I heard your first example as having a "pandiatonic
major" quality I think still serves as evidence that some kind of
psychoacoustic harmonic analysis is still taking place, and so I don't
know if it's possible to turn that off entirely.

-Mike

🔗djtrancendance@...

--"If the second one hadn't had that
--beating, I might well have said I preferred that one."
Fair enough...but the fact is that beating is a natural occurrence in the harmonic series: I certainly did not add it in there as a way to cheat.

--"Nobody ever claimed that the overtone series had a monopoly on
--pleasant sounding music."
It sure seems that way, though. JI, for example, is obviously based on the harmonic series (IE 4/3 (4th) and 5/3 (6th) are based on the 4/3,5/3,6/3...part of the series).
The counter question, as always, is why are there apparently so few examples of scales (or numerology of any sorts) around not based on rational-number-fractions (which are directly related to the harmonic series)...that are also being aimed as being
pleasant/relaxed sounding?

--"Chords don't have a fixed emotional content that is constant in every
--situation. If you play C minor and then E minor...(CUT)"
Of course...but I made absolutely sure to start both chords on exactly the middle C to avoid the "different root note, different emotion" issue.

--"Note that the order in which the two examples were played likely had
--an impact, and the aforementioned detuning of the harmonic series (or
--the timbre) is what killed it for me."
Firstly, yes, maybe the order did have an effect, but that's kind of a catch 22...if I put them in the opposite order I would have the exact same problem but "in the other direction". Also, you said you listened to both samples multiple times...so I wonder why (if you indeed did that) the order of presentation would be an issue.

--"the aforementioned detuning of the harmonic series (or
--the timbre) is what killed it for
me."
AS I SAID BEFORE the scale I used for the harmonic series example is 7/7, 8/7, 9/7, 10/7, 11/7, 12/7, 13/7, 14/7 There is ABSOLUTELY NO detuning of that scale and absolutely no detuning of the instrument used to play it. If it sounds detuned to you...perhaps the natural periodic beating/"periodic buzz" is tricking you into thinking it is de-tuned.

--"the second one blended into the sound of a
--low subtone with significant beating on top"
I agree with that statement...indeed the more obvious beating in the harmonic series (for better or worse) make it sound less like a timbre.

--"Intervals that aren't harmonics in nature can be perfectly natural
--sounding...(cut)...go look up some of the recent discussion about --metastable ratios that maximally avoid being near small-number JI --ratios on purpose"

I've read (and have responded to reading) a paper
about this several times. The paper is below (a paper about meta-stable ratios)
http://dkeenan.com/Music/NobleMediant.txt
And, again, for the record, that paper does not interest me as it reaches for the goal of non-relaxed-sounding tones IE maximum harmonic entropy. If you can give me an example actually based on the idea of finding less (AND NOT MORE) dissonant/"unpleasant" tones based on meta-stable ratios, though, I'd be happy to read it.

--"But for the record, your first example sounded like a C major scale ---that was significantly stretched."
Good ear, the scale was actually the subset of my PHI scale that sounded/felt to me most like C-major in an attempt to make the mood fairly similar to that of the harmonic series.
You can actually take C major and make a chord out of it to compare if you wish...I tried that and found the actually C-major scale played as a 7-note-per-octave
"chord" (for
better of worse) beats a LOT more. Whether or not that beating counts as undesired tension or desired movement you'll likely have to leave to your ears.

--"However, in this instance, the scale's stretch - its deviation from the ---overtone series - also carried a quite pleasant sound in and of itself."
In my theory, that "fluke" that it comes out sounding more and not less pleasant from being "stretched" is caused by the fact the beating rates are all powers of PHI relative to each other (showing the same A+B/A = A/B relationship with difference tones A and B).

--"(your) first example (had) a "pandiatonic
--major" quality...psychoacoustic harmonic analysis is still taking place, --and so I don't know if it's possible to turn that off entirely."

My theory is that, although the notes are fairly close (10 cents or less off) in many places between the PHI scale and c-major (minus the very skewed 5th)...the mind locks the "warped C-major" scale according to difference tones and not the usual harmonic series overtones.

However, you are right, the example does not make it blatantly obvious as in it is still quite likely the brain ends up tying it to the harmonic series in the end of the day, but just as "a harmonic series with somewhat more pleasant beating/difference-tone proportions". So I'll have to look further into this...perhaps with a 7-tone scale that is far less aligned with C-major yet displays similarly "nicely beating" properties.

-Michael

🔗Mike Battaglia <battaglia01@...>

> The counter question, as always, is why are there apparently so few
> examples of scales (or numerology of any sorts) around not based on
> rational-number-fractions (which are directly related to the harmonic
> series)...that are also being aimed as being pleasant/relaxed sounding?

JI is just one attempt at accessing a variety of new sounds and
colors. Just because it's a common approach doesn't mean it's the only
one. There is plenty of music that exists in temperaments that aren't
JI or 12-tet. And the reason that there aren't that many scales around
like that has to do with the fact that when we tend to hear harmonic
structures in such scales, so a lot of people have decided to screw
around with the harmonic structures directly and then
alter/stretch/temper them for different effects.

> Of course...but I made absolutely sure to start both chords on exactly
> the middle C to avoid the "different root note, different emotion" issue.

I was talking about where the chord is placed with respect to
surrounding chords. Cm -> Em will sound different than Bmaj -> Em,
even though it's Em at the end both times.

> AS I SAID BEFORE the scale I used for the harmonic series example is
> 7/7, 8/7, 9/7, 10/7, 11/7, 12/7, 13/7, 14/7 There is ABSOLUTELY NO detuning
> of that scale and absolutely no detuning of the instrument used to play it.

What timbre are you using to play it? Perhaps it's inharmonic.

> In my theory, that "fluke" that it comes out sounding more and not less
> pleasant from being "stretched" is caused by the fact the beating rates are
> all powers of PHI relative to each other (showing the same A+B/A = A/B
> relationship with difference tones A and B).

I do like the sound of the uniform beating. I think it sounds
"relaxing" just because of the synchronized chorusy effect that it
has. I'm not so sure it affects how I perceive the harmonic structures
in the scale.

> My theory is that, although the notes are fairly close (10 cents or less
> off) in many places between the PHI scale and c-major (minus the very skewed
> 5th)...the mind locks the "warped C-major" scale according to difference
> tones and not the usual harmonic series overtones.

You are confusing certain key concepts here.

The concept of a "difference tone" has to do with harmonic distortion.
If you take two sine waves and run them through a distortion pedal,
you'll get tones that are the sum and the difference of the two
original frequencies. You'll get the octave harmonic of each sine wave
as well (each sine wave summed with itself) and you'll also get sum
and difference tones of sum and difference tones and so on until you
have a whole harmonic series and a ton of these sum and difference
tones (also called combination tones).

A difference tone will manifest itself visually in a signal as an "up
and down" shift of the signal (aka an actual sine wave at that
frequency) and not just a volume envelope. A volume envelope isn't
really a "tone" per se.

If you have two sine waves going and some kind of distortion in the
air or in your ear creates a third difference tone and a fourth sum
tone, your brain will take all four of those tones and try to zap them
into some kind of harmonic series relationship. Difference tones exist
don't cause the "feeling" or emotional content of any chord - they
actually become just another part of the chord, and you'll try to hear
the harmonic relationship between not only the notes in the original
chord but these new difference tones at all.

Although you can get the frequency of beating by getting the
difference between two tones, this isn't the same thing as the
difference or combination tone as stated above.

As to the concept of one's determining a harmonic relationship between
two notes or a chord by beating instead of direct frequency analysis:
what evidence there is to indicate this? I don't see how the fact that
pleasant sounding chords exist outside of JI indicates anything about
psychoacoustic harmonic analysis mechanisms.

-Mike

🔗djtrancendance@...

--"the reason that there aren't that many scales around
--like that has to do with....(our) tend(ing) to hear harmonic
--structures in such scales" -Mike B
Exactly! So the harmonic series has somewhat of a "forced monopoly" in that sense, which was my original point. Maybe not a completely monopoly but, quite close (again going back to my "95% of scales follow...." quote).

--"so a lot of people have decided to screw

--around with the harmonic structures directly"
IE Sethares-type timbre changes (and then allowing far different scales to align the new timbres), if I read that correctly. But if so, then, yes, he's (Sethares) one of my favorite "tune-niks" for that reason.
Still, in that case...while the "Sethares-style" method is one way to do it, it has to do with aligning all partials/overtones with scales and each other (this aims toward eliminate beating), rather than allowing beating but making sure that when it happens beating is proportionate and pleasant (which is what, for example, noble number generated scales, including my own, can do). Again when you said that beating sounded oddly pleasant in my example...I think that points toward that.

--"Cm -> Em will sound different than Bmaj -> Em,
--even though it's Em at the end both times."
I'm still confused...the above
statement seems to imply a transition between two chords with different root where the mind finds a different mood based on the fact they are. I agree this phenomena does exist.
However my examples were one chord each and both with C-major as the root...and that situation does not seem to have a lot in common with your above example so far as I see.

----"absolutely no detuning of the instrument used to play it." -Me/Mike

--"What timbre are you using to play it? Perhaps it's inharmonic." -Mike B

I am using a plain old unmodified acoustic guitar sample. And, if I have it right, acoustic guitar gives a much purer version of the harmonic series, with many even tones, than something like a piano. My sense is that, since the difference between consecutive tones in the harmonic series are equal...the beating begins to stack up on one frequency and becomes overly dramatic it too many consecutive tones in the series have high amplitude peaks.

--"A difference tone will manifest itself visually in a signal as an "up
---and down" shift of the signal (aka an actual sine wave at that
---frequency) and not just a volume envelope."
Ok, you lost me there. So let me get this right, a 200hz and 300hz and 400hz sine wave do NOT form a 100hz difference tone?
I always
thought they did, in fact http://en.wikipedia.org/wiki/Combination_tone shows an example where a "missing fundamental" is found that way.

--"a third difference tone and a fourth sum
--tone, your brain will take all four of those tones and try to zap them
--into some kind of harmonic series relationship." -Mike B
I understand...but, at the same time, I believe the mind is also able to form different series relationships (IE a+b/a = a/b) if it sees enough overtones/partials/"mental equivalent of harmonics" following a consistant pattern the brain will be able to derive a root tone "anyhow". So while the harmonic series is a good example of difference tones pointing to a root...I am pretty sure it's not the only series through which they can do so.

--"Although you can get the frequency of beating by getting the
--difference between two tones, this isn't the same thing as the
--difference or combination
tone as stated above." -Mike B.

If the combination tone requires many tones following a pattern relative to each other where the difference tone's repetition between any partials causes a root to be found...my scale (and, in fact, virtually all noble-numbered scales) follow the difference tone concept.
******************important****************************************
However, if the difference tone concept is by definition ("anally limited" to the harmonic series). it obviously wouldn't apply to such scales as mine (noble-number generated scales)...and the question would become term be that I could use "legally"?
*********************************************************************

--"As to the concept of one's determining a harmonic relationship --"between
--"two notes or a chord by beating instead of direct frequency analysis:
--"what evidence there is to indicate
this?

Take the tones 1000hz 1618hz and 2000hz. Notice how if you move any of the three tones much the sense of one-ness falls apart completely. Not to mention that the rational approximation 13/8 (1.625) actually makes it sound significantly worse (at least to my ears)!

True, there's no
constant "difference tone" (IE 1618-1000=618hz is obviously != 2000-1618 = 382hz)...but the same sense of "the fluctations added merely add to the chord and don't distract from it" (the same sense that happens in the harmonic series) is achieved, IMVHO.

--"(I don't get why) pleasant sounding chords exist outside of JI --indicates anything about psychoacoustic harmonic analysis --mechanisms." -Mike B
It's still somewhat up for debate upon those who, say, try the above triad example I gave (again this has only been tested on about 8 people with no clear yes/no results). But, one thing I noticed: you (and others) keep on using the word harmonic which denotes the harmonic series. And the point is not to mathematically recreate the "harmonic-series difference tone" construct but, rather, to create a relationship of tones that add "hidden" tones which combine with the feel of the original chord rather than stick out like
a sore thumb. And
the fact at least some people thought the "PHI-aligned c-major" example sounded less jagged and more timbre-like than the harmonic series example seems to say, at least among some people, that their minds tie these extra results tones as while with differences between tones in noble-numbered scales as they do with the "constant difference toned" harmonic series.

And, you know, maybe the symmetry creates on emotional effect in the brain that only seems/feels like a psycho-acoustic alignment of beating...no matter; the point is, at least to some, it seems to create an equally, if not more, desirable feeling musically. Either of which is good enough for me.

-Michael

🔗Petr Parízek <p.parizek@...>

Mike Battaglia wrote:

> If you take two sine waves and run them through a distortion pedal,
> you'll get tones that are the sum and the difference of the two
> original frequencies. You'll get the octave harmonic of each sine wave
> as well (each sine wave summed with itself) and you'll also get sum
> and difference tones of sum and difference tones and so on until you
> have a whole harmonic series and a ton of these sum and difference
> tones (also called combination tones).

Not really. Difference tones as perceived by our hearing do not occur in the same way as they do in distorted sounds. Don't know about you, but if I hear a very loud sounding 11/8 pure sine dyad in some high octaves (like C6-F>6), I can quite clearly spot relative frequencies of 3 (i.e. hf-lf), 5 (2lf-hf), and sometimes 14 (2hf-lf). But when you také the very same sines of 11/8 and run this through some distortion, you won't find the 3rd harmonic in the spectrum unless the distortion is highly nonlinear and adds lot of extra frequencies. In the simplest case of just over-amplifiing something, what you'll get is 5, 8, 11, then softly 2 and 14, and then some higher harmonics with differences of 3 like 20, 23, 26, and so on. Similarly, if I hear a 13/8, I can easily "sense" 5 and 3, but if I run that through some ordinary distortion effect, I'll get 3, 8, 13, then softly 18, and then, with variing degrees of loudness, something like 28, 33, 38, 43 and so on.

Petr

🔗Petr Parízek <p.parizek@...>

🔗Daniel Forro <dan.for@...>

🔗Mike Battaglia <battaglia01@...>

> Not really. Difference tones as perceived by our hearing do not occur in the
> same way as they do in distorted sounds. Don’t know about you, but if I hear
> a very loud sounding 11/8 pure sine dyad in some high octaves (like C6-F>6),
> I can quite clearly spot relative frequencies of 3 (i.e. hf-lf), 5 (2lf-hf),
> and sometimes 14 (2hf-lf). But when you také the very same sines of 11/8 and
> run this through some distortion, you won’t find the 3rd harmonic in the
> spectrum unless the distortion is highly nonlinear and adds lot of extra
> frequencies. In the simplest case of just over-amplifiing something, what
> you’ll get is 5, 8, 11, then softly 2 and 14, and then some higher harmonics
> with differences of 3 like 20, 23, 26, and so on. Similarly, if I hear a
> 13/8, I can easily „sense“ 5 and 3, but if I run that through some ordinary
> distortion effect, I’ll get 3, 8, 13, then softly 18, and then, with variing
> degrees of loudness, something like 28, 33, 38, 43 and so on.
>
> Petr

Sure you would. Most likely you would certainly find 3 in the signal,
as it's a first order combination tone. That would be 11-8, as you
said yourself. 5 and 14 would be second order difference tones, as
they'd be 8+8 - 11 and 11+11-8 respectively. All of these things are
fairly common in distortion circuits, although a lot of them focus on
adding only odd-order difference tones - and so 5 and 14 wouldn't be
in there in that case.

All distortion is highly nonlinear - that's how it distorts. It could
be that the nonlinear characteristics of the ear canal are different
than the nonlinear characteristics of a common guitar distortion pedal
circuit, but it's still distortion nonetheless and the underlying
mechanism of production is the same. To be honest, I only used the
word "distortion" because I didn't want to throw terms like "nonlinear
systems" around as it's a pretty difficult concept to understand at
first.

> Which means that if you také a single periodic pure sine wave
> and run it through some ordinary distortion, this actually adds
> only odd harmonics and no even ones, unless there’s some
> additional DC offset contained in the original sound.

This is true, but it's a matter of convention and doesn't reflect any
underlying property of how distortion works. We like the sound of
odd-order distortion, so we come up with nonlinear systems that
produce mainly that. There are plenty of guitar distortion pedals that
throw even-order combination tones in as well - it's just a matter of
taste.

-Mike

🔗Mike Battaglia <battaglia01@...>

-Mike

🔗Petr Parízek <p.parizek@...>

🔗Mike Battaglia <battaglia01@...>

🔗djtrancendance@...

Mike and Petr,

Just a note: this is one of the reasons I find myself posting many messages.
This thread (believe it or not) just started as a list of conclusions to my sound listening test I posted here to give a "blind test" surveyed view over the harmonic series vs. a subset of my own scale which focussed on non-harmonic-series difference tone.

   And, believe me, I'd be more than happy just sitting here and listening to people talk/constructively argue about the actual topic trying to find what in it may be of use (rather than whining incessantly about what they think won't be of use and name-calling as has happend in past threads).
----------------------------------------------------------------
True, one of the issues at hand in the original discussion was
the definition of a
difference tone.
   However, Mike B, you never quite responded to my general comment (are difference tones EXCLUSIVE to the harmonic series)?
   And, for the record, so far I still am not so convinced they are: also Jacques Dudon and Kalle Aho, as I recall, apparently agreed with me that noble-numbered scales form valid difference tones and the same sense of "adding to a chord" rather than "throwing an alien secondary tone in the middle of it".
-------------------------------------------------------------------------------------------------
   But now here this thread is off on a TANGENT talking about distortion and how it introduces harmonics (and whether they are odd or even harmonics). Which has nothing to do with comparing the two scales/sound-samples this thread started out discussing or even difference tones directly (minus the fact HARMONIC SERIES difference tones do give a sense of missing tones in
the series (particularly the root) being there even when they are not).

But, is there any chance in hell I can post even a simple and honest thread...and actually NOT have it derailed within the first 5 or so replies. :-(

-Michael

PS-
To note, personally (far as distortion, which I generally care little about adding to instruments), I like even harmonics better...although my ears
aren't too averse to odd harmonics on even harmonic-intensive
instruments like guitars (which already have "too many" even harmonics
vs. odd ones). And, as usual, I don't really care to much about the math UNLESS the math produces something which connects with my ears as both beautiful and unique...and I can re-wire the math to recreate the same effect in a different/unique light.

🔗Kalle Aho <kalleaho@...>

🔗Mike Battaglia <battaglia01@...>

> IE Sethares-type timbre changes (and then allowing far different scales
> to align the new timbres), if I read that correctly. But if so, then, yes,
> he's (Sethares) one of my favorite "tune-niks" for that reason.

What I meant is that I perceive a major scale in your first example.
That means I have interpreted your first example as containing a
skewed section of harmonic series (or parts of related harmonic
series).

> My sense is that, since the difference between consecutive tones in the harmonic series are
> equal...the beating begins to stack up on one frequency and becomes overly
> dramatic it too many consecutive tones in the series have high amplitude
> peaks.

The timbre you're using is a full harmonic series in and of itself,
correct? Yet we don't hear any beating when a note is played in
unison.

> Ok, you lost me there. So let me get this right, a 200hz and 300hz and
> 400hz sine wave do NOT form a 100hz difference tone?

You keep talking about the psychoacoustic phenomenon of beating as if
it were the same thing as a difference tone. It is not. Beating has a
different psychoacoustic mechanism and isn't the same thing at all. If
I play 1000 Hz and 1 Hz together, you won't hear the signal fade in
and out with a frequency of 1 Hz. Volume changes aren't the same thing
as actual sine waves with certain frequencies existing in the signal,
even if the volume change is sinusoidal in nature.

Nonetheless, if I play 1000 Hz and 1001 Hz, you WILL hear the signal
fade in and out with a frequency of 1 Hz, and it has nothing to do
with some 1 Hz sine wave being created by distortion.

And both of these things have nothing to do with the concept of a
"virtual fundamental". It was once thought that fundamental processing
was caused by physical difference tones in the ear, but various
experiments have since shown that assumption to be suspect.

> So while the
> harmonic series is a good example of difference tones pointing to a root...I
> am pretty sure it's not the only series through which they can do so.

That is an intriguing idea - I don't know if it will work. Try coming
up with "false harmonic series" that are not the harmonic series and
see if virtual pitch detection still works. I could see that leading
to some cool "neutral" sounding tonalities (is that an oxymoron?),
especially if the timbres match the faux-harmonic series you used. Why
not run some phantom fundamental checks and see? See if a phantom
fundamental even comes to exist at all besides actual combination
tones from speaker distortion (i.e. do it at low volume).

> And the point
> is not to mathematically recreate the "harmonic-series difference tone"
> construct but, rather, to create a relationship of tones that add "hidden"
> tones which combine with the feel of the original chord rather than stick
> out like a sore thumb.

What you have essentially done is stretch and compress the harmonic
series (which is basically what happens if you try to create a bunch
of difference relationships like you're doing). I like it - the
stretch sounds good to me. However, it isn't really like you've broken
entirely away from the harmonic series because it still retains a
"major" kind of tonality to it, which implies a skewed 4:5:6
relationship.

A thought experiment for you:
If you take a major third and widen it until it becomes a perfect
fourth - at some point in the middle you'll hear a point where the
note sounds like both a major third AND a perfect fourth, and you can
"flip" your perception around to hear it whichever way you choose. And
when you "flip" your perception around this way, what you're really
doing is applying different harmonic templates to the signal. You're
saying to yourself, is this a major third (5/4)? Is this a perfect
fourth (4/3)? And both templates work equally well (or poorly,
depending on how you look at it).

The fact that you're hearing "majorness" in that first example of you
indicates that you're still applying harmonic templates to the signal.

🔗Michael Sheiman <djtrancendance@...>

Mike B> "What I meant is that I perceive a major scale in your first example. That means I have interpreted your first example as containing a skewed section of harmonic series (or parts of related harmonic series)."

Mike B> "However, it isn't really like you've broken entirely away from the harmonic series because it still retains a "major" kind of tonality to it, which implies a skewed 4:5:6 relationship."
*************************************************************************************
Right...it's an excellent point and fault with my example.

In my example, agreed, the subset of the PHI scale was close enough to diatonic to easily make it beyond a reasonable doubt if stability is coming from the "PHI-ness" or the fact many relationships are close to harmonic series ratios and "major" feel.
************************************************************************
So here's an "extreme" example:
7-notes of my PHI scale within a 2/1 interval NOT using major scale-style notes or feel: http://www.geocities.com/djtrancendance/PHI/7notesperoctavenonmajor2.wav

My original "bad" 7-note example where notes "felt like major tones"
http://www.geocities.com/djtrancendance/PHI/7notesperoctave1.wav
********************************************************
Note: the ratios used for the scale in the "non-major scale" example are approximately
1.065 or 109 cents       semi-tone
1.186 or 295 cents       tone
1.272 or 416 cents       about 1/8th off semi-tone "partly bent"
1.336 or 503 cents       semi-tone
1.386 or 565 cents      (a bit over 1/4 tone, "highly bent")
1.467 or 664 cents      (semi-tone, "highly bent")
1.618034 or 833 cents (3/4 tone gap, "highly bent")
****************************************************************
-Michael

🔗Mike Battaglia <battaglia01@...>

> So here's an "extreme" example:
> 7-notes of my PHI scale within a 2/1 interval NOT using major scale-style
> notes or feel:
> http://www.geocities.com/djtrancendance/PHI/7notesperoctavenonmajor2.wav

I still hear harmonies in it. This time it sounds like a stretched
major9 chord played in 4th inversion with some extra notes thrown in
at the bottom end. In 12-tet terms, I hear it as being a skewed
version of the following chord:

C Db Eb E F Ab C

That major 7 chord with the maj7 doubled in the bass stood out at me
as soon as I heard it, although I heard some rumbly sounding stuff in
the bottom end that didn't fit - I looked at your chart to see what
the cents values are, and the 12-tet chord I posted about has about
the same vibe.

Can you post an example of the same chord with the same sound with 416
cents omitted to see if it sounds like a major 7 chord?

I will say that the 565 and 833 cent intervals sound amazing - the
fact that they're sharp really adds to it. Nonetheless, I'd still like
to hear what the chord sounds like with that 416 omitted - I feel like
it'll sound like some kind of trippy alien major9 chord (and that's
the scientific term).

-Mike

🔗djtrancendance@...

************************************************************************
Note this discussion concerns the scale/chord played here http://www.geocities.com/djtrancendance/PHI/7notesperoctavenonmajor2.wav
...and the tuning below
1.065 or 109 cents       semi-tone
1.186 or 295 cents       tone
1.272 or 416 cents       about 1/8th off semi-tone "partly bent"
1.336 or 503 cents       semi-tone
1.386 or 565
cents      (a bit over 1/4 tone, "highly bent")
1.467 or 664 cents      (semi-tone, "highly bent")
1.618034 or 833 cents (3/4 tone gap, "highly bent")
****************************************************************

--Mike B> I still hear harmonies in it. This time it sounds like a stretched
--major9 chord played in 4th inversion with some extra notes thrown in
--at the bottom end.
Hmm...then either I've failed or perhaps you are simply right the mind will go "that far" to round things to harmonic series (even with, for example, some notes in the scale being almost dead-center in between 12TET tone IE "the maximum amount of error from them").

Mike B> --"C Db Eb E F Ab C...that major 7 chord...stood out at me
--as soon as I heard it, although I heard some rumbly sounding stuff in
--the bottom end that didn't fit "
Rumbly sounding, eh? I wonder how much of that it simply a side effect from beating and squeezing so many tones of such high amplitude within such a small frequency space...or do you have any other ideas what might be causing it?

--Mike B> "Can you post an example of the same chord with the same --sound with 416 cents omitted to see if it sounds like a major 7 chord?"
   Sure thing...I will. One odd thing I noticed in making the scale is using the usual 5/4 or 1.25 value kills the consonance terribly when played with some of the other "weird" notes that comprise this scale.
   I figure it may well be it's harmonics are simply in such a position they are "masked" well in general by other tones.
**********************************************************************
---Mike
B> "I will say that the 565 and 833 cent intervals sound amazing ---" the fact that they're sharp really adds to it."
    Glad you liked it. Indeed, at least to my ears as well, there's something about those last few notes in the scale that also sounds "distinctively noble-numbered" to me.

Mike B> "I feel like it'll sound like some kind of trippy alien major9 chord (and that's the scientific term)."

You know, one of my favorite pastimes is making odd chords in 12TET, specifically very jazzy sounding ones.
A tad off topic: I made the following "melodic loop/preview" in 12TET to mess around with "alien sounding" chord combinations a while ago just for fun. If you'd like, you can check it out at
http://www.geocities.com/djtrancendance/PHI/layerodrumsshrt.mp3

-Michael

--- On Thu, 4/16/09, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Sound test: conclusion
To: tuning@yahoogroups.com
Date: Thursday, April 16, 2009, 10:17 PM

> So here's an "extreme" example:

> 7-notes of my PHI scale within a 2/1 interval NOT using major scale-style

> notes or feel:

> http://www.geocitie s.com/djtrancend ance/PHI/ 7notesperoctaven onmajor2. wav

I still hear harmonies in it. This time it sounds like a stretched

major9 chord played in 4th inversion with some extra notes thrown in

at the bottom end. In 12-tet terms, I hear it as being a skewed

version of the following chord:

C Db Eb E F Ab C

That major 7 chord with the maj7 doubled in the bass stood out at me

as soon as I heard it, although I heard some rumbly sounding stuff in

the bottom end that didn't fit - I looked at your chart to see what

the cents values are, and the 12-tet chord I posted about has about

the same vibe.

Can you post an example of the same chord with the same sound with 416

cents omitted to see if it sounds like a major 7 chord?

I will say that the 565 and 833 cent intervals sound amazing - the

fact that they're sharp really adds to it. Nonetheless, I'd still like

to hear what the chord sounds like with that 416 omitted - I feel like

it'll sound like some kind of trippy alien major9 chord (and that's

the scientific term).

-Mike

Sound test: conclusion

🔗djtrancendance <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>

🔗djtrancendance@...

🔗Mike Battaglia <battaglia01@...>

🔗djtrancendance@...

🔗Petr Parízek <p.parizek@...>

🔗Petr Parízek <p.parizek@...>

🔗Daniel Forro <dan.for@...>

🔗Mike Battaglia <battaglia01@...>

🔗Mike Battaglia <battaglia01@...>

🔗Petr Parízek <p.parizek@...>

🔗Mike Battaglia <battaglia01@...>

🔗djtrancendance@...

🔗Kalle Aho <kalleaho@...>

🔗Mike Battaglia <battaglia01@...>

🔗Michael Sheiman <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>

🔗djtrancendance@...