Re: Where's all that hostility coming from?: what's the basic formul

Michael~
We will have to agree that at this point we are talking about the things that are subjective.
I will stand that Indian music can produced as much or more defined moods than tempered tunings. You can use any temperment you wish to get the moods you want.
Historically some of the biggest names in microtonality are people who used JI. Harry Partch, Lou Harrison, Ben Johnston, La Monte Young, Terry Riley. It is hard to come up with people who use temperaments that are as well known. There is much talk and explorations of the latter, but still difficulties make it more in theory than otherwise.

--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Dear Kraig,

You are wonderful and I love 'ya, but I believe you are biased (although you
call it subjective). All the composers you quote are American microtonalists
who use JI. But there are plenty of microtonalists as famous or more famous
in the world that use temperament, or even noise. Many JI users simply don't
have the patience to explore the myriad temperament induced sentiments.

Baroque well temperament and irregular tunings were extremely subtle in their
sentiments and moods. Basic 5-limit JI is boring in comparison. When there
is only one way to play an interval there is less variety, simply stated.

For the record, I am a JI composer. However, since I ALSO use a myriad of
other tunings, JI composers do not recognize this fact. This is more of a
minimalistic prejudice, from my point of view, than any objective fact.

best, Johnny Reinhard

----------------------------------------

Michael~
We will have to agree that at this point we are talking about the things
that are subjective.
I will stand that Indian music can produced as much or more defined
moods than tempered tunings. You can use any temperment you wish to get
the moods you want.
Historically some of the biggest names in microtonality are people who
used JI. Harry Partch, Lou Harrison, Ben Johnston, La Monte Young, Terry
Riley. It is hard to come up with people who use temperaments that are
as well known. There is much talk and explorations of the latter, but
still difficulties make it more in theory than otherwise.

**************Plan your next getaway with AOL Travel. Check out Today's Hot
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Kraig,

   I agree much of this is subjective.  I am just saying JI is far from the only way to skin this cat and I am all for people who suspect, like I do, that JI does not solve the whole puzzle of what makes music "consonant", not just mathematically but in having a cohesive mood. 

   Actually, Charles Lucy (Lucy-tuning) and Bill Sethares (composing in 10-TET using alternative overtone structures) have deviated from JI.  The way I think of it...JI is one way to help solve the "consonance puzzle", but surely not the only one. 

   Also...JI is built around the idea of whole-number-multiple harmonics, which not all instruments have (for example, look at Sethares' scales which are ideal for mallet-based instruments and note they do not match any JI scales).  But, to note...most acoustic instruments do, indeed, fit relatively closely to the ideal JI whole-number-multiple overtone schema.

   The other thing is, as I understand it, "purest" JI includes a usual 7-note JI scale approximated by 12-TET.  And scales like ones based on Partch's tonality diamond, for example, usually become far less consonant mathematically.  Hence we have 5-limit JI, 7-limit JI...until we get scales that are still JI, but far from mathematically consonant (at least according to Plompt and Llevelt, Helmholtz, etc.

   I agree most famous micro-tonalists have simply taken "spins" off Just-Intonation...but I also agree the area of scale creation with the most unlocked potential is non-just-intonation...even if it involves simply taking a JI scale and bending certain notes to create a more potent and cohesive mood.

-Michael

--- On Sat, 11/1/08, Kraig Grady <kraiggrady@...m> wrote:
From: Kraig Grady <kraiggrady@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Saturday, November 1, 2008, 12:47 AM

Michael~

We will have to agree that at this point we are talking about the things

that are subjective.

I will stand that Indian music can produced as much or more defined

moods than tempered tunings. You can use any temperment you wish to get

the moods you want.

Historically some of the biggest names in microtonality are people who

used JI. Harry Partch, Lou Harrison, Ben Johnston, La Monte Young, Terry

Riley. It is hard to come up with people who use temperaments that are

as well known. There is much talk and explorations of the latter, but

still difficulties make it more in theory than otherwise.

--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_

Mesotonal Music from:

_'''''''_ ^North/Western Hemisphere:

North American Embassy of Anaphoria Island <http://anaphoria. com/>

_'''''''_ ^South/Eastern Hemisphere:

Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
//
>    Also...JI is built around the idea of whole-number-multiple
> harmonics, which not all instruments have

All pitched instruments do.

> (for example, look at Sethares' scales which are ideal for
> mallet-based instruments and note they do not match any JI
> scales).

If the mallet-based instrument in question is pitched
(through the use of a resonator tuned to one of its prominent
partials, etc. etc.), it'll sound great when those pitches
are related by simple ratios. If it's not pitched (certain
bells), the amount of improvement available by using a
Sethares-type scale is actually quite small (chords will
tend to sound somewhat smoother/cleaner/simpler but not
necessarily more consonant in the traditional sense of
the word).

Where I think the adaptive timbre approach holds the most
promise is in cleaning up the medium-accuracy temperaments.
Scales like 15- and 26-ET for instance. Or in cleaning up
the 7-limit in 22-ET, or the 13-limit in 41-ET. Sethares
seems to prefer the more extreme examples like 10-ET. It's
certainly an interesting effect that's worth exploiting,
but I doubt anyone would say it has the power to make 10-ET
consonant in the sense that 7-limit JI is consonant.

> But, to note...most acoustic instruments do, indeed, fit
> relatively closely to the ideal JI whole-number-multiple
> overtone schema.

Indeed, all pitched instruments must. The piano seems to
be the most prominent deviant, and its deviations are so
small they can mostly be ignored. Tune a piano in JI with
no octave stretch and it'll sound fantastic through the
center 3-4 octaves at least. A small amount of uniform
stretch takes care of the rest.

>    The other thing is, as I understand it, "purest" JI
> includes a usual 7-note JI scale approximated by 12-TET.
>  And scales like ones based on Partch's tonality diamond,
> for example, usually become far less consonant
> mathematically.

How do you get that? Play all 7 tones of the 5-limit JI
diatonic scale at once, and then play the first 7 harmonics
at once -- which is more consonant?

> Hence we have 5-limit JI, 7-limit JI...until we get scales
> that are still JI, but far from mathematically consonant (at
> least according to Plompt and Llevelt, Helmholtz, etc.

The "roughness" models of consonance, central to the approach
of Plomp & Levelt, depend on critical-band effects and therefore
on absolute frequencies. JI-based models depend only on
the _relationships_ between frequencies. BOTH types of models
are required explain the phenomena of consonance and dissonance
to a level that is applicable to microtonal music.

-Carl

Carl,

---If the mallet-based instrument in question is pitched

(through the use of a resonator tuned to one of its prominent

partials, etc. etc.), it'll sound great when those pitches

are related by simple ratios. If it's not pitched (certain

bells), the amount of improvement available by using a

Sethares-type scale is actually quite small (chords will

tend to sound somewhat smoother/cleaner/ simpler but not

necessarily more consonant in the traditional sense of

the word).

  Great point.  I agree...the difference from the non-JI "Setharesian" scale is not much,
but the point is...it is there.  Whether you like it appears to be subjective: I've heard some people who love it, others who prefer JI (agreed, both sound good, at least to my ears).  Again, in my mind, it's just another option...

----------------------------------------------------------------------------------------------------------

---but I doubt anyone would say it has the power to make 10-ET

consonant in the sense that 7-limit JI is consonant.

   I agree, hence the example I gave in a message earlier on in this threads that "10 TET sounds odd, even using pure sine waves thus having no potential harmonic conflicts".

   Back to "sensory dissonance" vs. "musical dissonance".  I don't know the formal definition of which is which...but from what I have read from you I believe my point could be stated as "a 5 note widely spaced scale played with sine waves under 10-TET, although having more sensory consonance than a 7-note scale under 12-TET, fails to have the musical consonance of 12-TET". 

----How do you get that? Play all 7 tones of the 5-limit JI

diatonic scale at once, and then play the first 7 harmonics

at once -- which is more consonant?
  I believe I mis-stated my point, I never meant "harmonics vs. scales"...I meant to say that, say, a JI scale in a higher limit can become quite dissonant: JI does not instantly equal consonance.

----The "roughness" models of consonance, central to the approach

of Plomp & Levelt, depend on critical-band effects and therefore

on absolute frequencies. JI-based models depend only on

the _relationships_ between frequencies.

    The thing that gets me.....is that Plomp & Levelt's roughness model was used to form Sethares's consonance formula.  And, assuming harmonics of more-or-less equal volume and whole-number-ratio harmonics, the dissonance curve has troughs (IE minimization points) at the 7-tone JI scale.  Thus, they both ultimately appear to point in the same direction...

   But, again, the side issue seems to be, using Sethares' same formula that "proves JI" on odd scales like 10-TET (as he did in his "Ten Fingers" guitar piece) and weird "built-to-match" overtone structures seems to, as you said, never quite achieve the feel of musicality that 7-tone JI has.
  Hence we have a clear issue so far as I can figure...neither just intonation nor the "consonance formula" above can be considered the holy grail of tonality...it only seems to solve the equation with
whole-tone instruments and matching scales. 

   I have also found, for example, my own scale
Left channel                   Right Channel
1 (root tone)                      1.112 (2nd tone)
1.2405 (3rd tone)               1.345 (4th tone)
1.48 (5th tone)                   1.666 (6th tone)
1.868 (7th tone)                 2 (octave)
2.224 (9th tone) etc.

seems to have to best record to my ears with sine wave so far as
playing 7-notes per octave at once (IE a 7-note chord)
and
A) Subduing any types of beating that don't make musical sense (Helmholtz) AND
    making the effects of "binaural beating" not clash
B) Keeping notes far apart by strategically place-ing them far apart in different channels (Plomp & Levelt).  This allows the 7-note scale to sound about as consonant as a Gregorian chant-ish 4-note scale, at least to my ears.
C) A third factor which I believe has not been tackled: the notes fit in a same mood or character.  Note if you move notes in a closer to equal temperament, although the consonance goes down according to, say, Sethares' formula, it sounds worse far as mood.

This is my point...there has got to be something missing in the JI formula and the "consonance curves"...that we need to understand to truly explain "why certain notes sound good".

-Michael

--- On Sat, 11/1/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Saturday, November 1, 2008, 1:09 PM

--- In tuning@yahoogroups. com, Michael Sheiman <djtrancendance@ ...> wrote:

//

>    Also...JI is built around the idea of whole-number- multiple

> harmonics, which not all instruments have

All pitched instruments do.

> (for example, look at Sethares' scales which are ideal for

> mallet-based instruments and note they do not match any JI

> scales).

If the mallet-based instrument in question is pitched

(through the use of a resonator tuned to one of its prominent

partials, etc. etc.), it'll sound great when those pitches

are related by simple ratios. If it's not pitched (certain

bells), the amount of improvement available by using a

Sethares-type scale is actually quite small (chords will

tend to sound somewhat smoother/cleaner/ simpler but not

necessarily more consonant in the traditional sense of

the word).

Where I think the adaptive timbre approach holds the most

promise is in cleaning up the medium-accuracy temperaments.

Scales like 15- and 26-ET for instance. Or in cleaning up

the 7-limit in 22-ET, or the 13-limit in 41-ET. Sethares

seems to prefer the more extreme examples like 10-ET. It's

certainly an interesting effect that's worth exploiting,

but I doubt anyone would say it has the power to make 10-ET

consonant in the sense that 7-limit JI is consonant.

> But, to note...most acoustic instruments do, indeed, fit

> relatively closely to the ideal JI whole-number- multiple

> overtone schema.

Indeed, all pitched instruments must. The piano seems to

be the most prominent deviant, and its deviations are so

small they can mostly be ignored. Tune a piano in JI with

no octave stretch and it'll sound fantastic through the

center 3-4 octaves at least. A small amount of uniform

stretch takes care of the rest.

>    The other thing is, as I understand it, "purest" JI

> includes a usual 7-note JI scale approximated by 12-TET.

>  And scales like ones based on Partch's tonality diamond,

> for example, usually become far less consonant

> mathematically.

How do you get that? Play all 7 tones of the 5-limit JI

diatonic scale at once, and then play the first 7 harmonics

at once -- which is more consonant?

> Hence we have 5-limit JI, 7-limit JI...until we get scales

> that are still JI, but far from mathematically consonant (at

> least according to Plompt and Llevelt, Helmholtz, etc.

The "roughness" models of consonance, central to the approach

of Plomp & Levelt, depend on critical-band effects and therefore

on absolute frequencies. JI-based models depend only on

the _relationships_ between frequencies. BOTH types of models

are required explain the phenomena of consonance and dissonance

to a level that is applicable to microtonal music.

-Carl

Hi Michael,

>> ---but I doubt anyone would say it has the power to make 10-ET
>>
>> consonant in the sense that 7-limit JI is consonant.
>
>    I agree, hence the example I gave in a message earlier on in
> this threads that "10 TET sounds odd, even using pure sine waves
> thus having no potential harmonic conflicts".

Using pure sines to make music in 10-ET does NOT guarantee an
absence of beating or other critical band effects, if that's
what you meant by "harmonic conflicts".

>    Back to "sensory dissonance" vs. "musical dissonance".
> I don't know the formal definition of which is which...but from
> what I have read from you I believe my point could be stated as
> "a 5 note widely spaced scale played with sine waves under
> 10-TET, although having more sensory consonance than a 7-note
> scale under 12-TET, fails to have the musical consonance of
> 12-TET". 

Hm. Sensory consonance refers to the part of consonance that
exists solely in individual (isolated) sounds. Musical
consonance refers to the function of sounds within musical
compositions (it's more to do with grammar than just hearing).

Scales generally don't say much about either kind of consonance.
In most scales, you can easily create sounds that have high
sensory dissonance (just by mashing the keyboard). Some
theorists believe certain scale properties are required to
create musical consonance distinctions (e.g. must have a circle
of approximate 3/2 "fifths", etc.). But anyway, one doesn't
usually think of something like 12-ET as having consonance or
dissonance in and of itself. One might reference something
like 'common-practice music rendered in 12-ET'...

>> ----How do you get that? Play all 7 tones of the 5-limit JI
>> diatonic scale at once, and then play the first 7 harmonics
>> at once -- which is more consonant?
>
>   I believe I mis-stated my point, I never meant "harmonics
> vs. scales"...I meant to say that, say, a JI scale in a higher
>limit can become quite dissonant: JI does not instantly equal
>consonance.

One could argue that the sensory consonance of otonal chords
in JI actually increases as you add higher and higher
harmonics -- if the amplitude of each successive note
decreases. The same is not true of subharmonics (Partch's
"utonal" chords), which rapidly become dissonant as you go
up the series. However, the ratios required to spell extended
utonal chords also become more complex very quickly, and
usually "JI" entails something about ratios being simple.
Complex ratios are also needed to make small intervals that
would have strong critical band interactions. So JI does
indeed seem to guarantee sensory consonance for chords.
And by using Tenney Height (numerator * denominator of a
ratio in lowest terms, or, by extension, a * b * c... of the
notes in a chord, where a, b, and c are coprime integers over
a common fundamental), one can rank the consonance of
different JI chords.

The only problem is an inability to measure the consonance
of irrational intervals -- that's where harmonic entropy
comes in.

>> ----The "roughness" models of consonance, central to the
>> approach of Plomp & Levelt, depend on critical-band effects
>> and therefore on absolute frequencies. JI-based models
>> depend only on the _relationships_ between frequencies.
>
>     The thing that gets me.....is that Plomp & Levelt's
> roughness model was used to form Sethares's consonance formula.
> And, assuming harmonics of more-or-less equal volume and whole-
> number-ratio harmonics, the dissonance curve has troughs (IE
> minimization points) at the 7-tone JI scale.  Thus, they both
> ultimately appear to point in the same direction...

The model gives simple ratios when the timbres are harmonic,
and the JI diatonic scale is made up of the 7 simplest ratios.
But those graphs only show dyadic interactions, not larger
chords...

> But, again, the side issue seems to be, using Sethares' same
> formula that "proves JI"

There are lots of models that are capable of spitting out JI
in some cases. Which one actually corresponds to reality?

Harmonic entropy can be used to 'prove' the meantone diatonic,
which actually won the battle for musical praxis over JI.
If you play all 7 notes of a the diatonic scale at once, are
you better off to tune them in JI or in 31-ET? Harmonic
entropy says 31-ET. Try it and tell us what you think!

>on odd scales like 10-TET (as he did in his "Ten Fingers" guitar
>piece) and weird "built-to-match" overtone structures seems to,
>as you said, never quite achieve the feel of musicality that
>7-tone JI has.

I said 7-*limit* JI. Basically, if you stretch the partials
of a timbre out to 10-ET, you loose some of the 'pitchedness'
of the timbre. Consonance and pitch are very closely related
phenomena, so you can't have too much of one without the other,
though you can have some. Sethares' book and web site, in my
opinion, tends to overstate how much you can have. At any
rate, much of his music sounds rather bell-like -- would you
agree?

>   Hence we have a clear issue so far as I can figure...neither
> just intonation nor the "consonance formula" above can be
> considered the holy grail of tonality...it only seems to solve
> the equation with whole-tone instruments and matching scales.

Harmonic entropy is basically the holy grail of sensory
consonance -- though it's still a bit wishy-washy for larger
chords, we've seen glimpses of what it looks like for triads,
and it seems to agree with human listeners.

The holy grail of tonality is a much more elusive beast, because
you have to take into account all the values that work in music
which all affect our perception.

>    I have also found, for example, my own scale
> Left channel                   Right Channel
> 1 (root tone)                      1.112 (2nd tone)
> 1.2405 (3rd tone)               1.345 (4th tone)
> 1.48 (5th tone)                   1.666 (6th tone)
> 1.868 (7th tone)                 2 (octave)
> 2.224 (9th tone) etc.
>
> seems to have to best record to my ears with sine wave so far as
> playing 7-notes per octave at once (IE a 7-note chord)
> and
> A) Subduing any types of beating that don't make musical sense
(Helmholtz) AND
>     making the effects of "binaural beating" not clash
> B) Keeping notes far apart by strategically place-ing them far
> apart in different channels (Plomp & Levelt).  This allows the
> 7-note scale to sound about as consonant as a Gregorian
> chant-ish 4-note scale, at least to my ears.
> C) A third factor which I believe has not been tackled: the
> notes fit in a same mood or character.  Note if you move notes
> in a closer to equal temperament, although the consonance goes
> down according to, say, Sethares' formula, it sounds worse far
> as mood.

What's "mood"?

In cents, your scale is:
183.8 373.1 513.1 678.7 883.7 1081.8 1200.0

What do you think of
193.4 386.9 504.1 697.6 891.0 1084.4 1201.7
for comparison?

Or howabout:
182.4 369.7 498.0 663.0 884.3 1080.6 1200.0
?

-Carl

You are wonderful and I love 'ya too johnny . If you say you are aJI composer, i mill go along with that.
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

You make a couple of very perceptive points in this posting Carl, which trigger ideas which had never occurred to me before.

Your mention of distinguishing between sensory and musical dissonance, could throw new light on what is happening.

The traditional models of con/dissonance never seem to have worked satisfactorily; certainly neither in 12edo nor in JI.

This may be because each model has its own inherent restrictions and limitations.

a) In JI, because the intervals must conform to the small integer frequency ratio rules.

b) In 12 edo, because of the limitation of 100 cent intervals and a small number of possible notes per octave.

Each system is consistent within its own limitations for composition and performance of music, yet as tuning systems which can universally express musical harmonic relationships both fail dismally.

JI seems to have evolved from the wish to generate zero beating at particular intervals, and 12 edo (in the West) has evolved as a simplification of the meantone tradition as can been observed by the 12 edo note naming system which is still widely used.

(Many of the French musicians which I have worked with, still use a tonic solfa type naming system using do for C etc. instead of letter names (CDEFGAB) which is more common in English language cultures.)

Quarter comma, third comma, and other assorted meantones, refer back to JI as may be heard in the way in which they are named, suggesting that their heritage is from JI and the traditions which Helmholtz and many others have written about copiously.

The validity of equal temperaments usually seem to be evaluated by how closely they approach JI intervals.

Neither model can provide an entirely reliable or consistent method for mapping (Western) harmony, and we arrive at a situation in music theory (and tuning) where these "old" models are ripe for replacement.

To develop a new paradigm, the "traditionalists" will have to abandon their JI and "Helmholtz-type" assumptions.

[Neither an easy task, nor a comfortable place for most, as this will maroon them in a choppy ocean without a compass or even one of Harrison's clocks;-) ]

About a year ago, when I initially posted on the tuning list that I was developing a comprehensive list of scales, most tunaniks reacted by pointing me to the scala files, and/or questioning my sanity;
a few offered me encouragement and some very useful ideas.

Now I have completed ScaleCoding of 90% of the 2048 (+ others) 12edo scales, using the traditional note naming conventions of meantone (A - G + multiple sharps and flats), and find that it does manage to avoid both the JI and edo pitfalls.

The next stage is to explore the results and to attempt to completely reconcile the sensory/musical contradictions which Carl points out in his posting.

Anyone who has FileMaker ( .fp7 or above) (Carl?) ; it is unlocked and runs on PC or Mac; can watch my daily progress by downloading the link at:

http://www.lucytune.com/scales/

and develop their own thoughts and comments.

(Yes, I am slowly correcting the typos and other human errors;-)

Mahalo Carl.

On 2 Nov 2008, at 08:16, Carl Lumma wrote:

> Hi Michael,
>
> >> ---but I doubt anyone would say it has the power to make 10-ET
> >>
> >> consonant in the sense that 7-limit JI is consonant.
> >
> > I agree, hence the example I gave in a message earlier on in
> > this threads that "10 TET sounds odd, even using pure sine waves
> > thus having no potential harmonic conflicts".
>
> Using pure sines to make music in 10-ET does NOT guarantee an
> absence of beating or other critical band effects, if that's
> what you meant by "harmonic conflicts".
>
> > Back to "sensory dissonance" vs. "musical dissonance".
> > I don't know the formal definition of which is which...but from
> > what I have read from you I believe my point could be stated as
> > "a 5 note widely spaced scale played with sine waves under
> > 10-TET, although having more sensory consonance than a 7-note
> > scale under 12-TET, fails to have the musical consonance of
> > 12-TET".
>
> Hm. Sensory consonance refers to the part of consonance that
> exists solely in individual (isolated) sounds. Musical
> consonance refers to the function of sounds within musical
> compositions (it's more to do with grammar than just hearing).
>
> Scales generally don't say much about either kind of consonance.
> In most scales, you can easily create sounds that have high
> sensory dissonance (just by mashing the keyboard). Some
> theorists believe certain scale properties are required to
> create musical consonance distinctions (e.g. must have a circle
> of approximate 3/2 "fifths", etc.). But anyway, one doesn't
> usually think of something like 12-ET as having consonance or
> dissonance in and of itself. One might reference something
> like 'common-practice music rendered in 12-ET'...
>
> >> ----How do you get that? Play all 7 tones of the 5-limit JI
> >> diatonic scale at once, and then play the first 7 harmonics
> >> at once -- which is more consonant?
> >
> > I believe I mis-stated my point, I never meant "harmonics
> > vs. scales"...I meant to say that, say, a JI scale in a higher
> >limit can become quite dissonant: JI does not instantly equal
> >consonance.
>
> One could argue that the sensory consonance of otonal chords
> in JI actually increases as you add higher and higher
> harmonics -- if the amplitude of each successive note
> decreases. The same is not true of subharmonics (Partch's
> "utonal" chords), which rapidly become dissonant as you go
> up the series. However, the ratios required to spell extended
> utonal chords also become more complex very quickly, and
> usually "JI" entails something about ratios being simple.
> Complex ratios are also needed to make small intervals that
> would have strong critical band interactions. So JI does
> indeed seem to guarantee sensory consonance for chords.
> And by using Tenney Height (numerator * denominator of a
> ratio in lowest terms, or, by extension, a * b * c... of the
> notes in a chord, where a, b, and c are coprime integers over
> a common fundamental), one can rank the consonance of
> different JI chords.
>
> The only problem is an inability to measure the consonance
> of irrational intervals -- that's where harmonic entropy
> comes in.
>
> >> ----The "roughness" models of consonance, central to the
> >> approach of Plomp & Levelt, depend on critical-band effects
> >> and therefore on absolute frequencies. JI-based models
> >> depend only on the _relationships_ between frequencies.
> >
> > The thing that gets me.....is that Plomp & Levelt's
> > roughness model was used to form Sethares's consonance formula.
> > And, assuming harmonics of more-or-less equal volume and whole-
> > number-ratio harmonics, the dissonance curve has troughs (IE
> > minimization points) at the 7-tone JI scale. Thus, they both
> > ultimately appear to point in the same direction...
>
> The model gives simple ratios when the timbres are harmonic,
> and the JI diatonic scale is made up of the 7 simplest ratios.
> But those graphs only show dyadic interactions, not larger
> chords...
>
> > But, again, the side issue seems to be, using Sethares' same
> > formula that "proves JI"
>
> There are lots of models that are capable of spitting out JI
> in some cases. Which one actually corresponds to reality?
>
> Harmonic entropy can be used to 'prove' the meantone diatonic,
> which actually won the battle for musical praxis over JI.
> If you play all 7 notes of a the diatonic scale at once, are
> you better off to tune them in JI or in 31-ET? Harmonic
> entropy says 31-ET. Try it and tell us what you think!
>
> >on odd scales like 10-TET (as he did in his "Ten Fingers" guitar
> >piece) and weird "built-to-match" overtone structures seems to,
> >as you said, never quite achieve the feel of musicality that
> >7-tone JI has.
>
> I said 7-*limit* JI. Basically, if you stretch the partials
> of a timbre out to 10-ET, you loose some of the 'pitchedness'
> of the timbre. Consonance and pitch are very closely related
> phenomena, so you can't have too much of one without the other,
> though you can have some. Sethares' book and web site, in my
> opinion, tends to overstate how much you can have. At any
> rate, much of his music sounds rather bell-like -- would you
> agree?
>
> > Hence we have a clear issue so far as I can figure...neither
> > just intonation nor the "consonance formula" above can be
> > considered the holy grail of tonality...it only seems to solve
> > the equation with whole-tone instruments and matching scales.
>
> Harmonic entropy is basically the holy grail of sensory
> consonance -- though it's still a bit wishy-washy for larger
> chords, we've seen glimpses of what it looks like for triads,
> and it seems to agree with human listeners.
>
> The holy grail of tonality is a much more elusive beast, because
> you have to take into account all the values that work in music
> which all affect our perception.
>
> > I have also found, for example, my own scale
> > Left channel Right Channel
> > 1 (root tone) 1.112 (2nd tone)
> > 1.2405 (3rd tone) 1.345 (4th tone)
> > 1.48 (5th tone) 1.666 (6th tone)
> > 1.868 (7th tone) 2 (octave)
> > 2.224 (9th tone) etc.
> >
> > seems to have to best record to my ears with sine wave so far as
> > playing 7-notes per octave at once (IE a 7-note chord)
> > and
> > A) Subduing any types of beating that don't make musical sense
> (Helmholtz) AND
> > making the effects of "binaural beating" not clash
> > B) Keeping notes far apart by strategically place-ing them far
> > apart in different channels (Plomp & Levelt). This allows the
> > 7-note scale to sound about as consonant as a Gregorian
> > chant-ish 4-note scale, at least to my ears.
> > C) A third factor which I believe has not been tackled: the
> > notes fit in a same mood or character. Note if you move notes
> > in a closer to equal temperament, although the consonance goes
> > down according to, say, Sethares' formula, it sounds worse far
> > as mood.
>
> What's "mood"?
>
> In cents, your scale is:
> 183.8 373.1 513.1 678.7 883.7 1081.8 1200.0
>
> What do you think of
> 193.4 386.9 504.1 697.6 891.0 1084.4 1201.7
> for comparison?
>
> Or howabout:
> 182.4 369.7 498.0 663.0 884.3 1080.6 1200.0
> ?
>
> -Carl
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

I wrote:

> I said 7-*limit* JI. Basically, if you stretch the partials
> of a timbre out to 10-ET, you loose some of the 'pitchedness'
> of the timbre. Consonance and pitch are very closely related
> phenomena, so you can't have too much of one without the other,
> though you can have some. Sethares' book and web site, in my
> opinion, tends to overstate how much you can have. At any
> rate, much of his music sounds rather bell-like -- would you
> agree?

A perfect example of what I'm talking about is at the top
of this page:
http://eceserv0.ece.wisc.edu/~sethares/html/soundexamples.html
The four "simptun" examples... I hear the stretched timbre as
significantly less cohesive than the harmonic one. It's
possible to make dissonances with either timbre, but to my
ears the stretched timbre with the stretched scale isn't as
consonant as the harmonic timbre with the harmonic timbre.

-Carl

---Using pure sines to make music in 10-ET does NOT guarantee an

absence of beating or other critical band effects, if that's

what you meant by "harmonic conflicts".

   I meant that having individual sine waves placed far apart DOES guarantee an

absence of beating or other critical band effects...
   And that, for example, 10TET has each of its notes spaced further apart then 12TET, yet that further spacing does not automatically guarantee more musical sound even when overtones are "taken out of the picture".
   In other words, my point is the idea that eliminating critical band effects will automatically make something sound good is false regardless of what scale and instrument-overtone-schemas you use.
*******************************************************
---Hm. Sensory consonance refers to the part of consonance that

exists solely in individual (isolated) sounds. Musical

consonance refers to the function of sounds within musical

compositions (it's more to do with grammar than just hearing).

    Hmm...ok, if I have it right from the explanation "sensory" consonance would refer to the amount of consonance a single instrument has relative to itself IE a sine wave would have much higher sensory consonance than a trumpet. 
    Meanwhile it sounds like "musical consonance" is more like saying "how do I use the sweet and sour spots in the scales to promote a sense of contrast and emotion"...IE a good scale will likely have many good routes/choices this way and a bad scale far fewer.

*********************************************************************
----But anyway, one doesn't usually think of something like 12-ET as having consonance or

dissonance in and of itself. One might reference something

like 'common-practice music rendered in 12-ET'...

     Ok, then we're on different pages, it seems.  When I said "JI vs. other scale consonance" I meant "say you play every single note in the scales at once (with an instrument/overtone-schema intended to work with that scale)...which scale would produce the highest sense of musicality and/or consonance?"

   I understand that certain intervals like fifths and thirds will always sound "calm" because they are parts of "common-practice music".
    I am thinking more in terms of what kind of scale could open the most possibilities far as making more possible "common sweet intervals"...with the ultimate being a scale with many notes where it is virtually impossible to make a combination that feels out-of-tune.  The scale I created in my last example is a try at such a thing: you can get all 7 notes per octave without much feeling of "clash" and only rarely a feeling that a note "does not fit the same mood as the others".

>     The thing that gets me.....is that Plomp & Levelt's

> roughness model was used to form Sethares's consonance formula.

> And, assuming harmonics of more-or-less equal volume and whole-

> number-ratio harmonics, the dissonance curve has troughs (IE

> minimization points) at the 7-tone JI scale.  Thus, they both

> ultimately appear to point in the same direction...

---------The model gives simple ratios when the timbres are harmonic,
---------and the JI diatonic scale is made up of the 7 simplest ratios.
---------But those graphs only show dyadic interactions, not larger
---------chords...
    Right, then when I said "7-note JI" the technically correct term is "diatonic JI".
   So you are saying...that larger chords are possible with more complex ratios under JI?

---------Harmonic entropy can be used to 'prove' the meantone diatonic,
---------
which actually won the battle for musical praxis over JI.
---------
If you play all 7 notes of a the diatonic scale at once, are
---------
you better off to tune them in JI or in 31-ET? Harmonic
---------
entropy says 31-ET. Try it and tell us what you think!
          Hehe...ok, now this is getting more at the kind of crazy "all notes vs. all notes"
scale challenges I was aiming for.

       Though it does sound utterly to me like JI, mean-tone (much like a bunch a 5ths stacked on each other), and "harmonic entropy pointing near mean-tone" all seem to produce essentially the same diatonic scale off by only a few cents. 
    So it seems like trading apples for apples...my question is what is the significant difference (in mood of the resulting scales, not just math)?  It still seems to me, all math seems to point to generally the same place...and to go further you must use mood to "tweak" the scales.
******************************************************************************************

What's "mood"?

In cents, your scale is:

183.8 373.1 513.1 678.7 883.7 1081.8 1200.0

What do you think of

193.4 386.9 504.1 697.6 891.0 1084.4 1201.7

for comparison?

Or howabout:

182.4 369.7 498.0 663.0 884.3 1080.6 1200.0

?

Again, interesting challenge.  I will try these.
    ---------------------
    By mood I mean "which one is so flexible as to enable more possibilities far as chords and/or melodies"?
   And, of course, an ideal scale would (with sine waves) essentially enable a 7-note chord within an octave and, of course, against any note in the scale on any other octave. 
      5-TET can, more or less, do this and feel neither very consonant nor dissonant (I would be interested to hear why/how)...but you don't get the full 7 notes of flexibility and instead get stuck with 4-5 real 5 note chords and their inversions.

------------------------------

   As a side-note, I agree that JI gets close to "solving" the ideal set of scales for real-world instruments.  But using digital processing you could, for example, match all overtones of an instrument to my above scale (kind of like a guitar effects pedal, but for any instrument).
   My question again is, how to build a scale with a much larger possibility far as "sweet-sounding" chords, melodies...to the point where almost any combination of notes becomes possible and composition within it switches to an art of not rules but pure expression IE virtually everything becomes "in-tune".

-Michael

--- On Sun, 11/2/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Sunday, November 2, 2008, 1:16 AM

Hi Michael,

>> ---but I doubt anyone would say it has the power to make 10-ET

>>

>> consonant in the sense that 7-limit JI is consonant.

>

>    I agree, hence the example I gave in a message earlier on in

> this threads that "10 TET sounds odd, even using pure sine waves

> thus having no potential harmonic conflicts".

Using pure sines to make music in 10-ET does NOT guarantee an

absence of beating or other critical band effects, if that's

what you meant by "harmonic conflicts".

>    Back to "sensory dissonance" vs. "musical dissonance".

> I don't know the formal definition of which is which...but from

> what I have read from you I believe my point could be stated as

> "a 5 note widely spaced scale played with sine waves under

> 10-TET, although having more sensory consonance than a 7-note

> scale under 12-TET, fails to have the musical consonance of

> 12-TET". 

Hm. Sensory consonance refers to the part of consonance that

exists solely in individual (isolated) sounds. Musical

consonance refers to the function of sounds within musical

compositions (it's more to do with grammar than just hearing).

Scales generally don't say much about either kind of consonance.

In most scales, you can easily create sounds that have high

sensory dissonance (just by mashing the keyboard). Some

theorists believe certain scale properties are required to

create musical consonance distinctions (e.g. must have a circle

of approximate 3/2 "fifths", etc.). But anyway, one doesn't

usually think of something like 12-ET as having consonance or

dissonance in and of itself. One might reference something

like 'common-practice music rendered in 12-ET'...

>> ----How do you get that? Play all 7 tones of the 5-limit JI

>> diatonic scale at once, and then play the first 7 harmonics

>> at once -- which is more consonant?

>

>   I believe I mis-stated my point, I never meant "harmonics

> vs. scales"...I meant to say that, say, a JI scale in a higher

>limit can become quite dissonant: JI does not instantly equal

>consonance.

One could argue that the sensory consonance of otonal chords

in JI actually increases as you add higher and higher

harmonics -- if the amplitude of each successive note

decreases. The same is not true of subharmonics (Partch's

"utonal" chords), which rapidly become dissonant as you go

up the series. However, the ratios required to spell extended

utonal chords also become more complex very quickly, and

usually "JI" entails something about ratios being simple.

Complex ratios are also needed to make small intervals that

would have strong critical band interactions. So JI does

indeed seem to guarantee sensory consonance for chords.

And by using Tenney Height (numerator * denominator of a

ratio in lowest terms, or, by extension, a * b * c... of the

notes in a chord, where a, b, and c are coprime integers over

a common fundamental) , one can rank the consonance of

different JI chords.

The only problem is an inability to measure the consonance

of irrational intervals -- that's where harmonic entropy

comes in.

>> ----The "roughness" models of consonance, central to the

>> approach of Plomp & Levelt, depend on critical-band effects

>> and therefore on absolute frequencies. JI-based models

>> depend only on the _relationships_ between frequencies.

>

>     The thing that gets me.....is that Plomp & Levelt's

> roughness model was used to form Sethares's consonance formula.

> And, assuming harmonics of more-or-less equal volume and whole-

> number-ratio harmonics, the dissonance curve has troughs (IE

> minimization points) at the 7-tone JI scale.  Thus, they both

> ultimately appear to point in the same direction...

The model gives simple ratios when the timbres are harmonic,

and the JI diatonic scale is made up of the 7 simplest ratios.

But those graphs only show dyadic interactions, not larger

chords...

> But, again, the side issue seems to be, using Sethares' same

> formula that "proves JI"

There are lots of models that are capable of spitting out JI

in some cases. Which one actually corresponds to reality?

Harmonic entropy can be used to 'prove' the meantone diatonic,

which actually won the battle for musical praxis over JI.

If you play all 7 notes of a the diatonic scale at once, are

you better off to tune them in JI or in 31-ET? Harmonic

entropy says 31-ET. Try it and tell us what you think!

>on odd scales like 10-TET (as he did in his "Ten Fingers" guitar

>piece) and weird "built-to-match" overtone structures seems to,

>as you said, never quite achieve the feel of musicality that

>7-tone JI has.

I said 7-*limit* JI. Basically, if you stretch the partials

of a timbre out to 10-ET, you loose some of the 'pitchedness'

of the timbre. Consonance and pitch are very closely related

phenomena, so you can't have too much of one without the other,

though you can have some. Sethares' book and web site, in my

opinion, tends to overstate how much you can have. At any

rate, much of his music sounds rather bell-like -- would you

agree?

>   Hence we have a clear issue so far as I can figure...neither

> just intonation nor the "consonance formula" above can be

> considered the holy grail of tonality...it only seems to solve

> the equation with whole-tone instruments and matching scales.

Harmonic entropy is basically the holy grail of sensory

consonance -- though it's still a bit wishy-washy for larger

chords, we've seen glimpses of what it looks like for triads,

and it seems to agree with human listeners.

The holy grail of tonality is a much more elusive beast, because

you have to take into account all the values that work in music

which all affect our perception.

>    I have also found, for example, my own scale

> Left channel                   Right Channel

> 1 (root tone)                      1.112 (2nd tone)

> 1.2405 (3rd tone)               1.345 (4th tone)

> 1.48 (5th tone)                   1.666 (6th tone)

> 1.868 (7th tone)                 2 (octave)

> 2.224 (9th tone) etc.

>

> seems to have to best record to my ears with sine wave so far as

> playing 7-notes per octave at once (IE a 7-note chord)

> and

> A) Subduing any types of beating that don't make musical sense

(Helmholtz) AND

>     making the effects of "binaural beating" not clash

> B) Keeping notes far apart by strategically place-ing them far

> apart in different channels (Plomp & Levelt).  This allows the

> 7-note scale to sound about as consonant as a Gregorian

> chant-ish 4-note scale, at least to my ears.

> C) A third factor which I believe has not been tackled: the

> notes fit in a same mood or character.  Note if you move notes

> in a closer to equal temperament, although the consonance goes

> down according to, say, Sethares' formula, it sounds worse far

> as mood.

What's "mood"?

In cents, your scale is:

183.8 373.1 513.1 678.7 883.7 1081.8 1200.0

What do you think of

193.4 386.9 504.1 697.6 891.0 1084.4 1201.7

for comparison?

Or howabout:

182.4 369.7 498.0 663.0 884.3 1080.6 1200.0

?

-Carl

   Exactly...again far as the "consonance formula" says the stretched and non-stretched examples are equivalent in terms of consonance...but the is something else going on in the brain which says "something else just doesn't fit..."   My hope is people will try to pick up exactly what this "gap" is coming from...and then use that knowledge to open up new possibilities in music beyond JI...

--- On Sun, 11/2/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Sunday, November 2, 2008, 8:27 AM

I wrote:

> I said 7-*limit* JI. Basically, if you stretch the partials

> of a timbre out to 10-ET, you loose some of the 'pitchedness'

> of the timbre. Consonance and pitch are very closely related

> phenomena, so you can't have too much of one without the other,

> though you can have some. Sethares' book and web site, in my

> opinion, tends to overstate how much you can have. At any

> rate, much of his music sounds rather bell-like -- would you

> agree?

A perfect example of what I'm talking about is at the top

of this page:

http://eceserv0. ece.wisc. edu/~sethares/ html/soundexampl es.html

The four "simptun" examples... I hear the stretched timbre as

significantly less cohesive than the harmonic one. It's

possible to make dissonances with either timbre, but to my

ears the stretched timbre with the stretched scale isn't as

consonant as the harmonic timbre with the harmonic timbre.

-Carl

Hi Michael!

>> Using pure sines to make music in 10-ET does NOT guarantee
>> an absence of beating or other critical band effects, if that's
>> what you meant by "harmonic conflicts".
>
>    I meant that having individual sine waves placed far apart
> DOES guarantee an absence of beating or other critical band
> effects...

Indeed.

>    And that, for example, 10TET has each of its notes spaced
> further apart then 12TET,

...but still well within the critical band throughout much of
the traditional musical pitch range.

>    In other words, my point is the idea that eliminating critical
> band effects will automatically make something sound good is false
> regardless of what scale and instrument-overtone-schemas you use.

I can certainly agree with this!

>     Hmm...ok, if I have it right from the explanation "sensory"
> consonance would refer to the amount of consonance a single
> instrument has relative to itself IE a sine wave would have much
> higher sensory consonance than a trumpet.

Er, no. You can think of sensory consonance something about
*chords*, which are presented to a listener after a long period
of silence.

>     Meanwhile it sounds like "musical consonance" is more like
> saying "how do I use the sweet and sour spots in the scales to
> promote a sense of contrast and emotion"...IE a good scale will
> likely have many good routes/choices this way and a bad scale
> far fewer.

Er, it's more like, dominant 7th chords are musical dissonances
in classical music, but musical consonances in the blues.
Though it certainly builds on sensory consonance, it's mostly
a grammar thing. Think of it as having to do with *chord
progressions*. If a "dissonance must resolve", the kind of
dissonance being discussed is musical dissonance.

Note that Easley Blackwood proposed calling sensory consonance
and dissonance "concordance" and "discordance", which is a
great idea however it hasn't caught on. If you want to follow
that convention, though, I'm happy to oblige!

>> But anyway, one doesn't usually think of something like 12-ET
>> as having consonance or dissonance in and of itself
//
>      Ok, then we're on different pages, it seems.  When I said
> "JI vs. other scale consonance" I meant "say you play every
> single note in the scales at once

That's a chord then, not a scale. Sethares derives scales
directly from dissonance curves, but the procedure he seems to
use isn't valid, unless the only chords you intend to play are
dyads up from the tonic. For instance,
9/8 5/4 4/3 3/2 5/3
may be the minima for a given timbre, but if I play the chord
9/8 - 4/3 - 5/3
I'm getting the intervals 32/27, 5/4, and 40/27, which are
not minima.

>    I understand that certain intervals like fifths and thirds
> will always sound "calm" because they are parts of "common-
> practice music".

That would be cultural conditioning, which yet is another level
above either the sensory and musical consonances we've been
discussing.

>     I am thinking more in terms of what kind of scale could
> open the most possibilities far as making more possible "common
> sweet intervals"...with the ultimate being a scale with many
> notes where it is virtually impossible to make a combination
> that feels out-of-tune.

The only scales I know of like that are harmonic series
segments up to the 19th harmonic (with 21 we get 21/16, which
is discordant because of its proximity to 4/3). Try
for instance 8 9 10 11 12 13 14 15 16.

>> What's "mood"?
>
>> In cents, your scale is:
>> 183.8 373.1 513.1 678.7 883.7 1081.8 1200.0
>>
>> What do you think of
>> 193.4 386.9 504.1 697.6 891.0 1084.4 1201.7
>> for comparison?
>
>> Or howabout:
>> 182.4 369.7 498.0 663.0 884.3 1080.6 1200.0
>>
>> ?
>
> Again, interesting challenge.  I will try these.

Let us know how you make out!

> By mood I mean "which one is so flexible as to enable more
> possibilities far as chords and/or melodies"?

Well that's a tall order. What counts as a "chord"? What
counts as a "melody"? The theory developed on this list over
the last 15 years can be seen as an attempt to answer that
question, at least within the context of something like
Western music.

>    And, of course, an ideal scale would (with sine waves)
> essentially enable a 7-note chord within an octave and, of
> course, against any note in the scale on any other octave.

Harmonics 7 8 9 10 11 12 13 14 for instance, is a 7-note
scale that will be plenty consonant if you mash it, and
you don't even have to use sines. It also sounds interesting
melodically (at least to me). But it does have limitations
when the grammar stuff comes up. . . .

-Carl

Michael and I wrote:

>> A perfect example of what I'm talking about is at the top
>> of this page:
>> http://eceserv0. ece.wisc. edu/~sethares/ html/soundexampl es.html
>> The four "simptun" examples... I hear the stretched timbre as
>> significantly less cohesive than the harmonic one. It's
>> possible to make dissonances with either timbre, but to my
>> ears the stretched timbre with the stretched scale isn't as
>> consonant as the harmonic timbre with the harmonic timbre.
>
>  Exactly...again far as the "consonance formula" says the
> stretched and non-stretched examples are equivalent in terms of
> consonance...but the is something else going on in the brain
> which says "something else just doesn't fit..."   My hope is
> people will try to pick up exactly what this "gap" is coming
> from...and then use that knowledge to open up new possibilities
> in music beyond JI...

Well, I'll claim the gap has been identified. It's due to
the fact that the brain's virtual pitch processor has not
been triggered as strongly by the stretched timbre/scale
example as it has by the harmonic timbre/scale example,
because the brain's virtual pitch processor is tuned (by
evolution and/or early learning as infants) to pick out
harmonic spectra specifically (since that's what human voices
have). So JI is built into the brain -- there's no going
beyond it as far as raw sensory consonance is concerned,
except perhaps in a few isolated cases known as "magic chords"
(and it's debatable).

Now, there is a good argument that when it comes to musical
grammars, temperament can take you further. One of the
big theory items on this list is how to use temperament to
create richer grammar possibilities while staying very
close to JI on the chords... but again, it's debatable.

-Carl

---Er, no. You can think of sensory consonance something about

*chords*, which are presented to a listener after a long period

of silence.
     Hmm...so then sensory consonance = contrast with other parts IE "resolve" vs. "unresolved".

>    In other words, my point is the idea that eliminating critical

> band effects will automatically make something sound good is false

> regardless of what scale and instrument-overtone -schemas you use.

---I can certainly agree with this!
  Well then, is there any rationale that would prevent people from creating
scales outside JI that would sound equally musical and "sweet", if not "even"
better?

>      Ok, then we're on different pages, it seems.  When I said

> "JI vs. other scale consonance" I meant "say you play every

> single note in the scales at once
----That's a chord then, not a scale. Sethares derives scales
----
directly from dissonance curves, but the procedure he seems to
----
use isn't valid, unless the only chords you intend to play are

----dyads up from the tonic. For instance,

----9/8 5/4 4/3 3/2 5/3 may be the minima for a given timbre, but if I play the chord
----
9/8 - 4/3 - 5/3
----
I'm getting the intervals 32/27, 5/4, and 40/27, which are
----
not minima.
    Ok, if I am following, the point is as you move a chord to different "starting points" along the scale, the minimum points change.  In that case, wouldn't the ideal solution be a chain of chords that branch off each other (kind of like Debussy's chord-based modulations) and some sort of adaptive tuning to build each chord to be more in-tune to the root of that chord?
   And...wouldn't the C diatonic just-intonation scale fail at this task just as badly playing, say, a D triad?

   I am rather assuming...that the scale is fixed, and the optimum solution would be the "best average intervals for all chords", rather than one fitted to a certain chord.  And, if I have it right...that's what Sethares attempts to solve for.

>     I am thinking more in terms of what kind of scale could

> open the most possibilities far as making more possible "common

> sweet intervals".. .with the ultimate being a scale with many

> notes where it is virtually impossible to make a combination

> that feels out-of-tune.

----The only scales I know of like that are harmonic series

----
segments up to the 19th harmonic (with 21 we get 21/16, which

----
is discordant because of its proximity to 4/3). Try

----
for instance 8 9 10 11 12 13 14 15 16.
    Amazingly, this seems to work quite well: everything sounds "in mood" with everything else. 
     It seems I could only squeeze about 7 note or less scales (per octave) out of this without too many "critical band effects" even with pure sine waves (and that's with my trick of splitting every other note into the right channel and the rest into the left channel to eliminate excessive beating)...

  Still, that's every bit as good as my scale (at least for a nearly two-octave range).   My "binaural" interpretation of the scale was
Left channel    Right channel
5                     6
7                     8
9                     10
11                   12
13                    14 (octave)
15                    16
17                    18

      Are there any compositions you could recommend based on scales made from these "higher overtones"? 
   I could actually think of many cool ways software could "push" live instruments'
overtones to fit this schema...and perhaps even use this for "normal musicians".
   My real question is...why hasn't some form of this sort of thing become widely adopted?
This is WAY too much fun... :-)

   One the other hand...something that gives this much freedom, but has a range of more than about 2 octaves (with at least 7 notes per octave) would be nice (I am thinking 4 would be ideal)

----But it does have limitations when the grammar stuff comes up. . . .
Agreed, if I have it right: there doesn't seem any way to contrast consonance and dissonance...everything kind of feels "exactly the same" in "mood" under this scale model, even though, on the plus side, virtually all possibilities sound very "cohesive".
************************************************************************************************

-Michael

--- On Sun, 11/2/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Sunday, November 2, 2008, 2:57 PM

Hi Michael!

>> Using pure sines to make music in 10-ET does NOT guarantee

>> an absence of beating or other critical band effects, if that's

>> what you meant by "harmonic conflicts".

>

>    I meant that having individual sine waves placed far apart

> DOES guarantee an absence of beating or other critical band

> effects...

Indeed.

>    And that, for example, 10TET has each of its notes spaced

> further apart then 12TET,

...but still well within the critical band throughout much of

the traditional musical pitch range.

>    In other words, my point is the idea that eliminating critical

> band effects will automatically make something sound good is false

> regardless of what scale and instrument-overtone -schemas you use.

I can certainly agree with this!

>     Hmm...ok, if I have it right from the explanation "sensory"

> consonance would refer to the amount of consonance a single

> instrument has relative to itself IE a sine wave would have much

> higher sensory consonance than a trumpet.

Er, no. You can think of sensory consonance something about

*chords*, which are presented to a listener after a long period

of silence.

>     Meanwhile it sounds like "musical consonance" is more like

> saying "how do I use the sweet and sour spots in the scales to

> promote a sense of contrast and emotion"...IE a good scale will

> likely have many good routes/choices this way and a bad scale

> far fewer.

Er, it's more like, dominant 7th chords are musical dissonances

in classical music, but musical consonances in the blues.

Though it certainly builds on sensory consonance, it's mostly

a grammar thing. Think of it as having to do with *chord

progressions* . If a "dissonance must resolve", the kind of

dissonance being discussed is musical dissonance.

Note that Easley Blackwood proposed calling sensory consonance

and dissonance "concordance" and "discordance" , which is a

great idea however it hasn't caught on. If you want to follow

that convention, though, I'm happy to oblige!

>> But anyway, one doesn't usually think of something like 12-ET

>> as having consonance or dissonance in and of itself

//

>      Ok, then we're on different pages, it seems.  When I said

> "JI vs. other scale consonance" I meant "say you play every

> single note in the scales at once

That's a chord then, not a scale. Sethares derives scales

directly from dissonance curves, but the procedure he seems to

use isn't valid, unless the only chords you intend to play are

dyads up from the tonic. For instance,

9/8 5/4 4/3 3/2 5/3

may be the minima for a given timbre, but if I play the chord

9/8 - 4/3 - 5/3

I'm getting the intervals 32/27, 5/4, and 40/27, which are

not minima.

>    I understand that certain intervals like fifths and thirds

> will always sound "calm" because they are parts of "common-

> practice music".

That would be cultural conditioning, which yet is another level

above either the sensory and musical consonances we've been

discussing.

>     I am thinking more in terms of what kind of scale could

> open the most possibilities far as making more possible "common

> sweet intervals".. .with the ultimate being a scale with many

> notes where it is virtually impossible to make a combination

> that feels out-of-tune.

The only scales I know of like that are harmonic series

segments up to the 19th harmonic (with 21 we get 21/16, which

is discordant because of its proximity to 4/3). Try

for instance 8 9 10 11 12 13 14 15 16.

>> What's "mood"?

>

>> In cents, your scale is:

>> 183.8 373.1 513.1 678.7 883.7 1081.8 1200.0

>>

>> What do you think of

>> 193.4 386.9 504.1 697.6 891.0 1084.4 1201.7

>> for comparison?

>

>> Or howabout:

>> 182.4 369.7 498.0 663.0 884.3 1080.6 1200.0

>>

>> ?

>

> Again, interesting challenge.  I will try these.

Let us know how you make out!

> By mood I mean "which one is so flexible as to enable more

> possibilities far as chords and/or melodies"?

Well that's a tall order. What counts as a "chord"? What

counts as a "melody"? The theory developed on this list over

the last 15 years can be seen as an attempt to answer that

question, at least within the context of something like

Western music.

>    And, of course, an ideal scale would (with sine waves)

> essentially enable a 7-note chord within an octave and, of

> course, against any note in the scale on any other octave.

Harmonics 7 8 9 10 11 12 13 14 for instance, is a 7-note

scale that will be plenty consonant if you mash it, and

you don't even have to use sines. It also sounds interesting

melodically (at least to me). But it does have limitations

when the grammar stuff comes up. . . .

-Carl

----because the brain's virtual pitch processor is tuned (by

evolution and/or early learning as infants) to pick out

harmonic spectra specifically (since that's what human voices

have).
   Interesting...so it's almost like the brain is tuned to pick up music as sections of
whole-number-multiple harmonics (like those in human voice), then (almost as if to help it quickly deduce who a person is hearing speak IE their relative or just a random person)?

   The flip side...is does "easily distinguishable" necessarily equal "desirable"? 
   I will admit JI is often the easiest formulation to listen to but, at the same time, given some mental effort things like Lucytuning sound quite "sweet/pure/consonant". 
    At the same time, it makes sense they are less native: I couldn't imagine, say, driving a car safely while listening to, say, Sethares's "Ten Fingers" 10TET piece after a 12TET piece as my mind would be grinding a bit trying to "switch gears". 
    But, at the same time, I have found listening to several non JI (or near-JI) songs in a row my mind gets used to processing it, and it eventually begins to sound quite native.  Call it slowly breaking past a "sensory threshold"...but I wonder if the mind can be trained to accept "skewed tunings".  I can't tell you how many times people have commented on one 8-note scale 19TET piece I made (that uses a scale in no way based on JI) and said "on first listen this sounded like crap...but after I listened to it a few time I began to sense the cohesiveness and now it seems quite normal".
  
  

--- On Sun, 11/2/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Sunday, November 2, 2008, 3:12 PM

Michael and I wrote:

>> A perfect example of what I'm talking about is at the top

>> of this page:

>> http://eceserv0. ece.wisc. edu/~sethares/ html/soundexampl es.html

>> The four "simptun" examples... I hear the stretched timbre as

>> significantly less cohesive than the harmonic one. It's

>> possible to make dissonances with either timbre, but to my

>> ears the stretched timbre with the stretched scale isn't as

>> consonant as the harmonic timbre with the harmonic timbre.

>

>  Exactly...again far as the "consonance formula" says the

> stretched and non-stretched examples are equivalent in terms of

> consonance.. .but the is something else going on in the brain

> which says "something else just doesn't fit..."   My hope is

> people will try to pick up exactly what this "gap" is coming

> from...and then use that knowledge to open up new possibilities

> in music beyond JI...

Well, I'll claim the gap has been identified. It's due to

the fact that the brain's virtual pitch processor has not

been triggered as strongly by the stretched timbre/scale

example as it has by the harmonic timbre/scale example,

because the brain's virtual pitch processor is tuned (by

evolution and/or early learning as infants) to pick out

harmonic spectra specifically (since that's what human voices

have). So JI is built into the brain -- there's no going

beyond it as far as raw sensory consonance is concerned,

except perhaps in a few isolated cases known as "magic chords"

(and it's debatable).

Now, there is a good argument that when it comes to musical

grammars, temperament can take you further. One of the

big theory items on this list is how to use temperament to

create richer grammar possibilities while staying very

close to JI on the chords... but again, it's debatable.

-Carl

     Continuing on Carl's point that the harmonic scale is the only one he has heard of where virtually all notes sound good with any combination of any notes in the scale...

Assuming the 0th harmonic is the root note...

    The harmonic scale notes 5,6,7,8,9,10(octave),11,12,13,15,17,19,20(second octave) seem to sound both in-tune and in mood. 
    However both harmonics number 16 and 18 sound grossly out of tune.  Any clue why?
-------------------------------
   Also...again, the harmonic series seems to be limited to around 2 octaves without having notes be so far spaced (any higher or lower up the series and more and more notes sound out-of-tune.....IE for harmonics 20-39 only 20,23,27,30,and 35 sound in tune to me.

  According to the theory that the human ear is trained from birth to focus on whole-multiple harmonic spectra...how can you explain that certain whole-tone multiple overtones seem to sound "out of tune"?

-Michael

--- On Sun, 11/2/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Sunday, November 2, 2008, 3:12 PM

Michael and I wrote:

>> A perfect example of what I'm talking about is at the top

>> of this page:

>> http://eceserv0. ece.wisc. edu/~sethares/ html/soundexampl es.html

>> The four "simptun" examples... I hear the stretched timbre as

>> significantly less cohesive than the harmonic one. It's

>> possible to make dissonances with either timbre, but to my

>> ears the stretched timbre with the stretched scale isn't as

>> consonant as the harmonic timbre with the harmonic timbre.

>

>  Exactly...again far as the "consonance formula" says the

> stretched and non-stretched examples are equivalent in terms of

> consonance.. .but the is something else going on in the brain

> which says "something else just doesn't fit..."   My hope is

> people will try to pick up exactly what this "gap" is coming

> from...and then use that knowledge to open up new possibilities

> in music beyond JI...

Well, I'll claim the gap has been identified. It's due to

the fact that the brain's virtual pitch processor has not

been triggered as strongly by the stretched timbre/scale

example as it has by the harmonic timbre/scale example,

because the brain's virtual pitch processor is tuned (by

evolution and/or early learning as infants) to pick out

harmonic spectra specifically (since that's what human voices

have). So JI is built into the brain -- there's no going

beyond it as far as raw sensory consonance is concerned,

except perhaps in a few isolated cases known as "magic chords"

(and it's debatable).

Now, there is a good argument that when it comes to musical

grammars, temperament can take you further. One of the

big theory items on this list is how to use temperament to

create richer grammar possibilities while staying very

close to JI on the chords... but again, it's debatable.

-Carl

Carl wrote:
> One could argue that the sensory consonance of otonal chords
> in JI actually increases as you add higher and higher
> harmonics -- if the amplitude of each successive note
> decreases.

This statement is equal to the hypothesis that a sawtooth wave is less
dissonant than a sine wave -- under what definition of consonance and
dissonance is this true?

-Mike

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
>
>> Er, no. You can think of sensory consonance something about
>> *chords*, which are presented to a listener after a long period
>> of silence.
>
>      Hmm...so then sensory consonance = contrast with other
> parts IE "resolve" vs. "unresolved".

No, the exact opposite actually. I said resolve/unresolved
had to do with musical consonance. Sensory consonance pertains
to chords in complete and utter isolaton.

>> Sethares derives scales directly from dissonance curves, but
>> the procedure he seems to use isn't valid, unless the only
>> chords you intend to play are dyads up from the tonic. For
>> instance,
>> 9/8 5/4 4/3 3/2 5/3
>> may be the minima for a given timbre, but if I play the chord
>> 9/8 - 4/3 - 5/3
>> I'm getting the intervals 32/27, 5/4, and 40/27, which are
>> not minima.
>
>     Ok, if I am following, the point is as you move a chord to
> different "starting points" along the scale, the minimum points
> change.

The consonance minima of the timbre do NOT change, but the
intervals one gets when playing various chords are not always
obvious just by looking at one mode of the scale.

> In that case, wouldn't the ideal solution be a chain of chords
> that branch off each other (kind of like Debussy's chord-based
> modulations) and some sort of adaptive tuning to build each
> chord to be more in-tune to the root of that chord?

Yes, a chord-based approach is definitely preferable to a
scale-based approach as far as sensory consonance is concerned.

>    And...wouldn't the C diatonic just-intonation scale fail at
> this task just as badly playing, say, a D triad?

That is the example I'm providing above, yes.

>    I am rather assuming...that the scale is fixed, and the
> optimum solution would be the "best average intervals for all
> chords",

That's the right idea, yes. One way to go about it is to
ask how many tones you want in a scale (let's say 7) and then
start with that equal temperament (in this case 7-ET) and
compute the sensory dissonance using Sethares' formula, of
all 7 notes played together as a chord. Then move each note
of the scale slightly and see whether the total dissonance
goes up or down. One can then use a hill-climbing-type
algorithm to find the ideal scale. That may not be realistic
if you only intend to use triads from the scale, but a similar
process may be applied to the sum of the dissonances of all
triads in the scale.

Bill is a really really smart guy, and I assumed he must have
done something like this, so I went back through his book.
But I can't really find it. On pg. 233, he starts talking
about a very similar process to find scales optimized for
certain pieces of music. But throughout the book, he's taking
dyadic dissonance curves and making scales directly from them.
This approach is... wrong.

>> Try for instance 8 9 10 11 12 13 14 15 16.
>
>     Amazingly, this seems to work quite well: everything sounds
> "in mood" with everything else.

Bonus!

>      It seems I could only squeeze about 7 note or less scales
> (per octave) out of this without too many "critical band effects"

I've done it with 9 notes no problem, but you helps to space
the notes out by octaves.

>       Are there any compositions you could recommend based on
> scales made from these "higher overtones"?

Sure. I mentioned Jon Catler recently. The German organist
Hans Andre-Stamm has a CD out called Enharmonic Garden I
believe. Another German (I think) composer, Arnold Dreyblatt,
has a lifetype of work in harmonic series scales. Oh, and
Prent Rodgers of course. Lots of others, too.

>    My real question is...why hasn't some form of this sort
> of thing become widely adopted?

It's one of the deeper mysteries of our time.

> This is WAY too much fun... :-)

You betcha.

-Carl

Michael Scheiman wrote:

> Assuming the 0th harmonic is the root note...

The 0th harmonic is 0Hz which in most cases represents silence. The 1st harmonic is the fundamental.

> The harmonic scale notes 5,6,7,8,9,10(octave),11,12,13,15,17,19,20(second octave)
> seem to sound both in-tune and in mood.
> However both harmonics number 16 and 18 sound grossly out of tune. Any clue why?

To me they don't.

> Also...again, the harmonic series seems to be limited to around 2 octaves without having
> notes be so far spaced (any higher or lower up the series and more and more notes sound
> out-of-tune.....IE for harmonics 20-39 only 20,23,27,30,and 35 sound in tune to me.

I think this has something to do with the 21st harmonic as Carl has said.

> According to the theory that the human ear is trained from birth to focus on whole-multiple
> harmonic spectra...how can you explain that certain whole-tone multiple overtones seem to
> sound "out of tune"?

What do you mean by "whole tone multiple overtones"?

Petr

> people will try to pick up exactly what this "gap" is coming
> from...and then use that knowledge to open up new possibilities
> in music beyond JI...

Well, I'll claim the gap has been identified. It's due to
the fact that the brain's virtual pitch processor has not
been triggered as strongly by the stretched timbre/scale
example as it has by the harmonic timbre/scale example,
because the brain's virtual pitch processor is tuned (by
evolution and/or early learning as infants) to pick out
harmonic spectra specifically (since that's what human voices
have). So JI is built into the brain -- there's no going
beyond it as far as raw sensory consonance is concerned,
except perhaps in a few isolated cases known as "magic chords"
(and it's debatable).

Now, there is a good argument that when it comes to musical
grammars, temperament can take you further. One of the
big theory items on this list is how to use temperament to
create richer grammar possibilities while staying very
close to JI on the chords... but again, it's debatable.

-Carl

A few more comments:

>> Meanwhile it sounds like "musical consonance" is more like
>> saying "how do I use the sweet and sour spots in the scales to
>> promote a sense of contrast and emotion"...IE a good scale will
>> likely have many good routes/choices this way and a bad scale
>> far fewer.
>
> Er, it's more like, dominant 7th chords are musical dissonances
> in classical music, but musical consonances in the blues.
> Though it certainly builds on sensory consonance, it's mostly
> a grammar thing. Think of it as having to do with *chord
> progressions*. If a "dissonance must resolve", the kind of
> dissonance being discussed is musical dissonance.

I think that what Michael is saying has some meaning as well. There is
the cultural level of what is considered "appropriate" for the blues
and classical music and such, but you also have composers like
Stravinsky that use sensory dissonances in a musically consonant way
and vice versa. When the Rite of Spring came out, the whole thing was
considered musically dissonant, but the concept of using dissonances
in a consonant way still stands.

//
> The only scales I know of like that are harmonic series
> segments up to the 19th harmonic (with 21 we get 21/16, which
> is discordant because of its proximity to 4/3). Try
> for instance 8 9 10 11 12 13 14 15 16.

> Well, I'll claim the gap has been identified. It's due to
> the fact that the brain's virtual pitch processor has not
> been triggered as strongly by the stretched timbre/scale
> example as it has by the harmonic timbre/scale example,
> because the brain's virtual pitch processor is tuned (by
> evolution and/or early learning as infants) to pick out
> harmonic spectra specifically (since that's what human voices
> have). So JI is built into the brain -- there's no going
> beyond it as far as raw sensory consonance is concerned,
> except perhaps in a few isolated cases known as "magic chords"
> (and it's debatable).

It's hard to understand what you mean by raw sensory consonance in
this case -- I prefer the sound of a slightly sharp major third on a
piano to one that is a perfect 5/4. Perhaps the interval between the
just major third and the stretched 5th harmonic is discordant enough
to outweigh the concordance of the 5/4 -- I don't know.

I think it is noteworthy here that a 5/4 that is slightly sharp has a
slightly sadder quality to it -- 12tet's major third strikes me that
way. That quality is especially brought out when a major 7 or #11 is
brought into a major chord. The fact that said interval isn't quite
consonant carries its own emotional meaning.

-Mike

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:

>    Interesting...so it's almost like the brain is tuned to pick
> up music as sections of whole-number-multiple harmonics (like
> those in human voice), then (almost as if to help it quickly
> deduce who a person is hearing speak IE their relative or just
> a random person)?

More like, you don't want to hear 10 people talking when only
one person is (except at certain recreational times :).

Spoken language also uses changes in the relative amplitudes
of the harmonics of speech to encode different vowels. So
yes, differentiating speech sounds is definitely something
we're built to do, and something that would be aided by the
use of 'harmonic templates" in the brain.

-Carl

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
> Assuming the 0th harmonic is the root note...
>
>     The harmonic scale notes
> 5,6,7,8,9,10(octave),11,12,13,15,17,19,20(second octave) seem
> to sound both in-tune and in mood. 
>     However both harmonics number 16 and 18 sound grossly out
> of tune.  Any clue why?
//
>   According to the theory that the human ear is trained from
> birth to focus on whole-multiple harmonic spectra...how can
> you explain that certain whole-tone multiple overtones seem
> to sound "out of tune"?

Well, I can't reproduce that effect. I can just mash
15-20 and it sounds fine. What pitches would 16 and 18
be at? Are they still objectionable if you put them in
and take 17 and 19 out?

-Carl

2008/11/3 Carl Lumma <carl@...>:
> --- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
>
>> Interesting...so it's almost like the brain is tuned to pick
>> up music as sections of whole-number-multiple harmonics (like
>> those in human voice), then (almost as if to help it quickly
>> deduce who a person is hearing speak IE their relative or just
>> a random person)?
>
> More like, you don't want to hear 10 people talking when only
> one person is (except at certain recreational times :).

I think the most difficult task is when 10 people are talking and you
only want to listen to one. Knowing that each voice is a harmonic
timbre must surely help. And it's easy to speculate on how a feel for
harmony and counterpoint can grow out of this.

Graham

One last thing I forgot to throw in:

On Sun, Nov 2, 2008 at 5:57 PM, Carl Lumma <carl@...> wrote:
> The only scales I know of like that are harmonic series
> segments up to the 19th harmonic (with 21 we get 21/16, which
> is discordant because of its proximity to 4/3). Try
> for instance 8 9 10 11 12 13 14 15 16.

Don't forget about that pitch discrimination variable in the harmonic
entropy curves. This is why I very strongly oppose labeling a sound
absolutely concordant vs discordant -- while 21/16 to an untrained ear
sounds like a screwed up flat version of a perfect fourth, after
enough experimenting and soaking into the sound it starts to become
much more consonant sounding and take on its own character.

The same applies even more to 27/20, which is 4/3*81/80. You can find
that interval by just overlaying 9/8 on top of 6/5, and the resulting
triad has a different quality than just hearing 6/5 with 4/3 overlaid
on top of 1/1. Taking that minor third out and just leaving 27/20
still has its own character vs 4/3, and although the first time it
sounds like it's just a screwed up sharp version of 4/3, eventually
you start to hear that sharpness as having its own emotional character
- a bit exciting and at the same time sad for me.

Labeling an interval as fundamentally being a discordant version of
another interval is a psychological operation -- not a psychoacoustic
one. Psychoacoustically, it is possible to hear two JI-tuned intervals
that are in proximity to one another as being independent of one
another -- although the sound of 4/3 will still "color" 27/20 and
21/16, those intervals will stop sounding "wrong" after enough
listening.

Just my experience here.
-Mike

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> Carl wrote:
> > One could argue that the sensory consonance of otonal chords
> > in JI actually increases as you add higher and higher
> > harmonics -- if the amplitude of each successive note
> > decreases.
>
> This statement is equal to the hypothesis that a sawtooth wave
> is less dissonant than a sine wave -- under what definition of
> consonance and dissonance is this true?

Yep, that's about right. Sawtooth doesn't decrease as rapidly
as I had in mind (1/f vs. 1/f^2), causing it to tend to be a bit
'harsh'. But the idea is, consonance isn't just the absence of
dissonance, but also the presence of something. I sometimes find
it hard to nail the pitch of a sine accurately, whereas one would
never have this problem with a sawtooth. Back to the chord
example, if I have 6:7, the root is not as sure as if I have
6:7:8 or 6:7:9. etc. etc.

-Carl

Hi Petr,

> The 0th harmonic is 0Hz which in most cases represents
> silence. The 1st harmonic is the fundamental.

Actually, different conventions are used here. There was a
thread about this on MMM recently. Several people do it this
way, but several others take "1st harmonic" to mean 2:1.

-Carl

Hi Mike,

> >> Meanwhile it sounds like "musical consonance" is more like
> >> saying "how do I use the sweet and sour spots in the scales to
> >> promote a sense of contrast and emotion"...IE a good scale will
> >> likely have many good routes/choices this way and a bad scale
> >> far fewer.
> >
> > Er, it's more like, dominant 7th chords are musical dissonances
> > in classical music, but musical consonances in the blues.
> > Though it certainly builds on sensory consonance, it's mostly
> > a grammar thing. Think of it as having to do with *chord
> > progressions*. If a "dissonance must resolve", the kind of
> > dissonance being discussed is musical dissonance.
>
> I think that what Michael is saying has some meaning as well.
> There is the cultural level of what is considered "appropriate"
> for the blues and classical music and such, but you also have
> composers like Stravinsky that use sensory dissonances in a
> musically consonant way and vice versa. When the Rite of Spring
> came out, the whole thing was considered musically dissonant,
> but the concept of using dissonances in a consonant way still
> stands.

I didn't get that out of Michael's paragraph above... I was
just trying to steer things away from scales.

> It's hard to understand what you mean by raw sensory consonance
> in this case -- I prefer the sound of a slightly sharp major
> third on a piano to one that is a perfect 5/4.

You prefer it, or it sounds more consonant? FWIW, I both
prefer and think 5:4 is more consonant on pianos.

> Perhaps the interval between the
> just major third and the stretched 5th harmonic is discordant
> enough to outweigh the concordance of the 5/4 -- I don't know.

I doubt it. The 5th harmonic isn't that stretched on pianos,
especially not relative to the 4th harmonic.

-Carl

> Yep, that's about right. Sawtooth doesn't decrease as rapidly
> as I had in mind (1/f vs. 1/f^2), causing it to tend to be a bit
> 'harsh'. But the idea is, consonance isn't just the absence of
> dissonance, but also the presence of something. I sometimes find
> it hard to nail the pitch of a sine accurately, whereas one would
> never have this problem with a sawtooth. Back to the chord
> example, if I have 6:7, the root is not as sure as if I have
> 6:7:8 or 6:7:9. etc. etc.
>
> -Carl

It's an interesting idea. So you say 2/1 is more consonant than a
unison, and so on... what sorts of intervals are more dissonant than a
unison, and where does the cutoff lie? Is it different for every
person?

Furthermore, what are the qualities you are defining as being
dissonant and consonant here? I am having trouble determining what you
are defining as purely psychoacoustic consonance. What do you mean by
"nail the pitch" -- from an absolute pitch standpoint, or interval
identification? Does that factor into your definition of consonance?

-Mike

>> It's hard to understand what you mean by raw sensory consonance
>> in this case -- I prefer the sound of a slightly sharp major
>> third on a piano to one that is a perfect 5/4.
>
> You prefer it, or it sounds more consonant? FWIW, I both
> prefer and think 5:4 is more consonant on pianos.

I'm not sure, because I'm not sure exactly what sensory consonance is.
That I prefer it is I suppose one way of saying that I tend to find it
more musically consonant because I have a huge database of emotions
tied into a slightly sharp major third (as that's what I've been
exposed to my whole life). Hearing a slightly sharp major third
triggers all of those, and so I like it.

A pure 5/4 (or even more so, a pure 5/1) is a completely different
interval in a lot of ways to me than 12-tet's 5/4. It sounds almost
more like a doubling interval than a chord extension -- sort of like
how an octave is used as a doubling interval, or for some kind of
timbral adjustment. Either way, perhaps 5:4 is more psychoacoustically
concordant, but I prefer the sound of a sharp 5/4 in most contexts
that I am familiar with.

Honestly I just think they're two different intervals -- a pure 5/4
just functions different musically than a slightly sharp one does. I
don't know if that is something that is explored a lot from a tuning
standpoint, but that's just what I notice in my experiments and
compositions -- they are just different. To be perfectly honest, I
think that a slightly sharp 5/4 often carries more "emotional
information" than a pure 5/4 does.

>> Perhaps the interval between the
>> just major third and the stretched 5th harmonic is discordant
>> enough to outweigh the concordance of the 5/4 -- I don't know.
>
> I doubt it. The 5th harmonic isn't that stretched on pianos,
> especially not relative to the 4th harmonic.

Perhaps it's a cultural thing. Either way, I'm still not sure what the
sound of raw sensory consonance is at this point. Preferences are
clearly in the realm of psychology, and musical context is its own
thing, so what is sensory consonance? Lack of beating?

A slightly sharp octave when played with two sine waves will sound
"better" to me than a normal octave. Does that mean it's more
psychoacoustically consonant, or that I am culturally biased, or
either?

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > Yep, that's about right. Sawtooth doesn't decrease as rapidly
> > as I had in mind (1/f vs. 1/f^2), causing it to tend to be a bit
> > 'harsh'. But the idea is, consonance isn't just the absence of
> > dissonance, but also the presence of something. I sometimes find
> > it hard to nail the pitch of a sine accurately, whereas one would
> > never have this problem with a sawtooth. Back to the chord
> > example, if I have 6:7, the root is not as sure as if I have
> > 6:7:8 or 6:7:9. etc. etc.
> >
> > -Carl
>
> It's an interesting idea. So you say 2/1 is more consonant than
> a unison, and so on...

I just said the argument could be made, I didn't say I believed
it. The important point I was trying to make is that the
dissonance of utonal chords increases far more quickly with
harmonic extension than does the dissonance of otonal chords.

> Furthermore, what are the qualities you are defining as being
> dissonant and consonant here? I am having trouble determining
> what you are defining as purely psychoacoustic consonance.

Generally it is broken down into two components: one describing
the clarity of the spectrum reaching the brain, and the other
describing the strength of the virtual pitch produced there.

> What do you mean by "nail the pitch" -- from an absolute pitch
> standpoint // ? Does that factor into your definition of
> consonance?

Yes and yes. If I make you 'sing the pitch you hear' and
test you with both sines and natural timbers of varying
durations while recording your responses, I'll bet you a
banana split you do better with the natural timbres. In
fact I would guess this experiment has been performed many
times...

-Carl

>> What do you mean by "nail the pitch" -- from an absolute pitch
>> standpoint // ? Does that factor into your definition of
>> consonance?
>
> Yes and yes. If I make you 'sing the pitch you hear' and
> test you with both sines and natural timbers of varying
> durations while recording your responses, I'll bet you a
> banana split you do better with the natural timbres. In
> fact I would guess this experiment has been performed many
> times...
>
> -Carl

Indeed I would. This applies x10000 in the bass register. To be
honest, I think we should use a completely different word for
"consonance" if that's what you mean -- up until you clarified up
there I really had no idea that that was what you meant by that.
Consonance is usually meant musically to mean something completely
different. I always liked concordance myself.

//
> Generally it is broken down into two components: one describing
> the clarity of the spectrum reaching the brain, and the other
> describing the strength of the virtual pitch produced there.

This assumes that the most concordant signal is a perfect harmonic
spectrum -- how does this reconcile with the fact that a stretched
octave played with sines will sound more concordant than a
non-stretched one? Is there some kind of mathematically transformed
harmonic series that sounds more concordant than a natural one,
analogous to a stretched octave? Perhaps the stretching over the whole
series wouldn't be linear with respect to the octave.

Out of curiosity, do you have AP?

-Mike

On Mon, Nov 3, 2008 at 2:41 AM, Carl Lumma <carl@...> wrote:
> Hi Petr,
>
>> The 0th harmonic is 0Hz which in most cases represents
>> silence. The 1st harmonic is the fundamental.
>
> Actually, different conventions are used here. There was a
> thread about this on MMM recently. Several people do it this
> way, but several others take "1st harmonic" to mean 2:1.
>
> -Carl

I've never heard harmonic to mean that. I've heard the "first
overtone" referred to as 2/1 and the second overtone as 3/1 and such,
but I've never heard a harmonic series referred to as excluding 1/1.

-Mike

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> >> It's hard to understand what you mean by raw sensory consonance
> >> in this case -- I prefer the sound of a slightly sharp major
> >> third on a piano to one that is a perfect 5/4.
> >
> > You prefer it, or it sounds more consonant? FWIW, I both
> > prefer and think 5:4 is more consonant on pianos.
>
> I'm not sure, because I'm not sure exactly what sensory
> consonance is. That I prefer it is I suppose one way of
> saying that I tend to find it more musically consonant
> because I have a huge database of emotions tied into a
> slightly sharp major third (as that's what I've been exposed
> to my whole life). Hearing a slightly sharp major third
> triggers all of those, and so I like it.

A possibly-related anecdote: When I first heard piano in
7-limit JI, I thought it sounded sour. It took a little
while to get over it, and I chalk it up to a lifetime of
expectation that a piano has a certain sound. Once I
learned to hear the timbre in new ways, I found it sounded
more consonant in 7-limit JI.

> Either way, perhaps 5:4 is more psychoacoustically
> concordant, but I prefer the sound of a sharp 5/4 in most
> contexts that I am familiar with.

Sure.

> Honestly I just think they're two different intervals -- a pure
> 5/4 just functions different musically than a slightly sharp one
> does.

Sure it does. But they are similar in the scheme of things.
And I can take classical music and retune it in 5-limit JI
and retain the meaning of the music (as long as I use the right
adaptive tuning scheme for the melodic intervals).

> To be perfectly honest, I
> think that a slightly sharp 5/4 often carries more "emotional
> information" than a pure 5/4 does.

Maybe it does for you.

> I'm still not sure what the
> sound of raw sensory consonance is at this point.

Maybe you're not listening to intervals outside of musical
contexts, or on instruments other than what you're familiar
with in music.

> So what is sensory consonance? Lack of beating?

Adjectives like "smoothness", "rootedness", "calmness",
"richness" are often used. The pitch-matching test I
proposed earlier is a try at measuring it objectively
(though if you instruct people to rank chords by those
adjectives and 20 people give nearly identical rankings,
you know there's something objective going on). It
can be adapted to chords by asking people to sing the
root of the chord.

> A slightly sharp octave when played with two sine waves
> will sound "better" to me than a normal octave. Does that
> mean it's more psychoacoustically consonant, or that I am
> culturally biased, or either?

People are different. Some like leslie on their B3, others
don't. I don't, for example.

-Carl

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > Yes and yes. If I make you 'sing the pitch you hear' and
> > test you with both sines and natural timbers of varying
> > durations while recording your responses, I'll bet you a
> > banana split you do better with the natural timbres. In
> > fact I would guess this experiment has been performed many
> > times...
>
> Indeed I would. This applies x10000 in the bass register. To be
> honest, I think we should use a completely different word for
> "consonance" if that's what you mean -- up until you clarified up
> there I really had no idea that that was what you meant by that.
> Consonance is usually meant musically to mean something completely
> different. I always liked concordance myself.

Well that's why I've been saying "sensory consonance", which
is how the term is distinguished in most psychoacoustics
literature. But I also prefer concordance, as stated in a
recent post addressed to Michael.

> > Generally it is broken down into two components: one describing
> > the clarity of the spectrum reaching the brain, and the other
> > describing the strength of the virtual pitch produced there.
>
> This assumes that the most concordant signal is a perfect
> harmonic spectrum -- how does this reconcile with the fact that
> a stretched octave played with sines will sound more concordant
> than a non-stretched one?

That's an artifact of using sines. Early on, researchers assumed
they were getting at the truth of things by using sines, since
obviously people would just be avoiding beats otherwise. Wrong
approach! Because the brain uses the information in the partials
to place the octave. Not the partial near the octave! You can
do it with odd harmonics only and the pitch shift still goes away.

> Is there some kind of mathematically transformed
> harmonic series that sounds more concordant than a natural one,
> analogous to a stretched octave?

Nope.

> Out of curiosity, do you have AP?

Just the faintest hints, which I think is par for most musicians.
The short answer is "no".

-Carl

> I've never heard harmonic to mean that. I've heard the "first
> overtone" referred to as 2/1 and the second overtone as 3/1
> and such, but I've never heard a harmonic series referred to
> as excluding 1/1.
>
> -Mike

It's common in academic texts. 1/1 is f0.

-Carl

The purpose of JI is not the absence of beating. The purpose was to have clearly definable intervals and a completely modular system of building blocks to use as one wishes. The theoretical premise of JI (supposedly) have never been used that way, except possibly with La Monte Young, Mainly because of extended length in which things are held. Yet he does not use simple ratios anyways.

It is absurd to apply any concept of whether someone likes JI or not. It all depends on what someone is trying to do. Visual artist when they use different material, They use it for what it inherently does. One never complains that Pastel does not do what oil does. They use what it does in a way that fits the material. This is true of any scale or construct, one has to listen to it, and i don't mean downloading it and then doing ye ol habits in it without paying attention.

The Plomp test is a waste ( didn't make it past the first chart without experiencing conflicts). You cannot take the culture with the worse ears and test to see what people like. Westerners have been trained not to listen in the name of function. Take it to India and you might be able to tell something.
I have also recently heard the results of modeling for instruments done at MIT. My grade-FAIL. If this what science has to offer, we will lose nothing by placing our attention elsewhere, with ones ear. The last things this art needs is such "authorities" telling us what reality is.

--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

So what does one do ? all music is to be written in one single timbre that fits the defective product in the first place?
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

On Mon, Nov 3, 2008 at 3:23 AM, Carl Lumma <carl@...> wrote:
> --- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>>
>> > Yes and yes. If I make you 'sing the pitch you hear' and
>> > test you with both sines and natural timbers of varying
>> > durations while recording your responses, I'll bet you a
>> > banana split you do better with the natural timbres. In
>> > fact I would guess this experiment has been performed many
>> > times...
>>
>> Indeed I would. This applies x10000 in the bass register. To be
>> honest, I think we should use a completely different word for
>> "consonance" if that's what you mean -- up until you clarified up
>> there I really had no idea that that was what you meant by that.
>> Consonance is usually meant musically to mean something completely
>> different. I always liked concordance myself.
>
> Well that's why I've been saying "sensory consonance", which
> is how the term is distinguished in most psychoacoustics
> literature. But I also prefer concordance, as stated in a
> recent post addressed to Michael.

Is concordance fundamentally a term describing the information content
of the signal (being periodic) or the perceptual phenomenon of a
complex tone sounding as though it were "pitched"?

Also, perceptually, it feels like a completely different phenomenon
when I hear a chord that conveys complex emotions (such as an
augmented major seventh chord) than when I hear the "clarity of pitch"
of a guitar string vs the obfuscated pitch of a bell or something. I
don't hear an C+maj7 chord as sounding like an obfuscated "C" or
something. Put another way: when I hear a 4:5:6:7:8:9:10:11 chord
(assuming equal volume), I can flip my perception of it around to hear
it as either a complex timbre or as a chord. Is this indicative of two
brain processes yielding conflicting results, in the same way that
neural periodicity checks conflict with place information to yield
harmonic entropy? I assume part of the equation will be whether or not
there is a decrease in volume for each successive harmonic.

This ties more into the cognitive aspect of music, but I have interest
in this because I'd like to write a piece for orchestra that sounds
like being outside, for example. When you're outside, you're not
hearing everything as though it's musical. Similarly, when you hear
the sound of a bell, you don't hear it as a chord in the traditional
sense, but you hear it as a complex semi-pitched timbre, devoid of
chordal or musical content in and of itself. When you hear a complex
tone made up of the first 5 harmonics you are likely not perceiving it
as a major chord, but as a sawtooth wave sent through a low pass
filter -- just a timbre, not as a chord. You hear it as sound rather
than music. Similarly it would be interesting to have a piece for
orchestra that sounds more like an acoustic environment than a
concerto. Something that puts your brain in "sound" rather than
"music" mode.

>> > Generally it is broken down into two components: one describing
>> > the clarity of the spectrum reaching the brain, and the other
>> > describing the strength of the virtual pitch produced there.
>>
>> This assumes that the most concordant signal is a perfect
>> harmonic spectrum -- how does this reconcile with the fact that
>> a stretched octave played with sines will sound more concordant
>> than a non-stretched one?
>
> That's an artifact of using sines. Early on, researchers assumed
> they were getting at the truth of things by using sines, since
> obviously people would just be avoiding beats otherwise. Wrong
> approach! Because the brain uses the information in the partials
> to place the octave. Not the partial near the octave! You can
> do it with odd harmonics only and the pitch shift still goes away.

I don't understand what you mean here -- can you explain?

-Mike

> When you hear a complex
> tone made up of the first 5 harmonics you are likely not perceiving it
> as a major chord, but as a sawtooth wave sent through a low pass
> filter -- just a timbre, not as a chord.

To clarify, I meant out of sines here. Similarly, when you hear a
chord on piano that represents 1:2:3:4:5, it doesn't always fuse into
a more complex timbre, but sometimes sounds more like a chord.

-Mike

Carl wrote:

> One could argue that the sensory consonance of otonal chords

> in JI actually increases as you add higher and higher

> harmonics -- if the amplitude of each successive note

> decreases.

---This statement is equal to the hypothesis that a sawtooth wave is less

---dissonant than a sine wave -- under what definition of consonance and

---dissonance is this true?
   Hmm...of course, a saw wave is MORE dissonant (thus making the original statement sound quite odd, at least at first: nothing is more consonant than a single frequency "in unison").   I get the impression, of course, that if you create enough dissonant sounds, they begin to become consonant.  For example, a noise wave becomes so convoluted...it's as if your mind stops trying to tie all of its harmonics to a "root note"...and thus things like snares can be used in harmonic music.  Is this "over the top" situation a large chunk of what "harmonic entropy" is about?

--- On Sun, 11/2/08, Mike Battaglia <battaglia01@...> wrote:
From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Sunday, November 2, 2008, 10:41 PM

Carl wrote:

> One could argue that the sensory consonance of otonal chords

> in JI actually increases as you add higher and higher

> harmonics -- if the amplitude of each successive note

> decreases.

This statement is equal to the hypothesis that a sawtooth wave is less

dissonant than a sine wave -- under what definition of consonance and

dissonance is this true?

-Mike

>      Hmm...so then sensory consonance = contrast with other

> parts IE "resolve" vs. "unresolved" .

-------No, the exact opposite actually. I said resolve/unresolved

had to do with musical consonance. Sensory consonance pertains

to chords in complete and utter isolaton.

    Ah, ok.  So you mean chords in and of themselves so far as consonance (and then all the scales, I suppose, end up being just "possible methods to find more/less consonant chords".  Again, I think of the way Debussy composed around chords.

---The consonance minima of the timbre do NOT change, but the

intervals one gets when playing various chords are not always

obvious just by looking at one mode of the scale.
  Again, this seems to say "it's about the possible intervals (and their consonance levels) in chords that can be formed from the scale, rather than the scale itself, right?

---But throughout the book, he's taking dyadic dissonance curves and making scales directly from them.  This approach is... wrong.
  So his approach does not fully take into account the idea of chords branching on top of each other and fine-tuning the notes to fit the chords?  Ironically, the binaural scale I made was build from tuning triads on top of each other one-by-one...which sounds to me a whole lot like your method.  The other question is...what kind of results have you got from said above method so far as "very chord capable scales"? :-)

***************************************************

Sure. I mentioned Jon Catler recently. The German organist

Hans Andre-Stamm has a CD out called Enharmonic Garden I

believe. Another German (I think) composer, Arnold Dreyblatt,

has a lifetype of work in harmonic series scales. Oh, and

Prent Rodgers of course. Lots of others, too.
   I've heard Prent's work, I will have to check out the others.

>    My real question is...why hasn't some form of this sort

> of thing become widely adopted?

It's one of the deeper mysteries of our time

   READ LOUD AND CLEAR: THE HARMONIC SERIES CAN BE USED AS A VIABLE
HARMONICALLY-CAPABLE SCALE. :-)
***************************************************

-Michael

--- On Sun, 11/2/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Sunday, November 2, 2008, 10:50 PM

--- In tuning@yahoogroups. com, Michael Sheiman <djtrancendance@ ...> wrote:

>

>> Er, no. You can think of sensory consonance something about

>> *chords*, which are presented to a listener after a long period

>> of silence.

>

>      Hmm...so then sensory consonance = contrast with other

> parts IE "resolve" vs. "unresolved" .

-------No, the exact opposite actually. I said resolve/unresolved

had to do with musical consonance. Sensory consonance pertains

to chords in complete and utter isolaton.

>> Sethares derives scales directly from dissonance curves, but

>> the procedure he seems to use isn't valid, unless the only

>> chords you intend to play are dyads up from the tonic. For

>> instance,

>> 9/8 5/4 4/3 3/2 5/3

>> may be the minima for a given timbre, but if I play the chord

>> 9/8 - 4/3 - 5/3

>> I'm getting the intervals 32/27, 5/4, and 40/27, which are

>> not minima.

>

>     Ok, if I am following, the point is as you move a chord to

> different "starting points" along the scale, the minimum points

> change.

The consonance minima of the timbre do NOT change, but the

intervals one gets when playing various chords are not always

obvious just by looking at one mode of the scale.

> In that case, wouldn't the ideal solution be a chain of chords

> that branch off each other (kind of like Debussy's chord-based

> modulations) and some sort of adaptive tuning to build each

> chord to be more in-tune to the root of that chord?

Yes, a chord-based approach is definitely preferable to a

scale-based approach as far as sensory consonance is concerned.

>    And...wouldn' t the C diatonic just-intonation scale fail at

> this task just as badly playing, say, a D triad?

That is the example I'm providing above, yes.

>    I am rather assuming...that the scale is fixed, and the

> optimum solution would be the "best average intervals for all

> chords",

That's the right idea, yes. One way to go about it is to

ask how many tones you want in a scale (let's say 7) and then

start with that equal temperament (in this case 7-ET) and

compute the sensory dissonance using Sethares' formula, of

all 7 notes played together as a chord. Then move each note

of the scale slightly and see whether the total dissonance

goes up or down. One can then use a hill-climbing- type

algorithm to find the ideal scale. That may not be realistic

if you only intend to use triads from the scale, but a similar

process may be applied to the sum of the dissonances of all

triads in the scale.

Bill is a really really smart guy, and I assumed he must have

done something like this, so I went back through his book.

But I can't really find it. On pg. 233, he starts talking

about a very similar process to find scales optimized for

certain pieces of music. But throughout the book, he's taking

dyadic dissonance curves and making scales directly from them.

This approach is... wrong.

>> Try for instance 8 9 10 11 12 13 14 15 16.

>

>     Amazingly, this seems to work quite well: everything sounds

> "in mood" with everything else.

Bonus!

>      It seems I could only squeeze about 7 note or less scales

> (per octave) out of this without too many "critical band effects"

I've done it with 9 notes no problem, but you helps to space

the notes out by octaves.

>       Are there any compositions you could recommend based on

> scales made from these "higher overtones"?

Sure. I mentioned Jon Catler recently. The German organist

Hans Andre-Stamm has a CD out called Enharmonic Garden I

believe. Another German (I think) composer, Arnold Dreyblatt,

has a lifetype of work in harmonic series scales. Oh, and

Prent Rodgers of course. Lots of others, too.

>    My real question is...why hasn't some form of this sort

> of thing become widely adopted?

It's one of the deeper mysteries of our time.

> This is WAY too much fun... :-)

You betcha.

-Carl

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > When you hear a complex
> > tone made up of the first 5 harmonics you are likely not perceiving it
> > as a major chord, but as a sawtooth wave sent through a low pass
> > filter -- just a timbre, not as a chord.
>
> To clarify, I meant out of sines here. Similarly, when you hear a
> chord on piano that represents 1:2:3:4:5, it doesn't always fuse into
> a more complex timbre, but sometimes sounds more like a chord.
>
> -Mike
>

I'll get round to Sethares' simple tunes, but first... I do wish
people would either stop talking about pianos in JI, or decide whether
they mean real pianos tuned (hopefully) by ear or artificially
synthesized ones.

Real piano chords almost always don't fuse, because of the complicated
and differentiated intensity and timbre variations (particularly
during the first few milliseconds) and significantly non-harmonic
behaviour of higher overtones. I think it takes some sort of
consistency among the evolution of overtones for the brain to be happy
assigning them to a 'fused' single note. The great musical thing about
pianos is that different parts of their compass behave quite
differently - which is precisely what prevents 'fusion'.

As for inharmonicity, even the octave a-a' presents some element of
choice - witness Bill Bremmer's discussion of "2:1 vs 4:2 vs 6:3".
This doesn't mean that JI is meaningless on pianos, just that it's
probably going to be only 'just enough', rather than have any degree
of 'locking' or 'fusion'. Piano tones are inherently slightly unstable
and bell-like. When talking about '7-limit JI on piano' you have to be
quite careful whether you mean achieving certain frequency ratios of
fundamentals, or achieving coincidences of upper partials... they will
in general be acoustically different. Tuners need to find the 'right'
amount of stretch for a 7/5 just as they do for an octave.

Of course one can synthesize 'pianos' with any degree of inharmonicity
required, arguably Sethares has taken that to a logical extreme.
But quite a lot of the individual tones of the stretched 'simptun'
example sound wobbly or unrestful - that is, un'just' or dissonant
within themselves.
I expect there is some good mathematical (?) reason why adding sines
together at non-harmonic ratios will produce something that sounds
'wobblier', but I can't put my finger on it immediately apart from the
obvious fact that their waveforms are not even approximately periodic.

Remember Helmholtz's definition of consonance as a 'continuous
tone-sensation' - now even just one of Sethares' tones by itself
doesn't satisfy that. (Neither does the 'attack' of a piano tone...)

It might be interesting to try mixing sines in a
nearly-but-not-quite-harmonic way and see what degree of
non-periodicity can or cannot be detected aurally.
~~~T~~~

-----That's an artifact of using sines. Early on, researchers assumed

-----they were getting at the truth of things by using sines, since
-----
obviously people would just be avoiding beats otherwise. Wrong

-----approach! Because the brain uses the information in the partials

-----to place the octave. Not the partial near the octave! You can

-----do it with odd harmonics only and the pitch shift still goes away.

    Odd, maybe this partly explains why I have found, in making my own non-JI
scales by chaining chords on top of each other the following.  That certain tones an octave or so up will seem to "knock" the tones below them off center, even when tuned by tiny differences such as under 8 cents.  Perhaps this has something to do with the idea tones VERY close together can have very different moods, regardless of their not causing "critical band" effects.

--- On Mon, 11/3/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@lumma.org>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Monday, November 3, 2008, 12:23 AM

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

>

> > Yes and yes. If I make you 'sing the pitch you hear' and

> > test you with both sines and natural timbers of varying

> > durations while recording your responses, I'll bet you a

> > banana split you do better with the natural timbres. In

> > fact I would guess this experiment has been performed many

> > times...

>

> Indeed I would. This applies x10000 in the bass register. To be

> honest, I think we should use a completely different word for

> "consonance" if that's what you mean -- up until you clarified up

> there I really had no idea that that was what you meant by that.

> Consonance is usually meant musically to mean something completely

> different. I always liked concordance myself.

Well that's why I've been saying "sensory consonance", which

is how the term is distinguished in most psychoacoustics

literature. But I also prefer concordance, as stated in a

recent post addressed to Michael.

> > Generally it is broken down into two components: one describing

> > the clarity of the spectrum reaching the brain, and the other

> > describing the strength of the virtual pitch produced there.

>

> This assumes that the most concordant signal is a perfect

> harmonic spectrum -- how does this reconcile with the fact that

> a stretched octave played with sines will sound more concordant

> than a non-stretched one?

That's an artifact of using sines. Early on, researchers assumed

they were getting at the truth of things by using sines, since

obviously people would just be avoiding beats otherwise. Wrong

approach! Because the brain uses the information in the partials

to place the octave. Not the partial near the octave! You can

do it with odd harmonics only and the pitch shift still goes away.

> Is there some kind of mathematically transformed

> harmonic series that sounds more concordant than a natural one,

> analogous to a stretched octave?

Nope.

> Out of curiosity, do you have AP?

Just the faintest hints, which I think is par for most musicians.

The short answer is "no".

-Carl

---The purpose of JI is not the absence of beating. The purpose was to have

clearly definable intervals and a completely modular system of building

blocks to use as one wishes.

  Hmm...again this sounds a lot like "to aid the ability to build chords among the repeating clearly defined intervals in JI".

   I realize JI was not built to "eliminate beating"...however, as a side effect, it seems JI and most semi-popular/popular scales (IE mean-tone) do a good general job of at least regulating beating.  That's not to say any scale that regulates beating is "automatically good", but that it seems to generally be a step in the right direction.

   And I believe; that's no coincidence.  I still consider "regulated beating" a necessary step to make a scale (or series of chords) a majority of people think sound at least decent (IE take 20 people and show them 3 heavily beating scales vs. 3 barely-beating ones in any culture and likely a huge proportion will say "the barely beating ones are better").

-Michael

--- On Mon, 11/3/08, Kraig Grady <kraiggrady@...> wrote:
From: Kraig Grady <kraiggrady@...>
Subject: [tuning] Re: Where's all that hostility - reconciling the paradoxes.
To: tuning@yahoogroups.com
Date: Monday, November 3, 2008, 12:43 AM

The purpose of JI is not the absence of beating. The purpose was to have

clearly definable intervals and a completely modular system of building

blocks to use as one wishes. The theoretical premise of JI (supposedly)

have never been used that way, except possibly with La Monte Young,

Mainly because of extended length in which things are held. Yet he does

not use simple ratios anyways.

It is absurd to apply any concept of whether someone likes JI or

not. It all depends on what someone is trying to do. Visual artist when

they use different material, They use it for what it inherently does.

One never complains that Pastel does not do what oil does. They use what

it does in a way that fits the material. This is true of any scale or

construct, one has to listen to it, and i don't mean downloading it and

then doing ye ol habits in it without paying attention.

The Plomp test is a waste ( didn't make it past the first chart without

experiencing conflicts). You cannot take the culture with the worse ears

and test to see what people like. Westerners have been trained not to

listen in the name of function. Take it to India and you might be able

to tell something.

I have also recently heard the results of modeling for instruments done

at MIT. My grade-FAIL. If this what science has to offer, we will lose

nothing by placing our attention elsewhere, with ones ear. The last

things this art needs is such "authorities" telling us what reality is.

--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_

Mesotonal Music from:

_'''''''_ ^North/Western Hemisphere:

North American Embassy of Anaphoria Island <http://anaphoria. com/>

_'''''''_ ^South/Eastern Hemisphere:

Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

Mike wrote:

> Is concordance fundamentally a term describing the information
> content of the signal (being periodic) or the perceptual
> phenomenon of a complex tone sounding as though it were
> "pitched"?

It has no agreed-upon rigorous definition.

> I don't hear an C+maj7 chord as sounding like an obfuscated "C"
> or something.

Perhaps that's because bells don't generally have C+maj7 partials.
But anyway, the comparison of harmony to timbre isn't perfect.

> Put another way: when I hear a 4:5:6:7:8:9:10:11 chord
> (assuming equal volume), I can flip my perception of it
> around to hear it as either a complex timbre or as a chord.

Yes, me too.

> Is this indicative of two brain processes yielding conflicting
> results,

Perhaps.

> in the same way that neural periodicity checks conflict with
> place information to yield harmonic entropy?

That's not what yields harmonic entropy. Harmonic entropy
measures a degree of fit to a harmonic series, and that's
about it.

> I assume part of the equation will be whether or not
> there is a decrease in volume for each successive harmonic.

I'm not sure it looks at that. I just said it because, in
my example, the upper notes would get smashed by critical
band effects otherwise. If you just have a few partials,
it doesn't matter what their relative amplitudes are, if f0
has no amplitude at all, if even partials are missing, etc.

I've often thought of it as a recursive process taking out
harmonic templates with a greedy approach -- take out the
best-fit first, then repeat. I think it considers the
frequencies of the partials, and measures "fit" by how many
harmonics it's grabbing, how close they are to JI, how
low-numbered they are, etc. Now, it doesn't actually
"measure" these things, it's just that it's easier to be
sure of a fit when dealing with lower-numbered harmonics
(because higher ones are closer together). And it's not
really recursive -- it's happens continuously in huge
populations of neurons, where each neuron is tuned to be
receptive to certain "best frequencies" -- usually only
2-5 of them. e.g. neuron "Alex" fires strongly when it
hears 148-153 Hz, and almost as strongly when it hears
295-308 Hz. Such neurons have been studied in bats (and
I think cats too) using in vivo single-cell recordings.

> I'd like to write a piece for orchestra that sounds
> like being outside, for example.

There's simply no way to communicate abstract ideas like that
in music, unless you're talking about using bird-chip effects
and stuff like that. It's why when you hear the proverbial
rock star talk about what he was trying to get across in his
music, it's always a hoot. Even with lyrics they can't get
it across!

> Something that puts your brain in "sound" rather than
> "music" mode.

Well, that can be done. I think that's a big effect of
ambient music. You either avoid music grammars, or elongate
them to the point where they necessarily take a back seat
to the sound.

If you want to make chords that don't sound like individual
notes, but rather timbres, there are several approaches.
You can compose with sine waves, and mix to mono to eliminate
spatial source-separation cues. You can keep the fundamental
constant throughout a piece, which increases the odds any
changes will be heard as timbral. etc.

> >> how does this reconcile with the fact that
> >> a stretched octave played with sines will sound more concordant
> >> than a non-stretched one?
> >
> > That's an artifact of using sines. Early on, researchers assumed
> > they were getting at the truth of things by using sines, since
> > obviously people would just be avoiding beats otherwise. Wrong
> > approach! Because the brain uses the information in the partials
> > to place the octave. Not the partial near the octave! You can
> > do it with odd harmonics only and the pitch shift still goes away.
>
> I don't understand what you mean here -- can you explain?

Octave equivalence is part of the pitch-perception mechanism.
So you weaken it by using sines, and therefore people don't hit
the octaves. If you use a timbre with limited odd partials,
there's no beating to avoid, but people will still be able to
hit pure octaves then. Similarly, if you repeat Plomp & Levelt
with 3-partial chords with widely spaced partials, I bet you'll
get minima near JI ratios -- even though there's no beating to
avoid. I still have to dig up that Vos paper where he finds
JI minima just trying to reproduce Plomp & Levelt. . .

-Carl

> nothing is more consonant than a single frequency "in unison")

I don't agree, actually. There's not much consonance going
on in a sine wave, though there is a complete lack of dissonance.
I prefer a sweet, pure JI triad. And, as proposed, I bet one
can even measure this with a pitch-matching experiment.

> I get the impression, of course, that if you create enough
> dissonant sounds, they begin to become consonant. For example,
> a noise wave becomes so convoluted...it's as if your mind
> stops trying to tie all of its harmonics to a "root note"...and
> thus things like snares can be used in harmonic music.

They can be used, but they don't contribute to any consonance
in the music.

>Is this "over the top" situation a large chunk of what "harmonic
>entropy" is about?

Nope, harmonic entropy is a very clever way of measuring the
fit of a group of partials to a harmonic series.

-Carl

>>> Hmm...so then sensory consonance = contrast with other
>>> parts IE "resolve" vs. "unresolved" .
>>
>> No, the exact opposite actually. I said resolve/unresolved
>> had to do with musical consonance. Sensory consonance pertains
>> to chords in complete and utter isolaton.
>
>     Ah, ok.  So you mean chords in and of themselves so far as
> consonance

As far as sensory consonance.

> (and then all the scales, I suppose, end up being just
> "possible methods to find more/less consonant chords".

Yes.

> Again, this seems to say "it's about the possible intervals (and
> their consonance levels) in chords that can be formed from the
> scale, rather than the scale itself, right?

Exactly.

>> ---But throughout the book, he's taking dyadic dissonance curves
>> and making scales directly from them.  This approach is... wrong.
>
>   So his approach does not fully take into account the idea of
> chords branching on top of each other and fine-tuning the notes
> to fit the chords?

Uh, no. It doesn't take into account the kinds of things one
is bound to play if you use a scale to make music. If one only
ever plays dyads up from the tonic, the approach makes perfect
sense. Otherwise, it's meaningless.

> Ironically, the binaural scale I made was build from tuning
> triads on top of each other one-by-one...which sounds to me a
> whole lot like your method.  The other question is...what
> kind of results have you got from said above method so far
> as "very chord capable scales"? :-)

Your scale doesn't contain many concordant chords, if that's
your question.

-Carl

Tom wrote:

> Real piano chords almost always don't fuse, because of the
> complicated and differentiated intensity and timbre variations
> (particularl during the first few milliseconds) and
> significantly non-harmonic behaviour of higher overtones.

If you tune a piano in JI, even using a cheap electronic
tuner, I think you'll find the chords fuse pretty well.

> As for inharmonicity, even the octave a-a' presents some element
> of choice - witness Bill Bremmer's discussion of "2:1 vs 4:2 vs
> 6:3". This doesn't mean that JI is meaningless on pianos, just
> that it's probably going to be only 'just enough', rather than
> have any degree of 'locking' or 'fusion'. Piano tones are
> inherently slightly unstable and bell-like.

That's rubbish. It's only true for the extreme ends of the
keyboard. A grand piano in decent shape is plenty harmonic
enough to evoke an absolutely solid sense of f0 and work
absolutely perfectly with just intonation. You'll get a cleaner
sound if you tune by ear, or with an electronic tuner that
considers multiple partials, but you'll get a fine result even
without doing so.

> When talking about '7-limit JI on piano' you have to be
> quite careful whether you mean achieving certain frequency
> ratios of fundamentals, or achieving coincidences of upper
> partials... they will in general be acoustically different.

Not very different. You can't move f0 by switching from
aligning 4:2 to aligning 6:3.

> I expect there is some good mathematical (?)

Biological.

-Carl

> Ironically, the binaural scale I made was build from tuning

> triads on top of each other one-by-one.. .which sounds to me a

> whole lot like your method.  The other question is...what

> kind of results have you got from said above method so far

> as "very chord capable scales"? :-)

----Your scale doesn't contain many concordant chords, if that's

your question.

Hmm...this is confusing me.
     How can you have "non-concordant chords" in a scale where if you play all notes in the scale at once duplicated over 2 octaves they sound concordant? 
    Note I am assuming the instrument used is a sine wave.

    I tried the harmonic series scale and my own with sine waves over multiple octaves, and found a similar feeling of "resolve" in each scale.
-----------------------------------------------
    Or...are your ears telling you the 7 notes simply don't form a 7-note concordant chord...and if so do you have any ideas how come?  Is there a series of "rules of concordance" I need to follow in the same way there are rules to avoid nasty critical band effects?

    I am trying to create a "the scale is a chord and nearly all inversions of that chord sound "smooth" sort of scenario and any help would be much appreciated.

  The reason I want to try and go beyond the harmonic series is that higher harmonics IE 21+ seem to clash a lot on average and I would like a scale/chord schema that can enable an equal number of "clear" notes on any octave.

  Also I agree with your last question to me: in the harmonic scale it seems either you need to use the 16th and 18th OR 17th and 19th harmonic to maintain an "in key" feeling....and you can't use both at the same time without sounding like you are modulating between two different keys.  So it seems the harmonic scale does throw in a few annoying limitations...even though I will agree it is about the best "scale=chord" schema I have run into so far.

-Michael

--- On Mon, 11/3/08, Carl Lumma <carl@lumma.org> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Monday, November 3, 2008, 11:25 AM

>>> Hmm...so then sensory consonance = contrast with other

>>> parts IE "resolve" vs. "unresolved" .

>>

>> No, the exact opposite actually. I said resolve/unresolved

>> had to do with musical consonance. Sensory consonance pertains

>> to chords in complete and utter isolaton.

>

>     Ah, ok.  So you mean chords in and of themselves so far as

> consonance

As far as sensory consonance.

> (and then all the scales, I suppose, end up being just

> "possible methods to find more/less consonant chords".

Yes.

> Again, this seems to say "it's about the possible intervals (and

> their consonance levels) in chords that can be formed from the

> scale, rather than the scale itself, right?

Exactly.

>> ---But throughout the book, he's taking dyadic dissonance curves

>> and making scales directly from them.  This approach is... wrong.

>

>   So his approach does not fully take into account the idea of

> chords branching on top of each other and fine-tuning the notes

> to fit the chords?

Uh, no. It doesn't take into account the kinds of things one

is bound to play if you use a scale to make music. If one only

ever plays dyads up from the tonic, the approach makes perfect

sense. Otherwise, it's meaningless.

> Ironically, the binaural scale I made was build from tuning

> triads on top of each other one-by-one.. .which sounds to me a

> whole lot like your method.  The other question is...what

> kind of results have you got from said above method so far

> as "very chord capable scales"? :-)

Your scale doesn't contain many concordant chords, if that's

your question.

-Carl

Hi Michael,

>> ----Your scale doesn't contain many concordant chords, if that's
>> your question.
>
> Hmm...this is confusing me.
>      How can you have "non-concordant chords" in a scale where
> if you play all notes in the scale at once duplicated over 2
> octaves they sound concordant?

It doesn't sound concordant to me!

>     Note I am assuming the instrument used is a sine wave.

I'd rather not. I'm also not going to assume the stereo
spread you suggest. But I don't think it'd sound terribly
concordant (compared to alternatives) even then.

> Is there a series of "rules of concordance" I need to follow
> in the same way there are rules to avoid nasty critical band
> effects?

If you want a 7-note chord, the most consonant one is
1 2 3 4 5 6 7. Usually on this list the focus is on picking
out triads and tetrads from scales. Then you're looking at
things like meantone and pajara temperament.

>     I am trying to create a "the scale is a chord and nearly
> all inversions of that chord sound "smooth" sort of scenario
> and any help would be much appreciated.

With 7 notes or are you flexible on that? If you'll entertain
6 notes, you could try this for instance:

!
9-limit SSS chord/scale in 31-ET by Gene Smith.
6
!
232.258 !....6
425.806 !...11
619.355 !...16
812.903 !...21
1006.452 !..26
2/1 !.......31
!

>   The reason I want to try and go beyond the harmonic series
> is that higher harmonics IE 21+ seem to clash a lot on average
> and I would like a scale/chord schema that can enable an equal
> number of "clear" notes on any octave.

What about harmonics below 21? Take any 7 of them and then
extend by octaves as needed.

>   Also I agree with your last question to me: in the harmonic
> scale it seems either you need to use the 16th and 18th OR 17th
> and 19th harmonic to maintain an "in key" feeling....and you
> can't use both at the same time without sounding like you are
> modulating between two different keys.

I'm not sure what you're doing, but I can certainly use
all 16 17 18 19 without feeling like I'm modulating anywhere.
I suggested dropping them because I thought maybe you were
getting too much beating or something.

-Carl

>     Note I am assuming the instrument used is a sine wave.

-----I'd rather not. I'm also not going to assume the stereo

-----spread you suggest. But I don't think it'd sound terribly

-----
concordant (compared to alternatives) even then.
What are the alternatives, then?
Or...is the "harmonic scale" the only alternative?

    Note...the scale was built to be bin-aural using harmonics bent by a computer program (in the same way Sethares does).  That being said, if you play it monaurally or with sine waves...it probably won't work.  It presents a similar problem to if you play 10TET with a guitar (very discordant) vs. with one of Sethares' bent-overtone instrument sounds designed to fit with 10TET.

>>>>>Just for grins, I will try it tonight and post audio samples of (with sine wave and binaurallity) vs. (monoaural played with a guitar).  True, you may hate it, but I think there's a good chance it will at least make you think twice about use of binaural scales and digital alignment of overtones. <<<<<
---------------------------------------------------
   If I simply wanted to make a scale that matches with "real world instruments", I'd stick with JI or the harmonic series as they both make the overtones match (harmonic entropy) in general.
    I accept these are two ways to create a virtually ideal situation for non-binaural scales where computers can not be used to align overtones...but what's the point in trying to "solve a problem that, as you seem to state, has already been solved"?

   Yeah...I'm stubborn... :-D
___________________________________________________________________

-------------If you want a 7-note chord, the most consonant one is 1 2 3 4 5 6 7.
     True but because of the octave spread on this, good luck making it sound natural in a production environment: problem is it sounds like an arpeggiator stuck between a very high and low limit (nearly 3 octaves).  I actually like your more like 9-18th harmonic scale because it gets close to sounding "centered" far as octaves are concerned.

--------What about harmonics below 21? Take any 7 of them and then

extend by octaves as needed.

Again, I think you've already found the sweet spot for compositional flexibility within the harmonic series in your previous message to me. :-)

--------I'm not sure what you're doing, but I can certainly use
--------
all 16 17 18 19 without feeling like I'm modulating anywhere.
--------
I suggested dropping them because I thought maybe you were
--------
getting too much beating or something.
     I'm doing the "quasi-suicidal" test of playing all the notes at once and judging the concordance of that. 

    Once thing I really wonder is...what's so terrible about setting up notes binaurally?
Most sound systems nowadays have two speakers and it seems to be a great way to solve critical band issues so you can focus more on mood between notes.

   For the record, I found splitting all odd harmonics in the left channel and all even harmonics in the right for the harmonic scale does great things for concordance and "sense of rest".  Try it yourself if you don't believe me...the difference is HUGE.  Is there any reason why not to at least try the experiment of "which scales can benefit most from being binaurally split"?

-Michael

--- On Mon, 11/3/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Monday, November 3, 2008, 12:24 PM

Hi Michael,

>> ----Your scale doesn't contain many concordant chords, if that's

>> your question.

>

> Hmm...this is confusing me.

>      How can you have "non-concordant chords" in a scale where

> if you play all notes in the scale at once duplicated over 2

> octaves they sound concordant?

It doesn't sound concordant to me!

>     Note I am assuming the instrument used is a sine wave.

I'd rather not. I'm also not going to assume the stereo

spread you suggest. But I don't think it'd sound terribly

concordant (compared to alternatives) even then.

> Is there a series of "rules of concordance" I need to follow

> in the same way there are rules to avoid nasty critical band

> effects?

If you want a 7-note chord, the most consonant one is

1 2 3 4 5 6 7. Usually on this list the focus is on picking

out triads and tetrads from scales. Then you're looking at

things like meantone and pajara temperament.

>     I am trying to create a "the scale is a chord and nearly

> all inversions of that chord sound "smooth" sort of scenario

> and any help would be much appreciated.

With 7 notes or are you flexible on that? If you'll entertain

6 notes, you could try this for instance:

!

9-limit SSS chord/scale in 31-ET by Gene Smith.

6

!

232.258 !....6

425.806 !...11

619.355 !...16

812.903 !...21

1006.452 !..26

2/1 !.......31

!

>   The reason I want to try and go beyond the harmonic series

> is that higher harmonics IE 21+ seem to clash a lot on average

> and I would like a scale/chord schema that can enable an equal

> number of "clear" notes on any octave.

What about harmonics below 21? Take any 7 of them and then

extend by octaves as needed.

>   Also I agree with your last question to me: in the harmonic

> scale it seems either you need to use the 16th and 18th OR 17th

> and 19th harmonic to maintain an "in key" feeling....and you

> can't use both at the same time without sounding like you are

> modulating between two different keys.

I'm not sure what you're doing, but I can certainly use

all 16 17 18 19 without feeling like I'm modulating anywhere.

I suggested dropping them because I thought maybe you were

getting too much beating or something.

-Carl

> What are the alternatives, then?
> Or...is the "harmonic scale" the only alternative?

I gave you another alternative, in the very message to
which you're replying I believe.

>     Note...the scale was built to be bin-aural using harmonics
> bent by a computer program (in the same way Sethares does).
> That being said, if you play it monaurally or with sine waves...
> it probably won't work.  It presents a similar problem to if you
> play 10TET with a guitar (very discordant) vs. with one of
> Sethares' bent-overtone instrument sounds designed to fit
> with 10TET.

I can take any scale and potentially reduce beating by splitting
it over a couple of stereo channels (though I doubt it's as
effective as you seem to think). Therefore I can also compare
scales in mono and get the right relative ranking on them.

>     Once thing I really wonder is...what's so terrible about
> setting up notes binaurally?
> Most sound systems nowadays have two speakers and it seems to
> be a great way to solve critical band issues so you can focus
> more on mood between notes.

How exactly do you think stereo separation solves critical
band issues?

-Carl

So I only have one piano and lately I've been interested
in keeping it playable in all keys.

But back in '99, I tuned my 70-year-old baby grand in
a 7-limit scale using a strobe tuner and recorded this:

http://lumma.org/stuff/justpiano.mp3

That was recorded to minidisc with a cheap mic and exported
to the computer via an analog cable and a SoundBlaster card,
so don't expect wonders. I was trying to improvise a
progression without any wolf intervals, but wasn't entirely
successful.

I also have Pianoteq, a physically-modeled piano synthesizer.
Using a concert grand preset and turning the octave stretch
all the way down, I rendered this 11-limit hexad:

http://lumma.org/stuff/hexad.wav

What does anyone think of the fusion?

-Carl

----I can take any scale and potentially reduce beating by splitting

----it over a couple of stereo channels (though I doubt it's as
----
effective as you seem to think).

How to summarize this...
Of course binaurally splitting any scale can reduce beating.
But, at the same time, my idea is it can

A) Enable an ideal 3 note and 4 note chord
each of which is quite concordant within itself to be combined into a 7-note scale.
    Surely you can think of many 3 and 4-note chords within an octave, although making a 7-note chord within an octave become much trickier.

B) Strategically arrange each chord so the notes in each channel binaurally beat relative to notes in the other channel so the beating sounds pleasant.

----- Therefore I can also compare

----
scales in mono and get the right relative ranking on them.
Well if you want to start on those grounds try this
A) Split my scale into two scales comprised of the 3 and 4 notes in the left and right channel.
B) test the chords individually...do they sound concordant to you now?
C) if you dare, go all the way and test both "chord scales" played together at once in separate channels: do they still sound as concordant as when you played them by themselves, or at least close?

    Note, I have already tried splitting the usual 7-note scale from 12TET into 2 chords (a four and three note) and could not get it sounding significantly better than my scale.  And, when I played those 12TET chords together binaurally, I got binaural beating that threw things amok, unlike the result of my scale which had little such beating so far as I could tell.

   For the record...I realize you suggested using mean-tone and not just the harmonic scale.  However, last time I checked, you can't create a mean-tone 7-note chord within the space of an octave that sounds concordant...and you need to occupy many octaves to make concordance with 7 unique notes at once.  Which is why I am looking for another solution which can break this mold.

-Michael

--- On Mon, 11/3/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Monday, November 3, 2008, 1:03 PM

> What are the alternatives, then?

> Or...is the "harmonic scale" the only alternative?

I gave you another alternative, in the very message to

which you're replying I believe.

>     Note...the scale was built to be bin-aural using harmonics

> bent by a computer program (in the same way Sethares does).

> That being said, if you play it monaurally or with sine waves...

> it probably won't work.  It presents a similar problem to if you

> play 10TET with a guitar (very discordant) vs. with one of

> Sethares' bent-overtone instrument sounds designed to fit

> with 10TET.

I can take any scale and potentially reduce beating by splitting

it over a couple of stereo channels (though I doubt it's as

effective as you seem to think). Therefore I can also compare

scales in mono and get the right relative ranking on them.

>     Once thing I really wonder is...what's so terrible about

> setting up notes binaurally?

> Most sound systems nowadays have two speakers and it seems to

> be a great way to solve critical band issues so you can focus

> more on mood between notes.

How exactly do you think stereo separation solves critical

band issues?

-Carl

Michael wrote:

> A) Enable an ideal 3 note and 4 note chord
> each of which is quite concordant within itself to be combined
> into a 7-note scale.

If it enables it for the pair of chords you picked, it would
enable for any pair of chords, right?

Which pair did you pick, by the way? Ok, looks like a
10:12:15 triad in the right channel. How did you arrive
at the tones in the left channel?

>Which is why I am looking for another solution which can break
>this mold.

You haven't been answering my questions. I asked if it
had to be 7 tones, and if so, why. I also asked if you got
my 6-tone suggestion.

-Carl

----If it enables it for the pair of chords you picked, it would
----enable for any pair of chords, right?
   Right. I am not saying the chords I picked are ideal (if you can come up with better ones, great). 
     The tricky part comes with choosing chords that don't cause odd binaural beating
effects when played together in different channels.  That's why I didn't, say, just use two JI chords one in each channel: I couldn't find a way to make them match without odd binaural beating artifacts. 

---Which pair did you pick, by the way? Ok, looks like a
---10:12:15 triad in the right channel. How did you arrive
---at the tones in the left channel?
   I'm not going to pretend to be a PHD. :-D
   I simply did this all by ear...keeping in the back of my mind a few critical band limitations.
   I guess you could say the 10:12:15 triad was coincidence...and I'm pretty sure it's at least
a few cents off a "pure" 10:12:15.  I found myself adjusting notes slightly, as I said before, to keep undesired binaural beating effects under control.  So I came up with both "per channel" chords by experimentation, there's no formula involved other than "don't let notes get so close they beat excessively".

----You haven't been answering my questions. I asked if it

had to be 7 tones, and if so, why. I also asked if you got

my 6-tone suggestion.

   Sorry, I may have missed a few threads, nothing personal. 
I wanted (at least) 7 tones because
1) If I wanted only 5 tones relatively in tune sounding I could just use 5TET
2) I was hoping for something with at least the melodic flexibility of traditional 7-tone scales
3) In so many other tuning scales, you have to use several octaves to make 6+ note chords that sound resolved and not many of such chords are available. 
4) On a side note, experimentation I have done reveals that anything more than 7 notes will either cause
   A) "crashing" binaural beating effects when split among 2 channels and/or
   B) plain-old exaggerated beating effects within the same channel
   I haven't found a method of binaural separation so far that can prevent beating from becoming too harsh for 8+ note per octave arrangements.
5) Far as mixing and production (practical considerations), having several notes available at all octaves becomes a necessity in my book. 
    For example, even if you have 9 notes available for the lead melody in the harmonic scale you may have only 3-4 for the bass-line since naturally there are more notes per octave at "only" higher overtones.

    And, unless your 6 tone suggestion was either meantone or the harmonic scale, I am afraid I did not get it (it may have been lost within one of the 20+ messages in this winding thread).

-Michael

--- On Mon, 11/3/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Monday, November 3, 2008, 3:13 PM

Michael wrote:

> A) Enable an ideal 3 note and 4 note chord

> each of which is quite concordant within itself to be combined

> into a 7-note scale.

If it enables it for the pair of chords you picked, it would

enable for any pair of chords, right?

Which pair did you pick, by the way? Ok, looks like a

10:12:15 triad in the right channel. How did you arrive

at the tones in the left channel?

>Which is why I am looking for another solution which can break

>this mold.

You haven't been answering my questions. I asked if it

had to be 7 tones, and if so, why. I also asked if you got

my 6-tone suggestion.

-Carl

Michael wrote:
>     And, unless your 6 tone suggestion was either meantone or
> the harmonic scale, I am afraid I did not get it (it may have
> been lost within one of the 20+ messages in this winding thread).

/tuning/topicId_78905.html#78965

-Carl

> For the record...I realize you suggested using mean-tone and not just the
> harmonic scale. However, last time I checked, you can't create a mean-tone
> 7-note chord within the space of an octave that sounds concordant...and you
> need to occupy many octaves to make concordance with 7 unique notes at
> once. Which is why I am looking for another solution which can break this
> mold.

D-E-F-G-A-B-C-D in 12-tet is musically consonant, but it doesn't sound
like one unified pitch if that is the definition of "concordant" that
we're using here.
So is C-D-E-F#-G-A-Bb-C, so are a million other cluster chords that
are perfectly consonant sounding to me.

-Mike

----------D-E-F-G-A-B- C-D in 12-tet is musically consonant, but it doesn't sound
----------
like one unified pitch if that is the definition of "concordant" that
----------
we're using here.
-----------So is C-D-E-F#-G-A- Bb-C, so are a million other cluster chords that
-----------are perfectly consonant sounding to me.
   Man, you've got one flexible ear, then...because it sounds very "clustered" to me rather than resolves.
   I was referring to something that approaches the consonance level of the chord
C E G B...but with 7 notes. 
    One way that may be possible...is to scatter just the right chords from 12TET or JI into 2 channels.   One possible "easy" attempt at such a feat is:

C E G B  (left channel first octave)  D F A  (left channel second octave) C E G B  (left, 3rd)
and                             
D F A (right channel first octave)   C E G B (right channel second octave) D F A (right, 3rd)

   Although, for every combination I've tried within 12TET/meantone/JI or anything else
that centers around near-JI-ratios I have had trouble with nasty binaural beating artifacts
when all notes in both channels are played at once.

  Note: Carl's 6 note example (last link) is pretty close, though still a tad on the "unresolved"
side far as feeling and missing one note to be "melodically competitive" with standard
7-note scales.

-Michael

--- On Mon, 11/3/08, Mike Battaglia <battaglia01@...> wrote:
From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Monday, November 3, 2008, 4:48 PM

> For the record...I realize you suggested using mean-tone and not just the

> harmonic scale. However, last time I checked, you can't create a mean-tone

> 7-note chord within the space of an octave that sounds concordant.. .and you

> need to occupy many octaves to make concordance with 7 unique notes at

> once. Which is why I am looking for another solution which can break this

> mold.

D-E-F-G-A-B- C-D in 12-tet is musically consonant, but it doesn't sound

like one unified pitch if that is the definition of "concordant" that

we're using here.

So is C-D-E-F#-G-A- Bb-C, so are a million other cluster chords that

are perfectly consonant sounding to me.

-Mike

2008/11/4 Michael Sheiman <djtrancendance@...>:

> For the record...I realize you suggested using mean-tone and not just the
> harmonic scale. However, last time I checked, you can't create a mean-tone
> 7-note chord within the space of an octave that sounds concordant...and you
> need to occupy many octaves to make concordance with 7 unique notes at
> once. Which is why I am looking for another solution which can break this
> mold.

The best I know is Pajara. In major (T) and neutral (t) seconds, it's:

t T t T t T t

The neutral seconds could be 3 steps of 24, 4 steps of 31, and so on.
I think around 31-equal is the best tuning because there's a minor
third which follows meantone. It also implies 11-limit intervals,
particularly neutral thirds. Every interval approximates some
11-limit ratio.

I'll try and write it in 24-equal in cents.

C
Dv 150
Ev 350
F 500
G 700
Av 850
Bv 1050
C 1200

There's also Arabic Rast, which could be

T t t T T t t

I forget if that has an interval outside the 11-limit or not.

Graham

So what is the definition of 'fusion'? That is the whole problem.
Obviously reading my remarks BUT assuming a completely different
meaning of the word, they become meaningless and/or rubbish. But you
know (I hope) I don't often deliberately write rubbish.

If you mean 'that thing that JI chords do when they're pretty well in
tune' then the real piano is good up to some slow ~1 Hz beating.
(Can't get the .wav to play yet.)

But if people had read and TRIED TO UNDERSTAND the CONTEXT in which I
said "Real piano chords almost always don't fuse" it would not have
been rubbish. This sentence was directly below, was a REPLY to a
remark which said
"when you hear a chord on piano that represents 1:2:3:4:5, it doesn't
always fuse into a more complex timbre, but sometimes sounds more like
a chord."

So here 'fuse' means 'lose identity as a chord made of several tones
and appear instead as a single tone with complex timbre'.

A little later on I said
"I think it takes some sort of consistency among the evolution of
overtones for the brain to be happy assigning them to a 'fused' single
note."
Here "fused" means the same thing - 'fused SINGLE NOTE'.

And it's obvious that real piano chords don't do that, they sound like
chords not single complex timbres. In 'justpiano' they sound like JI
chords up to a slow beating or evolution of timbre - exactly what I
meant by 'just enough'.

Does anyone then have a reasonable definition or nomenclature for the
different phenomena we're talking about - 1) the loss of identity of
individual tones into a complex timbre and 2) the 'buzz' you get from
a (nearly enough) JI chord when overtones are coincident and the total
waveform is (nearly enough) periodic? ('Locking'?)

Anyway, wasn't there a big debate about pianos not too long ago? I
think it's clear that 19th and early 20th century pianos were
acoustically designed to minimize the consequences of ET and
things-close-to-ET in terms of thirds, in that certain harmonics are
suppressed and/or decay rapidly. Harmoniums (reed organs) and
harpsichords give a much more obvious JI-buzz, - and are technically
easier to tune - but much more difficult to lay one's hands on.
~~~T~~~

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> So I only have one piano and lately I've been interested
> in keeping it playable in all keys.
>
> But back in '99, I tuned my 70-year-old baby grand in
> a 7-limit scale using a strobe tuner and recorded this:
>
> http://lumma.org/stuff/justpiano.mp3
>
> That was recorded to minidisc with a cheap mic and exported
> to the computer via an analog cable and a SoundBlaster card,
> so don't expect wonders. I was trying to improvise a
> progression without any wolf intervals, but wasn't entirely
> successful.
>
> I also have Pianoteq, a physically-modeled piano synthesizer.
> Using a concert grand preset and turning the octave stretch
> all the way down, I rendered this 11-limit hexad:
>
> http://lumma.org/stuff/hexad.wav
>
> What does anyone think of the fusion?
>
> -Carl
>

Hi Tom,

Well first off, perhaps I shouldn't have have used such a
strong word as "rubbish". Secondly,

> So here 'fuse' means 'lose identity as a chord made of several tones
> and appear instead as a single tone with complex timbre'.

That _is_ the definition of fusion I was using.

> And it's obvious that real piano chords don't do that, they sound
> like chords not single complex timbres. In 'justpiano' they sound
> like JI chords up to a slow beating or evolution of timbre -
> exactly what I meant by 'just enough'.

The 4th chord in justpiano.mp3 and the chord in hexad.wav
fuse, to my ear, about as much as any chord in any musical
situation I can think of (barbershop and brass choirs being
some of the most-fusing).

> Does anyone then have a reasonable definition or nomenclature
//
>2) the 'buzz' you get from a (nearly enough) JI chord

That's been called "periodicity buzz" around here. But it
isn't what I was referring to. I think if you have periodicity
buzz, you're probably having a great deal of fusion. But
you can have fusion in the 5-limit, without periodicity buzz,
and indeed there are some triads in justpiano.mp3 that I think
qualify (not all of them though, because several triads were
only approximate under 225/224 in the scale I was using).

> Anyway, wasn't there a big debate about pianos not too long ago?
> I think it's clear that 19th and early 20th century pianos were
> acoustically designed to minimize the consequences of ET and
> things-close-to-ET in terms of thirds,

I think there was such a debate. And to refresh it, can you
name any specific design features that minimize the consequences
of ET?

> in that certain harmonics are
> suppressed and/or decay rapidly.

Evidence for this?

-Carl

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote/asked:
>
> So what is the definition of 'fusion'?
For organs:
http://arxiv.org/abs/physics/0506094v2
http://www.aes.org/e-lib/browse.cfm?elib=6621

Does anybody here knows something
about similar experiments with piano-strings?

bye
A.S.

On Mon, Nov 3, 2008 at 2:19 PM, Carl Lumma <carl@...> wrote:
>> nothing is more consonant than a single frequency "in unison")
>
> I don't agree, actually. There's not much consonance going
> on in a sine wave, though there is a complete lack of dissonance.
> I prefer a sweet, pure JI triad. And, as proposed, I bet one
> can even measure this with a pitch-matching experiment.

I wish we could all agree on the terminology. A sine wave often sounds
more musically consonant than a sawtooth wave because it's pure and
floaty sounding and such. However, if your definition of accordance
(which is apparently the correct term) is the strength of the
phenomenon of a pitch or a tone, then a sawtooth is much more
accordant than a sine wave. On the other hand, by that definition, a
3:4:5 triad might not be as accordant as a sine wave if it doesn't end
up fusing into a single timbre.

It is confusing to figure out what people mean by consonance at this
point -- sometimes people mean their personal preferences as to what
sounds "harsh" vs what doesn't, sometimes people mean what sounds good
in a certain style of music, and sometimes they mean the strength of
pitch produced in the brain. The last definition is one that I'm new
to, and I can see how under that definition a sawtooth is more
accordant than a sine wave. What does that say about the periodicity
mechanism in the brain? A sawtooth is equi-periodic to a sine wave.
And while a sawtooth has a full harmonic spectrum, it still doesn't
explain why a full harmonic spectrum produces a stronger pitch than a
pure tone, or why the periodicity mechanism in the brain somehow has
an easier time processing one vs. the other.

-Mike

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> On Mon, Nov 3, 2008 at 2:19 PM, Carl Lumma <carl@...> wrote:
> >> nothing is more consonant than a single frequency "in unison")
> >
> > I don't agree, actually. There's not much consonance going
> > on in a sine wave, though there is a complete lack of
> > dissonance. I prefer a sweet, pure JI triad. And, as
> > proposed, I bet one can even measure this with a pitch-
> > matching experiment.
>
> I wish we could all agree on the terminology. A sine wave
> often sounds more musically consonant than a sawtooth wave
> because it's pure and floaty sounding and such. However, if
> your definition of accordance (which is apparently the
> correct term)

No, that's just Monzo. The terms proposed by Blackwood
are discordance and concordance. Accordance implies that
concordance and discordance are two ends of the same thing.
But it's long been agreed by people such as Dave Keenan
and myself that they aren't. As illustrated by the example
of the sine wave, which is neither particularly discordant
or concordant.

> It is confusing to figure out what people mean by consonance
> at this point -- sometimes people mean their personal
> preferences as to what sounds "harsh" vs what doesn't,
> sometimes people mean what sounds good in a certain style
> of music, and sometimes they mean the strength of pitch
> produced in the brain.

Concordance (a.k.a. sensory consonance) is a subjective
thing, and that's OK.

Nevertheless, it is a subjective thing on which there is
wide, approximate agreement between subjects.

Pitch sensation in the brain is ONE COMPONENT of concordance;
the other is roughness (a.k.a. critical band effects).

'sounds good in music' is a COMPLETELY SEPARATE thing.

> A sawtooth is equi-periodic to a sine wave.
> And while a sawtooth has a full harmonic spectrum, it still
> doesn't explain why a full harmonic spectrum produces a
> stronger pitch than a pure tone,

Because there is more information present in the signal.

-Carl

----Pitch sensation in the brain is ONE COMPONENT of concordance;

----the other is roughness (a.k.a. critical band effects).
    This is a major terminology point "missing" from my education about micro-tonal music.  When I think "consonance" I think "degree of elimination of roughness". 

    I have to say I probably disagree with a lot of people about "pitch sensation".  While I agree having more overtones makes the location of a tone more obvious, it frustrated me
how few people seem to consider the "inverse" possibility of making instruments with bent overtones to fit scales (Sethares is one of the few I know of who does).  When you take away the "whole number overtones" limitation...in many ways, it gives you the freedom to create scales from sines again and know they will also work with instruments containing overtones needed for "pitch sensation". 
    One obvious pre-existing example of making overtones match a scale is the harmonic series where the overtone schema is also the scale schema.

    Any idea, with all the technology we have to do this (make arbitrary overtone schemas and then scales to match them), why people have not tried more of this?

BTW, I think we can almost all agree (80%+), that having the scale and overtone schemas match (IE using the harmonic series as a scale) sounds very concordant for the most part.  Can we?

-Michael

--- On Tue, 11/4/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@lumma.org>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Tuesday, November 4, 2008, 11:00 AM

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

>

> On Mon, Nov 3, 2008 at 2:19 PM, Carl Lumma <carl@...> wrote:

> >> nothing is more consonant than a single frequency "in unison")

> >

> > I don't agree, actually. There's not much consonance going

> > on in a sine wave, though there is a complete lack of

> > dissonance. I prefer a sweet, pure JI triad. And, as

> > proposed, I bet one can even measure this with a pitch-

> > matching experiment.

>

> I wish we could all agree on the terminology. A sine wave

> often sounds more musically consonant than a sawtooth wave

> because it's pure and floaty sounding and such. However, if

> your definition of accordance (which is apparently the

> correct term)

No, that's just Monzo. The terms proposed by Blackwood

are discordance and concordance. Accordance implies that

concordance and discordance are two ends of the same thing.

But it's long been agreed by people such as Dave Keenan

and myself that they aren't. As illustrated by the example

of the sine wave, which is neither particularly discordant

or concordant.

> It is confusing to figure out what people mean by consonance

> at this point -- sometimes people mean their personal

> preferences as to what sounds "harsh" vs what doesn't,

> sometimes people mean what sounds good in a certain style

> of music, and sometimes they mean the strength of pitch

> produced in the brain.

Concordance (a.k.a. sensory consonance) is a subjective

thing, and that's OK.

Nevertheless, it is a subjective thing on which there is

wide, approximate agreement between subjects.

Pitch sensation in the brain is ONE COMPONENT of concordance;

the other is roughness (a.k.a. critical band effects).

'sounds good in music' is a COMPLETELY SEPARATE thing.

> A sawtooth is equi-periodic to a sine wave.

> And while a sawtooth has a full harmonic spectrum, it still

> doesn't explain why a full harmonic spectrum produces a

> stronger pitch than a pure tone,

Because there is more information present in the signal.

-Carl

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
>
>>Pitch sensation in the brain is ONE COMPONENT of concordance;
>>the other is roughness (a.k.a. critical band effects).
>
>     This is a major terminology point "missing" from my education
> about micro-tonal music.  When I think "consonance" I think
> "degree of elimination of roughness".

Right! And you're in good company. The history of
psychoacoustics since the 19th century tells the story of
two competing theories -- "place" (roughness) and
"periodicity" (virtual pitch), with the place people
(Plomp Levelt et al) mostly winning until the 1980s, when
it started to become clear that BOTH theories are right.

Now we can just argue about which is more important for
music. And I'll argue that periodicity is.

> it frustrated me how few people seem to consider the
> "inverse" possibility of making instruments with bent
> overtones to fit scales

With 12-ET being an obvious candidate. I love the
beatless sound of tonewheel organs, for example.

>     Any idea, with all the technology we have to do this
> (make arbitrary overtone schemas and then scales to match
> them), why people have not tried more of this?

I'm going to say stupidity.

> BTW, I think we can almost all agree (80%+), that having
> the scale and overtone schemas match (IE using the harmonic
> series as a scale) sounds very concordant for the most part.
> Can we?

Not really, no. It works under two important conditions:

* That ALL the intervals of the scale are matched to the
overtone structure.

* That the overtone schema isn't too far from a harmonic
series.

-Carl

I feel like we are all using the same words to refer to different
things, and it is extremely confusing to carry on a conversation this
way. Since there seems to be no agreed-upon definition for some of
these words, then in order to provide some kind of uniform naming
convention, I propose the following definitions:

Musical consonance is something that is relative to each person
and has to do with how much "sense" you can make out of a chord. A
bunch of random notes in 24-tet might not sound like it makes any
sense to some observer, and so that'd be heard as dissonant for that
observer at this point in time. Maybe another observer hears it as
being perfectly coherent -- the "Rite of Spring" effect, if you will.
The Rite of Spring was heard as being completely disordered and
chaotic back when it first premiered, but to my modern ears I hear
consonances in that piece I had not known existed previously.
Besides the timbre that a chord is played on, what chords are
played before and after a certain chord can guide a listener to hear a
chord they would otherwise hear as "dissonant" as being "consonant" --
this is another way of saying that the ear can be "guided" to make
sense out of a chord that might be harder to digest immediately. I
don't know how or if this relates to Harmonic Entropy, but it is an
observation of mine nonetheless.

Then we have the "mood" of a scale or chord. I often hear people
saying things like that Ionian mode is "consonant" and that Phrygian
mode is "dissonant." Under the above definition, Phrygian mode can be
heard as being consonant, but it sounds rather "dark", "sad",
whatever. I propose that the "mood" of a scale, mode, or chord not be
tied in with evaluations of its sonance. If a listener is unable to
make any sense out of Phrygian mode and hears it as being completely
noisy and clangy, then that scale would sound "dissonant" to them.

Then we have what Carl termed "musical consonance", which is
whether or not a certain sound is "appropriate" in a certain gound of
music. As musical genres have the envelope pushed constantly, these
"rules" tend to be short-lived and broken rather quickly, so this I
think is a different thing than the phenomenon I called "sonance"
above.

And it seems like concordance is related, as you put it, to the
"strength of the virtual pitch" produced by a sound, so most chords
will not be perfectly concordant -- an augmented chord, for example,
will not. A sawtooth wave will sound more concordant than a sine wave
played at the same pitch, and I'd also say that a sine wave played in
the mid register will be more concordant than a sine wave played in
the bass register or extreme treble register (around 10,000 Hz or so),
as most people have an extremely hard time placing those as "pitches"
in a musical context.

The names we use for these things I don't really care about -- I
just want to point out that there are at least 4 distinct phenomena
that we've been lumping into two different words. The question: Are
the phenomena that I have labeled "accordance" and "sonance" above
really two sides of the same thing? Because if so, then the sounds
played before and after any one sound would affect its perception of
accordance, and repeated listenings would push a listener to hear a
discordant sound as being more concordant over time, perhaps
reflecting a gradual increase in the free variable in the HE equation
(or perhaps not, but the observation stands nonetheless). As it stands
now, I have never seen any parameter in HE that reflects how familiar
the listener is with a certain dyad (or chord), or how the accordance
of a dyad changes when surrounded with other dyads. If we really want
to lump what I have termed sonance in as being a certain type of
accordance, then those things should be taken into account, as they
certainly exist.

-Mike

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> I feel like we are all using the same words to refer to different
> things, and it is extremely confusing to carry on a conversation
> this way. Since there seems to be no agreed-upon definition for
> some of these words,

Speak for yourself, white man. I'm using the terms consistently,
in a manner generally consistent with psychoacoustics and
microtonal literature, and in a manner which was the consensus
of the active posters on this list in the 1998-2004 timeframe.

> If we really want
> to lump what I have termed sonance

You termed? That's funny, because Joe Monzo coined the same
term years ago and put it in his encyclopedia despite the fact
he was the only one who ever used it.

-Carl

>> Is concordance fundamentally a term describing the information
>> content of the signal (being periodic) or the perceptual
>> phenomenon of a complex tone sounding as though it were
>> "pitched"?
>
> It has no agreed-upon rigorous definition.

but then

>> I feel like we are all using the same words to refer to different
>> things, and it is extremely confusing to carry on a conversation
>> this way. Since there seems to be no agreed-upon definition for
>> some of these words,
>
> Speak for yourself, white man. I'm using the terms consistently,
> in a manner generally consistent with psychoacoustics and
> microtonal literature, and in a manner which was the consensus
> of the active posters on this list in the 1998-2004 timeframe.

This isn't Trivial Pursuit. The point was to communicate and have a
discussion. If you're the only one who knows what you're trying to
say, then we aren't having any discussion at all. This applies double
if you're using terms that aren't rigorously defined and if you resist
attempts to clarify as to what you're talking about.

>> If we really want
>> to lump what I have termed sonance
>
> You termed? That's funny, because Joe Monzo coined the same
> term years ago and put it in his encyclopedia despite the fact
> he was the only one who ever used it.
>
> -Carl

Joe Monzo's definition of sonance is not the same definition that I
used above. But yes, as your infinitely brilliant (and quick to
criticize) mind has realized, I did cop the name from Joe Monzo. I
never pretended to invent the name - I actually think I said I don't
care what names we use.

This is blindingly obvious, but as the subject of discussion -
accordance - isn't rigorously defined in psychoacoustics literature,
it is probably a good idea to agree on a definition before we try to
converse. Sadly, as the only point of conversing with you seems to be
to provoke some kind of argument as to who is more established within
the tuning community, efforts towards this direction might be
ultimately futile.

The real point of the post above was to point out that if what I
called "consonance" up there is really a special type of "accordance,"
then priming and other temporal effects have to be taken into account.

-Mike

Mike wrote:

> >> Is concordance fundamentally a term describing the information
> >> content of the signal (being periodic) or the perceptual
> >> phenomenon of a complex tone sounding as though it were
> >> "pitched"?
> >
> > It has no agreed-upon rigorous definition.
>
> but then
>
> >> I feel like we are all using the same words to refer to different
> >> things, and it is extremely confusing to carry on a conversation
> >> this way. Since there seems to be no agreed-upon definition for
> >> some of these words,
> >
> > Speak for yourself, white man. I'm using the terms consistently,
> > in a manner generally consistent with psychoacoustics and
> > microtonal literature, and in a manner which was the consensus
> > of the active posters on this list in the 1998-2004 timeframe.
>
> This isn't Trivial Pursuit. The point was to communicate and have a
> discussion. If you're the only one who knows what you're trying to
> say, then we aren't having any discussion at all. This applies
> double if you're using terms that aren't rigorously defined and
> if you resist attempts to clarify as to what you're talking about.

Right, maybe I shouldn't have said "rigorously defined".
If you read the text I was responding to, you were asking
about, like, is it defined in terms of the audio signal.
Well, it's not. It's a subjective perception that many
people agree on.

> This is blindingly obvious, but as the subject of discussion -
> accordance - isn't rigorously defined in psychoacoustics
> literature, it is probably a good idea to agree on a definition
> before we try to converse. Sadly, as the only point of conversing
> with you seems to be to provoke some kind of argument as to who
> is more established within the tuning community, efforts towards
> this direction might be ultimately futile.

I don't really care about the terminology at all, only
the concepts. They aren't that hard and I think you must
be grokking them by now.

> The real point of the post above was to point out that if what
> I called "consonance" up there is really a special type of
> "accordance," then priming and other temporal effects have to
> be taken into account.

What do you want me to say? The xxxcordance words were brought
in precisely to take priming out of the picture. If you want
to maximize confusion, go ahead and use them the exact opposite
purpose.

-Carl

> I don't really care about the terminology at all, only
> the concepts. They aren't that hard and I think you must
> be grokking them by now.

It's unclear to me what term you are using to denote which concept.
There are four distinct phenomena that we've mentioned:

1) the ability of an observer to make sense of a chord
2) the mood of a chord or scale
3) the strength of a pitch produced in the brain when a sound is heard, and
4) the appropriateness of a chord or scale to a certain type of music.

So far, the term "consonance" has been thrown around at different
times to mean all of these.

I proposed above that the "sonance" terms refer to the first
phenomenon and to keep discussions of "mood" separate. It seems like
you were saying that the strength of a pitch produced in the brain is
what "concordance" is. You also referred to "musical consonance" as
the appropriateness of a scale or chord in a certain genre of music,
such as how one interval might be consonant in the blues but dissonant
in Classical-era music, but I think that's a different phenomenon from
the first thing, which is how I hear consonance being discussed from a
musical standpoint.

What names would you propose for each of these four things? So far,
we've called them all "consonance" with the term "concordance" being
thrown around to sometimes mean the strength of a pitch and sometimes
to mean the coherence of a chord (with the implicit assumption that
all observers are equal).

> What do you want me to say? The xxxcordance words were brought
> in precisely to take priming out of the picture. If you want
> to maximize confusion, go ahead and use them the exact opposite
> purpose.

Well, it seemed like you were saying that phenomenon 1) and phenomenon
4) were really two sides of the same coin. After all, if we had
triadic harmonic entropy, wouldn't we be using it to model both 1) and
4)? But if they really ARE two sides of the same coin, then priming
effects and all of the things that apply to chords that are placed in
time would therefore carry over into the other domain as well.

But who cares about priming? What I'm really after is the effect
whereby someone listening to a chord might hear it as being a bunch of
clangy noise the first time, but after repeated listens starts to get
the "feeling" of the chord. It is reasonable to think that it might
correspond to some kind of "strengthening" of the way the brain
processes periodicity - but who knows? Either way, it exists. So let's
sum up from a to b:

1) Harmonies that sound "incoherent" under phenomenon 1) above will
eventually start to sound "coherent, yet complex" under repeated
listens.
2) Thus, the perception of harmony is not equal for every observer. A
chord might be perfectly coherent to one observer and incomprehensible
mush to another.
3) If what I've called the "coherence" of a chord is actually the
"con/discordance" of a chord, and that the "con/discordance" of a
chord is represented mainly by the amount of entropy in the
information going to the periodicity mechanism in the brain,
then:
4) "Discordant" chords will sound more "concordant" over time to some observer.
5) If real-life "discordance" or "concordance" truly is the output of
the harmonic entropy function, then the real-life harmonic entropy
function - how well the brain can "place" an interval - takes somehow
as input how "familiar" it is with an interval. The brain will less
confused by intervals that it has heard before, etc.

Is there any problem with that reasoning? If harmonic entropy solely
describes the information content of a signal, and if accordance
solely describes a perceptual attribute, then the theory around here
is that harmonic entropy causes accordance with no other variables
involved, correct? But observationally this doesn't apply to harmony -
that familiarity variable is in there, and I don't see how the two can
be rigorously and reasonably separated.

The information content of the input signal does not alone determine
the observer's ability to process it.

-Mike

    Consonance, concordance, sonance, musical vs sensory consonance, what JI is really made for or good for....  We could pointlessly fight over these terms and what they mean and things like "is JI the ultimate mathematics for tuning" for ages.

  But, was not the point in the first place to produce scales, be it from chords or otherwise, that are useful to musicians and listeners alike rather than prove each other right or wrong?

   Carl is an expert musical historian, that seems obvious and just about everything I've WIKI'd against his word has turned out to match his word.  But the title of this group appears to be "tuning" not "the history of tuning", so would not it be more useful if we all stuck to ideas which actually help create and/or use good scales?

  Also, granted, Carl knows a lot about this latter topic but, for sure, someone in this group likely has or will discover something is possible that Carl thought was not at some point in time.  So why the bitterness?
---------------------------------------------------
   Also, back to a comment from a previous post (paraphrased) if 19 of 20 people think a various scale sounds better, regardless of history, we are likely onto something.  And, even if it takes several tries to accomplish such a feat, aren't these the kind of discoveries a group like this is hoping for?

-Michael

--- On Tue, 11/4/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Tuesday, November 4, 2008, 5:31 PM

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

>

> I feel like we are all using the same words to refer to different

> things, and it is extremely confusing to carry on a conversation

> this way. Since there seems to be no agreed-upon definition for

> some of these words,

Speak for yourself, white man. I'm using the terms consistently,

in a manner generally consistent with psychoacoustics and

microtonal literature, and in a manner which was the consensus

of the active posters on this list in the 1998-2004 timeframe.

> If we really want

> to lump what I have termed sonance

You termed? That's funny, because Joe Monzo coined the same

term years ago and put it in his encyclopedia despite the fact

he was the only one who ever used it.

-Carl

----With 12-ET being an obvious candidate. I love the
----beatless sound of tonewheel organs, for example.
    This is one thing I simply don't understand is possible or, more importantly, can be elaborated on.
    I have found the 12TET notes a, a#, and b when played simultaneously, sound rough, even with 12TET-aligned overtones or even just pure sine waves. 
    And even the usual seven note scales, to me, with all notes played at once sound rough...even with pure sine waves.
    Granted though, the alignment of overtones, more like bin-aural splitting of alternative notes, both are definite keys to improving the "smoothness" of a scale...and I think both deserve lots of experimentation.

  About the closest I gave gotten to a scale
based on 12TET that sounds smooth enough for my ears is

Left Channel     Right Channel
C                     A#
C#                   D#
F                     G                    
G#                                         (first
octave)
                       C
A#                   C#
D#                   F
G                    G#                   (second octave)

C                                          

   And I assume aligning overtones of instruments to 12TET
would make it even smoother.  I am interested also to know if there is a theory which explains how/why the closely-spaced C and C# work together.

> BTW, I think we can almost all agree (80%+), that having

> the scale and overtone schemas match (IE using the harmonic

> series as a scale) sounds very concordant for the most part.

> Can we?

Not really, no. It works under two important conditions:

----* That ALL the intervals of the scale are matched to the

----overtone structure.
    That's what I meant when I said "scale and overtone schemas match".
I realize that for a non-equal-temperment scale the overtone schemas would
have to change per every note to "re-align" with the scale...this is a bit trickier, but can
still be done via digital processing.

-----* That the overtone schema isn't too far from a harmonic

series.
    I assume this is your tie to the "periodicity"/virtual pitch theory.  I will agree from my own experiments that the octave and the 5th pretty much MUST be a part of both the scale and overtone series.
  But, beyond that, I have found there are many ways to skew things and still end up with something which sounds fairly natural (long as the overtones and scales match)...and that path seems is great for experimentation.

-Michael

--- On Tue, 11/4/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Tuesday, November 4, 2008, 2:36 PM

--- In tuning@yahoogroups. com, Michael Sheiman <djtrancendance@ ...> wrote:

>

>>Pitch sensation in the brain is ONE COMPONENT of concordance;

>>the other is roughness (a.k.a. critical band effects).

>

>     This is a major terminology point "missing" from my education

> about micro-tonal music.  When I think "consonance" I think

> "degree of elimination of roughness".

Right! And you're in good company. The history of

psychoacoustics since the 19th century tells the story of

two competing theories -- "place" (roughness) and

"periodicity" (virtual pitch), with the place people

(Plomp Levelt et al) mostly winning until the 1980s, when

it started to become clear that BOTH theories are right.

Now we can just argue about which is more important for

music. And I'll argue that periodicity is.

> it frustrated me how few people seem to consider the

> "inverse" possibility of making instruments with bent

> overtones to fit scales

With 12-ET being an obvious candidate. I love the

beatless sound of tonewheel organs, for example.

>     Any idea, with all the technology we have to do this

> (make arbitrary overtone schemas and then scales to match

> them), why people have not tried more of this?

I'm going to say stupidity.

> BTW, I think we can almost all agree (80%+), that having

> the scale and overtone schemas match (IE using the harmonic

> series as a scale) sounds very concordant for the most part.

> Can we?

Not really, no. It works under two important conditions:

* That ALL the intervals of the scale are matched to the

overtone structure.

* That the overtone schema isn't too far from a harmonic

series.

-Carl

Hi Mike,

> It's unclear to me what term you are using to denote which
> concept. There are four distinct phenomena that we've
> mentioned:

Sorry. I've tried to explain it every way I can think of.
I'll try once more. I'm taking the time to proof-read this
post, since I've noticed typos and crappy wording creeping
in lately. I've also read yours entirely before starting
my reply, and I think we'll be better off if you do the
same (not to say you haven't been). Frankly, I don't think
reading before starting a reply is always necessary, but
when threads go on like this it's got to be the right way.

> 1) the ability of an observer to make sense of a chord

I don't know what you mean by "make sense". Determining
the pitch of a sound is one way of making sense of it.
There may be others.

> 2) the mood of a chord or scale

"Mood" is an ambiguous term. I've not used it at all in
this thread.

> 3) the strength of a pitch produced in the brain when a
> sound is heard, and

This is one principle component of concordance. The other
principle component being a lack of roughness/beating.

> 4) the appropriateness of a chord or scale to a certain
> type of music.

Completely out of the scope of anything psychoacoustics
can handle.

And these four are hardly a complete list of concepts
mentioned! It looks more like the four concepts you're
interested in.

> So far, the term "consonance" has been thrown around at
> different times to mean all of these.

Not by me. I've always said either "musical consonance"
and "sensory consonance" OR "consonance" and "concordance",
or replied directly to a block of text that made the context
clear. You'll notice in my posts that I take effort to
put my contributions directly below a clearly-quoted block
of text that contains the context for what I'm adding.

> I proposed above that the "sonance" terms refer to the first
> phenomenon and to keep discussions of "mood" separate.

You're a smart guy and obviously a decent musician. But
do you really think the time is apt for you to be coining
terms? I mean, you shouldn't complain that you don't
understand the existing concepts and coin new ones in the
same breath. At least, I wouldn't.

> It seems like
> you were saying that the strength of a pitch produced in the
> brain is what "concordance" is.

ONE part of it.

> You also referred to "musical consonance" as
> the appropriateness of a scale or chord in a certain genre
> of music, such as how one interval might be consonant in
> the blues but dissonant in Classical-era music, but I think
> that's a different phenomenon from the first thing, which is
> how I hear consonance being discussed from a musical standpoint.

I hardly need to tell you what musical consonance is. If
you've been to conservatory or taken college music theory
or even high school music theory or even worked through a
rudimentary guitar or piano book, you know how musicians
use the term "consonance". V7 (which is a chord not an
interval) is not a consonance in classical music, but is a
consonance in the blues. I have no idea what you mean by
"make sense of a chord" but it's probably correct.

What matters here is not defining what musical consonance
is, but simply agreeing what sensory consonance is not. It's
not #2 or #4, and until more meat is added, it's not #1
either. Does that help?

> What names would you propose for each of these four things?

I wouldn't. :)

> the term "concordance" being
> thrown around to sometimes mean the strength of a pitch and
> sometimes to mean the coherence of a chord (with the implicit
> assumption that all observers are equal).

That assumption has hardly been implicit. I've mentioned
already several times the partially-objective nature of
the phenomenon.

> > What do you want me to say? The xxxcordance words were brought
> > in precisely to take priming out of the picture. If you want
> > to maximize confusion, go ahead and use them the exact opposite
> > purpose.
>
> Well, it seemed like you were saying that phenomenon 1) and
> phenomenon 4) were really two sides of the same coin.

To me it seems like you are trying to interpret everything
I say in terms of what you want to hear. Let's back up.

Your original post in this microthread was, as I read it,
a complaint that nobody is addressing what I might call
'music psychology'. And you've basically made that same
complaint several times in the past.

As before, I can respond by saying that I (for one) am not
interested in psychology. And even if I were, I think it's
an inquiry on a fundamentally different level than what
theories of 'music intonation' (the subject of this mailing
list) can address. If you disagree, a sure way to make
progress would be to post a constructive theory relating
psychology and intonation.

> After all, if we had triadic harmonic entropy, wouldn't
> we be using it to model both 1)

Perhaps.

> and 4)?

No. How could we?

> What I'm really after is the effect whereby someone listening
> to a chord might hear it as being a bunch of clangy noise the
> first time, but after repeated listens starts to get the
> "feeling" of the chord. It is reasonable to think that it
> might correspond to some kind of "strengthening" of the way
> the brain processes periodicity

I don't think so, no. Because a "feeling" is a very high-level
abstraction that comes out of the most complex phenomenon in
the known universe (human intelligence). It involves many,
many kinds of perceptions and memories and the activity of
some neurons in the inferior colliculus are likely to play a
very small part in it. Does that make sense?

> 2) Thus, the perception of harmony is not equal for every
> observer.

harmony != consonance != concordance

So, I don't know what this means.

> Is there any problem with that reasoning?

Sorry, I've lost you. Perhaps it would be better to stick
to concrete examples as much as possible.

> If harmonic entropy solely describes the information
> content of a signal,

It doesn't.

> and if accordance solely describes a perceptual attribute,
> then the theory around here is that harmonic entropy causes
> accordance with no other variables involved, correct?

I don't think anyone's claiming harmonic entropy soley
captures anything. It's the "simplest possible model" of
concordance, according to Paul. I don't even agree with
that but it's certainly one of the simplest. Simple models
are good because they're powerful, but they're seldom
complete.

-Carl

Hi Michael!

>   But, was not the point in the first place to produce scales,
> be it from chords or otherwise, that are useful to musicians
> and listeners alike rather than prove each other right or wrong?

You bet! And boy, have we got 'em. Too many to use in a
lifetime.

>    Carl is an expert musical historian, that seems obvious and
> just about everything I've WIKI'd against his word has turned
> out to match his word.

That's probably because I've edited the wiki entry. ;)

> But the title of this group appears to be "tuning" not "the
> history of tuning", so would not it be more useful if we all
> stuck to ideas which actually help create and/or use
> good scales?

My main focus is actually on future theory! I didn't think
I was posting much about music history... there's been a lot
of talk about psychoacoustics because that's what people have
been asking about. If you're interested in new scales I'll
say this:

The only problem of tuning theory is that it is too easy to
create interesting scales. Just fire away! People have used
the same one tuning system for so long, it is so old and
decrepit that any change is good!

I can present reasoned arguments that if you really want to
create music as rich as that created by the masters of Western
music (including jazz and rock), that you need to use certain
kinds of scales that may not be obvious at first glance.
That argument is spelled out here:
http://lumma.org/music/theory/tctmo/

But it's important not to take such arguments too seriously.

>   Also, granted, Carl knows a lot about this latter topic but,
> for sure, someone in this group likely has or will discover
> something is possible that Carl thought was not at some point
> in time.  So why the bitterness?

I'm not bitter. Maybe Joseph B. is. I wanted to check out
his files, but the links he posted are giving 404 errors as
of last night, and I don't see them in the Files section here,
on the tuning_files list, or on the tuning_files2 list.

>    Also, back to a comment from a previous post (paraphrased)
> if 19 of 20 people think a various scale sounds better,
> regardless of history, we are likely onto something.

Unfortunately it takes a lot of money to do such experiments.
But as a musician (when I was one... now I just sit in front
of a damn computer all day), it was always enough that I
liked my stuff, and I knew a few other people who liked it
too. That's all any music needs. I don't think 19 out of 20
Americans like the Rite of Spring but I like it and Mike B.
likes it and that's all I need to know.

That said, the microtonal movement is growing. It's grown
so much since 1996, when I first became aware of the term
"just intonation" and could not for the life of me conceive
what it could even be. First, this list grew by leaps and
bounds. Then it split into 5 or 6 lists. And now with the
software synthesis revolution it's grown way beyond mailing
lists. It's just out there. People from the Czech republic
are posting mp3 files in linear temperaments discovered on
tuning-math, and discovering their own. Producers of major
pop stars are wondering about the spaces between the notes.
H-Pi instruments is a company devoted to microtonal
instruments. You can buy an AXiS honeycomb keyboard for
$2000. Jon Catler will sell you a ready-made microtonal
guitar. I have gigabytes of microtonal music on my PC, and
many dozen CDs. You can buy them on Amazon, download them
from iTunes.

By the way, Michael, are you a DJ? You might like
http://cdbaby.com/cd/googleplex
http://cdbaby.com/found?allsearch=marcus+satellite

-Carl

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
> ----With 12-ET being an obvious candidate. I love the
> ----beatless sound of tonewheel organs, for example.
>     This is one thing I simply don't understand is possible or,
> more importantly, can be elaborated on.
>     I have found the 12TET notes a, a#, and b when played
> simultaneously, sound rough, even with 12TET-aligned overtones
> or even just pure sine waves.

Anything, even pure sines, will sound rough when within
a critical band! Critical band is about a whole tone
in the middle of the keyboard, and much wider in the bass.
Which is why close voicings aren't common in the bass.

>     And even the usual seven note scales, to me, with all
> notes played at once sound rough...even with pure sine waves.

That's because 1200/7 = 171, which is probably within the
critical band (unless you play it really high). If you
use a harmonic series segment, you'll still get beating,
but the beat periods align (giving "periodicity buzz")
and the brain's pitch processor likes it, so it can still
sound concordant.

>     Granted though, the alignment of overtones, more like
> bin-aural splitting of alternative notes, both are definite
> keys to improving the "smoothness" of a scale...and I think
> both deserve lots of experimentation.

I agree.

> ----* That ALL the intervals of the scale are matched to the
> ----overtone structure.
>     That's what I meant when I said "scale and overtone
> schemas match". I realize that for a non-equal-temperment
> scale the overtone schemas would have to change per every
> note to "re-align" with the scale...this is a bit trickier,
> but can still be done via digital processing.

Yup. Or you can do a compromise, by using a static timbre
with the overtone structure that minimizes the average
beating over all intervals.

> -----* That the overtone schema isn't too far from a harmonic
> -----series.
>     I assume this is your tie to the "periodicity"/virtual pitch
> theory.

Yes.

-Carl

General note: I am trying to focus on what CAN be done rather than what can't.

----2) the mood of a chord or scale
My take on this is there IS an opening for putting notes that make a consistent emotion together.  It is VERY easy, even within consonant chords in JI in the same key, to make chords that don't emotionally sound good together. 

    If there were not...I am guessing all that would be needed to become a good song writer would be to "stay in key" and "play concordant chords", and I am pretty sure most of us can agree it's not that easy.

  Thus, I believe one way to make a good scale is to concoct it out of a melody but drone
noted from the melody together to make chords.  If any of the rest of you have other methods to make a scale that "can easy keep within the same mood"...I am eager to hear them.  I think...sense of "mood" and ways to create it is a point well worth elaborating on.

--------harmony != consonance != concordance
    This goes back to my other topic concerning "why all the fighting about terminology". 

    Whether they are or are not different does not seem to matter so long as it fails to help us open more musical possibilities.  Shouldn't we be trying to open doors, not close them?

-Michael

--- On Wed, 11/5/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Wednesday, November 5, 2008, 9:08 AM

Hi Mike,

> It's unclear to me what term you are using to denote which

> concept. There are four distinct phenomena that we've

> mentioned:

Sorry. I've tried to explain it every way I can think of.

I'll try once more. I'm taking the time to proof-read this

post, since I've noticed typos and crappy wording creeping

in lately. I've also read yours entirely before starting

my reply, and I think we'll be better off if you do the

same (not to say you haven't been). Frankly, I don't think

reading before starting a reply is always necessary, but

when threads go on like this it's got to be the right way.

> 1) the ability of an observer to make sense of a chord

I don't know what you mean by "make sense". Determining

the pitch of a sound is one way of making sense of it.

There may be others.

> 2) the mood of a chord or scale

"Mood" is an ambiguous term. I've not used it at all in

this thread.

> 3) the strength of a pitch produced in the brain when a

> sound is heard, and

This is one principle component of concordance. The other

principle component being a lack of roughness/beating.

> 4) the appropriateness of a chord or scale to a certain

> type of music.

Completely out of the scope of anything psychoacoustics

can handle.

And these four are hardly a complete list of concepts

mentioned! It looks more like the four concepts you're

interested in.

> So far, the term "consonance" has been thrown around at

> different times to mean all of these.

Not by me. I've always said either "musical consonance"

and "sensory consonance" OR "consonance" and "concordance" ,

or replied directly to a block of text that made the context

clear. You'll notice in my posts that I take effort to

put my contributions directly below a clearly-quoted block

of text that contains the context for what I'm adding.

> I proposed above that the "sonance" terms refer to the first

> phenomenon and to keep discussions of "mood" separate.

You're a smart guy and obviously a decent musician. But

do you really think the time is apt for you to be coining

terms? I mean, you shouldn't complain that you don't

understand the existing concepts and coin new ones in the

same breath. At least, I wouldn't.

> It seems like

> you were saying that the strength of a pitch produced in the

> brain is what "concordance" is.

ONE part of it.

> You also referred to "musical consonance" as

> the appropriateness of a scale or chord in a certain genre

> of music, such as how one interval might be consonant in

> the blues but dissonant in Classical-era music, but I think

> that's a different phenomenon from the first thing, which is

> how I hear consonance being discussed from a musical standpoint.

I hardly need to tell you what musical consonance is. If

you've been to conservatory or taken college music theory

or even high school music theory or even worked through a

rudimentary guitar or piano book, you know how musicians

use the term "consonance" . V7 (which is a chord not an

interval) is not a consonance in classical music, but is a

consonance in the blues. I have no idea what you mean by

"make sense of a chord" but it's probably correct.

What matters here is not defining what musical consonance

is, but simply agreeing what sensory consonance is not. It's

not #2 or #4, and until more meat is added, it's not #1

either. Does that help?

> What names would you propose for each of these four things?

I wouldn't. :)

> the term "concordance" being

> thrown around to sometimes mean the strength of a pitch and

> sometimes to mean the coherence of a chord (with the implicit

> assumption that all observers are equal).

That assumption has hardly been implicit. I've mentioned

already several times the partially-objective nature of

the phenomenon.

> > What do you want me to say? The xxxcordance words were brought

> > in precisely to take priming out of the picture. If you want

> > to maximize confusion, go ahead and use them the exact opposite

> > purpose.

>

> Well, it seemed like you were saying that phenomenon 1) and

> phenomenon 4) were really two sides of the same coin.

To me it seems like you are trying to interpret everything

I say in terms of what you want to hear. Let's back up.

Your original post in this microthread was, as I read it,

a complaint that nobody is addressing what I might call

'music psychology'. And you've basically made that same

complaint several times in the past.

As before, I can respond by saying that I (for one) am not

interested in psychology. And even if I were, I think it's

an inquiry on a fundamentally different level than what

theories of 'music intonation' (the subject of this mailing

list) can address. If you disagree, a sure way to make

progress would be to post a constructive theory relating

psychology and intonation.

> After all, if we had triadic harmonic entropy, wouldn't

> we be using it to model both 1)

Perhaps.

> and 4)?

No. How could we?

> What I'm really after is the effect whereby someone listening

> to a chord might hear it as being a bunch of clangy noise the

> first time, but after repeated listens starts to get the

> "feeling" of the chord. It is reasonable to think that it

> might correspond to some kind of "strengthening" of the way

> the brain processes periodicity

I don't think so, no. Because a "feeling" is a very high-level

abstraction that comes out of the most complex phenomenon in

the known universe (human intelligence) . It involves many,

many kinds of perceptions and memories and the activity of

some neurons in the inferior colliculus are likely to play a

very small part in it. Does that make sense?

> 2) Thus, the perception of harmony is not equal for every

> observer.

harmony != consonance != concordance

So, I don't know what this means.

> Is there any problem with that reasoning?

Sorry, I've lost you. Perhaps it would be better to stick

to concrete examples as much as possible.

> If harmonic entropy solely describes the information

> content of a signal,

It doesn't.

> and if accordance solely describes a perceptual attribute,

> then the theory around here is that harmonic entropy causes

> accordance with no other variables involved, correct?

I don't think anyone's claiming harmonic entropy soley

captures anything. It's the "simplest possible model" of

concordance, according to Paul. I don't even agree with

that but it's certainly one of the simplest. Simple models

are good because they're powerful, but they're seldom

complete.

-Carl

>     I have found the 12TET notes a, a#, and b when played

> simultaneously, sound rough, even with 12TET-aligned overtones

> or even just pure sine waves.

----Anything, even pure sines, will sound rough when within

----a critical band! Critical band is about a whole tone

----
in the middle of the keyboard, and much wider in the bass.

----
Which is why close voicings aren't common in the bass.
    This is why I say 12TET isn't "consonant" in the same way I hope an ideal scale would be.  
    Of course, you can't simply play every note in that scale together at once without such critical band issues...and even in 7-tone JI's CDEFGAB...E and F and B and C are close enough together to beat (E and F beating is tolerable to my ears but E and F + B and C beating seems to cross the line). 
     So one might think "there has got to be a different/better way to arrange 7 notes so that this problem does not occur..."

---If you use a harmonic series segment, you'll still get beating,

---but the beat periods align (giving "periodicity buzz")
---
and the brain's pitch processor likes it, so it can still

---sound concordant.
 

************ "Beat periods align", now that is a cool concept!  ************

I wonder if that also can be used to help split scales among 2 channels so the "binaural beating" also just creates "periodicity buzz" rather than sounds out-of-tune/dissonant.  Any idea what difference between sine waves in two different channels could generate "periodicity buzz"?

    Or...any clue how to do that or what binaurally split scale could produce such results?

    I think you may be on to something....

-Michael

--- On Wed, 11/5/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Wednesday, November 5, 2008, 9:43 AM

--- In tuning@yahoogroups. com, Michael Sheiman <djtrancendance@ ...> wrote:

> ----With 12-ET being an obvious candidate. I love the

> ----beatless sound of tonewheel organs, for example.

>     This is one thing I simply don't understand is possible or,

> more importantly, can be elaborated on.

>     I have found the 12TET notes a, a#, and b when played

> simultaneously, sound rough, even with 12TET-aligned overtones

> or even just pure sine waves.

Anything, even pure sines, will sound rough when within

a critical band! Critical band is about a whole tone

in the middle of the keyboard, and much wider in the bass.

Which is why close voicings aren't common in the bass.

>     And even the usual seven note scales, to me, with all

> notes played at once sound rough...even with pure sine waves.

That's because 1200/7 = 171, which is probably within the

critical band (unless you play it really high). If you

use a harmonic series segment, you'll still get beating,

but the beat periods align (giving "periodicity buzz")

and the brain's pitch processor likes it, so it can still

sound concordant.

>     Granted though, the alignment of overtones, more like

> bin-aural splitting of alternative notes, both are definite

> keys to improving the "smoothness" of a scale...and I think

> both deserve lots of experimentation.

I agree.

> ----* That ALL the intervals of the scale are matched to the

> ----overtone structure.

>     That's what I meant when I said "scale and overtone

> schemas match". I realize that for a non-equal-tempermen t

> scale the overtone schemas would have to change per every

> note to "re-align" with the scale...this is a bit trickier,

> but can still be done via digital processing.

Yup. Or you can do a compromise, by using a static timbre

with the overtone structure that minimizes the average

beating over all intervals.

> -----* That the overtone schema isn't too far from a harmonic

> -----series.

>     I assume this is your tie to the "periodicity" /virtual pitch

> theory.

Yes.

-Carl

Michael wrote,

> ----2) the mood of a chord or scale
> My take on this is there IS an opening for putting notes that
> make a consistent emotion together.  It is VERY easy, even within
> consonant chords in JI in the same key, to make chords that don't
> emotionally sound good together. 

Example?

>> --------harmony != consonance != concordance
>
>     This goes back to my other topic concerning "why all the
> fighting about terminology". 
> Whether they are or are not different does not seem to matter
> so long as it fails to help us open more musical possibilities.
> Shouldn't we be trying to open doors, not close them?

This is a discussion list. In order for anything to be
accomplished, we have to understand one another, at least
a little bit. And like it or not, that requires defining
terms, at least a few of them.

Harmony is a very broad word. I'm genuinely trying to
understand you and Mike B. And for my part, I've tried
very hard to define the terms I use, though I don't get
the feeling you or Mike B. are particularly interested in
those definitions, or, frankly, even reading my posts.

Maybe you are not interested in psychoacoustics? Feel
free to talk about anything you want, but I thought
(perhaps wrongly) that when you mention words like
"critical band" and "consonance" and "Bill Sethares" and
"beating" etc. etc. that you were, in fact, interested
in psychoacoustics.

If you do decide you're interested in psychoacoustics,
let me know, and I'd be happy to continue to try to
explain what I know about it.

-Carl

Michael wrote:

>     This is why I say 12TET isn't "consonant" in the same
> way I hope an ideal scale would be.

Yeah, I got that. But you cut out the part where I wrote
about 1200/7 = 171. That means that even if you use the
widest possible spacing for a 7-tone scale, you still can't
play all 7 tones in one octave without beating, like you
are trying to do. Doesn't matter what you do with the
timbres.

> "Beat periods align", now that is a cool concept!

Gladyoulikeit.

> I wonder if that also can be used to help split scales
> among 2 channels so the "binaural beating" also just creates
> "periodicity buzz" rather than sounds out-of-tune/dissonant.
>  Any idea what difference between sine waves in two different
> channels could generate "periodicity buzz"?

I don't know, I've never tried it, but it's an interesting
question. Why don't you post an example and people can
listen?

>     I think you may be on to something....

I can't take sole credit for the combined efforts of this
group.

-Carl

> ----2) the mood of a chord or scale

> My take on this is there IS an opening for putting notes that

> make a consistent emotion together.  It is VERY easy, even within

> consonant chords in JI in the same key, to make chords that don't

> emotionally sound good together. 

----Example?
   C E G and D G A.  At least when both are held one after the other,
D G A sounds much tenser and darker.  Dmitri Tymoczko http://music.princeton.edu/
has a theory about how chords that sound good together follow short paths in average
frequency changes between all notes in both chords...this may have something to do with it.

----Maybe you are not interested in psychoacoustics? Feel
----
free to talk about anything you want, but I thought
----
(perhaps wrongly) that when you mention words like
----
"critical band" and "consonance" and "Bill Sethares" and
----
"beating" etc. etc. that you were, in fact, interested
----
in psychoacoustics.

    Ok, I realize I REALLY need to clear this up.  This goes right into my topic of "why the arguing about terminology" as well.  Sethares was largely responsible for my interest in micro-tonal in the first place. 

Before him I though all micro-tonal was...was either

    A) Just Intonation, Mean tone, temperaments like 24TET that were basically used like 12TET with the option of using the other 12 notes as "neighboring tones", and other tunings all with the "mission" of estimating Just Intonation intervals in different ways.  IE it didn't really seem micro-tonal so much as "a different way to do the same thing"
-----------------or------------------------
   B) Many "random" scales that could be played melodically but NEVER consonantly in harmony...even though they are very fresh and interesting for melodies. 

     When I heard his song "Ten Fingers" in 10TET, which has intervals that are nothing like 12TET, I thought "wow...now this sounds completely fresh with completely new feel and moods...and yet is not too far from the usual Just Intonation sense of resolve/'consonance'".  And I read up on him and learned about critical bands, overtone shifting...and how he uses those things to bend timbers and scales to "match" each other.

     Ever since then I have been obsessed with the idea of trying to make a scale that's virtually as chord-capable as Just Intonation, but sounds distinctly very different from 12TET, mean-tone, or any other Just Intonation-like scale. 

    So I am here (in this case) to find "the minimum number of psychoacoustic principles I need to adhere to" and "psychoacoustic principle(s) that have not been fully exploited and can lead to more possibilities".  The principle Sethares found that opened things up was that of using technology to manipulate timbre/overtones to match scale.

     I realize if I adhere to virtually all of history's psychoacoustic ideas I just get stuck with something like Just Intonation or learn why 12TET is so annoyingly dominant. 
    This is why I want to learn more about psychoacoustics, but not to the point all I am doing is learning that what I am trying to do is impossible (LOL). :-D

    Simply put...I am trying to find a gap in psychoacoustics that allows me to take alternative routes to making new scales. 

   Which is why, for example, the idea of periodicity being necessary in scales for "concordance" interests me...though, at the same time, I am not interested in saying "oh well, current theories on that say I have to match either JI or the harmonic theories, so I give up".  
    I am hoping to find a clever gap in theories, much like Sethares did, at least in part, when he made 10TET "almost tolerable".
*****************************************************************************************

   For the record, Carl, I well understand you are interested in the future of micro-tonal and not simply regurgitating its history.  Yet, at the same time, listening to you I often feel like I am getting 10 different sets of directions to go to the same old Just Intonation or Harmonic Series related theories.

   So if you, like myself, are eager to express your knowledge in such a way it becomes obvious were "spots for possible innovation" lie I wish you would make it more obvious.  I am learning a lot from you, I just don't want to get so into history that I learn my way into giving up. :-)

-Michael

2008/11/6 Michael Sheiman <djtrancendance@...>:

> Of course, you can't simply play every note in that scale together at
> once without such critical band issues...and even in 7-tone JI's CDEFGAB...E
> and F and B and C are close enough together to beat (E and F beating is
> tolerable to my ears but E and F + B and C beating seems to cross the
> line).
> So one might think "there has got to be a different/better way to
> arrange 7 notes so that this problem does not occur..."

That's why I suggested Mohajira (although I called it Pajara and
nobody corrected me). All the seconds are either major or neutral.
You need to go to the 11-limit because the steps are smaller than any
9-limit interval.

In principle, any 7 note scale will have significant critical band
dissonance. Even the steps of 7-equal are in the roughness region.
So what you're looking for is really impossible. Hence you need
pentatonics to really get this to work, as used in change ringing,
gamelans, and so on. Maybe you can write a paper on why 5-equal is
the true scale of nature.

Graham

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
>> > My take on this is there IS an opening for putting notes
>> > that make a consistent emotion together.  It is VERY easy,
>> > even within consonant chords in JI in the same key, to make
>> > chords that don't emotionally sound good together. 
>>
>> Example?
>
>    C E G and D G A.  At least when both are held one after
> the other, D G A sounds much tenser and darker.

I hardly think that makes them not sound emotionally good
together!

> Dmitri
> Tymoczko http://music.princeton.edu/ has a theory about
> how chords that sound good together follow short paths in
> average frequency changes between all notes in both
> chords...this may have something to do with it.

I don't see the connection yet... Dmitri has discussed
his models here, by the way.

>      Ever since then I have been obsessed with the idea of
> trying to make a scale that's virtually as chord-capable as
> Just Intonation, but sounds distinctly very different from
> 12TET, mean-tone, or any other Just Intonation-like scale.

Well, it's a fine obsession I'd say. If you're looking for
some objectivity, I'm sure people here would be interested
in seeing the scales you try out, and especially in hearing
any audio examples you might post, and sharing their
experiences.

>     So I am here (in this case) to find "the minimum number
> of psychoacoustic principles I need to adhere to"

Well, there are probably more than you realized at first. :)
But ultimately not that many.

>      I realize if I adhere to virtually all of history's
> psychoacoustic ideas I just get stuck with something like
> Just Intonation or learn why 12TET is so annoyingly dominant.

You are maybe unfamiliar with linear and planar temperaments,
etc.?

>    Which is why, for example, the idea of periodicity being
> necessary in scales for "concordance" interests me...though,
> at the same time, I am not interested in saying "oh well,
> current theories on that say I have to match either JI or
> the harmonic theories, so I give up".

Nobody's said that. If you want a no-roughness 7-note chord
in any single octave, though, it is impossible.

-Carl

----That's why I suggested Mohajira (although I called it Pajara and
----
nobody corrected me). All the seconds are either major or neutral.
----
You need to go to the 11-limit because the steps are smaller than any
----
9-limit interval.
    I have tried that...I will agree it works better than 12-TET or JI in that sense.

----
In principle, any 7 note scale will have significant critical band

----dissonance. Even the steps of 7-equal are in the roughness region.
----
So what you're looking for is really impossible.
I believe so considering the following usual standards are enforced
A) whole number multiple over-tones
B) use of mono-aural separation IE not forcing different notes to appear in different stereo channels
C) not using the phenomenon where beat periods align in the harmonic series scale that Carl noted where beats generate "periodicity buzz" that the brain still agrees with (unlike most beating)

    Surely taking advantage of alleviating all 3 of those "standards" IE using binaural separation, "periodicity buzz", and shifted non-whole-number overtones (where the scale and overtones  are digitally manipulated to match each other's frequencies) there must be some way to make a 7-note perfectly consonant scale work... 
Why not?

In fact, I am praying someone can come up with a clever way to do this.
It would likely lead to a compositional utopia: a scale that's infinitely flexible about itself concerning note combinations that is not limited to 5 notes.

    Also...maybe there are further (maybe a fourth and fifth) psychoacoustic standard we can take advantage of/alleviate to twist our way to a "perfectly consonant" seven-plus note scale that could compete with, if not super-cede, 12-TET and other scales that simply approximate Just Intonation.

-Michael

--- On Wed, 11/5/08, Graham Breed <gbreed@gmail.com> wrote:
From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Wednesday, November 5, 2008, 6:50 PM

2008/11/6 Michael Sheiman <djtrancendance@ yahoo.com>:

> Of course, you can't simply play every note in that scale together at

> once without such critical band issues...and even in 7-tone JI's CDEFGAB...E

> and F and B and C are close enough together to beat (E and F beating is

> tolerable to my ears but E and F + B and C beating seems to cross the

> line).

> So one might think "there has got to be a different/better way to

> arrange 7 notes so that this problem does not occur..."

That's why I suggested Mohajira (although I called it Pajara and

nobody corrected me). All the seconds are either major or neutral.

You need to go to the 11-limit because the steps are smaller than any

9-limit interval.

In principle, any 7 note scale will have significant critical band

dissonance. Even the steps of 7-equal are in the roughness region.

So what you're looking for is really impossible. Hence you need

pentatonics to really get this to work, as used in change ringing,

gamelans, and so on. Maybe you can write a paper on why 5-equal is

the true scale of nature.

Graham

>    C E G and D G A.  At least when both are held one after

> the other, D G A sounds much tenser and darker.

---I hardly think that makes them not sound emotionally good
---
together!
    It's a hard thing to prove...but, essentially, some chord progressions will always have better emotional impact (on average) than others.  Otherwise...wouldn't anything the was played "in key" automatically become a catchy pop song and every musician who could produce a chord could be a hit songwriter? :-D

> Dmitri

> Tymoczko http://music. princeton. edu/ has a theory about

> how chords that sound good together follow short paths in

> average frequency changes between all notes in both

> chords...this may have something to do with it.
---I don't see the connection yet... Dmitri has discussed
---his models here, by the way.
   It had something to do with certain chords represent certain dimensions in space and composer styles/chord-progressions lean toward certain space.  I'm not an expert at string theory so it's hard for me to elaborate further
     I actually read about him at first in Time Magazine...I just got a strong impression that different chords would and would not match well in space in his model.

>      Ever since then I have been obsessed with the idea of

> trying to make a scale that's virtually as chord-capable as

> Just Intonation, but sounds distinctly very different from

> 12TET, mean-tone, or any other Just Intonation-like scale.
----Well, it's a fine obsession I'd say. If you're looking for
----
some objectivity, I'm sure people here would be interested

----in seeing the scales you try out, and especially in hearing

----any audio examples you might post, and sharing their

----experiences.
Sure thing...I just have to put something together
In the meantime at
www.myspace.com/spectrafloor
   I have a track Sutrated which has two 10-note scales optimized for instruments with
mostly only odd and mostly only even harmonics, respectively.  And one part of the song is just in plain old 12TET.  And the 10 note scales look absolutely nothing like Just Intonation or Mean-tone. 

    But...I have fooled a handful of people into saying 12TET was the micro-tonal part and vice-versa (which was half the point of making that track)...I am just hoping to open people up to the idea of using odd timbres to open up new scales without sounding significantly more discordant.  :-)

   And when I have my "evil 7-note chord per octave binaural scale" in the form of a song I will gladly post it here. :-)
*********************************************************************************************
---Nobody's said that. If you want a no-roughness 7-note chord
---in any single octave, though, it is impossible.
We will have to see about that... :-)

-Michael

--- On Wed, 11/5/08, Carl Lumma <carl@...> wrote:
From: Carl Lumma <carl@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Wednesday, November 5, 2008, 7:30 PM

--- In tuning@yahoogroups. com, Michael Sheiman <djtrancendance@ ...> wrote:

>> > My take on this is there IS an opening for putting notes

>> > that make a consistent emotion together.  It is VERY easy,

>> > even within consonant chords in JI in the same key, to make

>> > chords that don't emotionally sound good together. 

>>

>> Example?

>

>    C E G and D G A.  At least when both are held one after

> the other, D G A sounds much tenser and darker.

I hardly think that makes them not sound emotionally good

together!

> Dmitri

> Tymoczko http://music. princeton. edu/ has a theory about

> how chords that sound good together follow short paths in

> average frequency changes between all notes in both

> chords...this may have something to do with it.

I don't see the connection yet... Dmitri has discussed

his models here, by the way.

>      Ever since then I have been obsessed with the idea of

> trying to make a scale that's virtually as chord-capable as

> Just Intonation, but sounds distinctly very different from

> 12TET, mean-tone, or any other Just Intonation-like scale.

Well, it's a fine obsession I'd say. If you're looking for

some objectivity, I'm sure people here would be interested

in seeing the scales you try out, and especially in hearing

any audio examples you might post, and sharing their

experiences.

>     So I am here (in this case) to find "the minimum number

> of psychoacoustic principles I need to adhere to"

Well, there are probably more than you realized at first. :)

But ultimately not that many.

>      I realize if I adhere to virtually all of history's

> psychoacoustic ideas I just get stuck with something like

> Just Intonation or learn why 12TET is so annoyingly dominant.

You are maybe unfamiliar with linear and planar temperaments,

etc.?

>    Which is why, for example, the idea of periodicity being

> necessary in scales for "concordance" interests me...though,

> at the same time, I am not interested in saying "oh well,

> current theories on that say I have to match either JI or

> the harmonic theories, so I give up".

Nobody's said that. If you want a no-roughness 7-note chord

in any single octave, though, it is impossible.

-Carl

Michael wrote:
>    It had something to do with certain chords represent certain
> dimensions in space and composer styles/chord-progressions lean
> toward certain space.  I'm not an expert at string theory so
> it's hard for me to elaborate further

I know which model you were referring to; I meant I didn't see
the connection to the example you gave. Dmitri's got several
models, but none of them are particularly involved with
string theory.

> Sure thing...I just have to put something together
> In the meantime at
> www.myspace.com/spectrafloor
>    I have a track Sutrated which has two 10-note scales
> optimized for instruments with mostly only odd and mostly only
> even harmonics, respectively.  And one part of the song is just
> in plain old 12TET.  And the 10 note scales look absolutely
> nothing like Just Intonation or Mean-tone. 

Cool! I'm listening now.

>> ---Nobody's said that. If you want a no-roughness 7-note chord
>> ---in any single octave, though, it is impossible.
>
> We will have to see about that... :-)

Now you're talking!

-Carl

It seems to me that the minimal "roughness" that you are going to find is any chord that has seven contiguous notes on the spiral of fourths and fifths.

Now the only "problem" is to decide what to use as the Large interval for this meantone arrangement.

How about 1200/(2*pi) cents ;-)?

In my list of thousands of scales the only candidates using a Tonic of C are listed on this page:

http://www.lucytune.com/new_to_lt/pitch_03.html

On 6 Nov 2008, at 03:51, Michael Sheiman wrote:
> ***************************
> ---Nobody's said that. If you want a no-roughness 7-note chord
> ---in any single octave, though, it is impossible.
> We will have to see about that... :-)
>
>
>
>
>
>

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

2008/11/6 Michael Sheiman <djtrancendance@...>:
> ----That's why I suggested Mohajira (although I called it Pajara and
> ---- nobody corrected me). All the seconds are either major or neutral.
> ---- You need to go to the 11-limit because the steps are smaller than any
> ---- 9-limit interval.
> I have tried that...I will agree it works better than 12-TET or JI in
> that sense.
>
> ---- In principle, any 7 note scale will have significant critical band
> ----dissonance. Even the steps of 7-equal are in the roughness region.
> ---- So what you're looking for is really impossible.
> I believe so considering the following usual standards are enforced
> A) whole number multiple over-tones
> B) use of mono-aural separation IE not forcing different notes to appear in
> different stereo channels
> C) not using the phenomenon where beat periods align in the harmonic series
> scale that Carl noted where beats generate "periodicity buzz" that the brain
> still agrees with (unlike most beating)

I assumed (B) so you got me there. The other two don't matter. 7
sine waves per octave will have roughness. Beat periods don't matter
for avoiding roughness.

> Surely taking advantage of alleviating all 3 of those "standards" IE
> using binaural separation, "periodicity buzz", and shifted non-whole-number
> overtones (where the scale and overtones are digitally manipulated to match
> each other's frequencies) there must be some way to make a 7-note perfectly
> consonant scale work...
> Why not?

Why doesn't a regular meantone diatonic, with tempered overtones, work
if you move the semitones to different ears? You can do the same with
Mohajira. There are two sets of notes, each a chain of fifths. In a
meantone temperament they're 9-limit intervals with no 7s. So temper
the scale accordingly, use the right timbre, and but each chain on a
different ear.

> In fact, I am praying someone can come up with a clever way to do this.
> It would likely lead to a compositional utopia: a scale that's infinitely
> flexible about itself concerning note combinations that is not limited to 5
> notes.

If you want infinitely flexible there's also adaptive tuning. I've
thought about this with miracle temperament. You can write with 10
notes to the octave and let the computer decide the inequality. This
is also, of course, related to Sethares' work with 10-equal.

Another thing I've thought about: the miraculous decimal scale
naturally breaks down into two pentatonics. Each is roughly the
"Pygmy" scale

1/1 7/8 21/16 3/2 12/7 2/1

That's a no 5's scale with only the 21:16 intervals outside the
9-limit. I've tried retuning the 5th partial to give 21:16 instead of
5:4 but I'm afraid it doesn't blend very well. Still, it's a thought
and it might still be better than a 10-equal timbre. And then you can
put on of these scales in each ear to get a total of 10 notes (3 more
than you ordered).

You can also try mixing this with adaptive temperament to get 4:3
instead of 21:16 when you need it. Or Negri temperament, where the
two pentatonics are naturally 9-limit but further from JI.

> Also...maybe there are further (maybe a fourth and fifth) psychoacoustic
> standard we can take advantage of/alleviate to twist our way to a "perfectly
> consonant" seven-plus note scale that could compete with, if not super-cede,
> 12-TET and other scales that simply approximate Just Intonation.

One thing I think's missing from this thread is that there seem to be
two different kinds of fusion. One, octave equivalent, gives us chord
roots and the strike notes of bells. The perceived pitch corresponds
to a low, strong partial. Then there's a stronger kind of fusion
where the pitch is heard as the virtual pitch even when that doesn't
correspond to a real partial. If the weaker kind's all you need for
harmony then maybe you don't have to worry about partials higher than
4 or 5 matching the harmonic series. That gives you more freedom in
choosing timbres.

Graham

By coincidence, it seems the first chord (left channel) for my current attempt falls smack on that spiral. :-) 
   I'll definitely take a look into this...  Still think binaural will be necessary, though, as I have had no luck getting 7 notes into one channel consonantly due to obvious critical band issues.
 
-Michael

--- On Wed, 11/5/08, Charles Lucy <lucy@harmonics.com> wrote:

From: Charles Lucy <lucy@...>
Subject: [tuning] The "pleasant sounding" seven note chord problem - a recipe?
To: tuning@yahoogroups.com
Date: Wednesday, November 5, 2008, 8:16 PM

It seems to me that the minimal "roughness" that you are going to find is any chord that has seven contiguous notes on the spiral of fourths and fifths.

Now the only "problem" is to decide what to use as the Large interval for this meantone arrangement.

How about 1200/(2*pi) cents ;-)?

In my list of thousands of scales the only candidates using a Tonic of C are listed on this page:

http://www.lucytune .com/new_ to_lt/pitch_ 03.html

On 6 Nov 2008, at 03:51, Michael Sheiman wrote:

********* ********* *********
---Nobody's said that. If you want a no-roughness 7-note chord
---in any single octave, though, it is impossible.
We will have to see about that... :-)

Charles Lucy
lucy@lucytune. com

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune .com

For LucyTuned Lullabies go to:
http://www.lullabie s.co.uk

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
>
> I also have Pianoteq, a physically-modeled piano synthesizer.
> Using a concert grand preset and turning the octave stretch
> all the way down, I rendered this 11-limit hexad:
>
> http://lumma.org/stuff/hexad.wav
>
> What does anyone think of the fusion?
>
> -Carl
>

This does indeed 'fuse' well in the sense of blending almost
immediately into a single pitch of non-piano-like timbre. Everything
is just a little (maybe a lot!) more perfect than you could get with a
wood-and-metal instrument, and it works nicely.

Conceivably the real piano might give you this single-pitch fusion if
Carl had played otonal chords carefully voiced and synchronized.
'Justpiano' comes closest around 0'12'' with the 4-5-6 triad, but for
me it doesn't really suggest a richly-timbred 1/1 as the first few
harmonics are missing.
~~~T~~~

> This does indeed 'fuse' well in the sense of blending almost
> immediately into a single pitch of non-piano-like timbre.
> Everything is just a little (maybe a lot!) more perfect than
> you could get with a wood-and-metal instrument, and it works
> nicely.

It's physically modeled and should most of the inharmonicity
of a real instrument. The parameters are soundboard impedance
and Q factor, piano size, "quadratic effect", and then as far
as tuning: unison width, temperament, and octave stretch.
The timbre produced is indistinguishable from the best sampled
pianos in some cases.

Unfortunately a series made the same day as "justpiano" are the
only JI piano recordings I have, but I've done a better job of
JI-tuning pianos on other occasions -- justpiano was my first
attempt. Still, to my ear the fusion is pretty good.

At any rate, I repeat my assertion that the inharmonicity in
the middle 5 octaves of a modern piano in good condition is
no barrier to its employ in just intonation music, either
when compared to other typical acoustic musical instruments
or indeed to ideal electronic ones.

-Carl

Graham wrote:

> I assumed (B) so you got me there.

Stereo (or other multi-channel setups) may help reduce
roughness, but can't eliminate it. Even with headphones
one will get binaural effects.

> The other two don't matter. 7 sine waves per octave
> will have roughness. Beat periods don't matter
> for avoiding roughness.

Indeed. Part of the key to the pleasantness of periodicity
buzz is that it occurs mostly in the very high harmonics --
not between the fundamentals as would be the case with
7 tones in a single octave.

-Carl

---Why doesn't a regular meantone diatonic, with tempered overtones, work

---if you move the semitones to different ears?
    That was actually my first experiment.  There problem was I could not find a way to align the intervals between each ear to avoid "bin-aural beating".  If you know any way to arrange diatonic intervals to avoid this, be my guest. :-)

---If you want infinitely flexible there's also adaptive tuning. I've

---thought about this with miracle temperament. You can write with 10

---notes to the octave and let the computer decide the inequality. This

---is also, of course, related to Sethares' work with 10-equal.

   Not a bad idea...however I am interested in how it would be done well.  Most adaptive tuning I have heard seems to sound a bit mushy and hard to keep track of due to the arbitrary "sliding" of notes to avoid beating. 
    In addition (I assume this has to do with the "periodicity" element of consonance Carl described before), the notes in 10TET, even when played in a monophonic melody, seem to sound significantly more tense than running between all the notes in 12TET, for example.

--- If the weaker kind's all you need for

---
harmony then maybe you don't have to worry about partials higher than

---
4 or 5 matching the harmonic series. That gives you more freedom in

---
choosing timbres.
This is where I was thinking relieving the restriction of A)
    A) whole number multiple over-tones
would come in handy.  Even using bin-aural separation to eliminate beating, you can still have the problem with "virtual tones", right?  Aligning harmonics is intended to solve this dilemma...I am hoping I don't have to run a "low pass filter" over all my instruments to make the higher-level (6,7,8,etc.) overtones match.

-Michael

--- On Thu, 11/6/08, Graham Breed <gbreed@...> wrote:
From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Thursday, November 6, 2008, 5:44 AM

2008/11/6 Michael Sheiman <djtrancendance@ yahoo.com>:

> ----That's why I suggested Mohajira (although I called it Pajara and

> ---- nobody corrected me). All the seconds are either major or neutral.

> ---- You need to go to the 11-limit because the steps are smaller than any

> ---- 9-limit interval.

> I have tried that...I will agree it works better than 12-TET or JI in

> that sense.

>

> ---- In principle, any 7 note scale will have significant critical band

> ----dissonance. Even the steps of 7-equal are in the roughness region.

> ---- So what you're looking for is really impossible.

> I believe so considering the following usual standards are enforced

> A) whole number multiple over-tones

> B) use of mono-aural separation IE not forcing different notes to appear in

> different stereo channels

> C) not using the phenomenon where beat periods align in the harmonic series

> scale that Carl noted where beats generate "periodicity buzz" that the brain

> still agrees with (unlike most beating)

I assumed (B) so you got me there. The other two don't matter. 7

sine waves per octave will have roughness. Beat periods don't matter

for avoiding roughness.

> Surely taking advantage of alleviating all 3 of those "standards" IE

> using binaural separation, "periodicity buzz", and shifted non-whole-number

> overtones (where the scale and overtones are digitally manipulated to match

> each other's frequencies) there must be some way to make a 7-note perfectly

> consonant scale work...

> Why not?

Why doesn't a regular meantone diatonic, with tempered overtones, work

if you move the semitones to different ears? You can do the same with

Mohajira. There are two sets of notes, each a chain of fifths. In a

meantone temperament they're 9-limit intervals with no 7s. So temper

the scale accordingly, use the right timbre, and but each chain on a

different ear.

> In fact, I am praying someone can come up with a clever way to do this.

> It would likely lead to a compositional utopia: a scale that's infinitely

> flexible about itself concerning note combinations that is not limited to 5

> notes.

If you want infinitely flexible there's also adaptive tuning. I've

thought about this with miracle temperament. You can write with 10

notes to the octave and let the computer decide the inequality. This

is also, of course, related to Sethares' work with 10-equal.

Another thing I've thought about: the miraculous decimal scale

naturally breaks down into two pentatonics. Each is roughly the

"Pygmy" scale

1/1 7/8 21/16 3/2 12/7 2/1

That's a no 5's scale with only the 21:16 intervals outside the

9-limit. I've tried retuning the 5th partial to give 21:16 instead of

5:4 but I'm afraid it doesn't blend very well. Still, it's a thought

and it might still be better than a 10-equal timbre. And then you can

put on of these scales in each ear to get a total of 10 notes (3 more

than you ordered).

You can also try mixing this with adaptive temperament to get 4:3

instead of 21:16 when you need it. Or Negri temperament, where the

two pentatonics are naturally 9-limit but further from JI.

> Also...maybe there are further (maybe a fourth and fifth) psychoacoustic

> standard we can take advantage of/alleviate to twist our way to a "perfectly

> consonant" seven-plus note scale that could compete with, if not super-cede,

> 12-TET and other scales that simply approximate Just Intonation.

One thing I think's missing from this thread is that there seem to be

two different kinds of fusion. One, octave equivalent, gives us chord

roots and the strike notes of bells. The perceived pitch corresponds

to a low, strong partial. Then there's a stronger kind of fusion

where the pitch is heard as the virtual pitch even when that doesn't

correspond to a real partial. If the weaker kind's all you need for

harmony then maybe you don't have to worry about partials higher than

4 or 5 matching the harmonic series. That gives you more freedom in

choosing timbres.

Graham

2008/11/7 Michael Sheiman <djtrancendance@...>:
> ---Why doesn't a regular meantone diatonic, with tempered overtones, work
> ---if you move the semitones to different ears?
> That was actually my first experiment. There problem was I could not
> find a way to align the intervals between each ear to avoid "bin-aural
> beating". If you know any way to arrange diatonic intervals to avoid this,
> be my guest. :-)

So what was the problem? The only one I remember in this thread is
that the semitones are wrong. So it's easy to put semitone pairs in
different ears. If that isn't good enough you can try Mohajira.

If the whole tones are a problem, you can bounce alternate notes to
different ears, giving a 2-octave pattern. If that doesn't work
you're pretty much shafted, aren't you? There are no 7 note scales
with no intervals at least as large as a whole tone.

Oh, incidentally, there's another way of cheating. You can have very
small intervals that beat but don't have roughness.

> ---If you want infinitely flexible there's also adaptive tuning. I've
> ---thought about this with miracle temperament. You can write with 10
> ---notes to the octave and let the computer decide the inequality. This
> ---is also, of course, related to Sethares' work with 10-equal.
>
> Not a bad idea...however I am interested in how it would be done well.
> Most adaptive tuning I have heard seems to sound a bit mushy and hard to
> keep track of due to the arbitrary "sliding" of notes to avoid beating.

It'd be more like musica ficta than normal adaptive tuning. Notes
would move by steps of about 30 cents. All dyads can be tuned to at
least 11-limit consonances (7-limit except for 1 and 9 steps, which
there's not much you can do about). Maybe you can hear the steps.
Maybe there are some pathological triads that can't be properly tuned.
So you'd come up with dissonance resolution patterns.

I generally don't like adaptive tuning because I prefer to keep
control of the dissonance. So I wrote directly in miracle temperament
instead of trying to get an algorithm to do it for me.

> In addition (I assume this has to do with the "periodicity" element of
> consonance Carl described before), the notes in 10TET, even when played in a
> monophonic melody, seem to sound significantly more tense than running
> between all the notes in 12TET, for example.

Was that because of the tuning or the timbre? I didn't have problems
with melody in miracle temperament, anyway. I think I put the decimal
counterpoint examples back:

http://x31eq.com/music/counterpoint.html

> --- If the weaker kind's all you need for
> --- harmony then maybe you don't have to worry about partials higher than
> --- 4 or 5 matching the harmonic series. That gives you more freedom in
> --- choosing timbres.
> This is where I was thinking relieving the restriction of A)
> A) whole number multiple over-tones
> would come in handy. Even using bin-aural separation to eliminate beating,
> you can still have the problem with "virtual tones", right? Aligning
> harmonics is intended to solve this dilemma...I am hoping I don't have to
> run a "low pass filter" over all my instruments to make the higher-level
> (6,7,8,etc.) overtones match.

Yes, but it's no good if you already have roughness between the sine
waves. Most of the attention for this weak fusion seems to be paid to
fifths and octaves. So you probably want an octave repeating scale
with reasonably good fifths. Maybe you can go with a no-5s scale
where 9:7 substitutes for 5:4. And I can't see any way for all chords
to fuse. They have to look like harmonic series segments -- which
means something like triads.

Graham

For those tunaniks without FileMaker, you can now get the listing of scales in .xls format, as I have now completed the first draft of all the possible 12edo scales, and at least one meantone version of each scale and a list of triads which can be played for each scale.

Download is linked from this page:

http://www.lucytune.com/scales/

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

I find nothing wrong with the chords presented. In fact if you spread the d and tho A and octave you can increase the beating which is OFTEN musically useful on the other hand 10ET for 20 minutes would be unbearable . There is good reason why no one likes tunes ET by ear. no one likes the sound of it. 10,000 years of musical experiments and developments over time has some how rejected ETs. & ET which some may like i find horrible and insensitive and lacking any subtlety at all. One has only to play at the near 7ET scales to feel a sigh of relief.
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

If we listen to Beethoven's fifth with all the dissonant notes separated by stereo would it sound better, or more importantly would it be better musically.
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

----If we listen to Beethoven's fifth with all the dissonant notes separated
----
by stereo would it sound better, or more importantly would it be better
----
musically.
Without care, I doubt it......

The thing I have realized is...binaural scale music simply presents different issues than mono-aural scale music.  For example:

A) Reducing binaural beating to a reasonable level instead of normal beating becomes an issue.  The advantage is the ear seems much less picky about binaural beating thus allowing closer note spacing across channels than in the same channel...but pushing too close can still cause problems.
B) My experiments so far by ear seem to say chords in mean-tone and 12ET have binaural beating problems.  That's why I am trying to create special scales for binaural use rather than just shove sections/chords of 12ET or other just-intonation-like scales in separate channels.
C) Much like with adaptive tuning, I have found random tone separation "on demand" leaves the mind struggling to catch up with the adaptive panning changes, regardless of how consonant they are. 
    So for binaural panning to "work", I think it helps a lot if each frequency is assigned a permanent panning position.  This is done as common knowledge in professional production of instruments like drums anyhow. 
D) The other thing is, the notes panned to each side must be aligned to produce consonant chords on each side of the spectrum. 
__________________________________________________

    I think, for sure, you need both C) and D) to be satisfied to improve a piece musically by making it "binaural": you can't just snap random panning positions on any notes that clash. 
    And, to do both C) and D), you most likely have to compose the piece to fit those demands in the first place.

--- On Thu, 11/6/08, Kraig Grady <kraiggrady@...> wrote:
From: Kraig Grady <kraiggrady@...>
Subject: [tuning] Re: Where's all that hostility coming from?: what's the basic formul
To: tuning@yahoogroups.com
Date: Thursday, November 6, 2008, 10:19 PM

If we listen to Beethoven's fifth with all the dissonant notes separated

by stereo would it sound better, or more importantly would it be better

musically.

--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_

Mesotonal Music from:

_'''''''_ ^North/Western Hemisphere:

North American Embassy of Anaphoria Island <http://anaphoria. com/>

_'''''''_ ^South/Eastern Hemisphere:

Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

Michael wrote:
>     So for binaural panning to "work", I think it helps a lot
> if each frequency is assigned a permanent panning position.

Still, I would think the hocketing, though interesting at
first, might get annoying pretty quickly. Have you found
that not to be the case?

Also, you keep talking about the stereo split eliminating
beating (I mean regular, not binaural, beating). Are you
assuming headphones will be used? All but the most
carefully designed speaker systems in the most carefully
configured rooms will mix channels in the room a great deal.

-Carl

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote/asked:
> >
> > So what is the definition of 'fusion'?
> For organs:
> http://arxiv.org/abs/physics/0506094v2
> http://www.aes.org/e-lib/browse.cfm?elib=6621
>
>
> Does anybody here knows something
> about similar experiments with piano-strings?
>

http://link.aip.org/link/?JASMAN/62/1474/1

> There's simply no way to communicate abstract ideas like that
> in music, unless you're talking about using bird-chip effects
> and stuff like that. It's why when you hear the proverbial
> rock star talk about what he was trying to get across in his
> music, it's always a hoot. Even with lyrics they can't get
> it across!
>
> > Something that puts your brain in "sound" rather than
> > "music" mode.
>
> Well, that can be done. I think that's a big effect of
> ambient music. You either avoid music grammars, or elongate
> them to the point where they necessarily take a back seat
> to the sound.
>
> If you want to make chords that don't sound like individual
> notes, but rather timbres, there are several approaches.
> You can compose with sine waves, and mix to mono to eliminate
> spatial source-separation cues. You can keep the fundamental
> constant throughout a piece, which increases the odds any
> changes will be heard as timbral. etc.

Many composers already compose with notes being heard as a timbre
rather than pitches, although in an imperfect manner.

By using excessively dissonant chords, with ambiguous roots, on can
focus more on the rhythm and timbre of the instrument-and the timbre
of a particular area of the instrument as any collection of notes will
sound subtly (or not so subtly) different in different registers.

But it still is not very well served by our tuning system.

Chords like (spelled low to high)
G C F# B
E A# F B
C F# B F A# E
B C C#
G# A A# B C
and we cannot forget Igor Stravinsky's famous
E G# B E G Bb Db Eb

These types of chords don't give a very strong sense of pitch, but
they don't really sound like timbres either, it is, however a step in
that direction I do believe.
However these are all fairly harsh sounding, and within 12TET we do
not have 'pleasant' equivalent of this.

That strange boundary between notes and timbre is quite a beautiful
thing to hear.

caleb rites: welcome, and please don't think I'm arguing with you. I just got interested in the chords you posted.

> to my ear, a 12-tone et "012" is very dissonant, in fact "beyond the > pale" for tonal harmony--although it occurs in contrapuntal > combinations and in the Neapolitan situation, where, in C, you'd > have a Db quickly moving through C down to a B, or skipping C.

so, I'd instinctively sort these chords below into several groups:

G C F# B
E A# F B 016-y, octotonic-ish, dissonant because of tritones and minor seconds, but not that unusual. voicing upward: C1 G2, B3, F#4 hardly dissonant at all 1-3-15-45

> C F# B F A# E just way too gnarly, man, unless you really spread > them wide apart
> B C C#
> G# A A# B C

E G# B E G Bb Db Eb hardly dissonant at all: rich, but Eb triad over E triad. Eb Lydian #3. G# harmonic minor. Scale-group 3.

> By using excessively dissonant chord...
>
>

>
> Chords like (spelled low to high)
> G C F# B
> E A# F B
> C F# B F A# E
> B C C#
> G# A A# B C
> and we cannot forget Igor Stravinsky's famous
> E G# B E G Bb Db Eb
>
> These types of chords don't give a very strong sense of pitch, but
> they don't really sound like timbres either, it is, however a step in
> that direction I do believe.
> However these are all fairly harsh sounding, and within 12TET we do
> not have 'pleasant' equivalent of this.
>
> That strange boundary between notes and timbre is quite a beautiful
> thing to hear.
>
>
>

caleb writes: caleb, think before you hit send:

should have been E lydian #3.

and:

> G C F# B voicing upward: C1 G2, B3, F#4 hardly dissonant at all > 1-3-15-45
> E A# F B 016-y, octotonic-ish, dissonant because of tritones and > minor seconds, but not that unusual.

a little more clear.

On Nov 8, 2008, at 9:36 AM, caleb morgan wrote:

>
> caleb rites: welcome, and please don't think I'm arguing with you. > I just got interested in the chords you posted.
>
>
>> to my ear, a 12-tone et "012" is very dissonant, in fact "beyond >> the pale" for tonal harmony--although it occurs in contrapuntal >> combinations and in the Neapolitan situation, where, in C, you'd >> have a Db quickly moving through C down to a B, or skipping C.
>
> so, I'd instinctively sort these chords below into several groups:
>
> G C F# B
> E A# F B 016-y, octotonic-ish, dissonant because of tritones and > minor seconds, but not that unusual. voicing upward: C1 G2, B3, > F#4 hardly dissonant at all 1-3-15-45
>
>
>> C F# B F A# E just way too gnarly, man, unless you really spread >> them wide apart
>> B C C#
>> G# A A# B C
>
>
>
> E G# B E G Bb Db Eb hardly dissonant at all: rich, but Eb triad > over E triad. Eb Lydian #3. G# harmonic minor. Scale-group 3.
>
>
>
>
>> By using excessively dissonant chord...
>>
>>
>
>>
>> Chords like (spelled low to high)
>> G C F# B
>> E A# F B
>> C F# B F A# E
>> B C C#
>> G# A A# B C
>> and we cannot forget Igor Stravinsky's famous
>> E G# B E G Bb Db Eb
>>
>> These types of chords don't give a very strong sense of pitch, but
>> they don't really sound like timbres either, it is, however a step in
>> that direction I do believe.
>> However these are all fairly harsh sounding, and within 12TET we do
>> not have 'pleasant' equivalent of this.
>>
>> That strange boundary between notes and timbre is quite a beautiful
>> thing to hear.
>>
>>
>
>
>

Lord Vodka wrote:
> That strange boundary between notes and timbre is quite a beautiful
> thing to hear.

Indeed! -Carl

Lord Vodka wrote:
> That strange boundary between notes and timbre is quite a beautiful
> thing to hear.

Indeed! -Carl

in turn applies to consonance and dissonance as this same territory.
The notion of pitch and "noise" too
The most interesting stuff is in between.
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> The 4th chord in justpiano.mp3 and the chord in hexad.wav
> fuse, to my ear, about as much as any chord in any musical
> situation I can think of (barbershop and brass choirs being
> some of the most-fusing).

I have to disagree slightly, in that although I am quite OK with
saying that barbershops 'fuse' nicely in some sense, as do a few of
the 'real' piano chords, I don't hear (say) a barbershop 4:5:6:7 as an
interestingly-timbred single note at the fundamental pitch 1/1 (as I
did with the synthesized hexad). I hear it as a very well-tuned chord...

Anyway, since most chords in JI music aren't otonal, they don't ever
'fuse' in the sense of fooling the ear into hearing a single note.
They can be made 'as united as possible' (to use a nice 16th century
phrase) but not completely and absolutely unitary.

> any specific design features that minimize the consequences
> of ET?

In general, the greatly increasing amount of padding on hammers,
suppressing higher harmonics? ... Though even Schumann's piano
(c.1830-40) only had fairly thin leather on top of the wood. And I
believe the greatly increased mass of the whole assembly (considering
6-7 octave triple strung in comparison to 5-octave double-strung and
wooden framed) generally meant that high frequencies decay quickly.

> > in that certain harmonics are
> > suppressed and/or decay rapidly.
>
> Evidence for this?

Listening to the old Bechstein grand in the lecture theatre here for
one... I find actually most mid-19th to early-20th century pianos I've
heard to be rather devoid of strong-and-persistent high frequency
upper partials, at least in a moderate dynamic. It's usually
advertised as 'transparency' of tone. But the great contrast here is
really around 1800 when the harpsichord-like ringing tone of early
pianos (eg J.A. Stein) started to yield to a more 'rounded' one. Of
course beats are absolutely still there, but they are much less
sharply prominent.

The hammer padding, different decay time of various modes etc etc may
have something (a lot!) to do with a new style of playing too, using
lots of force and big chords and pedal. But imagine trying to play
Chopin pedalled accompaniments if the upper harmonics were strong and
persistent (as on certain famous modern pianos...), if every sixth and
tenth gave you an obvious and persistent beating.

So I don't go so far as to claim that piano makers consiously and
specifically planned to reduce the audibility of beating thirds &
sixths, but a lot of the changes made by influential and successful
makers between 1780 and 1880 did seem to effect this, and composers
and performers seemed to take advantage freely. Now somehow since
maybe 1950 a more overtoney sound has come heavily back into fashion...
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > The 4th chord in justpiano.mp3 and the chord in hexad.wav
> > fuse, to my ear, about as much as any chord in any musical
> > situation I can think of (barbershop and brass choirs being
> > some of the most-fusing).
>
> I have to disagree slightly, in that although I am quite OK with
> saying that barbershops 'fuse' nicely in some sense, as do a few
> of the 'real' piano chords, I don't hear (say) a barbershop
> 4:5:6:7 as an interestingly-timbred single note at the fundamental
> pitch 1/1 (as I did with the synthesized hexad). I hear it as a
> very well-tuned chord...

I think it depends on the degree of analytical listening.
Musicians tend to listen analytically all the time, but I think
many people hear barbershop more like a melody, and I can
remember hearing it more that way as a child. Ditto harmonica.

> Anyway, since most chords in JI music aren't otonal,

Did you mean utonal?

> they don't ever
> 'fuse' in the sense of fooling the ear into hearing a single
> note. They can be made 'as united as possible' (to use a nice
> 16th century phrase) but not completely and absolutely unitary.

Not sure I'm following. But I've proposed in the past that
voice leading rules like 'no parallel fifths' are due to
reducing timbre-fusing potential. I've also argued that the
central property of a "generalized diatonic" scale must be
its capacity to offer certain interval classes (such as 3rds)
which are consonant in most modes, but via different intervals.
This allows them to be 'parallelized' with much less risk of
timbre-fusing.

> > any specific design features that minimize the consequences
> > of ET?
>
> In general, the greatly increasing amount of padding on hammers,
> suppressing higher harmonics? ... Though even Schumann's piano
> (c.1830-40) only had fairly thin leather on top of the wood.
> And I believe the greatly increased mass of the whole assembly
> (considering 6-7 octave triple strung in comparison to 5-octave
> double-strung and wooden framed) generally meant that high
> frequencies decay quickly.

The greatly increased mass of the whole assembly was chiefly
to support greater string tension, which should improve
harmonicity as long as you don't have to make the strings much
thicker as a result (and the switch to steel should have helped
there). It also supported longer string lengths, which again
helps harmonicity. As for it suppressing higher harmonics,
I'm dubious. If anything, that has to do with the sound board,
and it should be possible to put a light soundboard in a heavy
instrument.

As far as eliminating the 5th harmonic, normal pianos have no
features which do this to my knowledge, but there is at least
one piano that does (though even there only for the bass
strings I think). Unfortunately, I can't now find the web
site for this "Apental piano", which was around circa 2005.

But as for whether, at the end of the day, 3rds do beat less
on modern instruments than fortepianos, I can't say I remember
one way or the other. It's been a few years since I've played,
or even heard live, a fortepiano.

-Carl

Tom:
>> I have to disagree slightly, in that although I am quite OK with
>> saying that barbershops 'fuse' nicely in some sense, as do a few
>> of the 'real' piano chords, I don't hear (say) a barbershop
>> 4:5:6:7 as an interestingly-timbred single note at the fundamental
>> pitch 1/1 (as I did with the synthesized hexad). I hear it as a
>> very well-tuned chord...

Carl:
> I think it depends on the degree of analytical listening.
> Musicians tend to listen analytically all the time, but I think
> many people hear barbershop more like a melody, and I can
> remember hearing it more that way as a child. Ditto harmonica.

Isn't the issue the virtual 1/1? I hear all kinds of chord sequences
melodically, but I don't hear them as very low pitched notes. That's
one of Tom's criteria for whatever kind of fusion he's talking about.

Graham

Carl wrote:

> Did you mean utonal?

I think he meant otonal because he was mentioning the overall "synchronicity" which makes otonal chords so well distinguishable by ear. A common guide tone, which occurs in utonal chords, is often overheard until one of the tones introduces beats by slight mistuning.

Petr

> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > > any specific design features that minimize the consequences
> > > of ET?
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
> >
> >
> > In general, the greatly increasing amount of padding on hammers,
> > suppressing higher harmonics? ... Though even Schumann's piano
> > (c.1830-40) only had fairly thin leather on top of the wood.
> > And I believe the greatly increased mass of the whole assembly
> > (considering 6-7 octave triple strung in comparison to 5-octave
> > double-strung and wooden framed) generally meant that high
> > frequencies decay quickly.
>
--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
>
> The greatly increased mass of the whole assembly was chiefly
> to support greater string tension, which should improve
> harmonicity as long as you don't have to make the strings much
> thicker as a result (and the switch to steel should have helped
> there). It also supported longer string lengths, which again
> helps harmonicity. As for it suppressing higher harmonics,
> I'm dubious. If anything, that has to do with the sound board,
> and it should be possible to put a light soundboard in a heavy
> instrument.

About the same time higher strength wire became available
some manufacturers like Broadwood and Chickering put felt in
places current ones wouldn't, like the bridge
http://tinyurl.com/6r8wqg or the nut http://tinyurl.com/5nqdxg
I think Erard's and Herce & Mainé's and Aucher's putting
agraffes on the bridge during the same period could've had the
opposite result, same as screwed-in agraffes and capotastos/
harmonic bars/suspended bridges that started to be used more
instead of pinned wooden nuts.

Clark

> > > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > >
> > > > any specific design features that minimize the consequences
> > > > of ET?
> > --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
> > >
> > >
> > > In general, the greatly increasing amount of padding on hammers,
> > > suppressing higher harmonics? ... Though even Schumann's piano
> > > (c.1830-40) only had fairly thin leather on top of the wood.
> > > And I believe the greatly increased mass of the whole assembly
> > > (considering 6-7 octave triple strung in comparison to 5-octave
> > > double-strung and wooden framed) generally meant that high
> > > frequencies decay quickly.
> >
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> >
> > The greatly increased mass of the whole assembly was chiefly
> > to support greater string tension, which should improve
> > harmonicity as long as you don't have to make the strings much
> > thicker as a result (and the switch to steel should have helped
> > there). It also supported longer string lengths, which again
> > helps harmonicity. As for it suppressing higher harmonics,
> > I'm dubious. If anything, that has to do with the sound board,
> > and it should be possible to put a light soundboard in a heavy
> > instrument.

http://web.ecs.baylor.edu/faculty/gravagnei/piano/

--- In tuning@yahoogroups.com, "threesixesinarow" <CACCOLA@...> wrote:

> > > The greatly increased mass of the whole assembly was chiefly
> > > to support greater string tension, which should improve
> > > harmonicity as long as you don't have to make the strings much
> > > thicker as a result (and the switch to steel should have helped
> > > there). It also supported longer string lengths, which again
> > > helps harmonicity. As for it suppressing higher harmonics,
> > > I'm dubious. If anything, that has to do with the sound board,
> > > and it should be possible to put a light soundboard in a heavy
> > > instrument.
>
> http://web.ecs.baylor.edu/faculty/gravagnei/piano/

Hi Clark- Thanks for the link, that's interesting, but I'm
not sure how it relates to harmonicity over the evolution of
the piano. It just seems to talk about bridge/soundboard
impedance, not string material, tension, length, cross-section,
or hammer material.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "threesixesinarow" <CACCOLA@> wrote:
>
> > > > The greatly increased mass of the whole assembly was chiefly
> > > > to support greater string tension, which should improve
> > > > harmonicity as long as you don't have to make the strings
> > > > much thicker as a result (and the switch to steel should
> > > > have helped there). It also supported longer string
> > > > lengths, which again helps harmonicity. As for it
> > > > suppressing higher harmonics, I'm dubious. If anything,
> > > > that has to do with the sound board, and it should be
> > > > possible to put a light soundboard in a heavy instrument.
> >
> > http://web.ecs.baylor.edu/faculty/gravagnei/piano/
>
> Hi Clark- Thanks for the link, that's interesting, but I'm
> not sure how it relates to harmonicity over the evolution of
> the piano. It just seems to talk about bridge/soundboard
> impedance, not string material, tension, length, cross-section,
> or hammer material.

You might find more practical insight on these topics from
Welcker:

Durch Filz lässt sich der dicke gedeckte Verdische
Clavierton, welcher in England und Frankreich Mode ist,
am leichtesten ausführen, während mit gutem Leder ein
hellklingender, weicher Ton mit feuriger Klangfarbe (der
Wiener Clavierton) weit leichter hervorgebracht werden kann.
(p.324)

http://books.google.com/books?id=SdsPAAAAYAAJ

--- In tuning@yahoogroups.com, "threesixesinarow" <CACCOLA@...> wrote:
>
> You might find more practical insight on these topics from
> Welcker:
>
> Durch Filz lässt sich der dicke gedeckte Verdische
> Clavierton, welcher in England und Frankreich Mode ist,
> am leichtesten ausführen, während mit gutem Leder ein
> hellklingender, weicher Ton mit feuriger Klangfarbe (der
> Wiener Clavierton) weit leichter hervorgebracht werden kann.
> (p.324)
>
> http://books.google.com/books?id=SdsPAAAAYAAJ
>
Here my tr. of that passage on p.324;

Using felt (hammers) allows to gain G.Verdi's thick
(low-partials) muted piano-tone in the easiest way,
that is (now) on vouge in England and France,
whereas good leather allows much easier to produce
an twang sounding, mellow tone with flamy timbre
(the Vienna piano-tone).

That agrees almost with
http://en.wikipedia.org/wiki/Julius_Bl%C3%BCthner
views,
that invented in 1873 additional
http://en.wikipedia.org/wiki/Sympathetic_strings
for
http://en.wikipedia.org/wiki/Aliquot_stringing
"Opinions differ on whether this actually happens in Blüthner pianos.
The noted piano authority Larry Fine says of Blüthner pianos "the
sustain is good, but at a low level of volume, giving the tone a
refined, delicate character."

Larry Fine's opinion, quoted above, is from The Piano Book (4th
edition 2001; Jamaica Plain, MA: Brookside Press; ISBN 1-929145-01-2).

On the other hand, the Blüthner company claims that the effect of
aliquot stringing is apparent only in loud playing."

http://www.bluthner.co.uk/bluthner/special.html#aliquot
"For optimum effect, precise tuning is essential. In today's
instruments the 'aliquot strings' are tuned in unison with the trichords."

But
http://wiki.hammerfluegel.net/index.php/Conrad_Graf
"Ludwig van Beethoven erhielt 1826 im Rahmen einer Reparatur seines
Broadwood-Flügels von Graf einen Flügel mit vierchörigem Saitenbezug
als Leihinstrument, welchen Graf ihm später auf Lebenszeit zur
Verfügung stellte."

tr:
'Ludwig van Beethoven obtained from Graf in 1826 during a repair of
his Broadwood-grand another 4-stringed grand-piano by way of lending.
Later Graf provided van B. that instrument tenure for whole life.

now located in:
"im Beethoven-Haus Bonn:
vierchöriger Hammerflügel aus Beethovens Besitz"
(4-choirs-stringed piano-forte out of B.'s property)

bye
A.S.

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:

>
> On the other hand, the Blüthner company claims that the effect of
> aliquot stringing is apparent only in loud playing."
>
> "For optimum effect, precise tuning is essential. In today's
> instruments the 'aliquot strings' are tuned in unison with the
trichords."
>
> But
> http://wiki.hammerfluegel.net/index.php/Conrad_Graf
> "Ludwig van Beethoven erhielt 1826 im Rahmen einer Reparatur seines
> Broadwood-Flügels von Graf einen Flügel mit vierchörigem Saitenbezug
> als Leihinstrument, welchen Graf ihm später auf Lebenszeit zur
> Verfügung stellte."
>
> tr:
> 'Ludwig van Beethoven obtained from Graf in 1826 during a repair of
> his Broadwood-grand another 4-stringed grand-piano by way of lending.
> Later Graf provided van B. that instrument tenure for whole life.

Now, THAT'S a classic example of a distinction without a difference.
Considering old B. kicked-off in March of 1827...

;-)

I don't get the connection, though. The "Beethoven" Graf is not
aliquot, it is just quad-strung. Graf experimented with quad-stringing
in the late 18-teens, but quickly abandoned the idea because it was a
tuner's nightmare, as anyone who has ever tuned a 6 1/2 octave
triple-strung instrument would tell you. Somewhere we have a surviving
quote saying as much, I forget where, either the conversation books or
Giesinger.

The one thing we know is that the stated claim that Graf made this
piano for Beethoven because of his hearing problem is a fabrication.
My take on it, which is only my take, but strongly suggested by the
circumstancial evidence, is that Graf simply hauled one of these
disasters out of the store room and put it back in working order in
order to entice the overly-possessive B into letting him take away the
Broadwood to his shop, ostensibly to repair it, but actually to study
it in detail, as the idea that English instruments were louder was a
myth in fashion in Vienna at the time. Graf knew all to well that B's
hearing would prevent him from hearing the fact that the ting couldn'
really be put in proper tune, and in any event, he wasn't long for
this world. Graf's further motivation is demonstrated by what he
actually did; on the day after B died, he had the boys from the
factory go round B's house, returning the Broadwood and collecting his
instrument. He then had the guys down in veneering engrave "L. van
Beethoven" across the front of the damper rail, and he promptly sold
"the Instrument of the Great Master" to some unsuspecting Viennese
doctor, effectively turning a sow's ear into a silk purse. The
duplicity is further supported by the "certificate of authenticity"
Graf issued, which use some slippery language, can't remember exactly
what the wording is, but something to the effect of "made by me *a few
years* before the great master's death". Graf was a very slick
operator who invested heavily in Viennese real estate, and sold the
piano biz in 1839 just before the bottom fell out of the market for
the Viennese style.

Ciao,

P

--- In tuning@yahoogroups.com, "Paul Poletti" <paul@...> wrote:
>
>
>
> >In today's
> > instruments the 'aliquot strings' are tuned in unison with the
> trichords."
> >

Please attend here, that I introduced my statement with the word:
> > !!! But !!!...

> > http://wiki.hammerfluegel.net/index.php/Conrad_Graf

> > 'Ludwig van Beethoven obtained from Graf in 1826 during a repair of
> > his Broadwood-grand another 4-stringed grand-piano by way of lending.
> > Later Graf provided van B. that instrument tenure for whole life.
>
> Now, THAT'S a classic example of a distinction without a difference.

...In order differ two types of the function of quadruple-strings:

1. Aliqout (Bluethner)
2. Also exited by the hammer (Graf)

> ;-)

>
> I don't get the connection, though. The "Beethoven" Graf is not
> aliquot, it is just quad-strung.
Right.

> Graf experimented with quad-stringing
> in the late 18-teens, but quickly abandoned the idea because it was a
> tuner's nightmare,
Yes,
my old guild-master agreed with you in that view,
consequently he smashed in the early 1950s such an old
quad-stringed Graf-"monster" with his axe and burnt it in the fire,
as many other old forte-pianos.
Probably that award-winning craftsman was inept and overstrained
to tune 4 strings properly into unisono, or was simply just to lazy...

> as anyone who has ever tuned a 6 1/2 octave
> triple-strung instrument would tell you.
All you need for that is:

1. Adaequate tools (tuning-wrench, pices of felt)
2. Good ears
3. Patient nerves of steel.

>
> The one thing we know is that the stated claim that Graf made this
> piano for Beethoven because of his hearing problem is a fabrication.

http://www.tamino-klassikforum.at/thread.php?postid=159492
"...Haus aufbewahrten Graf-Flügel von 1824 (baugleich mit dem
Graf-Flügel, den Beethoven besessen hatte, aber in viel besserem
Zustand) gegeben..."

hence the "Bonn" Graf-grand is only
"baugleich" = 'constructed in the same way'

"Der Klang des Instrumentes ist gewöhnungsbedürftig,..."
'The sound of the instrument needs getting used to...."

Sorry, but sadly the instrument at:
http://www.musikwissenschaft.uni-hd.de/termine/orlando08.shtml
"...historischen Graf-Flügel des Musikwissenschaftlichen Seminars..."
http://publicus.culture.hu-berlin.de/sammlungen/detail.php?dsn=895
"...einen Graf-Flügel aus der Zeit Beethovens ..."
is
an so horrible condition,
so that i can't judge fair
about Graf's skills in piano-building.

bye
A.S.