Theory of harmony between multiple chords

Lobawad>"Leaving aside ideas like "major triad" is, IMO, pretty much "step number one"."
   Some a side questions I have are

A) What can we use to determine if a chord can act as a point of resolve or point of discord (or, in some cases, either of the two)?  This could easily be a sort of psychoacoustic measure for individual chords that would work through, say, JI and a list of tempered/error variations on JI chords...  Better yet, once we figure this out, why not make this a feature in SCALA IE the ability to list chords on a scale of 1 to 10 in terms of how well they act as points of resolution (with 1 meaning they act best as points of tension)?

B) How much/long and area of discord (or how many non-resolved chords) can the mind take before music starts to sound unstable?

C) What ratios, so far as the root, achieve the strongest resolve (IE often a resolved chord has a root a fifth under a tense chord)? This builds on an idea Igs communicated to me.

   Combining A,B, and C someone, I figure, could make a program that creates chord progressions that build and resolve tension in a very listenable fashion using a huge variety of microtonal chords.  Making it work with something simple like a scale with 7 or 8 notes would be a great start...then we could move on to things like 12+ tones.

--- On Mon, 6/13/11, lobawad <lobawad@...> wrote:

From: lobawad <lobawad@...>
Subject: [tuning] Re: guts of my scheme
To: tuning@yahoogroups.com
Date: Monday, June 13, 2011, 7:39 AM

My opinion is that your assumptions and the basics of your thinking, only as I glean from this post of course, are the very embodiment of one of major "glass cieling"s holding microtonal music back. Leaving aside ideas like "major triad" is, IMO, pretty much "step number one".

--- In tuning@yahoogroups.com, Ralph Hill <ASCEND11@...> wrote:

>

>

>

> Begin forwarded message:

>

> > From: Ralph Hill <ascend11@...>

> > Date: June 12, 2011 11:52:34 PM PDT

> > To: Jonathan Glasier <jonathan.sonicarts@...>, Brink Mcgoogy <mahagoogy@...

> > >, Elizabeth Glasier <glasier2@...>, Joe Monzo

> > <monzojoe@...>

> > Subject: Fwd: ...general post to Tuning: Battaglia .....

> > Vaisaval ..... I appreciate your feedback. I take init.

> > responses as MAYBE guts of my scheme

> >

> >

> > I've rushed to "get down on paper" the heart of a systematic scheme

> > for ordering and classifying a set of building blocks composers of a

> > post 12 equal temperament music can use which I believe has the

> > power to "electrify their workshops" and enable them to break

> > through a kind of "glass ceiling veil" which has lain draped unseen

> > over the 20th century era music so familiar to us.

> >

> > I'd hoped - and do hope - to do a much better explained and complete

> > job than this,

> >

> > Hello -

> >

> > I'll start by posting to Tuning - verbally only for now - the few

> > core ideas underlying my scheme for classifying the body of

> > "comoponents" or "molecules" which form the basic palette of

> > uniquely distinct harmonies available to composers out of which to

> > construct their musical creations. I'm leaving out music's other

> > key elements - rhythm and timing, amplitudes over the music's flow,

> > stereo balance, emotional meanings touched on over the course of the

> > music, ... and so many other things. Also I'm not looking at

> > melodic contour on it's own, but concentrating on the harmonies

> > sounded in succession as the music proceeds.

> >

> > In my particular scheme, I take what I call CHORD TRANSITIONS as

> > the basic building blocks the composer uses in constructing his

> > composition. Generally music's basic harmonic elements tend to be

> > thought to be the chords sounded as the music proceeds ..... eg "

> > major triad on C harmonic seventh chord on F major triad on

> > C minor triad on A harmonic seventh chord on F major

> > triad on C " could be analyzed into a stream of six chords the

> > composer had used there.

> >

> > That's how I used to think, but at some point it started to dawn on

> > me that it is really pairs of chords, one sounded after the other

> > with a first chord "leading into" a second destination chord which

> > are needed to say something which can stand on its own musically. A

> > single chord sounded by itself with no other harmony, not even any

> > implied partner harmony, tends to leave one hanging in suspense.

> > "Is it supposed to be part of music being played? Or is it the

> > doorbell. or......"

> >

> > A major triad on G followed by a major triad on C is a pair of

> > chords having a degree of completeness. Probably an authentic

> > cadence occurring in a piece of music in the key of C - at least

> > with no other information that's what that pair of chords suggests.

> >

> > In short, I take pairs of chords having direction (C major triad

> > followed by G major triad is not the same as G major triad first,

> > followed by C major triad) ...... but C major triad followed by G

> > major triad IS the same as F major triad followed by C major

> > excepting for the fact that the latter CHORD TRANSITION sounds at a

> > pitch level a fourth higher than the former ..... or at a pitch

> > level a fifth lower than the former.

> >

> > In my proposed scheme, there can be any of 12 chord root shift

> > intervals - 1 up a fifth (eg C to G) 2 down a fifth 3 up a major

> > second (C to D) 4 down a major second (C to B-flat) 5 down a

> > just minor third (C to A) 6 up a just minor third (C to E-flat)

> > 7 up a major third (second chord's root frequency 5/4 - just - times

> > the first chord's root frequency) 8 down a just major third (eg C

> > to A-flat) 9 down a 15/16 diatonic semitone (C to B) 10 up a

> > 15/16 diatonic semitone (C to C-sharp) 11 up an augmented fourth

> > (C to F-sharp) *** very close to down an augmented fourth 12

> > first and 2nd chords are on the same root i.e. root shift is zero.

> >

> > Then (first cut) I take it that the first chord can be any one of

> > five "types" of chord and 2nd chord can be any one of these five

> > "types" of chord as I'll explain. This makes the number of possible

> > combinations - 12 possible root shifts, 5 possible types for the

> > first chord, 5 possible types for the second or destination chord

> > (12 times 5 times 5 equals 300).

> >

> > For "chord type" I'm taking it roughly that a chord can be: 1 a

> > major triad, the highest small whole integer to which one of its

> > note frequencies is proportional being 5 2 a harmonic seventh

> > chord, the highest small whole integer to which one of its note

> > frequencies is proportional being 7, its other notes having

> > frequencies proportional to 5, 3, and 1 (root note) - or a related

> > inversion perhaps having only two other notes with frequencies

> > proportional to 5 and 3 - or 5 and 1 - or 3 and 1 **** note - these

> > inversions aren't totally identical or equivalent, but they seem to

> > belong to a "close family" of harmonically similar chords *****

> > Then beyond the harmonic 7th chord we have the harmonic 9th chord

> > with one of its notes having a frequency proportional to 9 (other

> > notes having note frequencies proportional to odd integers less than

> > 9). I'm cutting the odd integers off at 11 and a six note chord

> > with note frequencies proportional to 1, 3, 5, 7, 9, and 11 is

> > certainly a striking and unique animal. Added to these four "chord

> > types" are the minor chords with note frequencies proportional to 3,

> > 5, and 15 as well as the root having frequency proportional to 1.

> >

> > This scheme seems arbitrary as laid out in sketch form here, but a

> > lot of ear testing and experimentation with chord construction on

> > overtones and undertones etc., etc., etc. lies behind it. I don't

> > propose it as a final product, but as something which does embrace a

> > large swath of the most important "molecular elements" in musical

> > harmony. These elements in the palette of musical harmonies have

> > their own unique psychological perceptual effects and merit a place

> > in the post 12 equal temperament/common practice composer's tool

> > kit. Very sweet harmonious music can be composed out of these

> > elements or intriging mysterious sounding music can be built from

> > them. They put a great deal more power and flexibility and

> > capability for creating striking, rarely heard novel effects into

> > composers' hands. By contrast, the harmonic materials 12 equal

> > temperament puts into a composer's hands have a slight bland

> > "sameness" which seems to hang over music composed and/or performed

> > in that system. Quarter comma mean tone gives the composer more

> > power and if extended beyond 12 notes per octave to 14, 15, ..... 24

> > notes per octave laid out in a spiral of fifths flattened by 1/4

> > comma (approximating 31 equal temperament) provides a powerful

> > harmonic toolkit intermediate between the 12 equal tool kit and the

> > one based on chord transitions with 12 possible root shifts and

> > chords having note frequencies, the highest integer to which its

> > note frequency is proportional being 5, 7, 9, 11, or 15. Two such

> > chords separated by one of the 12 possible root shifts form a unique

> > "molecule" in this most advanced system I'm proposing.

> >

> > To repeat a key idea characterizing this palette of harmonies, I

> > take not the single chord, but rather a chord TRANSITION having

> > directionally ordered origin and destination chords whose roots are

> > separated by one of 12 possible integer ratio intervals as the

> > fundamental element or "molecule" out of which a musical composition

> > (in its harmonic aspect) is constructed.

> >

> > My initial first cut system offers about 300 unique building block

> > elements out of which a composition may be said to be constructed.

> > Of course there's much more to music, but this system is to bear its

> > harmonic aspects.

> >

> >

> >

> > Begin forwarded message:

> >

> >> From: Ralph Hill <ascend11@...>

> >> Date: June 11, 2011 10:25:05 PM PDT

> >> To: tuning@yahoogroups.com, Jonathan Glasier <jonathan.sonicarts@...

> >> >, Brink Mcgoogy <mahagoogy@...>, Elizabeth Glasier <glasier2@...

> >> >, Joe Monzo <monzojoe@...>

> >> Subject: Fwd: ...general post to Tuning:... Corr. in last

> >> paragraph - "White Christmas" melody begins on E, not C; C is the

> >> tonic Re: Twinkletits in 23-EDO

> >>

> >>

> >>

> >> Begin forwarded message:

> >>

> >>> From: Ralph Hill <ascend11@...>

> >>> Date: June 11, 2011 10:04:35 PM PDT

> >>> To: tuning@yahoogroups.com, Jonathan Glasier <jonathan.sonicarts@...

> >>> >, Brink Mcgoogy <mahagoogy@...>, Elizabeth Glasier <glasier2@...

> >>> >, Joe Monzo <monzojoe@...>

> >>> Subject: This is a general post to Tuning not specifically

> >>> directed: JI based "body of thought" on musical pitch &

> >>> harmony. Re: Twinkletits in 23-EDO

> >>>

> >>> " Sending 10:25 PM PDT Sat. June 11th, 2011

> >>>

> >>> Hello -

> >>>

> >>> I used to be active posting to the Tuning List about 10 years ago

> >>> but have since then gotten to being much less active, and have

> >>> contributed posts much less frequently.

> >>>

> >>> However I've been developing a fairly specific system for

> >>> organizing the pitch/harmonic side of music one is studying or

> >>> composing which I believe has value and deserves the attention of

> >>> musicians (composers, teachers, music lovers)....... "

> >>>

> >> **********************************

> >>

> >>> I hope some will give me the benefit of their thoughts as to the

> >>> suitability of my getting a draft of my thoughts on an organized

> >>> way of thinking about musical pitch/harmony which could form a

> >>> replacement (or core of a replacement) for the current compound of

> >>> common practice quarter comma mean tone systematization

> >>> confusingly subposed beneath the 12 equal pitch step per octave

> >>> 20th century piano tuning system which makes no distinction (the

> >>> latter) between the 24/25 frequency ratio chromatic semitone (eg E-

> >>> flat to E) and the 15/16 frequency ratio diatonic semitone found

> >>> in the step E to F. THINK OF THE MELODY STARTING ON C FOR "I'M

> >>> DREAMING OF A WHITE CHRISTMAS"

> >>

> >>

> >>> Melody starts on E, not C. C is tonic.

> >>

> >>

> >>

> >>> - the upward step between the 1st and 2nd note of the melody

> >>> (diatonic semitone) and the downward step between the 3rd and 4th

> >>> notes of the melody (chromatic semitone) (or upward again between

> >>> the 4th and 5th notes of the melody (again chromatic semitone)).

> >>>

> >>> Best wishes, Ralph David Hill

> >>

> >

>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Lobawad>"Leaving aside ideas like "major triad" is, IMO, pretty much "step number one"."
>    Some a side questions I have are
>
> A) What can we use to determine if a chord can act as a point of >resolve or point of discord

Really I think the best thing to use is simply our ears. "Resolution" is so relative anyway. And why should we hold music to less complex standards, that is, less resonant of real life, than other art forms? Do you expect of every movie an ending with the hero kissing the girl while he raises his blood-stained sword and the crowds cheer (i.e., V7-I)?

Igs: "Really I think the best thing to use is simply our ears. 'Resolution'
is so relative anyway. And why should we hold music to less complex
standards, that is, less resonant of real life, than other art forms? Do you
expect of every movie an ending with the hero kissing the girl while he
raises his blood-stained sword and the crowds cheer (i.e., V7-I)?"

True, for instance, a segment might play on known motifs or sarcastic
neoclassicism etc. It sounds like what you describe, Michael, is what on the
Craik & Lockhart scale might register as semi-deep processing or something.
With enough data, one could use a basic Markov model to predict the next
chord that sounds somewhat acceptable given the last N chords, but that also
wouldn't be a terribly deep model. I think what Michael wants, though, is
not a model that can accurately analyze all given possibilities, but instead
a tool that can help a composer or performer navigate that space, and the
sort of model he describes could likely do that pretty well most of the
time.

Instead of considering larger segments, though, analyzing 2 chords in
isolation and defining ways of combining them into larger perceived
structures is a pretty valid method of analysis. The question is, how many
and what factors are important psychologically for effectively navigating
musical structures? I've brought this up before, but one method that has
proven some merit in social psychology is the EPA space, or Evaluation
(good/bad)-Potency (powerful/weak)-Activity (active/passive). Every symbol
has a position in this space, and each observer has an impression formation
matrix that is built up over time from encountering these symbols. This EPA
processing then forms an associative memory shortcut for understanding the
interactions of many different types of elements: in musical terms these
might be dynamics, harmony, melody, rhythm, articulation, timbre, etc.
Assuming this model, determining how EPA maps to musical elements is a more
difficult issue. After all, that could be nearly as complex as human
invention, irony upon irony.

What drives the model is the idea of affect control - that affect is defined
by roles, settings, available props, and impressions of events, and that the
actors will try to maintain their roles; i.e.,if a teacher makes a mistake
that causes them to look unknowledgeable (less powerful) or possibly
disingenuous (less good), that teacher will need to remove the deflection by
doing something that pushes the E and P factors back into the "teacher"
position. However, when the teacher takes a trip to Atlantic City, the role
of "teacher" might change to "gambler", and actions will change if that role
is to be maintained.

I think Michael is looking for compound sound-objects which are, if not inherently "at rest", at least highly suitable for being used as points of rest. The major triad is of course the classic example.

--- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
>
> Igs: "Really I think the best thing to use is simply our ears. 'Resolution'
> is so relative anyway. And why should we hold music to less complex
> standards, that is, less resonant of real life, than other art forms? Do you
> expect of every movie an ending with the hero kissing the girl while he
> raises his blood-stained sword and the crowds cheer (i.e., V7-I)?"
>
> True, for instance, a segment might play on known motifs or sarcastic
> neoclassicism etc. It sounds like what you describe, Michael, is what on the
> Craik & Lockhart scale might register as semi-deep processing or something.
> With enough data, one could use a basic Markov model to predict the next
> chord that sounds somewhat acceptable given the last N chords, but that also
> wouldn't be a terribly deep model. I think what Michael wants, though, is
> not a model that can accurately analyze all given possibilities, but instead
> a tool that can help a composer or performer navigate that space, and the
> sort of model he describes could likely do that pretty well most of the
> time.
>
> Instead of considering larger segments, though, analyzing 2 chords in
> isolation and defining ways of combining them into larger perceived
> structures is a pretty valid method of analysis. The question is, how many
> and what factors are important psychologically for effectively navigating
> musical structures? I've brought this up before, but one method that has
> proven some merit in social psychology is the EPA space, or Evaluation
> (good/bad)-Potency (powerful/weak)-Activity (active/passive). Every symbol
> has a position in this space, and each observer has an impression formation
> matrix that is built up over time from encountering these symbols. This EPA
> processing then forms an associative memory shortcut for understanding the
> interactions of many different types of elements: in musical terms these
> might be dynamics, harmony, melody, rhythm, articulation, timbre, etc.
> Assuming this model, determining how EPA maps to musical elements is a more
> difficult issue. After all, that could be nearly as complex as human
> invention, irony upon irony.
>
> What drives the model is the idea of affect control - that affect is defined
> by roles, settings, available props, and impressions of events, and that the
> actors will try to maintain their roles; i.e.,if a teacher makes a mistake
> that causes them to look unknowledgeable (less powerful) or possibly
> disingenuous (less good), that teacher will need to remove the deflection by
> doing something that pushes the E and P factors back into the "teacher"
> position. However, when the teacher takes a trip to Atlantic City, the role
> of "teacher" might change to "gambler", and actions will change if that role
> is to be maintained.
>

--- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
>
> Igs: "Really I think the best thing to use is simply our ears. 'Resolution'
> is so relative anyway. And why should we hold music to less complex
> standards, that is, less resonant of real life, than other art forms? Do you
> expect of every movie an ending with the hero kissing the girl while he
> raises his blood-stained sword and the crowds cheer (i.e., V7-I)?"

Uh, that wasn't I who said that. That quote belongs to the venerable Lobawad.

-igs

On Tue, Jun 14, 2011 at 1:00 PM, cityoftheasleep <igliashon@...>wrote:
>
> Uh, that wasn't I who said that. That quote belongs to the venerable
> Lobawad.
> -igs
>

Oops - apologize for the miscite.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
>
> --- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@> wrote:
> >
> > Igs: "Really I think the best thing to use is simply our ears. 'Resolution'
> > is so relative anyway. And why should we hold music to less complex
> > standards, that is, less resonant of real life, than other art forms? Do you
> > expect of every movie an ending with the hero kissing the girl while he
> > raises his blood-stained sword and the crowds cheer (i.e., V7-I)?"
>
> Uh, that wasn't I who said that. That quote belongs to the venerable Lobawad.
>
> -igs
>

That's "venereal", I would think.

A example of the kind of sonority Michael is looking for would be
1:2*phi(mod2):phi:2

The difference-tone structure is very simple, the internal intervals are exceptionally vague as to suggesting specific diatonic/12-tET intervals, there is a great amount of complex beating if you've got rich harmonic timbres, masking any specific beating, and no single dominant chugging or wobbling in the beating. All this, I believe, is what creates the "metastability" of this sonority.

Plus, it is well approximated in a number of relatively accessible tunings- 13, 23 and 36 edo for example. In addition, it can be created using ancient Greek tetrachords, without modifying them (other than using polyphony of course). It's kind of a "signature chord" for me, but I'd love to hear others using it.

Lobawad>"I think Michael is looking for compound sound-objects which are, if not
inherently "at rest", at least highly suitable for being used as points
of rest. The major triad is of course the classic example."

     Exactly.  Of course, someone could go out on a limb and say something moderately dissonant like an add2 or suspended chord could be used as resolve...no need to restrict oneself to "only the absolute most resolved chords".  Although, on the other hand, something like a diminished 13th isn't exactly likely to be used for a function other than tension...

Far as the "hero with the sword" metaphor...the idea was not to follow absolute rules, but establish a continuum of how likely to unlikely a chord is to be able to be used as a point of resolve.  So the "hero with the sword" could just as well be the "mad scientist finishing the time machine" or even "the kid's first ride without training wheels"...just a relative "positive point" in the plot of a piece of music with no further "strict criteria".
 

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

> Far as the "hero with the sword" metaphor...the idea was not to follow absolute rules, but establish a continuum of how likely to unlikely a chord is to be able to be used as a point of resolve.  So the "hero with the sword" could just as well be the "mad scientist finishing the time machine" or even "the kid's first ride without training wheels"...just a relative "positive point" in the plot of a piece of music with no further "strict criteria".
>  
>

Yeah that's exactly how I was thinking of it. There's also "sudden cut to black", "the lady or the tiger?", etc. etc.

Daniel>"I
think what Michael wants, though, is not a model that can accurately
analyze all given possibilities, but instead a tool that can help a
composer or performer navigate that space, and the sort of model he
describes could likely do that pretty well most of the time."

Right, it wouldn't give exact answers, but rather as many options as possible that are fairly likely to sound right IE give a good average sense of tension and resolve, building and relaxing tension.

>",if
a teacher makes a mistake that causes them to look unknowledgeable
(less powerful) or possibly disingenuous (less good), that teacher will
need to remove the deflection by doing something that pushes the E and P
factors back into the "teacher" position."

Right, music can/should veer off a bit, but should always be close enough to maintain a recognizable and consistent mood/goal/point.  Ironically if a piece of music, by intention, is meant to sound more dissonant it may actually use a minor chord for a "resolve" point and a major for a "tension" point.  Both chords would be "consonant enough on their own to work as resolve points"...but the role of the song would have a more minor-key mood, hence the minor chord seeming more normal/predictable in that song.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> Plus, it is well approximated in a number of relatively accessible
> tunings- 13, 23 and 36 edo for example.

How is it tuned in 23-EDO? I know phi is 16 degrees of 23 (thereabouts, anyway).

-Igs

Didn't John O'Sullivan do just that?

That is how I understand what John's calculator is, and his book explains how he arrived at his definitions. So, this has been done already as far as I can see.

http://www.johnsmusic7.com/

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Daniel>"I
> think what Michael wants, though, is not a model that can accurately
> analyze all given possibilities, but instead a tool that can help a
> composer or performer navigate that space, and the sort of model he
> describes could likely do that pretty well most of the time."
>
> Right, it wouldn't give exact answers, but rather as many options as possible that are fairly likely to sound right IE give a good average sense of tension and resolve, building and relaxing tension.
>
> >",if
> a teacher makes a mistake that causes them to look unknowledgeable
> (less powerful) or possibly disingenuous (less good), that teacher will
> need to remove the deflection by doing something that pushes the E and P
> factors back into the "teacher" position."
>
> Right, music can/should veer off a bit, but should always be close enough to maintain a recognizable and consistent mood/goal/point.  Ironically if a piece of music, by intention, is meant to sound more dissonant it may actually use a minor chord for a "resolve" point and a major for a "tension" point.  Both chords would be "consonant enough on their own to work as resolve points"...but the role of the song would have a more minor-key mood, hence the minor chord seeming more normal/predictable in that song.
>

John's system is consonance metric for individual chords; it doesn't address
voice leading between chords. Other systems do address both issues at once.
I think it would be neat to combine HE with a function that is basically a
minimal path integral that represents voice leading, and then tie that
evaluation to a haptic control system.

On Tue, Jun 14, 2011 at 7:49 PM, christopherv <chrisvaisvil@...>wrote:

>
>
> Didn't John O'Sullivan do just that?
>
> That is how I understand what John's calculator is, and his book explains
> how he arrived at his definitions. So, this has been done already as far as
> I can see.
>
> http://www.johnsmusic7.com/
>
>

Chris>"Didn't John O'Sullivan do just that?"

Hmm....
   John's calculator is for dyadic consonance only.  You could assume that (or, perhaps more acceptably, Tenney Height or TRIADIC Harmonic Entropy) defines resolved-ness.  Any of the above could do a fair job of at least ruling out chords so dissonant they can virtually never be used as resolving points (in the case of the dyadic formulas, of course, you'd have to do something like take the average of three dyads in a chord to get a "triadic dissonance"..

    But the there is another factor...desired mood IE in a minor-key piece of music a minor chord may sound more "resolved" than a major chord for that music's mood.

  And I don't think psychoacoustics alone can summarize that kind of thing that well...only lots of examples of micro-tonal composition, surveyed by ear without the listeners' knowing what the underlying scales are.  For sure though...anything that notoriously
dissonant so far as Tenney Height, Triadic HE, John's calculator...is unlikely to serve as a resolving point in music.  But so far and the huge amount of chords in the range of "mildly dissonant to major triad-like consonant"...there are so many possibilities that only our ears can tell which ones (in terms of mood and not just psychoacoustic "ease of hearing") can work as resolving points in music.

--- On Tue, 6/14/11, christopherv <chrisvaisvil@...> wrote:

From: christopherv <chrisvaisvil@...>
Subject: [tuning] Re: Theory of harmony between multiple chords
To: tuning@yahoogroups.com
Date: Tuesday, June 14, 2011, 5:49 PM

Didn't John O'Sullivan do just that?

That is how I understand what John's calculator is, and his book explains how he arrived at his definitions. So, this has been done already as far as I can see.

http://www.johnsmusic7.com/

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

>

> Daniel>"I

> think what Michael wants, though, is not a model that can accurately

> analyze all given possibilities, but instead a tool that can help a

> composer or performer navigate that space, and the sort of model he

> describes could likely do that pretty well most of the time."

>

> Right, it wouldn't give exact answers, but rather as many options as possible that are fairly likely to sound right IE give a good average sense of tension and resolve, building and relaxing tension.

>

> >",if

> a teacher makes a mistake that causes them to look unknowledgeable

> (less powerful) or possibly disingenuous (less good), that teacher will

> need to remove the deflection by doing something that pushes the E and P

> factors back into the "teacher" position."

>

> Right, music can/should veer off a bit, but should always be close enough to maintain a recognizable and consistent mood/goal/point.  Ironically if a piece of music, by intention, is meant to sound more dissonant it may actually use a minor chord for a "resolve" point and a major for a "tension" point.  Both chords would be "consonant enough on their own to work as resolve points"...but the role of the song would have a more minor-key mood, hence the minor chord seeming more normal/predictable in that song.

>

On Tue, Jun 14, 2011 at 11:03 PM, Michael <djtrancendance@...> wrote:
>
>   And I don't think psychoacoustics alone can summarize that kind of thing that well...only lots of examples of micro-tonal composition, surveyed by ear without the listeners' knowing what the underlying scales are.  For sure though...anything that notoriously
> dissonant so far as Tenney Height, Triadic HE, John's calculator...is unlikely to serve as a resolving point in music.  But so far and the huge amount of chords in the range of "mildly dissonant to major triad-like consonant"...there are so many possibilities that only our ears can tell which ones (in terms of mood and not just psychoacoustic "ease of hearing") can work as resolving points in music.

Does it sound like there are resolutions in this?

http://www.youtube.com/watch?v=KV_MzdtU2WQ&feature=related

-Mike

On Tue, Jun 14, 2011 at 10:03 PM, Michael <djtrancendance@...> wrote:

> John's calculator is for dyadic consonance only. You could assume that
> (or, perhaps more acceptably, Tenney Height or TRIADIC Harmonic Entropy)
> defines resolved-ness...
>

Not to keep bringing up the O'Sullivan metric, but it actually can be
evaluated for any n-ad. Whether it is any good (like TH>10) is up to you to
decide.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > Plus, it is well approximated in a number of relatively accessible
> > tunings- 13, 23 and 36 edo for example.
>
> How is it tuned in 23-EDO? I know phi is 16 degrees of 23 (thereabouts, anyway).
>
> -Igs
>

O, 9, 16, 23

I wonder how it sounds on your 23-edo guitar!

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> O, 9, 16, 23
>
> I wonder how it sounds on your 23-edo guitar!
>

So it's basically harmonics 16:21:26:32, but with a slight irrationality adding some extra mojo. Let's see...oh, it's also an inverted Dicot triad with octave doubling, there's 5 of them in the 3L4s MOS scale. Cool, I'll try that out and maybe post a little goober in a day or two.

-Igs

21/16 is a bit wide, there are better harmonic approximations via the Fibonacci series. But yeah, that's the most simple harmonic structure that approximates. Tuning strictly with phi is what creates the unique difference tone structure, though, so the nearer the approximation the better. phi is the only interval (other than 1/1) that returns itself as a first order difference tone.

Don't know about the online community, but out here in physical reality I've found pretty much universal agreement that it's a very trippy sonority, but not dissonant or jarring.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > O, 9, 16, 23
> >
> > I wonder how it sounds on your 23-edo guitar!
> >
>
> So it's basically harmonics 16:21:26:32, but with a slight irrationality adding some extra mojo. Let's see...oh, it's also an inverted Dicot triad with octave doubling, there's 5 of them in the 3L4s MOS scale. Cool, I'll try that out and maybe post a little goober in a day or two.
>
> -Igs
>

On Wed, Jun 15, 2011 at 3:25 AM, lobawad <lobawad@...> wrote:
>
> 21/16 is a bit wide, there are better harmonic approximations via the Fibonacci series. But yeah, that's the most simple harmonic structure that approximates. Tuning strictly with phi is what creates the unique difference tone structure, though, so the nearer the approximation the better. phi is the only interval (other than 1/1) that returns itself as a first order difference tone.
>
> Don't know about the online community, but out here in physical reality I've found pretty much universal agreement that it's a very trippy sonority, but not dissonant or jarring.

I'll assume that you're referring to buzz/amplitude modulation rather
than actual combination tones here. Even so, I would expect the whole
thing to sound terrible unless you were using timbres that were also
based on a linear phi series. Otherwise, all of the buzz in the
harmonics is going to be at a different rate from one another, whereas
if you use phi-based timbres, the buzz will be completely in sync all
around.

This is also, incidentally, why it is that for harmonic timbres it's
these "isoharmonic," RI chords in particular that buzz the most -
because that's the only way to get it so that all of the harmonics end
up buzzing in sync with everything else. Of course, that's only if
you're shooting for the theoretical ideal of there being this
omni-sync buzz; slight temperings of this will probably be useful in a
way that people haven't figured out yet.

If you are actually talking about difference tones, despite my
skepticism that combination tones have anything to do with anything,
all of the above should still apply. So it would be an interesting
experiment if anyone has the time for it.

-Mike

First-order difference tones. You doubt their significance, but I find that what Dudon calls "-c", differentially coherent, tunings to go over nicely. As far as beating and buzzing, as I have said, the sheer amount of unsynchronized buzz masks any concrete beating. And it's not just an interesting potential experiment, it's something I've been using regularly in music for several years now, with very positive reactions.

Heh, I'll find an example in which it's demonstrated clearly, and post it.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Jun 15, 2011 at 3:25 AM, lobawad <lobawad@...> wrote:
> >
> > 21/16 is a bit wide, there are better harmonic approximations via the Fibonacci series. But yeah, that's the most simple harmonic structure that approximates. Tuning strictly with phi is what creates the unique difference tone structure, though, so the nearer the approximation the better. phi is the only interval (other than 1/1) that returns itself as a first order difference tone.
> >
> > Don't know about the online community, but out here in physical reality I've found pretty much universal agreement that it's a very trippy sonority, but not dissonant or jarring.
>
> I'll assume that you're referring to buzz/amplitude modulation rather
> than actual combination tones here. Even so, I would expect the whole
> thing to sound terrible unless you were using timbres that were also
> based on a linear phi series. Otherwise, all of the buzz in the
> harmonics is going to be at a different rate from one another, whereas
> if you use phi-based timbres, the buzz will be completely in sync all
> around.
>
> This is also, incidentally, why it is that for harmonic timbres it's
> these "isoharmonic," RI chords in particular that buzz the most -
> because that's the only way to get it so that all of the harmonics end
> up buzzing in sync with everything else. Of course, that's only if
> you're shooting for the theoretical ideal of there being this
> omni-sync buzz; slight temperings of this will probably be useful in a
> way that people haven't figured out yet.
>
> If you are actually talking about difference tones, despite my
> skepticism that combination tones have anything to do with anything,
> all of the above should still apply. So it would be an interesting
> experiment if anyone has the time for it.
>
> -Mike
>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > Plus, it is well approximated in a number of relatively accessible
> > > tunings- 13, 23 and 36 edo for example.
> >
> > How is it tuned in 23-EDO? I know phi is 16 degrees of 23 (thereabouts, anyway).
> >
> > -Igs
> >
>
> O, 9, 16, 23

How come I get 0, 7, 16, 23 for

1:2*phi(mod2):phi:2

?

Isn't 2*phi(mod2)=2*Phi-2?

Kalle

On Wed, Jun 15, 2011 at 5:20 AM, lobawad <lobawad@...> wrote:
>
> First-order difference tones. You doubt their significance, but I find that what Dudon calls "-c", differentially coherent, tunings to go over nicely.

You'll have to point it out for me, because what I know of Dudon's
work involved him calling things "difference tones" often but meaning
"proportional beating" more often. The two have similar mathematical
origins.

It should be noted that my experience with "difference tones" comes
from a strict audio engineering perspective, which is what I studied
in school. So I don't associate any sort of artistic meaning with them
whatsoever. To me they're just things that happens when a nonlinear
operation is carried out on a waveform. So I have no vested interest
in them, and the way that people use the term here is inconsistent
with what I understand them to be.

I think that people are referring often to amplitude modulation that
occurs at a rate equal to the difference between two frequencies,
which they've termed a "difference frequency," or a "difference tone."
However, that sort of thing has a phenomenological origin that is
distinct from actual combination tones, which are caused by
"nonlinearities" of the inner ear. I think when people hear the phrase
"phi-based difference tone timbre" they probably imagine some sort of
sweet alien-sounding fused timbre from Jupiter. Although I think that
little quantum units of inspiration like that are real, and that
people are imagining a real sound, it doesn't have to do with the
technical, mathematical meaning of the word difference tone as I
learned it. Unless I'm missing something very subtle.

> As far as beating and buzzing, as I have said, the sheer amount of unsynchronized buzz masks any concrete beating. And it's not just an interesting potential experiment, it's something I've been using regularly in music for several years now, with very positive reactions.

Buzzing = beating. Carl's going to have a fit, but I'll just say it,
because the data supports that theory and I've yet to see a model that
makes better predictions. Plus, once he's ready to resurrect that
discussion, I'm ready to pounce on his argument with the force of a
thousand vicious tigers plus three dying suns. But I'm getting off
track, because what I actually mean to say here is that I don't
understand what you wrote above.

> Heh, I'll find an example in which it's demonstrated clearly, and post it.

OK. In the meantime, here's a little experiment to show you why I
think difference tones just aren't involved at all: load up a timbre
that looks like 1:1+phi:1+2phi:1+3phi:... so that the difference
between every harmonic is phi. Or you can make it 1:phi:2phi-1:etc. A
"phi-timbre," let's call it.

It should sound trippy and cool and bell-like. Now put some distortion
on it and crank it up, which actually will generate real combination
tones and in abundance, and watch as the whole transforms into a
beating, convulsant, discordant mess. What happened, you ask? Where is
the self-reinforcing combination tone phi behavior that I was told
about? How could things have gone so terribly wrong?

Well I'll tell you what happened, Cameron. What happened is that
first-order difference tones don't travel alone. They're accompanied
by other order difference tones, like second and third order ones, and
they're also accompanied by sum tones of all orders as well. Now
"HALT!" you might say, "that makes no sense, because all of the
difference and sum tones should still be in some kind of phi-like
proportion with one another, thus rendering your mathematical
reasoning absurd and your very personality contemptible!" Yes, but
don't forget that you have to factor in the sum of each tone with
-itself- -- aka for some frequency f, you're going to get f+f in the
output (first-order sum tone) and f+f+f (second-order sum tone) and
f+f+f+f and so on. Now you have a harmonic series to contend with
alongside the phi one.

The former is what they call "intermodulation distortion," and the
latter is what they call "harmonic distortion," but they both have
their origin in the combination of the spectrum with itself (or
"convolution" of the spectrum with itself, if you're really hip). The
two don't come separately from one another. If actual combination
tones were involved, then phi timbres by themselves should beat like
crazy, because the harmonic distortion products would clash with the
intermodulation ones. But they don't, and hence we know we're talking
more about amplitude modulation, and abstract applications of
periodicity estimation, and so on, all of which might involve
"frequency differences" without involving actual difference "tones."

H0h0! Anyway, now that you've heard my mathematicizing, if you still
have an experiment to demonstrate combination tones, and you're sure
even after the above that they really are combination tones, I'm all
for it.

-Mike

>"Does it sound like there are resolutions in this?

http://www.youtube.com/watch?v=KV_MzdtU2WQ&feature=related"

To my ear, the chords at 5 seconds and again at 10 seconds, at 19 seconds, 36 and 46 seconds, 1:25...definitely qualify.  There is, of course, a whole lot of repeating of the above "resolution chords".

   To be honest, the phrasing is spunky and enthusiastic, the general mood seems fun, the solos very skillful...but half of the chords beside the "resolved" ones sound off...almost as if they were musical mistakes (think diminished chords with one note off key).
  They veer "of course" far as tension for a little bit too long and I find myself losing track before the resolution chords occur...it's fine they are tense, but being that tense almost demands immediate resolution to balance that tensity.

   So it sounds a bit like a technical exercise, but with some great small sections that could be made into a very convincing piece of music.

--- On Tue, 6/14/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Theory of harmony between multiple chords
To: tuning@yahoogroups.com
Date: Tuesday, June 14, 2011, 8:14 PM

On Tue, Jun 14, 2011 at 11:03 PM, Michael <djtrancendance@...> wrote:

>

>   And I don't think psychoacoustics alone can summarize that kind of thing that well...only lots of examples of micro-tonal composition, surveyed by ear without the listeners' knowing what the underlying scales are.  For sure though...anything that notoriously

> dissonant so far as Tenney Height, Triadic HE, John's calculator...is unlikely to serve as a resolving point in music.  But so far and the huge amount of chords in the range of "mildly dissonant to major triad-like consonant"...there are so many possibilities that only our ears can tell which ones (in terms of mood and not just psychoacoustic "ease of hearing") can work as resolving points in music.

Does it sound like there are resolutions in this?

http://www.youtube.com/watch?v=KV_MzdtU2WQ&feature=related

-Mike

On Wed, Jun 15, 2011 at 10:12 AM, Michael <djtrancendance@...> wrote:
>
> >"Does it sound like there are resolutions in this?
> http://www.youtube.com/watch?v=KV_MzdtU2WQ&feature=related"
>
>
> To my ear, the chords at 5 seconds and again at 10 seconds, at 19 seconds, 36 and 46 seconds, 1:25...definitely qualify.  There is, of course, a whole lot of repeating of the above "resolution chords".
>
>    To be honest, the phrasing is spunky and enthusiastic, the general mood seems fun, the solos very skillful...but half of the chords beside the "resolved" ones sound off...almost as if they were musical mistakes (think diminished chords with one note off key).
>   They veer "of course" far as tension for a little bit too long and I find myself losing track before the resolution chords occur...it's fine they are tense, but being that tense almost demands immediate resolution to balance that tensity.
>
>    So it sounds a bit like a technical exercise, but with some great small sections that could be made into a very convincing piece of music.

It is a technical exercise, it wasn't really supposed to be a finished
song. It also happens to be in 9-EDO. So resolutions are possible even
in tunings that have really high harmonic entropy and all that.

-Mike

MikeB>"It also happens to be in 9-EDO. So resolutions are possible even

in tunings that have really high harmonic entropy and all that."

    Indeed...sounds VERY convincing, considering it is 9-EDO.  Just for grins...what are the chords I pointed out as resolution points (in scale steps and the nearest just chord)?

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Reviewing MikeB's "guess the scale" musical example (was "multiple chords")
To: tuning@yahoogroups.com
Date: Wednesday, June 15, 2011, 7:15 AM

On Wed, Jun 15, 2011 at 10:12 AM, Michael <djtrancendance@...> wrote:

>

> >"Does it sound like there are resolutions in this?

> http://www.youtube.com/watch?v=KV_MzdtU2WQ&feature=related"

>

>

> To my ear, the chords at 5 seconds and again at 10 seconds, at 19 seconds, 36 and 46 seconds, 1:25...definitely qualify.  There is, of course, a whole lot of repeating of the above "resolution chords".

>

>    To be honest, the phrasing is spunky and enthusiastic, the general mood seems fun, the solos very skillful...but half of the chords beside the "resolved" ones sound off...almost as if they were musical mistakes (think diminished chords with one note off key).

>   They veer "of course" far as tension for a little bit too long and I find myself losing track before the resolution chords occur...it's fine they are tense, but being that tense almost demands immediate resolution to balance that tensity.

>

>    So it sounds a bit like a technical exercise, but with some great small sections that could be made into a very convincing piece of music.

It is a technical exercise, it wasn't really supposed to be a finished

song. It also happens to be in 9-EDO. So resolutions are possible even

in tunings that have really high harmonic entropy and all that.

-Mike

On Wed, Jun 15, 2011 at 10:19 AM, Michael <djtrancendance@...> wrote:
>
> MikeB>"It also happens to be in 9-EDO. So resolutions are possible even
> in tunings that have really high harmonic entropy and all that."
>
>     Indeed...sounds VERY convincing, considering it is 9-EDO.  Just for grins...what are the chords I pointed out as resolution points (in scale steps and the nearest just chord)

They're all C major, which happens also to be the key of the song. In
steps it's 1-4-6, which is 0-400-667 cents. They're all really flat
4:5:6 chords. There's a more "in tune" sounding version here, in
16-equal

http://www.youtube.com/watch?v=y8MXbFtw4rM&feature=related

It's just that in this version, I don't get to claim I'm only using 9 notes.

-Mike

>"They're all C major, which happens also to be the key of the song"

Makes sense.  Now here's a challenge (any takers?): compose a short example where you make odd microtonal chords IE neither near standard major or minor chords, as resting points.  What I really want to find is...how weird a chord can we get to still work as a point of resolution...

--- On Wed, 6/15/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Reviewing MikeB's "guess the scale" musical example (was "multiple chords")
To: tuning@yahoogroups.com
Date: Wednesday, June 15, 2011, 7:29 AM

On Wed, Jun 15, 2011 at 10:19 AM, Michael <djtrancendance@yahoo.com> wrote:

>

> MikeB>"It also happens to be in 9-EDO. So resolutions are possible even

> in tunings that have really high harmonic entropy and all that."

>

>     Indeed...sounds VERY convincing, considering it is 9-EDO.  Just for grins...what are the chords I pointed out as resolution points (in scale steps and the nearest just chord)

They're all C major, which happens also to be the key of the song. In

steps it's 1-4-6, which is 0-400-667 cents. They're all really flat

4:5:6 chords. There's a more "in tune" sounding version here, in

16-equal

http://www.youtube.com/watch?v=y8MXbFtw4rM&feature=related

It's just that in this version, I don't get to claim I'm only using 9 notes.

-Mike

On Wed, Jun 15, 2011 at 10:43 AM, Michael <djtrancendance@...> wrote:
>
> >"They're all C major, which happens also to be the key of the song"
>
> Makes sense.  Now here's a challenge (any takers?): compose a short example where you make odd microtonal chords IE neither near standard major or minor chords, as resting points.  What I really want to find is...how weird a chord can we get to still work as a point of resolution...

These major chords have 667 cent fifths. The major chord in 9-equal
has a 400 cent major third, a 267 cent minor third, and a 667 cent
fifth. How much odder do you want to get than that? I'm not sure you
can crank the oddness up any more.

-Mike

>"These major chords have 667 cent fifths. The major chord in 9-equal has a 400 cent major third, a 267 cent minor third, and a 667 cent fifth. How much odder do you want to get than that? I'm not sure you can crank the oddness up any more."

The real odd thing here, if any, is the 667 cent major fifth.  Some counter observations:
A) 667 cents is near 22/15...a diminished fifth that has always come across to me as one of the least objectionable "non-perfect" fifths.  I use it a lot, and leading scales like Mohajira take advantage of it.

B) The 400 cent major third is normal...far as 12TET...and really not that far off Just considering the strong field of attraction of the 5/4 Just major third.  In fact, the strong third seems to do a good job offsetting the "a bit off" fifth.

...and it still comes across, more or less, as a standard major triad (just as you noticed).

   Now if you want weird...I was thinking of something more like a 1/1 11/9 22/15 chord.  Note the 22/15 and 11/9 form an unexpected 6/5 minor third.  It's one of those really weird chords that, to my ears at least, still sounds stable enough (if barely) to work as a point of resolution.

--- On Wed, 6/15/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Reviewing MikeB's "guess the scale" musical example (was "multiple chords")
To: tuning@yahoogroups.com
Date: Wednesday, June 15, 2011, 7:51 AM

On Wed, Jun 15, 2011 at 10:43 AM, Michael <djtrancendance@...> wrote:

>

> >"They're all C major, which happens also to be the key of the song"

>

> Makes sense.  Now here's a challenge (any takers?): compose a short example where you make odd microtonal chords IE neither near standard major or minor chords, as resting points.  What I really want to find is...how weird a chord can we get to still work as a point of resolution...

These major chords have 667 cent fifths. The major chord in 9-equal

has a 400 cent major third, a 267 cent minor third, and a 667 cent

fifth. How much odder do you want to get than that? I'm not sure you

can crank the oddness up any more.

-Mike

Perhaps this Bill Wesley video can provide some insight into the emotional part.

http://www.youtube.com/watch?v=MzD5riY9ZnE

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Chris>"Didn't John O'Sullivan do just that?"
>
>
> Hmm....
>    John's calculator is for dyadic consonance only.  You could assume that (or, perhaps more acceptably,

>"Perhaps this Bill Wesley video can provide some insight into the emotional part.

http://www.youtube.com/watch?v=MzD5riY9ZnE"

   I know this guy is trying to be funny and a bit crazy...but I honestly think he gets it.  Being a good musician is about successfully conveying a certain emotion...and doing it well means alienating certain people who HATE that emotion, but getting respect at being "good at what you aim to express" regardless.  IE his example "I hate the Eagles...but I'd never call them bad musicians...they are great song writers, performers...they just express very well...feelings I don't want to feel".

  Back to microtonality...my fear is that any music that is too unstable would only have one prevalent emotion: chaos.  And meanwhile music that is too stable (think a straight harmonic series) would convey a simple "hazy" emotion...with no interesting contrast.  However, finding a pattern in which microtonal chords and pairs of chords people think are generally happy, angry, tense, non-tense...musicians can choose a palette with suitable emotions for music easily and most likely get the mood they want.  12TET already has such obvious trends IE minor chords for trance and metal (esp. E minor for metal)...but the question becomes what new chords and progressions would create similar moods (and even enhanced ones) in microtonality without becoming so chaotic the mood can be decoded...or respected by listeners.  Realizing, of course, that there's a huge difference between being respected as a musician and liked as a musician.

--- On Wed, 6/15/11, christopherv <chrisvaisvil@...> wrote:

From: christopherv <chrisvaisvil@...>
Subject: [tuning] Re: Theory of harmony between multiple chords
To: tuning@yahoogroups.com
Date: Wednesday, June 15, 2011, 6:14 PM

Perhaps this Bill Wesley video can provide some insight into the emotional part.

http://www.youtube.com/watch?v=MzD5riY9ZnE

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

>

> Chris>"Didn't John O'Sullivan do just that?"

>

>

> Hmm....

>    John's calculator is for dyadic consonance only.  You could assume that (or, perhaps more acceptably,

On Wed, Jun 15, 2011 at 11:30 PM, Michael <djtrancendance@...> wrote:
>
>   Back to microtonality...my fear is that any music that is too unstable would only have one prevalent emotion: chaos.  And meanwhile music that is too stable (think a straight harmonic series) would convey a simple "hazy" emotion...with no interesting contrast.  However, finding a pattern in which microtonal chords and pairs of chords people think are generally happy, angry, tense, non-tense...musicians can choose a palette with suitable emotions for music easily and most likely get the mood they want.  12TET already has such obvious trends IE minor chords for trance and metal (esp. E minor for metal)...but the question becomes what new chords and progressions would create similar moods (and even enhanced ones) in microtonality without becoming so chaotic the mood can be decoded...or respected by listeners.  Realizing, of course, that there's a huge difference between being respected as a musician and liked as a musician.

I'm not sure about the respected/liked as a musician thing, but how
does 6:9:10:11:12 grab you? That's basically a 2:3:4 trine on the
outside with some notes that fit in the wrong way (the 9:10:11:12 in
the upper fourth), just like a 10:12:15 is a 3/2 dyad with a 5/4 in
there fitting in the wrong way.

-Mike

   Just a quick look at the lowest common denominator...
   All the triads below should consonant enough to work as resolving points in composition...for me.
  Do any of you have any chords to add to the list and/or delete from it?

I figure once we all, more or less, agree on a list we can start looking around to find some mathematical properties/patterns we can use in microtonal scales to, in general, locate "resolved enough" sounding chords with fair precision...
  (btw I already am pretty sure I notice one pattern...tri-tones are out far as "resolution-point chords")

C C# D#
C D F
C D A
C D# G#

C D# A#
C E F

C E G
C F G#
C F A

C F A#

C F B
C G A
C G B

C C# F

--- On Wed, 6/15/11, Michael <djtrancendance@...> wrote:

From: Michael <djtrancendance@...>
Subject: Re: [tuning] Re: Theory of harmony between multiple chords
To: tuning@yahoogroups.com
Date: Wednesday, June 15, 2011, 8:30 PM

>"Perhaps this Bill Wesley video can provide some insight into the emotional part.

http://www.youtube.com/watch?v=MzD5riY9ZnE"

   I know this guy is trying to be funny and a bit crazy...but I honestly think he gets it.  Being a good musician is about successfully conveying a certain emotion...and doing it well means alienating certain people who HATE that emotion, but getting respect at being "good at what you aim to express" regardless.  IE his example "I hate the Eagles...but I'd never call them bad musicians...they are great song writers, performers...they just express very well...feelings I don't want to feel".

  Back to microtonality...my fear is that any music that is too unstable would only have one prevalent emotion: chaos.  And meanwhile music that is too stable (think a straight harmonic series) would convey a simple "hazy" emotion...with no interesting contrast.  However, finding a pattern in which microtonal chords and pairs of chords people think are generally happy, angry, tense, non-tense...musicians can choose a
palette with suitable emotions for music easily and most likely get the mood they want.  12TET already has such obvious trends IE minor chords for trance and metal (esp. E minor for metal)...but the question becomes what new chords and progressions would create similar moods (and even enhanced ones) in microtonality without becoming so chaotic the mood can be decoded...or respected by listeners.  Realizing, of course, that there's a huge difference between being respected as a musician and liked as a musician.

--- On Wed, 6/15/11, christopherv <chrisvaisvil@...> wrote:

From: christopherv <chrisvaisvil@...>
Subject: [tuning] Re: Theory of harmony between multiple chords
To: tuning@yahoogroups.com
Date: Wednesday, June 15, 2011, 6:14 PM

Perhaps this Bill Wesley video can provide some insight into the emotional part.

http://www.youtube.com/watch?v=MzD5riY9ZnE

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

>

> Chris>"Didn't John O'Sullivan do just that?"

>

>

> Hmm....

>    John's calculator is for dyadic consonance only.  You could assume that (or, perhaps more acceptably,

MikeB>"I'm not sure about the respected/liked as a musician thing, but how

does 6:9:10:11:12 grab you? That's basically a 2:3:4 trine on the

outside with some notes that fit in the wrong way (the 9:10:11:12 in

the upper fourth), just like a 10:12:15 is a 3/2 dyad with a 5/4 in

there fitting in the wrong way."

    Sounds decent, somewhere near the edge of what could work as a  "point of resolution".  The only reason I say "edge" is that the 10:11:12 cluster takes up most of the slack given for dissonance due to critical band issues.  But, in general...great example of what's "just good enough to work as a point of resolution"...in my book at least.  Even if people don't like it's mood...I'm pretty sure they could identify it as a foundation/resolve point and not a "strictly experimental chord".

On Wed, Jun 15, 2011 at 11:58 PM, Michael <djtrancendance@...> wrote:
>
>    Just a quick look at the lowest common denominator...
>    All the triads below should consonant enough to work as resolving points in composition...for me.
>   Do any of you have any chords to add to the list and/or delete from it?
>
> I figure once we all, more or less, agree on a list we can start looking around to find some mathematical properties/patterns we can use in microtonal scales to, in general, locate "resolved enough" sounding chords with fair precision...
>   (btw I already am pretty sure I notice one pattern...tri-tones are out far as "resolution-point chords")

C-E-F# can be decently resolved, as can C-#F-G, especially if you
resolve them to C-E-G afterward. C F# Bb can be really resolved,
especially if you voice the F# up an octave. C E Bb can be resolved in
the blues. But a lot of the ones you listed are the same chord in
inversion, so you might want to check that.

-Mike

   In addition, I think the chord 1 11/9 22/15 11/6 2/1 is "just good enough to work as a point of resolution".  So is 1/1 5/4 5/3 11/6 and 1 11/9 3/2 11/6 2/1

   However 1 11/9 5/3 11/6 fails to me as a possible point of resolution...for example.

  The weird thing is some of the "non-resolved chords" seem to be of lower otonal odd limit than the "resolved" ones...

--- On Wed, 6/15/11, Michael <djtrancendance@yahoo.com> wrote:

From: Michael <djtrancendance@...>
Subject: Re: [tuning] Re: Theory of harmony between multiple chords
To: tuning@yahoogroups.com
Date: Wednesday, June 15, 2011, 9:08 PM

MikeB>"I'm not sure about the respected/liked as a musician thing, but how

does 6:9:10:11:12 grab you? That's basically a 2:3:4 trine on the

outside with some notes that fit in the wrong way (the 9:10:11:12 in

the upper fourth), just like a 10:12:15 is a 3/2 dyad with a 5/4 in

there fitting in the wrong way."

    Sounds decent, somewhere near the edge of what could work as a  "point of resolution".  The only reason I say "edge" is that the 10:11:12 cluster takes up most of the slack given for dissonance due to critical band issues.  But, in general...great example of what's "just good enough to work as a point of resolution"...in my book at least.  Even if people don't like it's mood...I'm pretty sure they could identify it as a foundation/resolve point and not a "strictly experimental chord".

Mike, I think all we need is more or less out there.

Wasn't the reason you liked my UnTweleve entry so much was because it did, in fact, convey a lot of emotion? If I have that right then my point is - its time to write the music and to stop thinking we don't have the tools to do it.

In fact I've found some profound emotional microtonal music in places like Beauty in the Beast, Neil Haverstick, Igs' work, people I've heard in Urbana and the Mills demonstration CD and music posted to this forum.

I'm not saying theory is worthless - the work that Gene and others do with devising tunings is very important. The point I'm making is that very good, emotional, and timeless music was written in 12 equal and near 12 equal before composers obtained the depth of knowledge about the tuning that exists today. Even in the "hard" sciences not everything is known about any subject yet useful applications and answers are found every day.

Chris

>
>   Back to microtonality...my fear is that any music that is too unstable would only have one prevalent emotion: chaos.  And meanwhile music that is too stable (think a straight harmonic series) would convey a simple "hazy" emotion...with no interesting contrast.  However, finding a pattern in which microtonal chords and pairs of chords people think are generally happy, angry, tense, non-tense...musicians can choose a palette with suitable emotions for music easily and most likely get the mood they want.  12TET already has such obvious trends IE minor chords for trance and metal (esp. E minor for metal)...but the question becomes what new chords and progressions would create similar moods (and even enhanced ones) in microtonality without becoming so chaotic the mood can be decoded...or respected by listeners.  Realizing, of course, that there's a huge difference between being respected as a musician and liked as a musician.
>

Please, I'm getting exhausted with reading this same thing over and over
again. I joined this list because I was interested in learning about
"alternate tuning" methods, not to read a hundred thousand posts about how
we need to stop analyzing alternate tunings.

On Thu, Jun 16, 2011 at 11:52 AM, christopherv <chrisvaisvil@...>wrote:

>
>
> Mike, I think all we need is more or less out there.
>
> Wasn't the reason you liked my UnTweleve entry so much was because it did,
> in fact, convey a lot of emotion? If I have that right then my point is -
> its time to write the music and to stop thinking we don't have the tools to
> do it.
>
> In fact I've found some profound emotional microtonal music in places like
> Beauty in the Beast, Neil Haverstick, Igs' work, people I've heard in Urbana
> and the Mills demonstration CD and music posted to this forum.
>
> I'm not saying theory is worthless - the work that Gene and others do with
> devising tunings is very important. The point I'm making is that very good,
> emotional, and timeless music was written in 12 equal and near 12 equal
> before composers obtained the depth of knowledge about the tuning that
> exists today. Even in the "hard" sciences not everything is known about any
> subject yet useful applications and answers are found every day.
>
> Chris
>
> >
> > Â Back to microtonality...my fear is that any music that is too unstable
> would only have one prevalent emotion: chaos. And meanwhile music that is
> too stable (think a straight harmonic series) would convey a simple "hazy"
> emotion...with no interesting contrast. However, finding a pattern in
> which microtonal chords and pairs of chords people think are generally
> happy, angry, tense, non-tense...musicians can choose a palette with
> suitable emotions for music easily and most likely get the mood they want.Â
> 12TET already has such obvious trends IE minor chords for trance and metal
> (esp. E minor for metal)...but the question becomes what new chords and
> progressions would create similar moods (and even enhanced ones) in
> microtonality without becoming so chaotic the mood can be decoded...or
> respected by listeners. Realizing, of course, that there's a huge
> difference between being respected as a musician and liked as a musician.
> >
>
>
>

I'm sorry. I didn't realize you were steering the discussion.

Please by all means carry on.

Chris

--- In tuning@yahoogroups.com, Daniel Nielsen <nielsed@...> wrote:
>
> Please, I'm getting exhausted with reading this same thing over and over
> again. I joined this list because I was interested in learning about
> "alternate tuning" methods, not to read a hundred thousand posts about how
> we need to stop analyzing alternate tunings.
>
>
>
> On Thu, Jun 16, 2011 at 11:52 AM, christopherv <chrisvaisvil@...>wrote:
>
> >
> >
> > Mike, I think all we need is more or less out there.
> >
> > Wasn't the reason you liked my UnTweleve entry so much was because it did,
> > in fact, convey a lot of emotion? If I have that right then my point is -
> > its time to write the music and to stop thinking we don't have the tools to
> > do it.
> >
> > In fact I've found some profound emotional microtonal music in places like
> > Beauty in the Beast, Neil Haverstick, Igs' work, people I've heard in Urbana
> > and the Mills demonstration CD and music posted to this forum.
> >
> > I'm not saying theory is worthless - the work that Gene and others do with
> > devising tunings is very important. The point I'm making is that very good,
> > emotional, and timeless music was written in 12 equal and near 12 equal
> > before composers obtained the depth of knowledge about the tuning that
> > exists today. Even in the "hard" sciences not everything is known about any
> > subject yet useful applications and answers are found every day.
> >
> > Chris
> >
> > >
> > > Â Back to microtonality...my fear is that any music that is too unstable
> > would only have one prevalent emotion: chaos. And meanwhile music that is
> > too stable (think a straight harmonic series) would convey a simple "hazy"
> > emotion...with no interesting contrast. However, finding a pattern in
> > which microtonal chords and pairs of chords people think are generally
> > happy, angry, tense, non-tense...musicians can choose a palette with
> > suitable emotions for music easily and most likely get the mood they want.Â
> > 12TET already has such obvious trends IE minor chords for trance and metal
> > (esp. E minor for metal)...but the question becomes what new chords and
> > progressions would create similar moods (and even enhanced ones) in
> > microtonality without becoming so chaotic the mood can be decoded...or
> > respected by listeners. Realizing, of course, that there's a huge
> > difference between being respected as a musician and liked as a musician.
> > >
> >
> >
> >
>

On Thu, Jun 16, 2011 at 12:08 AM, Michael <djtrancendance@...> wrote:
>
> MikeB>"I'm not sure about the respected/liked as a musician thing, but how
> does 6:9:10:11:12 grab you? That's basically a 2:3:4 trine on the
> outside with some notes that fit in the wrong way (the 9:10:11:12 in
> the upper fourth), just like a 10:12:15 is a 3/2 dyad with a 5/4 in
> there fitting in the wrong way."
>
>     Sounds decent, somewhere near the edge of what could work as a  "point of resolution".  The only reason I say "edge" is that the 10:11:12 cluster takes up most of the slack given for dissonance due to critical band issues.  But, in general...great example of what's "just good enough to work as a point of resolution"...in my book at least.  Even if people don't like it's mood...I'm pretty sure they could identify it as a foundation/resolve point and not a "strictly experimental chord".

Man, I can't believe you're still harping on this critical band thing.
Don't you realize that if you play 10:11:12, all of these mysterious
and evil critical band interactions will actually end up being in
perfect sync with one another? That's what this periodicity buzz stuff
is. Since when is that bad?

Critical band interactions are bad if they interfere with the
intelligibility of the sound. If they don't, then they're not bad. If
I put LFO on a square wave, it's creating "beating." So what?

-Mike

Chris>"Wasn't the reason you liked my UnTweleve entry so much was because it did, in fact, convey a lot of emotion? "
   Indeed.

>"If I have that right then my point is - its time to write the music and to stop thinking we don't have the tools to do it."
   For me it's always the same complaints...mainly about lack of building tension and "variety".  And that's even in songs like "Dimension", my Untwelve entry where I spent a month, a little time each day, adding variation to the piece.  Simply put...I've come to the conclusion I'm really not made to be a musician (far as finding people who understand my music and/or want to collaborate on making music).   It's, admittedly, by and large just a self-indulgence for me...a way to wind down: I don't except any amount of work can make me a "respected musician"...because I've done so much work and the responses virtually haven't changed.

   And that my time is likely more productively spent making software, theories...to make it easier for other to make music.  Even then...I've had people applaud, say, my meter/rhythm rotation techniques and then not even take 2 minutes to look at the theory I've posted on it.  So I've perhaps kind of hit a dead end.

>"The point I'm making is that very good, emotional, and timeless music
was written in 12 equal and near 12 equal before composers obtained the
depth of knowledge about the tuning that exists today."

  Indeed.  Although the caveat is...it's hard to do something in 12TET, far as composition and general mood, that hasn't already been done in some form.  So microtonal music, to me, is like getting access to "secondary colors" of mood instead of just primary ones.   I'm not a master artist/"painter"...but I figure I can at least try to make some new contributions to the palette.

>"Don't you realize that if you play 10:11:12, all of these mysterious

and evil critical band interactions will actually end up being in

perfect sync with one another? That's what this periodicity buzz stuff

is. Since when is that bad?"

Call me alien eared...but too much periodicity buzz, to me, is actually annoying...like running a huge mechanical-sounding amplitude modulator over a sound.  Its another one of those things...that seems to work best in moderation

>"If I put LFO on a square wave, it's creating "beating." So what?".
  Again, too much of such things just begin to sound mechanical, almost robotic, to me.  Especially when it comes to fast beating (slow beating sounds far less mechanical).  I actually love 9:10:11 or 10:11:12 chords...but acknowledge that I'd be hard-pressed to find fourth and fifth notes I could add to them while being able to use them as points of resolve.  For example, a 9:10:11:12 chord, to me, would sound over the edge...and I would, indeed, have a very tough time recognizing the individual notes due to all the quick beating involved...though 9:10:11 is fine.

--- On Thu, 6/16/11, Mike Battaglia <battaglia01@...> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: Theory of harmony between multiple chords
To: tuning@yahoogroups.com
Date: Thursday, June 16, 2011, 11:21 AM

On Thu, Jun 16, 2011 at 12:08 AM, Michael <djtrancendance@yahoo.com> wrote:

>

> MikeB>"I'm not sure about the respected/liked as a musician thing, but how

> does 6:9:10:11:12 grab you? That's basically a 2:3:4 trine on the

> outside with some notes that fit in the wrong way (the 9:10:11:12 in

> the upper fourth), just like a 10:12:15 is a 3/2 dyad with a 5/4 in

> there fitting in the wrong way."

>

>     Sounds decent, somewhere near the edge of what could work as a  "point of resolution".  The only reason I say "edge" is that the 10:11:12 cluster takes up most of the slack given for dissonance due to critical band issues.  But, in general...great example of what's "just good enough to work as a point of resolution"...in my book at least.  Even if people don't like it's mood...I'm pretty sure they could identify it as a foundation/resolve point and not a "strictly experimental chord".

Man, I can't believe you're still harping on this critical band thing.

Don't you realize that if you play 10:11:12, all of these mysterious

and evil critical band interactions will actually end up being in

perfect sync with one another? That's what this periodicity buzz stuff

is. Since when is that bad?

Critical band interactions are bad if they interfere with the

intelligibility of the sound. If they don't, then they're not bad. If

I put LFO on a square wave, it's creating "beating." So what?

-Mike

On Thu, Jun 16, 2011 at 2:38 PM, Michael <djtrancendance@...> wrote:
>
> >"If I put LFO on a square wave, it's creating "beating." So what?".
> For example, a 9:10:11:12 chord, to me, would sound over the edge...and I would, indeed, have a very tough time recognizing the individual notes due to all the quick beating involved...though 9:10:11 is fine.

I don't think that this is true. All of the beating will be
synchronized, so you should still be able to identify the notes. And
even so, it's not hard to adapt to learn to pick notes out of a
cluster. At one point, I had trained myself to identify the missing
note in an octave of notes played simultaneously minus 1 (assuming you
hit the notes decently close to the same volume). This was a stupid
party trick, so I haven't kept up with it, and I don't know how good
I'd do anymore with a full octave, but I guarantee you if you want to
test me with a fifth now I'll get it. (That's right, try me, skeptics!
I will crush your puny skepticism with the power of my iron will.)

Beating just sends a more chaotic signal to your brain, sometimes by
even creating FM in addition to AM (props to Graham for calling this
back in the day, and you can see a visual diagram of it on some of the
Gammatone plots), but there's nothing stopping your brain from
learning to adapt and make use of the signal anyway. So I urge you to
adapt!

-Mike

Mike, honestly, it pains me to hear you say that. You have produced a number of interesting ideas. Though it can be hard to make musical constructions that other people can appreciate - since they don't understand completely what went into the making of the music.

I've thrown a lot of books at you in the past - but this one is not dry theory, and you probably can find it in your local library.

"What to Listen for in Music" by Aaron Copeland. If you have not had a music history / humanities or music appreciation class this book might change the way you view music and make it easier to compose.

Here is a review for the book that makes me think it could be useful to you.

Anybody who has any interest in music owes it to themselves to read this book. In this definitive guide to musical enjoyment, Aaron Copeland takes a look at how to listen to music intelligently. Two questions are addressed in this interesting, in-depth study: Are you hearing everything that is going on? Are you really being sensitive to it?

It doesn't matter what kind of music you enjoy, everyone can get something out of this book. Though relating more closely to classical music, Aaron Copeland's ideas for listening to music will give the reader a better appreciation and understanding of whatever music they listen to.

From reading this book you will gain insight into the creative process of a composer. In laymen's terms, the book describes the way composers write music as well as how they actually listen to it. It explains that there are three separate planes upon which music is listened to. They are the sensuous plane, the expressive plane, and the sheerly musical plane. Copeland goes on to tell how music is heard on each plane and explains how each works, which I found very interesting.

Overall, Aaron Copeland's What To Listen For In Music is a good book that I recommend to anyone who has an interest in music or enjoys listening to it. A whole new level of listening ability can be gained from reading this book. It explains music from the composer's point of view, giving you insight into how music is composed, and how to listen to it, which gives you a deeper appreciation of music.

link at Amazon

http://www.amazon.com/What-Listen-Music-Aaron-Copland/dp/0451528670

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> For me it's always the same complaints...mainly about lack of building tension and "variety".  And that's even in songs like "Dimension", my Untwelve entry where I spent a month, a little time each day, adding variation to the piece.  Simply put...I've come to the conclusion I'm really not made to be a musician

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > > Plus, it is well approximated in a number of relatively accessible
> > > > tunings- 13, 23 and 36 edo for example.
> > >
> > > How is it tuned in 23-EDO? I know phi is 16 degrees of 23 (thereabouts, anyway).
> > >
> > > -Igs
> > >
> >
> > O, 9, 16, 23
>
> How come I get 0, 7, 16, 23 for
>
> 1:2*phi(mod2):phi:2
>
> ?
>
> Isn't 2*phi(mod2)=2*Phi-2?
>
> Kalle
>

phi^2, sorry

Thanks for taking the time to write this. Note that I was referring to phi-based relations for the fundamentals of harmonic spectra, not about phi spectra.

Before debating the whys and hows of these things, let's take a listen to what we're talking about. You predicted "probably awful" for the chord I described. Here is that chord (1st and 2nd chords of this example, the last chord is in a different voicing)

http://soundcloud.com/cameron-bobro/agapanthus-cbobro

Does that chord sound awful to you?

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
I think when people hear the phrase
> "phi-based difference tone timbre" they probably imagine some sort of
> sweet alien-sounding fused timbre from Jupiter. Although I think that
> little quantum units of inspiration like that are real, and that
> people are imagining a real sound, it doesn't have to do with the
> technical, mathematical meaning of the word difference tone as I
> learned it. Unless I'm missing something very subtle.
>
> > As far as beating and buzzing, as I have said, the sheer amount of unsynchronized buzz masks any concrete beating. And it's not just an interesting potential experiment, it's something I've been using regularly in music for several years now, with very positive reactions.
>
> Buzzing = beating. Carl's going to have a fit, but I'll just say it,
> because the data supports that theory and I've yet to see a model that
> makes better predictions. Plus, once he's ready to resurrect that
> discussion, I'm ready to pounce on his argument with the force of a
> thousand vicious tigers plus three dying suns. But I'm getting off
> track, because what I actually mean to say here is that I don't
> understand what you wrote above.
>
> > Heh, I'll find an example in which it's demonstrated clearly, and post it.
>
> OK. In the meantime, here's a little experiment to show you why I
> think difference tones just aren't involved at all: load up a timbre
> that looks like 1:1+phi:1+2phi:1+3phi:... so that the difference
> between every harmonic is phi. Or you can make it 1:phi:2phi-1:etc. A
> "phi-timbre," let's call it.
>
> It should sound trippy and cool and bell-like. Now put some distortion
> on it and crank it up, which actually will generate real combination
> tones and in abundance, and watch as the whole transforms into a
> beating, convulsant, discordant mess. What happened, you ask? Where is
> the self-reinforcing combination tone phi behavior that I was told
> about? How could things have gone so terribly wrong?
>
> Well I'll tell you what happened, Cameron. What happened is that
> first-order difference tones don't travel alone. They're accompanied
> by other order difference tones, like second and third order ones, and
> they're also accompanied by sum tones of all orders as well. Now
> "HALT!" you might say, "that makes no sense, because all of the
> difference and sum tones should still be in some kind of phi-like
> proportion with one another, thus rendering your mathematical
> reasoning absurd and your very personality contemptible!" Yes, but
> don't forget that you have to factor in the sum of each tone with
> -itself- -- aka for some frequency f, you're going to get f+f in the
> output (first-order sum tone) and f+f+f (second-order sum tone) and
> f+f+f+f and so on. Now you have a harmonic series to contend with
> alongside the phi one.
>
> The former is what they call "intermodulation distortion," and the
> latter is what they call "harmonic distortion," but they both have
> their origin in the combination of the spectrum with itself (or
> "convolution" of the spectrum with itself, if you're really hip). The
> two don't come separately from one another. If actual combination
> tones were involved, then phi timbres by themselves should beat like
> crazy, because the harmonic distortion products would clash with the
> intermodulation ones. But they don't, and hence we know we're talking
> more about amplitude modulation, and abstract applications of
> periodicity estimation, and so on, all of which might involve
> "frequency differences" without involving actual difference "tones."
>
> H0h0! Anyway, now that you've heard my mathematicizing, if you still
> have an experiment to demonstrate combination tones, and you're sure
> even after the above that they really are combination tones, I'm all
> for it.
>
> -Mike
>

On Fri, Jun 17, 2011 at 8:09 AM, lobawad <lobawad@...> wrote:
>
> Thanks for taking the time to write this. Note that I was referring to phi-based relations for the fundamentals of harmonic spectra, not about phi spectra.

OK, I see. The phi spectra example was just to make a psychoacoustic point.

> Before debating the whys and hows of these things, let's take a listen to what we're talking about. You predicted "probably awful" for the chord I described. Here is that chord (1st and 2nd chords of this example, the last chord is in a different voicing)
>
> http://soundcloud.com/cameron-bobro/agapanthus-cbobro
>
> Does that chord sound awful to you?

It sounds like a minor chord in second inversion with a really sharp
minor third. Since my days of JI drug addiction are long since past, I
think this sounds nicely detuned and rather interesting. That's my
impression of it. I would be surprised if my enjoyment of this chord
was coming from any subliminal perception of colliding difference
tones, because it seems to be coming from a combination of its
proximity to a minor chord and its being detuned. No, it does not
sound awful, although in the original context I was referring more to
some kind of overarching phi-based system. I may have misunderstood.

Why not run it through some distortion and force the difference tones
to pop out of the woodwork in abundance? Then try some ones that are
slightly off from it and we'll hear if there's any notable difference,
if it locks in at the phi ratio, etc.

-Mike

...but 2phi(mod2) is another "shadow" interval, which I probably use even more in harmony, the "first position" voicing being
1, 2phi(mod2),phi,2.

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> > > >
> > > > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > > > Plus, it is well approximated in a number of relatively accessible
> > > > > tunings- 13, 23 and 36 edo for example.
> > > >
> > > > How is it tuned in 23-EDO? I know phi is 16 degrees of 23 (thereabouts, anyway).
> > > >
> > > > -Igs
> > > >
> > >
> > > O, 9, 16, 23
> >
> > How come I get 0, 7, 16, 23 for
> >
> > 1:2*phi(mod2):phi:2
> >
> > ?
> >
> > Isn't 2*phi(mod2)=2*Phi-2?
> >
> > Kalle
> >
>
> phi^2, sorry
>

BTW, is this a live recording? If not, what did you use to render
this? This is great.

-Mike

On Fri, Jun 17, 2011 at 8:27 AM, Mike Battaglia <battaglia01@...> wrote:
> On Fri, Jun 17, 2011 at 8:09 AM, lobawad <lobawad@...> wrote:
>>
>> Thanks for taking the time to write this. Note that I was referring to phi-based relations for the fundamentals of harmonic spectra, not about phi spectra.
>
> OK, I see. The phi spectra example was just to make a psychoacoustic point.
>
>> Before debating the whys and hows of these things, let's take a listen to what we're talking about. You predicted "probably awful" for the chord I described. Here is that chord (1st and 2nd chords of this example, the last chord is in a different voicing)
>>
>> http://soundcloud.com/cameron-bobro/agapanthus-cbobro
>>
>> Does that chord sound awful to you?
>
> It sounds like a minor chord in second inversion with a really sharp
> minor third. Since my days of JI drug addiction are long since past, I
> think this sounds nicely detuned and rather interesting. That's my
> impression of it. I would be surprised if my enjoyment of this chord
> was coming from any subliminal perception of colliding difference
> tones, because it seems to be coming from a combination of its
> proximity to a minor chord and its being detuned. No, it does not
> sound awful, although in the original context I was referring more to
> some kind of overarching phi-based system. I may have misunderstood.
>
> Why not run it through some distortion and force the difference tones
> to pop out of the woodwork in abundance? Then try some ones that are
> slightly off from it and we'll hear if there's any notable difference,
> if it locks in at the phi ratio, etc.
>
> -Mike
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jun 17, 2011 at 8:09 AM, lobawad <lobawad@...> wrote:
> >
> > Thanks for taking the time to write this. Note that I was referring to phi-based relations for the fundamentals of harmonic spectra, not about phi spectra.
>
> OK, I see. The phi spectra example was just to make a psychoacoustic point.
>
> > Before debating the whys and hows of these things, let's take a listen to what we're talking about. You predicted "probably awful" for the chord I described. Here is that chord (1st and 2nd chords of this example, the last chord is in a different voicing)
> >
> > http://soundcloud.com/cameron-bobro/agapanthus-cbobro
> >
> > Does that chord sound awful to you?
>
> It sounds like a minor chord in second inversion with a really sharp
> minor third. Since my days of JI drug addiction are long since >past, I
> think this sounds nicely detuned and rather interesting. That's my
> impression of it.

A minor third of 367 cents? That is a curiosity worthy of note, I'd say. It can't be a matter of proximity to coincident partials, or "harmonic entropy", for those would point to a detuned major chord. An overbearing diatonic grid might concievably suggest a Db minor with the fifth doubled and in the bass, but that too would be pretty extreme and if the case, quite a mockery of JI and HE reasoning.

I also hear a "minorness" as one of the feelings of the chord, as does my son. His description was "minor-like", but he recognized it as not actually "minor", which I thought was very interesting.

>I would be surprised if my enjoyment of this chord
> was coming from any subliminal perception of colliding difference
> tones, because it seems to be coming from a combination of its
> proximity to a minor chord and its being detuned.

I think the question is, why isn't the chord beating like hell? Simply any-ol' detuning of a minor chord runs a good chance of being very discordant.

>No, it does not
> sound awful,>although in the original context I was referring more to
> some kind of overarching phi-based system.

I don't know about "phi-based". I think that there are a good number of ways to create sonorities which sound far less discordant in actual practice than they do on paper. Without altering timbre, that's a neat thing but not my cup of tea.

>
> Why not run it through some distortion and force the difference >tones
> to pop out of the woodwork in abundance? Then try some ones that are
> slightly off from it and we'll hear if there's any notable >difference,
> if it locks in at the phi ratio, etc.

I've tried distortions, doesn't change anything except to make the same thing only in garish colors, and I've found the window of mellowness to be quite narrow. It sounds like wobbly chugging "xenharmonic" music if you stray more than few cents. Really I'd like other people to try for themselves.

Thanks! I played the clarinet, multitrack. On this one I used headphone guide tracks throughout, because the "phi" vertical sonorities are finicky and the beating gets heavy with the smallest drift. The bass is synth, pretty much "sawtoothy", and on the middle two clarinet voices I used a sneaky digital process to increase the harmonic content of the clarinets so it's more toward quarter-duty pulse than the usual squarish content.

The truer and richer the harmonic content, I find, the better these kinds of sonorities, and more complex rational intervals as well, work.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> BTW, is this a live recording? If not, what did you use to render
> this? This is great.
>
> -Mike
>
>
>
> On Fri, Jun 17, 2011 at 8:27 AM, Mike Battaglia <battaglia01@...> wrote:
> > On Fri, Jun 17, 2011 at 8:09 AM, lobawad <lobawad@...> wrote:
> >>
> >> Thanks for taking the time to write this. Note that I was referring to phi-based relations for the fundamentals of harmonic spectra, not about phi spectra.
> >
> > OK, I see. The phi spectra example was just to make a psychoacoustic point.
> >
> >> Before debating the whys and hows of these things, let's take a listen to what we're talking about. You predicted "probably awful" for the chord I described. Here is that chord (1st and 2nd chords of this example, the last chord is in a different voicing)
> >>
> >> http://soundcloud.com/cameron-bobro/agapanthus-cbobro
> >>
> >> Does that chord sound awful to you?
> >
> > It sounds like a minor chord in second inversion with a really sharp
> > minor third. Since my days of JI drug addiction are long since past, I
> > think this sounds nicely detuned and rather interesting. That's my
> > impression of it. I would be surprised if my enjoyment of this chord
> > was coming from any subliminal perception of colliding difference
> > tones, because it seems to be coming from a combination of its
> > proximity to a minor chord and its being detuned. No, it does not
> > sound awful, although in the original context I was referring more to
> > some kind of overarching phi-based system. I may have misunderstood.
> >
> > Why not run it through some distortion and force the difference tones
> > to pop out of the woodwork in abundance? Then try some ones that are
> > slightly off from it and we'll hear if there's any notable difference,
> > if it locks in at the phi ratio, etc.
> >
> > -Mike
> >
>

On Fri, Jun 17, 2011 at 9:00 AM, lobawad <lobawad@...> wrote:
>
> A minor third of 367 cents? That is a curiosity worthy of note, I'd say. It can't be a matter of proximity to coincident partials, or "harmonic entropy", for those would point to a detuned major chord.

If that's 367 cents, then I'm going to lose my mind. I swear I hear
that as being more around 333 cents or so, not 367. Are you sure it's
367 cents? Does anyone have melodyne?

Actually, upon listening to it again, it might be 367 cents if that
fourth on the bottom is really flat. Is the outer dyad close to 8/5?
That's how I hear it.

> An overbearing diatonic grid might concievably suggest a Db minor with the fifth doubled and in the bass, but that too would be pretty extreme and if the case, quite a mockery of JI and HE reasoning.

I've been long aware that crazy distortions of categorical perception
are possible - I was at Paul Erlich's house, playing on his keyboard,
and went about 10 minutes before realizing that I was actually playing
in mavila, and that these insane ultra-flat major chords I was playing
were actually minor chords. They actually sounded like flat major
chords - not minor chords. It was insane. Then, when I figured it out,
I snapped my perception of things to hear them as minor chords, and
then I got "stuck" and couldn't switch it back. So yeah, I have no
idea how to explain any of that. But no matter how hard I try I can't
hear this chord as anything but minor.

> >I would be surprised if my enjoyment of this chord
> > was coming from any subliminal perception of colliding difference
> > tones, because it seems to be coming from a combination of its
> > proximity to a minor chord and its being detuned.
>
> I think the question is, why isn't the chord beating like hell? Simply any-ol' detuning of a minor chord runs a good chance of being very discordant.

I think it's not beating like hell because you're playing it on
separate multitracked clarinet tracks with a lot of reverb. For
starters, clarinets are instruments that have only even overtones.
Rather than me delving into another long explanation, try playing a
16-equal mavila fifth with a square wave, then try it with a saw wave,
and you'll see what I mean. I'm curious to see how all of this would
sound with a sawtooth wave or something.

Either way, beating and difference tones definitely do not have the
same origin, not at all, so if you're using difference tones to
explain beating, I'll have to take whatever your observation is and do
a bit of translating.

> >No, it does not
> > sound awful,>although in the original context I was referring more to
> > some kind of overarching phi-based system.
>
> I don't know about "phi-based". I think that there are a good number of ways to create sonorities which sound far less discordant in actual practice than they do on paper. Without altering timbre, that's a neat thing but not my cup of tea.

I would agree, but nowadays I chalk this up to the fact that paper
underestimates of the brain's capacity to adapt to extract information
from a signal, and to learn after repeated exposure to a "discordant,"
"noisy," chaotic stimulus to separate the figure from the ground.

After spending the last few weeks getting my head wrapped around
father temperament and mavila, everything sounds amazing. You cannot
play an unpleasant chord to me anymore. Mistuning now adds a lot of
character to things, so when you use these phi or pi or e-based
methods to deliberately generate chords that are far from just ratios,
you end up with a result that has a lot of character. That's my
perception, anyway.

> > Why not run it through some distortion and force the difference >tones
> > to pop out of the woodwork in abundance? Then try some ones that are
> > slightly off from it and we'll hear if there's any notable >difference,
> > if it locks in at the phi ratio, etc.
>
> I've tried distortions, doesn't change anything except to make the same thing only in garish colors, and I've found the window of mellowness to be quite narrow. It sounds like wobbly chugging "xenharmonic" music if you stray more than few cents. Really I'd like other people to try for themselves.

I can come up with some examples when I have some time, if you can
give me the specs for the chords to try out. What chord are you using
here?

Also, why do you say that distortion makes it sound garish? Do you
mean it starts to clash? Distortion is effectively a difference tone
generating machine, that's how distortion works, so if difference
tones are really contributing positively to the above chord, I would
expect adding more of them should enrich whatever the effect is.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jun 17, 2011 at 9:00 AM, lobawad <lobawad@...> wrote:
> >
> > A minor third of 367 cents? That is a curiosity worthy of note, I'd say. It can't be a matter of proximity to coincident partials, or "harmonic entropy", for those would point to a detuned major chord.
>
> If that's 367 cents, then I'm going to lose my mind. I swear I hear
> that as being more around 333 cents or so, not 367. Are you sure it's
> 367 cents? Does anyone have melodyne?

Told you it was trippy. :-)
>
> Actually, upon listening to it again, it might be 367 cents if that
> fourth on the bottom is really flat. Is the outer dyad close to 8/5?
> That's how I hear it.

Outer dyad is an octave. It is, in round cents, 0, 466, 833, 1200.
>
> > An overbearing diatonic grid might concievably suggest a Db minor with the fifth doubled and in the bass, but that too would be pretty extreme and if the case, quite a mockery of JI and HE reasoning.
>
> I've been long aware that crazy distortions of categorical perception
> are possible - I was at Paul Erlich's house, playing on his keyboard,
> and went about 10 minutes before realizing that I was actually playing
> in mavila, and that these insane ultra-flat major chords I was playing
> were actually minor chords. They actually sounded like flat major
> chords - not minor chords. It was insane. Then, when I figured it out,
> I snapped my perception of things to hear them as minor chords, and
> then I got "stuck" and couldn't switch it back. So yeah, I have no
> idea how to explain any of that. But no matter how hard I try I can't
> hear this chord as anything but minor.
>
> > >I would be surprised if my enjoyment of this chord
> > > was coming from any subliminal perception of colliding difference
> > > tones, because it seems to be coming from a combination of its
> > > proximity to a minor chord and its being detuned.
> >
> > I think the question is, why isn't the chord beating like hell? Simply any-ol' detuning of a minor chord runs a good chance of being very discordant.
>
> I think it's not beating like hell because you're playing it on
> separate multitracked clarinet tracks with a lot of reverb.

But I use this chord with all kinds of timbres- it never "chugs" or does that "wonky" thing.

>For
> starters, clarinets are instruments that have only even overtones.

Nope- sawtooth on the bottom, middle voices processed to have more or less the content of quarter-duty pulse, only the top voice is squarish. The first, piano, instance, has synth on top as well, so it's two saw(ish) and two quarter-duty pulse(ish).

> Rather than me delving into another long explanation, try playing a
> 16-equal mavila fifth with a square wave, then try it with a saw wave,
> and you'll see what I mean. I'm curious to see how all of this would
> sound with a sawtooth wave or something.

Well I'll find or make some more examples, it's not like I don't have years of the stuff lying around. :-)

> I would agree, but nowadays I chalk this up to the fact that paper
> underestimates of the brain's capacity to adapt to extract information
> from a signal, and to learn after repeated exposure to a "discordant,"
> "noisy," chaotic stimulus to separate the figure from the ground.
>
> After spending the last few weeks getting my head wrapped around
> father temperament and mavila, everything sounds amazing. You cannot
> play an unpleasant chord to me anymore. Mistuning now adds a lot of
> character to things, so when you use these phi or pi or e-based
> methods to deliberately generate chords that are far from just ratios,
> you end up with a result that has a lot of character. That's my
> perception, anyway.

I think that's part of it. It's hard for me to think that that's "all" there is to it, because I'm tripping on clearly percieved "minor" elements in what would better be described on paper as an aug. chord.

>
> Also, why do you say that distortion makes it sound garish? Do you
> mean it starts to clash?

No- doesn't clash, just sounds like the same thing but "loud".

Distortion is effectively a difference tone
> generating machine, that's how distortion works, so if difference
> tones are really contributing positively to the above chord, I would
> expect adding more of them should enrich whatever the effect is.

Yes, distortion enrichens the "oneness" of it.

Lemmee float you some "shadow" chords and see what you make of them, but at this very moment I have to run get my kid from school, so c-ya later!

On Fri, Jun 17, 2011 at 9:43 AM, lobawad <lobawad@...> wrote:
>
> > Actually, upon listening to it again, it might be 367 cents if that
> > fourth on the bottom is really flat. Is the outer dyad close to 8/5?
> > That's how I hear it.
>
> Outer dyad is an octave. It is, in round cents, 0, 466, 833, 1200.

I put in those figures here:

http://www.mikebattagliamusic.com/microscalegen/midigenerator.html

{0.0, 466.0, 833.0, 1200.0}

The result is that I do get something that sounds more augmented-ish.
So I still wonder if some kind of slight intonational difference from
what you originally played might have tipped the scales a bit towards
minor for me.

But you win: I hear the synchronous beating. And if I change the 466.0
to 476.0, the beating gets all messed up.

This chord is 1:1.309:1.618:2. Except for the doubled bottom note (the
2 on top, ignore it), this is a linearly even "isoharmonic" chord,
since there is a constant frequency difference here of (phi-1)/2.
These are exactly the chords that we were studying with the
periodicity buzz thread and the kind that were shown to cause
periodicity buzz. JI chords cause it because they're a type of these,
not because they're periodic, so it should really be called
isoharmonicity buzz, but the unfortunate misnomer may be here to stay.
The effect is very fragile, and is much more sensitive to mistuning
than f0 estimation is. If instead you have a chord like 8:9:11, the
beating/buzzing will be in a 2:1 polyrhythm, as you can see visually
by going back to the gammatone plots, and by noting that 11-9 is 2 and
9-8 is 1. This behavior will manifest for these sorts of chords
whether or not the frequency difference is based on phi, e, pi, or an
integer. That's how they work.

You can also try 17:20:23:26, 17:20:23:26:29, 17:20:23:26:29:35, or
17:20:23:26:29:32:35 for some interesting chords that sound like
father in 13-equal, but also buzz very coherently. They have nothing
to do with phi, but isoharmonicity carries a power all its own.

Now, I have a question: which one of these five chords do you think
sounds the most fused?

/tuning/files/MikeBattaglia/phitest.mid

> > I think it's not beating like hell because you're playing it on
> > separate multitracked clarinet tracks with a lot of reverb.
>
> But I use this chord with all kinds of timbres- it never "chugs" or does that "wonky" thing.

See above - now that I realize we're dealing with an isoharmonic chord
it all makes sense.

-Mike

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:

> Outer dyad is an octave. It is, in round cents, 0, 466, 833, 1200.

With some effort I deduce this must be 1, (phi+1)/2, phi, 2.

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

> The result is that I do get something that sounds more augmented-ish.

If you think 2 phi - 2 is like a major third, I guess. The step sizes of 1:(phi+1)/2:phi:2 go (phi+1)/2, 2 phi - 2, 2 phi - 2.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > The result is that I do get something that sounds more augmented-ish.
>
> If you think 2 phi - 2 is like a major third, I guess. The step sizes of 1:(phi+1)/2:phi:2 go (phi+1)/2, 2 phi - 2, 2 phi - 2.

Another phi doodad like a major third is sqrt(phi), which is 416.545 cents, less than a cent shy of 14/11. I've mentioned before that this could serve as a generator for the 49&72 temperament, and I'll add to that if it didn't already get mentioned that the 2.5/3.7/3.11/3 subgroup has a complexity in this system low enough for a lot of people. So you get 5:7:11 chords and 1:phi:phi^2 chords both with this.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Jun 17, 2011 at 9:43 AM, lobawad <lobawad@...> wrote:
> >
> > > Actually, upon listening to it again, it might be 367 cents if that
> > > fourth on the bottom is really flat. Is the outer dyad close to 8/5?
> > > That's how I hear it.
> >
> > Outer dyad is an octave. It is, in round cents, 0, 466, 833, 1200.
>
> I put in those figures here:
>
> http://www.mikebattagliamusic.com/microscalegen/midigenerator.html
>
> {0.0, 466.0, 833.0, 1200.0}
>
> The result is that I do get something that sounds more augmented-ish.
> So I still wonder if some kind of slight intonational difference from
> what you originally played might have tipped the scales a bit towards
> minor for me.

I suspect that it's probably a matter of relationship(s) of emphasized frequencies somewhere within the overall specrtum of the chord.

The most simple example of this kind of thing would be two tones in unison, the spectrum of one with a radically emphasized fifth partial, of the other with a radically emphasized fourth partial. I think it's safe to say that there will be a tendency to percieve this unison dyad as having a "major" quality, don't you? Of course you can test this for yourself.

If this is the case, we can make the prediction that this "phi" chord could assume a feeling of other character classes as well. Highly ambiguous and inharmonic by any traditional analysis, therefore offering a great number of intraspectral relation possibilities to be emphasized, the chord performed with other timbres could concievably sound "major", "neutral" etc. With sines or straight raw waveforms such as sawtooth, I think it should sound more or less "augmented".

You know that this is true of any highly complex vertical sonority, and you've probably guessed that when I speak of making predictions I have, of course, already tested to be sure that they are likely to be sound. :-)

>
> But you win: I hear the synchronous beating. And if I change the >466.0
> to 476.0, the beating gets all messed up.

"Winning" is when we can describe things such that running the description backwards, i.e., as part of a generative process, and create more useful material for music.

>
> This chord is 1:1.309:1.618:2. Except for the doubled bottom note (the
> 2 on top, ignore it), this is a linearly even "isoharmonic" chord,
> since there is a constant frequency difference here of (phi-1)/2.
> These are exactly the chords that we were studying with the
> periodicity buzz thread and the kind that were shown to cause
> periodicity buzz. JI chords cause it because they're a type of these,
> not because they're periodic, so it should really be called
> isoharmonicity buzz, but the unfortunate misnomer may be here to stay.

Yip. Michael Sheiman pointed this out a couple of years ago here. He did not articulate the point well, hardly suprising considering the incessant jeering and being told to buzz off he recieved, but he did bring this up. I for one will not use the bogus term "periocicity buzz" and will use "isoharmonicity".

> The effect is very fragile, and is much more sensitive to mistuning
> than f0 estimation is. If instead you have a chord like 8:9:11, the
> beating/buzzing will be in a 2:1 polyrhythm, as you can see visually
> by going back to the gammatone plots, and by noting that 11-9 is 2 and
> 9-8 is 1.

Yes. Fragility is something of a problem for me: for all that I work with and love synthesizers, my background and biggest axe are acoustic, as was my point of entry into microtonalism. These particular materials are, for me, reserved for synthesizers or acoustic instruments combined (and let's face it, guided by) synthesizers.

>This behavior will manifest for these sorts of chords
> whether or not the frequency difference is based on phi, e, pi, or an
> integer. That's how they work.

Yes. phi has positive attributes I mentioned earlier, but it's certainly not the only possiblity.
>
> You can also try 17:20:23:26, 17:20:23:26:29, 17:20:23:26:29:35, or
> 17:20:23:26:29:32:35 for some interesting chords that sound like
> father in 13-equal, but also buzz very coherently. They have nothing
> to do with phi, but isoharmonicity carries a power all its own.

Yes, it's a concrete sensation. Dismissing "rational intonation" on account of "complexity" is numerology, for intervals which are complex on paper do not necessarily fail to produce tangible or even "simple" things in the realm of perception.

>
> Now, I have a question: which one of these five chords do you think
> sounds the most fused?
>
> /tuning/files/MikeBattaglia/phitest.mid

I am unable to critically segregate the individual vertical sonorities from the passage as a whole, which a good sign musically, but means that any given window of the vertical flip-flops in my perception as far as being the "most" or "least" of anything. Sorry- could you offer a slow version?

>
> > > I think it's not beating like hell because you're playing it on
> > > separate multitracked clarinet tracks with a lot of reverb.
> >
> > But I use this chord with all kinds of timbres- it never "chugs" or does that "wonky" thing.
>
> See above - now that I realize we're dealing with an isoharmonic chord
> it all makes sense.
>
> -Mike
>
Note that I earlier used a dry, verifiable description: simple difference-tone structure. If we reduce the variety or complexity of what is created (doesn't matter how) by combination tones, we do tend to get tangible psychoacoustic phenomena (however they're caused). That's not mystical or numerological.

So you can see what I mean by "shadow" sonorities. Inharmonicity/great complexity in the spectra, but sharing simplicities with simple Just chords, e.g. isoharmonic buzz. A different sound to that of straight inharmonicity/complexity, but related in feel to that of simple rational chords performed with imperfect and noisy spectra. There's more to it than that- monkeying with the "diatonic grid" is important to me- but that's the basic psychoacoustic description.