Re: [tuning] Re: PHI interval tuning (for Michael S): with "Phicicles" song example :-)

Mike B>"Nonetheless, I can't ignore the simple fact that your phi scale does sound great."

   Thanks...it's nice to know I'm not the only one around (beside maybe Chris and Rick) with "alien ears". :-)

>"Is it that you're taking equal divisions of phi and using that as a period instead of 2/1?"

  There are no "equal divisions", at least if you mean that in the same way as you do with 12TET IE 2^(x/12) divisions of 2/1.

  But, yes, I am using PHI as the period in place of the 2/1 octave.  And then I am taking "inverse powers" of PHI IE (1/PHI)^x + 1 to get the other tones.  Note that (1/PHI)^1 + 1 = the "PHI-tave" itself, and (1/PHI)^2 + 1, (1/PHI)^2 + 1 keeps on dividing these smaller areas in the same fashion that 1.618034 divides 2/1...until you get to about (1/PHI)^6 + 1 =
1.0557 and can't go any further due to excessive beating roughness for values under 1.05.

>"If so, I think the unique sound that it has stems from the fact the phi ratio itself is extremely high entropy, but when you stack a bunch of copies of phi on top of each other you eventually come close to familiar small-integer ratios."
  Could well be true.  I noticed my scale has quite a few (around 60-70%) of the notes fairly near to in common with the x/8 harmonic series (8/8 9/8 10/8 etc.)...yet, at least to my ears, the beating sounds much more relaxed in the PHI scale than with the harmonic series (a bit like the sound of a string section vs. an organ).  That became obvious when I made my last sound example using that harmonic series.

>"I do notice that it does seem to have a lot of maximally different

"tone colors" as you mentioned above, or tone chroma, as I prefer to

call it - "
  This is good news because the other thrust advantage I am going for, beside more relaxed-sounding beating vs. the harmonic series, is a larger range of tonal color (particularly since the harmonic series itself refers back to the tonal color of the tonic).

>"The pattern I notice is that the farther harmonically "out" you

get from a tone, the more the tone chroma changes. "
   I will admit, I have not heard the term chroma...what does it mean?     
   Though I will admit a huge reason I was attracted to working with PHI is the mystery "why does an interval so statistically far from 12TET somehow sound so natural to me"?

>"The fact that this scale uses the opposite approach is something I

especially like. Perhaps the fact that the period itself is so

dissonant has something to do with it as well."
   That, however, I do actually doubt a bit.  In fact I purposefully round the period to 1.625 or 13/8...because it is the only fraction on the harmonic series I found that beats with octave-like smooth-ness against 1/1 and yet maintains virtually the same sense of tonal color as 1.618 (unlike 8/5 AKA 1.6, for example).  So basically 1.625 "sounds like PHI minus the excessive beating", at least to my ears.
  
   But I do suspect very strongly...that the PHI scale has a weird property of not increasing dissonance notice-ably as more notes are played within the PHI-tave.  Meaning where-as
A) Playing any one interval in 12TET will likely sound cleaner than in my PHI scale
B) Playing any two in 12TET will sound a tad cleaner

C) Playing three will sound more or less the same
D) Playing four will actually begin to sound more natural in my PHI scale
etc.

   Simply put, the PHI scale seems to lean itself more toward a sense of relaxation and resolve with large chords and not small ones.  It indeed has a somewhat opposite effect on perceived consonance when adding extra notes to a chord...and the "consonance penalty" for adding notes seems much lower than with JI, at least to my ears.

  So, if you're not over-glorifying it, it means that my PHI scale is achieving the exact goal I designed it for: to make it possible to make huge chords with huge degrees of tonal color within a small interval space sound fairly relaxed.

   The final challenge, of course, is do you think my scale sounds better than the x/8 harmonic series when all tones of both my scale and the series are played at once (and, if not, what makes the harmonic series better that I can research more into and improve)?

-Michael

> But, yes, I am using PHI as the period in place of the 2/1 octave. And
> then I am taking "inverse powers" of PHI IE (1/PHI)^x + 1 to get the other
> tones. Note that (1/PHI)^1 + 1 = the "PHI-tave" itself, and (1/PHI)^2 + 1,
> (1/PHI)^2 + 1 keeps on dividing these smaller areas in the same fashion that
> 1.618034 divides 2/1...until you get to about (1/PHI)^6 + 1 =
> 1.0557 and can't go any further due to excessive beating roughness for
> values under 1.05.

That's interesting. What's the reason for this approach?

Also, what about the fact that the fact that the bandwidth of each
cochlear auditory filter is going to change per register? What might
beat in a low register might not beat up at 8K.

> Could well be true. I noticed my scale has quite a few (around 60-70%) of
> the notes fairly near to in common with the x/8 harmonic series (8/8 9/8
> 10/8 etc.)...yet, at least to my ears, the beating sounds much more relaxed
> in the PHI scale than with the harmonic series (a bit like the sound of a
> string section vs. an organ). That became obvious when I made my last sound
> example using that harmonic series.

There is something pleasant about the beating pattern you have... I
don't know if it really sounds "better" than the harmonic series or if
the harmonic series is just different.

> I will admit, I have not heard the term chroma...what does it mean?
> Though I will admit a huge reason I was attracted to working with PHI is
> the mystery "why does an interval so statistically far from 12TET somehow
> sound so natural to me"?

Tone chroma is also referred to as "pitch color" and refers to a
perceptual quality that a note will have; this quality is usually
shared by all notes of a certain pitch class regardless of what octave
they are in. For example, a C has a certain chroma, D has a different
chroma, etc. Supposedly anyone can become aware of these subtle
characteristics of different notes, although people with absolute
pitch have greater ease at assigning them labels and recognizing them
later.

What is your justification for using PHI in this case though? The PHI
interval is a pretty cool sound, although what I like about it is that
it is almost maximally atonal from an HE standpoint - that doesn't
seem like the reason you're using it though. Then again, sometimes
13/8 itself sounds pretty out there to my ears.

> The final challenge, of course, is do you think my scale sounds better
> than the x/8 harmonic series when all tones of both my scale and the series
> are played at once (and, if not, what makes the harmonic series better that
> I can research more into and improve)?

You can't hope to quantify something like that. You might think some
kind of organizational pattern like 5-limit JI sounds better than
random notes being played, but atonal music sounds great as well. They
are simply different.

-Mike

One more thing... Have you tried making any examples using timbres
with overtones rooted in your "faux-harmonix" phi series rather than
the harmonic series? That would likely sound very cool.

-Mike

On Thu, May 7, 2009 at 11:05 PM, Mike Battaglia <battaglia01@...> wrote:
>> But, yes, I am using PHI as the period in place of the 2/1 octave. And
>> then I am taking "inverse powers" of PHI IE (1/PHI)^x + 1 to get the other
>> tones. Note that (1/PHI)^1 + 1 = the "PHI-tave" itself, and (1/PHI)^2 + 1,
>> (1/PHI)^2 + 1 keeps on dividing these smaller areas in the same fashion that
>> 1.618034 divides 2/1...until you get to about (1/PHI)^6 + 1 =
>> 1.0557 and can't go any further due to excessive beating roughness for
>> values under 1.05.
>
> That's interesting. What's the reason for this approach?
>
> Also, what about the fact that the fact that the bandwidth of each
> cochlear auditory filter is going to change per register? What might
> beat in a low register might not beat up at 8K.
>
>> Could well be true. I noticed my scale has quite a few (around 60-70%) of
>> the notes fairly near to in common with the x/8 harmonic series (8/8 9/8
>> 10/8 etc.)...yet, at least to my ears, the beating sounds much more relaxed
>> in the PHI scale than with the harmonic series (a bit like the sound of a
>> string section vs. an organ). That became obvious when I made my last sound
>> example using that harmonic series.
>
> There is something pleasant about the beating pattern you have... I
> don't know if it really sounds "better" than the harmonic series or if
> the harmonic series is just different.
>
>> I will admit, I have not heard the term chroma...what does it mean?
>> Though I will admit a huge reason I was attracted to working with PHI is
>> the mystery "why does an interval so statistically far from 12TET somehow
>> sound so natural to me"?
>
> Tone chroma is also referred to as "pitch color" and refers to a
> perceptual quality that a note will have; this quality is usually
> shared by all notes of a certain pitch class regardless of what octave
> they are in. For example, a C has a certain chroma, D has a different
> chroma, etc. Supposedly anyone can become aware of these subtle
> characteristics of different notes, although people with absolute
> pitch have greater ease at assigning them labels and recognizing them
> later.
>
> What is your justification for using PHI in this case though? The PHI
> interval is a pretty cool sound, although what I like about it is that
> it is almost maximally atonal from an HE standpoint - that doesn't
> seem like the reason you're using it though. Then again, sometimes
> 13/8 itself sounds pretty out there to my ears.
>
>> The final challenge, of course, is do you think my scale sounds better
>> than the x/8 harmonic series when all tones of both my scale and the series
>> are played at once (and, if not, what makes the harmonic series better that
>> I can research more into and improve)?
>
> You can't hope to quantify something like that. You might think some
> kind of organizational pattern like 5-limit JI sounds better than
> random notes being played, but atonal music sounds great as well. They
> are simply different.
>
> -Mike
>

Me> 1.618034 divides 2/1...until you get to about (1/PHI)^6 + 1 =

> 1.0557 and can't go any further due to excessive beating roughness for

> values under 1.05.

Mike B>That's interesting. What's the reason for this approach?
It splits the PHI-tave in the exact same fashion PHI splits a line from 1 to 2 in art.
    If you look at http://en.wikipedia.org/wiki/File:Fibonacci_spiral_34.svg...you'll see how the sides of the squares become smaller at a fixed rate.  My taking 0.618034^x has the same effect: it makes the distance between (1/PHI)^6 + 1 and 1/1 fold into smaller parts in the same way the squares fold into smaller parts in the Fibonacci spiral.  You'll also notice, far as distances from one tone to the next, that 0.05557 + 0.09017 (the next note in the scale) = about 0.1459 (the third note in the scale) and so on...thus the scale has the bizarre property of being both exponential (in the sense of 0.618^x) and additive (in the sense that taking the distance of each note from 1 and then adding those differences enables you to find the next note by adding the last two).  And, then, of course...there's the coincidence that 0.618 + 1 = 1.618 and 1.618 * 1.23607 (the fourth note in the scale) perfectly intersects the 2/1 octave.  So many symmetries are
possible...

>"Also, what about the fact that the fact that the bandwidth of each

cochlear auditory filter is going to change per register? What might

beat in a low register might not beat up at 8K."
   
True but, as we know, there is nothing dissonant about non-beating tones.  The idea is that when there is beating...it occurs in such a way that it forms something symmetric enough to be easily interpreted (in the same way even complex art using the golden ratio is able to be easily interpreted).

>"Tone chroma is also referred to as "pitch color" and refers to a

perceptual quality that a note will have; this quality is usually

shared by all notes of a certain pitch class regardless of what octave

they are in.
  Right, meaning C5 and C6 have the same chroma. 

>"although what I like about it is that it is almost maximally atonal from an HE standpoint - that doesn't seem like the reason you're using it though."
  I realize PHI itself is maximally a-tonal from music theory, but I also realize much of that is based on the idea of just having one interval playing.

   Also, I agree with you 13/8 is a fairly weird interval by itself, but once you start adding a few tones to "center" it...it begins to feel more natural (at least to my ears).  Whereas most scales I hear become less natural when more than a certain # of notes are played closely together...doing that seems to have an opposite effect in these PHI scales...an effect of making the structure (of the chord formed by all the notes) feel more aligned and relaxed.

Me> "The final challenge, of course, is do you think my scale sounds better than the x/8 harmonic series when all tones of both my scale and the series are played at once (and, if not, what makes the harmonic series better that I can research more into and improve)?"

Mike B>"You can't hope to quantify something like that. You might think some

kind of organizational pattern like 5-limit JI sounds better than

random notes being played, but atonal music sounds great as well. They

are simply different."

   One thing I have noticed, is that having music with low consonance that seems steady in its level of consonance actually often sounds much more resolved than very consonant and structured music with sudden dips in consonance.  The whole feeling of a composition's having a steady goal so far as introducing consonance/dissonance in a way that feels guided seems crucial to me.
    Another way to say it is I wonder if any of the notes/intervals in my scales stick out as being considerably more-or-less consonant than the rest.  That's what I want to try and avoid...the sense something was put there by accident that makes you have to really grind your mind to try and figure out how consonant/dissonant what's coming up next may sound.

-Michael

>"One more thing... Have you tried making any examples using timbres

with overtones rooted in your "faux-harmonix" phi series rather than

the harmonic series? That would likely sound very cool."
   Hmm...that would likely be quite cool...but any ideas how on earth I would make such instruments/sounds?

-Michael

--- On Thu, 5/7/09, Mike Battaglia <battaglia01@gmail.com> wrote:

From: Mike Battaglia <battaglia01@...>
Subject: Re: [tuning] Re: PHI interval tuning (for Michael S): with "Phicicles" song example :-)
To: tuning@yahoogroups.com
Date: Thursday, May 7, 2009, 8:29 PM

One more thing... Have you tried making any examples using timbres

with overtones rooted in your "faux-harmonix" phi series rather than

the harmonic series? That would likely sound very cool.

-Mike

On Thu, May 7, 2009 at 11:05 PM, Mike Battaglia <battaglia01@ gmail.com> wrote:

>> But, yes, I am using PHI as the period in place of the 2/1 octave. And

>> then I am taking "inverse powers" of PHI IE (1/PHI)^x + 1 to get the other

>> tones. Note that (1/PHI)^1 + 1 = the "PHI-tave" itself, and (1/PHI)^2 + 1,

>> (1/PHI)^2 + 1 keeps on dividing these smaller areas in the same fashion that

>> 1.618034 divides 2/1...until you get to about (1/PHI)^6 + 1 =

>> 1.0557 and can't go any further due to excessive beating roughness for

>> values under 1.05.

>

> That's interesting. What's the reason for this approach?

>

> Also, what about the fact that the fact that the bandwidth of each

> cochlear auditory filter is going to change per register? What might

> beat in a low register might not beat up at 8K.

>

>> Could well be true. I noticed my scale has quite a few (around 60-70%) of

>> the notes fairly near to in common with the x/8 harmonic series (8/8 9/8

>> 10/8 etc.)...yet, at least to my ears, the beating sounds much more relaxed

>> in the PHI scale than with the harmonic series (a bit like the sound of a

>> string section vs. an organ). That became obvious when I made my last sound

>> example using that harmonic series.

>

> There is something pleasant about the beating pattern you have... I

> don't know if it really sounds "better" than the harmonic series or if

> the harmonic series is just different.

>

>> I will admit, I have not heard the term chroma...what does it mean?

>> Though I will admit a huge reason I was attracted to working with PHI is

>> the mystery "why does an interval so statistically far from 12TET somehow

>> sound so natural to me"?

>

> Tone chroma is also referred to as "pitch color" and refers to a

> perceptual quality that a note will have; this quality is usually

> shared by all notes of a certain pitch class regardless of what octave

> they are in. For example, a C has a certain chroma, D has a different

> chroma, etc. Supposedly anyone can become aware of these subtle

> characteristics of different notes, although people with absolute

> pitch have greater ease at assigning them labels and recognizing them

> later.

>

> What is your justification for using PHI in this case though? The PHI

> interval is a pretty cool sound, although what I like about it is that

> it is almost maximally atonal from an HE standpoint - that doesn't

> seem like the reason you're using it though. Then again, sometimes

> 13/8 itself sounds pretty out there to my ears.

>

>> The final challenge, of course, is do you think my scale sounds better

>> than the x/8 harmonic series when all tones of both my scale and the series

>> are played at once (and, if not, what makes the harmonic series better that

>> I can research more into and improve)?

>

> You can't hope to quantify something like that. You might think some

> kind of organizational pattern like 5-limit JI sounds better than

> random notes being played, but atonal music sounds great as well. They

> are simply different.

>

> -Mike

>

> You'll also notice, far as distances from one tone to the next, that 0.05557
> + 0.09017 (the next note in the scale) = about 0.1459 (the third note in the scale) and so on...thus the
> scale has the bizarre property of being both exponential (in the sense of
> 0.618^x) and additive (in the sense that taking the distance of each note
> from 1 and then adding those differences enables you to find the next note
> by adding the last two).

I don't understand this. You claim that the scale's "additive"
properties cause some kind of pleasant reinforcement whereby the
"difference tone" between each frequency matches the previous note in
the scale, correct? What are you saying the acoustic end result of
this "exponential" property is?

> And, then, of course...there's the coincidence
> that 0.618 + 1 = 1.618 and 1.618 * 1.23607 (the fourth note in the scale)
> perfectly intersects the 2/1 octave. So many symmetries are possible...

This is very cool and I can see it being used to create some pretty
cool sounds. I would doubt if it sounded anything like familiar tonal
music though. I think the concept would work best with sounds whose
overtones are detuned to match your phi scale a la Sethares, though
I'm not sure how you would really match them up in this case. I could
see that doing that might lead to some very interesting "pseudo-tonal"
heirarchies, though.

> Right, meaning C5 and C6 have the same chroma.

Right, and they have a different "tone-height".

> I realize PHI itself is maximally a-tonal from music theory, but I also
> realize much of that is based on the idea of just having one interval
> playing.

Maximally inharmonic, I should say. It's pretty close to 13/8, but
13/8 is difficult to place as an isolated interval for me.

> Also, I agree with you 13/8 is a fairly weird interval by itself, but
> once you start adding a few tones to "center" it...it begins to feel more
> natural (at least to my ears). Whereas most scales I hear become less
> natural when more than a certain # of notes are played closely
> together...doing that seems to have an opposite effect in these PHI
> scales...an effect of making the structure (of the chord formed by all the
> notes) feel more aligned and relaxed.

Something to think about... If you play in a C major scale CDEGAB,
that still sounds pretty "aligned" and "relaxed" and "resonant" to me
(especially if you tune the A to 27/16). If you throw the F in there,
CDEFGAB, the whole thing sounds much less relaxed, no matter whether
you put the A in there or leave it out. I doubt if it has anything to
do with beating. Some food for thought.

> One thing I have noticed, is that having music with low consonance that
> seems steady in its level of consonance actually often sounds much more
> resolved than very consonant and structured music with sudden dips in
> consonance. The whole feeling of a composition's having a steady goal so
> far as introducing consonance/dissonance in a way that feels guided seems
> crucial to me.

Do you have any examples of this?

-Mike

Mike B>"The phi interval is the noble mediant between 1/1 and 2/1. "

  I'll come back to this....
  Now I realize the paper was indeed using a similar way to split between tones to make a scale.  What threw me off was the fact it was taking the noble mediant between pre-existing diatonic scale fractions rather than between 1/1 and 2/1 and then between the noble mediant of the result and 1 and so forth (as I do in my scale).  So the result is completely different in their case (and I still don't see the usefulness of the paper beyond saying "noble mediant" is another term to describe PHI by)...but at least now I know that term.

Mike B>"What is likely is that the scale structure repeating at phi is an easily

recognizable pattern that leads to some perceptual nature of

"equivalence, " although it's not the same type of equivalence as 2/1

chroma equivalence."

    Exactly, and the perceptual equivalence, so far as the equivalence of periodic buzz, is what I call "proportionate beating" or "symmetrical beating".
  It's hard to explain why in pure and simple mathematics, but it does seem like the mind is good at aligning PHI based ratios (the obvious one being 1.618034) to mesh with harmonic-series ratios like 1.625 when needed.  This is one phenomena I am having a heck of a time explaining with math...just like Plompt and Llevelt's theory of dissonance curves (which were derived by hearing tests rather than mathematical equations)...you really just have to listen to get a sense for what the continuum of beating-proportionality is like.

-Michael

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > But, yes, I am using PHI as the period in place of the 2/1 octave. And
> > then I am taking "inverse powers" of PHI IE (1/PHI)^x + 1 to get the other
> > tones. Note that (1/PHI)^1 + 1 = the "PHI-tave" itself, and (1/PHI)^2 + 1,
> > (1/PHI)^2 + 1 keeps on dividing these smaller areas in the same fashion that
> > 1.618034 divides 2/1...until you get to about (1/PHI)^6 + 1 =
> > 1.0557 and can't go any further due to excessive beating roughness for
> > values under 1.05.
>

But Mike (S),

I already proved that not all powers of x in (1/PHI)^x + 1 are PHI numbers (Tuning digest no 6173 on 6/5/09, answer 5a). Also that calling the generating interval of PHI an "equivalence" like the 8ve will lead to all notes having the same name. eg 1: in 36TET, all 35 notes can be generated from PHI 25 or its inverse 11, eg 2: for pure PHI's, these will spiral off to infinity and beyond?? So I'm not sure what you're saying here.

-Rick
> That's interesting. What's the reason for this approach?
>
> Also, what about the fact that the fact that the bandwidth of each
> cochlear auditory filter is going to change per register? What might
> beat in a low register might not beat up at 8K.
>
> > Could well be true. I noticed my scale has quite a few (around 60-70%) of
> > the notes fairly near to in common with the x/8 harmonic series (8/8 9/8
> > 10/8 etc.)...yet, at least to my ears, the beating sounds much more relaxed
> > in the PHI scale than with the harmonic series (a bit like the sound of a
> > string section vs. an organ). That became obvious when I made my last sound
> > example using that harmonic series.
>
> There is something pleasant about the beating pattern you have... I
> don't know if it really sounds "better" than the harmonic series or if
> the harmonic series is just different.
>
> > I will admit, I have not heard the term chroma...what does it mean?
> > Though I will admit a huge reason I was attracted to working with PHI is
> > the mystery "why does an interval so statistically far from 12TET somehow
> > sound so natural to me"?
>
> Tone chroma is also referred to as "pitch color" and refers to a
> perceptual quality that a note will have; this quality is usually
> shared by all notes of a certain pitch class regardless of what octave
> they are in. For example, a C has a certain chroma, D has a different
> chroma, etc. Supposedly anyone can become aware of these subtle
> characteristics of different notes, although people with absolute
> pitch have greater ease at assigning them labels and recognizing them
> later.
>
> What is your justification for using PHI in this case though? The PHI
> interval is a pretty cool sound, although what I like about it is that
> it is almost maximally atonal from an HE standpoint - that doesn't
> seem like the reason you're using it though. Then again, sometimes
> 13/8 itself sounds pretty out there to my ears.
>
> > The final challenge, of course, is do you think my scale sounds better
> > than the x/8 harmonic series when all tones of both my scale and the series
> > are played at once (and, if not, what makes the harmonic series better that
> > I can research more into and improve)?
>
> You can't hope to quantify something like that. You might think some
> kind of organizational pattern like 5-limit JI sounds better than
> random notes being played, but atonal music sounds great as well. They
> are simply different.
>
> -Mike
>