Golden ratio discovered in a quantum world

here is a tuning relevant science article

Golden ratio discovered in a quantum world

"Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture."

http://esciencenews.com/articles/2010/01/07/golden.ratio.discovered.a.quantum.world

Don't see that every day...

Michael !! More Golden tunings please!!

Chris

Chris,

Interesting, so the first two notes match the quantum ratio and the resonance is symmetrical.
But, to establish a pattern used for a scale I'd need more notes from the experiment to see a true pattern (PHI could be used only multipicatively, additively....based on the information given).

The highest symmetry IMVHO acheivable is to make the whole scale out of consecutive Golden Sections the same way architects do (which is what I did in my scale, bearing no "homage" to any other popular tuning system IE meantone, JI, etc.).

But it well could be, that the notes in said below experiment have a different type of symmetry or additional symmetry (additive, logarithmic, etc.)
One of the reasons I gave up improving the Golden Sections PHI scale was that I could get all notes of the Silver Ratio scale to have additive AND multiplication symmetries (and not just multicative ones). And still, I think the Silver Ratio scale sounds a good deal better...but that may be about to change if I can find a newly researched way to arrange the symmetry.

________________________________
From: christopherv <chrisvaisvil@...>
To: tuning@yahoogroups.com
Sent: Sat, January 9, 2010 11:05:28 AM
Subject: [tuning] Golden ratio discovered in a quantum world

here is a tuning relevant science article

Golden ratio discovered in a quantum world

"Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618…, which is the golden ratio famous from art and architecture. "

http://esciencenews .com/articles/ 2010/01/07/ golden.ratio. discovered. a.quantum. world

Don't see that every day...

Michael !! More Golden tunings please!!

Chris

What would happen if PHI was used to generate a PHI harmonic series and then
the notes of that series collapsed into one PHI octave just like the octave
based harmonic series?

Ie. C, C, g, c, e, b flat.... etc but in PHI intervals.

Just a thought. I might even be able to do this.

Chris

On Sat, Jan 9, 2010 at 1:05 PM, Michael <djtrancendance@...> wrote:

>
>
> Chris,
>
> Interesting, so the first two notes match the quantum ratio and the
> resonance is symmetrical.
> But, to establish a pattern used for a scale I'd need more notes from the
> experiment to see a true pattern (PHI could be used only multipicatively,
> additively....based on the information given).
>
> The highest symmetry IMVHO acheivable is to make the whole scale out of
> consecutive Golden Sections the same way architects do (which is what I did
> in my scale, bearing no "homage" to any other popular tuning system IE
> meantone, JI, etc.).
>
> But it well could be, that the notes in said below experiment have a
> different type of symmetry or additional symmetry (additive, logarithmic,
> etc.)
> One of the reasons I gave up improving the Golden Sections PHI scale was
> that I could get all notes of the Silver Ratio scale to have additive AND
> multiplication symmetries (and not just multicative ones). And still, I
> think the Silver Ratio scale sounds a good deal better...but that may be
> about to change if I can find a newly researched way to arrange the
> symmetry.
>
>

How would this work? Would a PHI harmonic series just be the normal harmonic
series compressed so that 2/1 now equals phi/1?

-Mike

On Sat, Jan 9, 2010 at 1:28 PM, Chris Vaisvil <chrisvaisvil@...>wrote:

>
>
> What would happen if PHI was used to generate a PHI harmonic series and
> then the notes of that series collapsed into one PHI octave just like the
> octave based harmonic series?
>
> Ie. C, C, g, c, e, b flat.... etc but in PHI intervals.
>
> Just a thought. I might even be able to do this.
>
> Chris
>
>
> On Sat, Jan 9, 2010 at 1:05 PM, Michael <djtrancendance@...> wrote:
>
>>
>>
>> Chris,
>>
>> Interesting, so the first two notes match the quantum ratio and the
>> resonance is symmetrical.
>> But, to establish a pattern used for a scale I'd need more notes from the
>> experiment to see a true pattern (PHI could be used only multipicatively,
>> additively....based on the information given).
>>
>> The highest symmetry IMVHO acheivable is to make the whole scale out of
>> consecutive Golden Sections the same way architects do (which is what I did
>> in my scale, bearing no "homage" to any other popular tuning system IE
>> meantone, JI, etc.).
>>
>> But it well could be, that the notes in said below experiment have a
>> different type of symmetry or additional symmetry (additive, logarithmic,
>> etc.)
>> One of the reasons I gave up improving the Golden Sections PHI scale
>> was that I could get all notes of the Silver Ratio scale to have additive
>> AND multiplication symmetries (and not just multicative ones). And still, I
>> think the Silver Ratio scale sounds a good deal better...but that may be
>> about to change if I can find a newly researched way to arrange the
>> symmetry.
>>
>>
>
>

That is how I'd attempt it yes. Of course then the idea of temperament would
come into play - should one temper or no?. How many notes per PHI-tave?

I actually did a piece (or two?) in 12th root pf PHI tuning, and
surprisingly it wasn't too bad. But it was odd.

One of them is here with the .scl

http://clones.soonlabel.com/public/micro/12th-root-phi/

On Sat, Jan 9, 2010 at 1:29 PM, Mike Battaglia <battaglia01@...>wrote:

>
>
> How would this work? Would a PHI harmonic series just be the normal
> harmonic series compressed so that 2/1 now equals phi/1?
>
> -Mike
>
>
>
> On Sat, Jan 9, 2010 at 1:28 PM, Chris Vaisvil <chrisvaisvil@...>wrote:
>
>>
>>
>> What would happen if PHI was used to generate a PHI harmonic series and
>> then the notes of that series collapsed into one PHI octave just like the
>> octave based harmonic series?
>>
>> Ie. C, C, g, c, e, b flat.... etc but in PHI intervals.
>>
>> Just a thought. I might even be able to do this.
>>
>> Chris
>>
>>
>> On Sat, Jan 9, 2010 at 1:05 PM, Michael <djtrancendance@yahoo.com> wrote:
>>
>>>
>>>
>>> Chris,
>>>
>>> Interesting, so the first two notes match the quantum ratio and the
>>> resonance is symmetrical.
>>> But, to establish a pattern used for a scale I'd need more notes from the
>>> experiment to see a true pattern (PHI could be used only multipicatively,
>>> additively....based on the information given).
>>>
>>> The highest symmetry IMVHO acheivable is to make the whole scale out of
>>> consecutive Golden Sections the same way architects do (which is what I did
>>> in my scale, bearing no "homage" to any other popular tuning system IE
>>> meantone, JI, etc.).
>>>
>>> But it well could be, that the notes in said below experiment have a
>>> different type of symmetry or additional symmetry (additive, logarithmic,
>>> etc.)
>>> One of the reasons I gave up improving the Golden Sections PHI scale
>>> was that I could get all notes of the Silver Ratio scale to have additive
>>> AND multiplication symmetries (and not just multicative ones). And still, I
>>> think the Silver Ratio scale sounds a good deal better...but that may be
>>> about to change if I can find a newly researched way to arrange the
>>> symmetry.
>>>
>>>
>>
>
>

>"What would happen if PHI was used to generate a PHI harmonic series and
then the notes of that series collapsed into one PHI octave just like
the octave based harmonic series?"

I can try that again.
I did that once, but with bad results and I realize MANY MANY people had tried the exact same thing and gotten a huge range of resulting scales due to the lousy ambiguity (and inefficiency and producing well spaced tones) of the formula.

Again, I already noticed when you do phi^x/2^y (where y = the # of octaves), you get a lot of intervals way too closely spaced to be used for the scale and have to "cherry pick" the good ones out of many (if not most) that work bad.

However if you relax the octave restraint and do phi^x/any-number up to where x = 6 (6th harmonic in the series) you get mostly intervals that are fairly spaced apart and/or almost directly match each other, for example

1.059 (PHI^3/4)
1.1089 (PHI^5/10)
1.232 (PHI^5/9)
1.309 (PHI^2/2)
1.38625 (PHI^5/8)
1.495 (PHI^6/12)
1.618 PHI!!
1.713 (PHI^4/4)
1.848 (PHI^5/6)
2
...........note this way that no two notes are any closer than the half step in 12TET.
See how that one works out for you........
You can also try using PHI as the period/"octave equivalent" and forget about the 1.713 and 1.848 notes.

________________________________
From: Chris Vaisvil <chrisvaisvil@...>
To: tuning@yahoogroups.com
Sent: Sat, January 9, 2010 12:28:32 PM
Subject: Re: [tuning] Golden ratio discovered in a quantum world

What would happen if PHI was used to generate a PHI harmonic series and then the notes of that series collapsed into one PHI octave just like the octave based harmonic series?

Ie. C, C, g, c, e, b flat.... etc but in PHI intervals.

Just a thought. I might even be able to do this.

Chris

On Sat, Jan 9, 2010 at 1:05 PM, Michael <djtrancendance@ yahoo.com> wrote:

>
>
>
>
>
>
>
>
>
>
>
>
>
> >
>
>>
>
>>
>
>Chris,
>
> Interesting, so the first two notes match the quantum ratio and the resonance is symmetrical.
>But, to establish a pattern used for a scale I'd need more notes from the experiment to see a true pattern (PHI could be used only multipicatively, additively.. ..based on the information given).
>
> The highest symmetry IMVHO acheivable is to make the whole scale out of consecutive Golden Sections the same way architects do (which is what I did in my scale, bearing no "homage" to any other popular tuning system IE meantone, JI, etc.).
>
> But it well could be, that the notes in said below experiment have a different type of symmetry or additional symmetry (additive, logarithmic, etc.)
> One of the reasons I gave up improving
> the Golden Sections PHI scale was that I could get all notes of the Silver Ratio scale to have additive AND multiplication symmetries (and not just multicative ones). And still, I think the Silver Ratio scale sounds a good deal better...but that may be about to change if I can find a newly researched way to arrange the symmetry.
>
>

Ack - I forgot you are a consonance junkie :-)

Did you listen to the 12th root of PHI piece I posted?

You can have extra notes in a tuning system, like 12 edo, and simply not use
them all until you want to modulate or be a dissonant SOB like me.

I don't understand your math - you seem to be using 2/1 as the octave and
just picking notes within the octave based on a PHI influenced formula -
which would be different from using PHI as the "octave".

Chris

On Sat, Jan 9, 2010 at 2:00 PM, Michael <djtrancendance@...m> wrote:

>
>
> >"What would happen if PHI was used to generate a PHI harmonic series and
> then the notes of that series collapsed into one PHI octave just like the
> octave based harmonic series?"
>
> I can try that again.
> I did that once, but with bad results and I realize MANY MANY people
> had tried the exact same thing and gotten a huge range of resulting scales
> due to the lousy ambiguity (and inefficiency and producing well spaced
> tones) of the formula.
>
> Again, I already noticed when you do phi^x/2^y (where y = the # of
> octaves), you get a lot of intervals way too closely spaced to be used for
> the scale and have to "cherry pick" the good ones out of many (if not most)
> that work bad.
>
> However if you relax the octave restraint and do phi^x/any-number up
> to where x = 6 (6th harmonic in the series) you get mostly intervals that
> are fairly spaced apart and/or almost directly match each other, for example
>
> 1.059 (PHI^3/4)
> 1.1089 (PHI^5/10)
> 1.232 (PHI^5/9)
> 1.309 (PHI^2/2)
> 1.38625 (PHI^5/8)
> 1.495 (PHI^6/12)
> 1.618 PHI!!
> 1.713 (PHI^4/4)
> 1.848 (PHI^5/6)
> 2
> ...........note this way that no two notes are any closer than the half
> step in 12TET.
> See how that one works out for you........
> You can also try using PHI as the period/"octave equivalent" and forget
> about the 1.713 and 1.848 notes.
>
>
> ------------------------------
> *From:* Chris Vaisvil <chrisvaisvil@...>
> *To:* tuning@yahoogroups.com
> *Sent:* Sat, January 9, 2010 12:28:32 PM
> *Subject:* Re: [tuning] Golden ratio discovered in a quantum world
>
>
>
> What would happen if PHI was used to generate a PHI harmonic series and
> then the notes of that series collapsed into one PHI octave just like the
> octave based harmonic series?
>
> Ie. C, C, g, c, e, b flat.... etc but in PHI intervals.
>
> Just a thought. I might even be able to do this.
>
> Chris
>
> On Sat, Jan 9, 2010 at 1:05 PM, Michael <djtrancendance@ yahoo.com<djtrancendance@...>
> > wrote:
>
>>
>>
>> Chris,
>>
>> Interesting, so the first two notes match the quantum ratio and the
>> resonance is symmetrical.
>> But, to establish a pattern used for a scale I'd need more notes from the
>> experiment to see a true pattern (PHI could be used only multipicatively,
>> additively.. ..based on the information given).
>>
>> The highest symmetry IMVHO acheivable is to make the whole scale out of
>> consecutive Golden Sections the same way architects do (which is what I did
>> in my scale, bearing no "homage" to any other popular tuning system IE
>> meantone, JI, etc.).
>>
>> But it well could be, that the notes in said below experiment have a
>> different type of symmetry or additional symmetry (additive, logarithmic,
>> etc.)
>> One of the reasons I gave up improving the Golden Sections PHI scale
>> was that I could get all notes of the Silver Ratio scale to have additive
>> AND multiplication symmetries (and not just multicative ones). And still, I
>> think the Silver Ratio scale sounds a good deal better...but that may be
>> about to change if I can find a newly researched way to arrange the
>> symmetry.
>>
>>
>
>

By "PHI harmonic series", I think he means taking PHI^x to make the series (correct me if I'm wrong).

Since the harmonic series is 1*root freq, 2 * root freq, 3 * root freq...you'd think it would be PHI, 2*PHI, 3*PHI, but I and many others have used PHI*root freq, PHI^2 * root freq, PHI^2 * root freq.

Though it would be interesting to try PHI, 2*PHI, 3*PHI as well. Using the octave IE dividing by 2^x...that can give
1
1.112 ( * 11/16)
1.2135 (* 3)
1.3146 ( * 13 / 16)
1.41575 (*7 /8 )
1.5168 (* 15 / 16)
1.618 ( * 4 / 4)
1.82025 (*9 / 8)
2

-Michael

Yes I mean as your first sentence. However outside of fitting a standard keyboard nicely there would seem to be no other reason to stick with 12 notes or therefore 12 iterations of the phi series.
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Michael <djtrancendance@yahoo.com>
Date: Sat, 9 Jan 2010 11:18:12
To: <tuning@yahoogroups.com>
Subject: Re: [tuning] Golden ratio discovered in a quantum world

By "PHI harmonic series", I think he means taking PHI^x to make the series (correct me if I'm wrong).

Since the harmonic series is 1*root freq, 2 * root freq, 3 * root freq...you'd think it would be PHI, 2*PHI, 3*PHI, but I and many others have used PHI*root freq, PHI^2 * root freq, PHI^2 * root freq.

Though it would be interesting to try PHI, 2*PHI, 3*PHI as well. Using the octave IE dividing by 2^x...that can give
1
1.112 ( * 11/16)
1.2135 (* 3)
1.3146 ( * 13 / 16)
1.41575 (*7 /8 )
1.5168 (* 15 / 16)
1.618 ( * 4 / 4)
1.82025 (*9 / 8)
2

-Michael

>"I don't understand your math - you seem to be using 2/1 as the octave
and just picking notes within the octave based on a PHI influenced
formula - which would be different from using PHI as the "octave"."

As I stated
"You can also try using PHI as the period/"octave equivalent" and forget about the 1.713 and 1.848 notes."
which would make the scale simply

1.059 (PHI^3/4)
1.1089 (PHI^5/10)
1.232 (PHI^5/9)
1.309 (PHI^2/2)
1.38625 (PHI^5/8)
1.495 (PHI^6/12)
1.618 PHI!!

I also read your "compress the harmonic series to the "PHI-tave" message and admit I've never tried that.
In that case I'd try x/8 * 0.618 for starters (note that 0.618 = 1 / PHI). So that gives

9/8 = 1.0625 * 0.618 = 1.07725
10/8 = 1.25 * 0.618 = 1.1545
11/8 = 1.375 * 0.618 = 1.23175
12/8 = 1.5 * 0.618 = 1.309
13/8 = 1.625 * 0.618 = 1.38625
14/8 = 1.75 * 0.618 = 1.4635
15/8 = 1.875 * 0.618 = 1.54075
16/8 = PHI (phi-tave AKA compressed octave)

I ,_._,___

>Yes I mean as your first sentence.

In that case, you can actually take any existing octave-based scale and take each note of it and do

(RATIOorNOTE - 1) * 0.618(AKA 1/PHI) + 1 = resulting PHI-compressed-octave ratio.

Although I'd again recommend using 0.625 IE 1/(13/8) instead of 1/PHI if you want consonance (like I usually do)...but it sounds like you might not. ;-)

________________________________
From: Chris <chrisvaisvil@gmail.com>
To: tuning@yahoogroups.com
Sent: Sat, January 9, 2010 1:40:22 PM
Subject: Re: [tuning] Golden ratio discovered in a quantum world

Yes I mean as your first sentence. However outside of fitting a standard keyboard nicely there would seem to be no other reason to stick with 12 notes or therefore 12 iterations of the phi series.
Sent via BlackBerry from T-Mobile
________________________________

From: Michael <djtrancendance@ yahoo.com>
Date: Sat, 9 Jan 2010 11:18:12 -0800 (PST)
To: <tuning@yahoogroups. com>
Subject: Re: [tuning] Golden ratio discovered in a quantum world

By "PHI harmonic series", I think he means taking PHI^x to make the series (correct me if I'm wrong).

Since the harmonic series is 1*root freq, 2 * root freq, 3 * root freq...you'd think it would be PHI, 2*PHI, 3*PHI, but I and many others have used PHI*root freq, PHI^2 * root freq, PHI^2 * root freq.

Though it would be interesting to try PHI, 2*PHI, 3*PHI as well. Using the octave IE dividing by 2^x...that can give
1
1.112 ( * 11/16)
1.2135 (* 3)
1.3146 ( * 13 / 16)
1.41575 (*7 /8 )
1.5168 (* 15 / 16)
1.618 ( * 4 / 4)
1.82025 (*9 / 8)
2

-Michael