Yahoo Tuning Groups Ultimate Backup tuning Why the Golden Ratio Scale works (WITH audio example)

http://www.geocities.com/djtrancendance/micro/goldenscaletrans.mp3
My real question: biases and hate for old scale systems aside...do
you think this sounds good and why/why not?

This is an example of
A) a 9-note per 2/1 octave (approximately) scale playing a melody
B) that same melody transposed two "steps" up IE in the equivalent
grammatically of a different "key".

It seems so obvious to me this is system is comparable or better
than the Pythagorean system >>IF you use 1.618 as the octave and NOT
2/1<<...regardless of when it was invented.

BTW, the ratios used in the tuning are
*1
1.05902
*1.12151
*1.18765
*1.25779
*1.30898
1.38627
*1.46808
1.55472
*1.61803 -octave

And the notes used in the SCALE under the tuning have a * next to them.
I am pretty sure the actual scale I used in the example IS original,
but if there is documentation on the exact same scale I'd love to
research it.
*****************************************************************

BTW >>IMPORTANT NOTE<< using 2 as the octave all the overtones
clash (this, I think, was the one major flawed assumption in Petr's
Golden Ratio scale). This scale completely disobeys the "rational
numbered fraction" type rules which govern Pythagorean-type scales.

In fact, the most beautiful thing about the scale mathematically is
that it achieves the equivalent of a "circle of 5ths" (with the 1.618
being the generator of the circle) AND an octave that intersects
perfectly with the circle (again, 1.618). With all the arguments over
whether maintaining perfect just-intonation intervals IE adaptive JI
is best, or the ability to maintain just one to a couple of constant
intervals (EDO and MOS tunings)...to mean-tone and keeping a perfect
"circle of 5ths"...you'd think someone would have stopped and said
"wow...a golden ratio scale statisfies virtually all of these conditions!)
-------------------------------------------------------

So maybe the Babylonians used it. In fact, the Golden Ratio has
obviously been around in some form since the Ancient Greeks who used
it as the "proportion of beauty" in architecture. So has PI...and
even the best engineers today, for example, use PI all the time. Even
calculus is hugely aged, people just keep finding new ways to use it.

BTW I don't know where all this "let's use or not use this not
because it's good or bad, but because some person of "high prestige"
recently created it" attitude seems to have gotten started. The
response to the Golden Ratio scale question I asked at first seemed to
be "uh...already been done, useless..."...and yet the same people work
with only slightly modified Pythagorean-like scales all the time.

Realistically, I don't care how much >>I<< get counted as an
original founder for a scale or way to use a scale...I wouldn't care
if someone else took credit for a scale I made, for example. So long
as I see people using it and the Lord knows I created something useful.
**********************
All I really care about here...is that someone somewhere manages to
find a musical alternative both more flexible (for as the number of
notes available for melody and chords for harmony) and more easy to
use for the average musician.
And, REGARDLESS of who thought it up or how many (thousands of?)
years ago it was originally considered...I swear the Golden Ratio is a
fantastic building block for making scales and one which deserves a
second look.

-Michael

🔗Michael Sheiman <djtrancendance@...>

---I personally consider this trend of westernization as
--->>devastating original cultures, not as a fruitful synthesis<<. This is
---just cheap consumer pop where the most common harmonic cliches ---of western pop are combined with some local pentatonics or other ---cliches in the melody.

Agreed, it seems people are taking the scales under 12TET that also coincide with "cut-down" pentatonic "sub-scales" from different cultures, rather than "building up" Western music to include more notes, longer scales...that truly "build up" toward capturing scales from other cultures rather than cut down the theory.

   A few somewhat good examples of "building up" the theory I what kind of things I feel should be done as a "compromise":
A) 9-tone blues scale using two extra "blue" quarter tones, one between the major and minor (3rd and 7th) keys, to emulate the original African tuning while still allowing Western harmony
B) 24-tone Arab tunings which also, on one hand, allow 12TET style chords and, on the other, more complex Arab melodies.
C) Ideally, a tuning of which you can create a consonant scale with several notes (say 9 to 10) that allows easy access to chord harmony AND, on the other hand, several other notes that can be used as neighboring tones to provide the kind of more closely-spaced melodic lines and intervals common in other cultures.
     My experiments say about 9 tones is the maximum number you can use for a chord-capable scale...but you can probably add another 9 or so tones in between for neighboring-tone/melodic purposes to emulate things like the 22-tone Indian scale. Between all the chords of a 9-tone scale...you should be able to find plenty of chords to match the emotional feel of all those neighboring tones.
***********************************************************
   When you look at Arab and Indian micro-tonal melodies, for example, I am sorry but there is no way you can authentically mimic the melodic feel of, say, Indian Srutis, just by, say, using pentatonic subsets of 12TET that are in common between the Indian 22-tone tuning and the Western 12-tone one. You can't build up by cutting cultures down to "fit" 12TET, in other words.

-Michael

--- On Tue, 2/10/09, Daniel Forro <dan.for@...> wrote:

From: Daniel Forro <dan.for@...>
Subject: Re: [tuning] Why the Golden Ratio Scale works (WITH audio example)
To: tuning@yahoogroups.com
Date: Tuesday, February 10, 2009, 8:06 AM

Oh so, but this has not so much to do with the traditional music of

those cultures nor with their original microtonality (with some

exceptions), even they don't use their traditional instruments, or

use them tuned to 12ET and combined with synthesizers and western

instruments. I personally consider this trend of westernization as

devastating original cultures, not as a fruitful synthesis. This is

just cheap consumer pop where the most common harmonic cliches of

western pop are combined with some local pentatonics or other cliches

in the melody. I see enough bad examples in Japan where I live,

starting with Meiji educational songs shoka, continuing in enka and J-

pop. Same with afro-pop, Turkish, Iranian, Indian bhangra, Chinese,

Korean, Indonesian pop... Most of Hawaiian music was created

artificially in 19th century by European missionaries and German

bandleader Berger, if somebody wonders why it sounds like Serbian/

Croatian/Austrian songs... I wouldn't call it homogenization. This is

rather decadence. Unfortunately nothing can be done against it when

those cultures want it this way. Sometimes we foreigners living here

know more about their own music.

Daniel Forro

On 10 Feb 2009, at 8:50 PM, Chris Vaisvil wrote:

> take the time to listen to *popular* music from India or the middle

> east.

> or from the central asian republics or japan for that matter.

> therein you will find the true answer

> internet radio is a wonderful thing.

> except that music, like culture, is tending towards homogenization

> ala world village.

> On Mon, Feb 9, 2009 at 5:53 PM, Daniel Forro <dan.for@tiscali. cz>

> wrote:

> Not exactly. What you describe is accompanied monody. Homophony

> itself doesn't need melodic line far from the other voices like in

> your example (which even doesn't sound well). Very often one of the

> voices is melody, usually the highest one, but not always.

> And beg you pardon, which world music follows the Western homophonic

> model? There are still living musical cultures which preserve their

> own ways, far from homophony. Not only Indian music. And opposite

> there are some which developped their own using of harmony, and some

> are based on very advanced polyphony different from European.

> Daniel Forro

🔗Carl Lumma <carl@...>

I think it sounds good, but not necessarily consonant
The chord you posted the other day, which you called
consonant -- I thought it was dissonant.

> It seems so obvious to me this is system is comparable or better
> than the Pythagorean system >>IF you use 1.618 as the octave and
> NOT 2/1<<...regardless of when it was invented.

Why is it better?

> BTW >>IMPORTANT NOTE<< using 2 as the octave all the overtones
> clash (this, I think, was the one major flawed assumption in Petr's
> Golden Ratio scale). This scale completely disobeys the "rational
> numbered fraction" type rules which govern Pythagorean-type scales.

Howso?

> In fact, the most beautiful thing about the scale
> mathematically is that it achieves the equivalent of a "circle
> of 5ths" (with the 1.618 being the generator of the circle) AND
> an octave that intersects perfectly with the circle (again,
> 1.618).

You're using phi as the generator, 2:1 as the period (to reduce
the chain of generators as you go), and phi as the interval of
equivalence. Why is this beautiful?

> With all the arguments over
> whether maintaining perfect just-intonation intervals IE adaptive
> JI is best, or the ability to maintain just one to a couple of
> constant intervals (EDO and MOS tunings)...to mean-tone and
> keeping a perfect "circle of 5ths"...you'd think someone would
> have stopped and said "wow...a golden ratio scale statisfies
> virtually all of these conditions!)

I'm not aware of anything about the golden ratio that helps
us satisfy any of these conditions.

> In fact, the Golden Ratio has obviously been around in some
> form since the Ancient Greeks who used it as the "proportion of
> beauty" in architecture.

That's a myth, actually. There's no evidence the greeks used
it in architecture. See:
http://www.maa.org/devlin/devlin_06_04.html
and
http://www.maa.org/devlin/devlin_05_07.html

> BTW I don't know where all this "let's use or not use this
> not because it's good or bad, but because some person of "high
> prestige" recently created it" attitude seems to have gotten
> started.

Who, in your judgment, has that attitude?

-Carl

🔗caleb morgan <calebmrgn@...>

yes, I do think this sounds good. hard piano-sound and quantization aside.

heard as a single harmony, though, I'm not sure I like it more than some of the other things you've posted.

fwiw

On Feb 5, 2009, at 7:10 AM, djtrancendance wrote:

> http://www.geocities.com/djtrancendance/micro/goldenscaletrans.mp3
> My real question: biases and hate for old scale systems aside...do
> you think this sounds good and why/why not?
>
> This is an example of
> A) a 9-note per 2/1 octave (approximately) scale playing a melody
> B) that same melody transposed two "steps" up IE in the equivalent
> grammatically of a different "key".
>
> It seems so obvious to me this is system is comparable or better
> than the Pythagorean system >>IF you use 1.618 as the octave and NOT
> 2/1<<...regardless of when it was invented.
>
> BTW, the ratios used in the tuning are
> *1
> 1.05902
> *1.12151
> *1.18765
> *1.25779
> *1.30898
> 1.38627
> *1.46808
> 1.55472
> *1.61803 -octave
>
> And the notes used in the SCALE under the tuning have a * next to > them.
> I am pretty sure the actual scale I used in the example IS original,
> but if there is documentation on the exact same scale I'd love to
> research it.
> *****************************************************************
>
> BTW >>IMPORTANT NOTE<< using 2 as the octave all the overtones
> clash (this, I think, was the one major flawed assumption in Petr's
> Golden Ratio scale). This scale completely disobeys the "rational
> numbered fraction" type rules which govern Pythagorean-type scales.
>
> In fact, the most beautiful thing about the scale mathematically is
> that it achieves the equivalent of a "circle of 5ths" (with the 1.618
> being the generator of the circle) AND an octave that intersects
> perfectly with the circle (again, 1.618). With all the arguments over
> whether maintaining perfect just-intonation intervals IE adaptive JI
> is best, or the ability to maintain just one to a couple of constant
> intervals (EDO and MOS tunings)...to mean-tone and keeping a perfect
> "circle of 5ths"...you'd think someone would have stopped and said
> "wow...a golden ratio scale statisfies virtually all of these > conditions!)
> -------------------------------------------------------
>
> So maybe the Babylonians used it. In fact, the Golden Ratio has
> obviously been around in some form since the Ancient Greeks who used
> it as the "proportion of beauty" in architecture. So has PI...and
> even the best engineers today, for example, use PI all the time. Even
> calculus is hugely aged, people just keep finding new ways to use it.
>
> BTW I don't know where all this "let's use or not use this not
> because it's good or bad, but because some person of "high prestige"
> recently created it" attitude seems to have gotten started. The
> response to the Golden Ratio scale question I asked at first seemed to
> be "uh...already been done, useless..."...and yet the same people work
> with only slightly modified Pythagorean-like scales all the time.
>
> Realistically, I don't care how much >>I<< get counted as an
> original founder for a scale or way to use a scale...I wouldn't care
> if someone else took credit for a scale I made, for example. So long
> as I see people using it and the Lord knows I created something > useful.
> **********************
> All I really care about here...is that someone somewhere manages to
> find a musical alternative both more flexible (for as the number of
> notes available for melody and chords for harmony) and more easy to
> use for the average musician.
> And, REGARDLESS of who thought it up or how many (thousands of?)
> years ago it was originally considered...I swear the Golden Ratio is a
> fantastic building block for making scales and one which deserves a
> second look.
>
> -Michael
>
>
>

🔗Petr Parízek <p.parizek@...>

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, "djtrancendance" <djtrancendance@...>
wrote:
>
> http://www.geocities.com/djtrancendance/micro/goldenscaletrans.mp3
> My real question: biases and hate for old scale systems
aside...do
> you think this sounds good and why/why not?
>
>
> This is an example of
> A) a 9-note per 2/1 octave (approximately) scale playing a melody
> B) that same melody transposed two "steps" up IE in the equivalent
> grammatically of a different "key".
>
> It seems so obvious to me this is system is comparable or better
> than the Pythagorean system >>IF you use 1.618 as the octave and NOT
> 2/1<<...regardless of when it was invented.
>
> BTW, the ratios used in the tuning are
> *1
> 1.05902
> *1.12151
> *1.18765
> *1.25779
> *1.30898
> 1.38627
> *1.46808
> 1.55472
> *1.61803 -octave
>
> And the notes used in the SCALE under the tuning have a * next
to them.
> I am pretty sure the actual scale I used in the example IS
original,
> but if there is documentation on the exact same scale I'd love to
> research it.
> *****************************************************************
>
> BTW >>IMPORTANT NOTE<< using 2 as the octave all the overtones
> clash (this, I think, was the one major flawed assumption in Petr's
> Golden Ratio scale). This scale completely disobeys the "rational
> numbered fraction" type rules which govern Pythagorean-type scales.
>
> In fact, the most beautiful thing about the scale mathematically
is
> that it achieves the equivalent of a "circle of 5ths" (with the
1.618
> being the generator of the circle) AND an octave that intersects
> perfectly with the circle (again, 1.618). With all the arguments
over
> whether maintaining perfect just-intonation intervals IE adaptive JI
> is best, or the ability to maintain just one to a couple of constant
> intervals (EDO and MOS tunings)...to mean-tone and keeping a perfect
> "circle of 5ths"...you'd think someone would have stopped and said
> "wow...a golden ratio scale statisfies virtually all of these
conditions!)
> -------------------------------------------------------
>
> So maybe the Babylonians used it. In fact, the Golden Ratio has
> obviously been around in some form since the Ancient Greeks who used
> it as the "proportion of beauty" in architecture. So has PI...and
> even the best engineers today, for example, use PI all the time.
Even
> calculus is hugely aged, people just keep finding new ways to use
it.
>
> BTW I don't know where all this "let's use or not use this not
> because it's good or bad, but because some person of "high prestige"
> recently created it" attitude seems to have gotten started. The
> response to the Golden Ratio scale question I asked at first seemed
to
> be "uh...already been done, useless..."...and yet the same people
work
> with only slightly modified Pythagorean-like scales all the time.
>
> Realistically, I don't care how much >>I<< get counted as an
> original founder for a scale or way to use a scale...I wouldn't care
> if someone else took credit for a scale I made, for example. So long
> as I see people using it and the Lord knows I created something
useful.
> **********************
> All I really care about here...is that someone somewhere manages
to
> find a musical alternative both more flexible (for as the number of
> notes available for melody and chords for harmony) and more easy to
> use for the average musician.
> And, REGARDLESS of who thought it up or how many (thousands of?)
> years ago it was originally considered...I swear the Golden Ratio
is a
> fantastic building block for making scales and one which deserves a
> second look.
>
> -Michael
>
Michael said "It seems so obvious to me this is system is comparable
or better
> than the Pythagorean system >>IF you use 1.618 as the octave and NOT
> 2/1<<...regardless of when it was invented.".
This is nonsense. First 1:2 IS the octave, not 1.618 which is close
to a min 6. Second, Pythagoras didn't "invent" it and it
wasn't "thought up" but it is the name given to the first overtone
(2nd harmonic), which is a fact of nature and wave theory. "using 2
as the octave all the overtones
> clash (this, I think, was the one major flawed assumption in Petr's
> Golden Ratio scale). This scale completely disobeys the "rational
> numbered fraction" type rules which govern Pythagorean-type
scales." On the one hand you say "the overtones clash" when you apply
the octave. But since the octave IS an overtone, you are therefore
admitting the validity of overtones by deciding whether they "clash"
or not as a standard against which to measure. Then,just to further
compound your self contradictions, you say "it disobeys the rational
numbered fraction type rule which govern Pythagorean type scales".
However, rational numbered fractions are not specific to Pythagorean
scales. They apply to all periodic waves without exception of which
there are infinitely many. You appeal to the fact that the Greeks
used the golden proportion in architecture as a defense of your scale
yet deny the fact that Pythagoras' discovery of the harmonic series
gave birth to the entire field of music-maths.
But at the end of the day, what has the Golden mean really got to do
with music? First we have 1:1.618. Then 1.618: 1.618 squared, the
1.618 squared: 1.618 cubed and so on ad infinitum. Or to apply it
another way, from a C=1 we get 1.618 up giving approx G# and 0.618
down giving approx an E below. This is an out of tune augmented
triad. But musical harmony already comes with its own recursive
augmented triad, 2 power 1/3 up and 2 power -1/3 down. (Now try using
1.618 to the power of...What, can't find any meaning for it??).

"high prestige" Rick

Why the Golden Ratio Scale works (WITH audio example)

🔗djtrancendance <djtrancendance@...>

🔗Michael Sheiman <djtrancendance@...>

🔗Carl Lumma <carl@...>

🔗caleb morgan <calebmrgn@...>

🔗Petr Parízek <p.parizek@...>

🔗rick_ballan <rick_ballan@...>

🔗Kraig Grady <kraiggrady@...>

🔗Kraig Grady <kraiggrady@...>

🔗Carl Lumma <carl@...>

🔗Carl Lumma <carl@...>

🔗Kraig Grady <kraiggrady@...>

🔗Petr Parízek <p.parizek@...>