LHP Only: Sacred Geometry

[jasonwill2]

Lack of understanding does not equal chaos. I bet everything follows patterns, just ones more complex than the golden ratio and such.

Like this?

I love that equation... but I prefer instead of l^2p to put

there instead, as that is how Roger Penrose liked to lay out the equation in his book, and is was the only darn thing past page 100 I could understand at the age of 15. (The Road to Reality was the book)

Things follow patterns. They are called equations

 

[apophenia]

That's cool, sure. But I think you completely missed the point. Most artwork is beautiful in its own way, but that does not mean it is anything deeper than human creation. We are capable of amazing things as human beings, but this thread is not about beauty, it is about fundamental patterns and aspects of reality, in which the golden pentagram seemingly has no place. Even music, I love music and it can be amazing. But it is man made, your favorite bands are not channeling some fundamental aspect of reality, not making it come to life. Music is beautiful and created. Touching but not "spiritual".

Regards the highlighted section -

Do you know what the overtone series is ?

from - Overtone

"Overtones or harmonics are the natural parts of any pitch heard when it is sounded. That is to say, that each pitch that we hear contains addition pitches within it that are termed overtones or harmonics. The relative strength or weakness of these overtones determines the tone color or timbre of the pitch. This is why no two instruments sound alike.When a pitch is played, the main note heard is the fundamental (the note itself), but there is also present a series of other pitches above it called overtones or harmonics. The first overtone is an octave above the fundamental, the second is an octave and a fifth above the fundamental, the third is two octaves, the fourth is two octaves and a third, and so on, with each following overtone closer to the last than the last was to the tone before it.
The series of overtones (harmonic series) for the fundamental pitch C would consist of C-C3-G3-C4-E4 G4-B-Flat4*-C5-D5 E5-F-Sharp5*-G5-A5*-B Flat5*-B5-C6."

Here are some snippets of musicology you may find interesting. I'm leaving out any use of the term 'spiritual', because it's one of those effectively meaningless words... though I may return to Gurdjieff's idea "The Law of Octaves" which he expressed half a century before Mandelbrot sets and fractals become known.


There are two aspects to the overtone series that I would like to draw to your attention, in relation to your statement (highlighted) about music.

The first is the historical development of music. As it happens, the notes in the overtone series are a sort of schema of the evolution of music over the last few thousand years.

Here is a quick cut and paste to save me from too much work -

"The overtone series can actually be used to trace the progression of harmonic development through Western music. As George Frederick McKay points out in The Technique of Modern Harmony, different eras throughout musical history became more accepting of higher reaching chord tones in conjunction with the overtone series.
Octaves and 5ths are primal intervals, natural to ancient music. The use of the third became prominent in the Renaissance and with composers such as Palestrina in the 1500s. Bach and his contemporaries began to exploit the 7th in the 16th and 17th centuries. The 9th didn’t become an important chord tone until the time of Wagner in the mid 19th Century, and the extended tones of #11 and 13th weren’t commonly accepted until the music of early 20th century composers like Debussy and Stravinsky."
-Quick Tip: The Overtone Series


"But it is man made, your favorite bands are not channeling some fundamental aspect of reality, not making it come to life"

As you can see, the historical development of music in fact does " channel some fundamental aspect of reality, not making it come to life".

And there was no "central music committee" driving this. This was done spontaneously over many generations and cultures.

The second aspect of the overtone series I would like to tell you about is the Indian melakarta raga system.


Without going into a load of arcane musical maths, there is a musical 'problem' called the Pythagorean comma. I am not going to attempt to define that here, the post would become a Wikipedia entry. Suffice to say that to maintain the ratios of the different musical intervals over multiple octaves is an impossibility. Our (western) assignment of frequencies to the 12 notes of the octave is a best-fit compromise, the equal-tempered scale.

Here's some further information -
Equal Temperament -- from Eric Weisstein's Treasure Trove of Music

The Indians are a very clever bunch, and arrived at their own way of dealing with this. The Indian system uses srutis (microtones). The octave is divided into 22 notes rather than 12. They still use 7 note scales, but most of the notes have 2 or 3 variations, one of which is chosen for a given scale.

The raga system has 72 ragas. A raga is a combination of a specific scale selected from the 22 srutis (sometimes 2 scales, one for ascending notes and another for descending notes), plus a specific tala (time signature - though some of them are very strange and complicated to western musicians, except maybe some demented metal-heads) and a set of characteristic musical motifs (riffs) which serve as the prototypes for improvisation. Each raga is also associated with a specific emotion, time of year and time of day, but that is not relevant to this post ( in any way that I could 'prove').

Here is the important point about raga - the 22 srutis are all integer relationships to the tonic (root note of the scale). Thus they all have a direct relationship to frequencies of the overtone series of the tonic.

So each raga exploits the overtone series of the tonic which is always maintained as a drone (pedal note).Unlike western music, where choices have been made which disallow this level of consonance, each note of the scale resonates with one of the natural harmonics of the drone.

So there you have two examples of how the intrinsic nature, the physics, of sound underlies the historical development of music throughout human history, and is the underlying principle of one of the most sophisticated musical forms to have ever existed.

"not channeling some fundamental aspect of reality" ?

Yes it does. Musical forms have grown around the natural phenomenon of the overtone series. Not arbitrary.

 

[jasonwill2]

I can never hope to understand the mechanics of music.

 

[apophenia]

I can never hope to understand the mechanics of music.

Of course you could. It is pretty straightforward, you just need an explanation that is concise, accurate, and suits your cognitive style.

 

[jasonwill2]

Of course you could. It is pretty straightforward, you just need an explanation that is concise, accurate, and suits your cognitive style.

I'm right-brain hemisphere dominant, if that means anything. Visual representations might work good because of that, but I don't know.

I'm also tone deaf. I can differentiate different tones in other people's voices (as well as Music but I probably can't identify specifically what parts are what), but not my own. Some weird thing about how the sound waves from my voice-box vibrates in the bones of my skull to my ears and my brain can't figure it out... or something. That's just what my brother told me (he's been in his HighSchool Choir for ages so he probably knows) though, he also says he learned that it's (Tone Deafness) common with people who have Aspergers, which I do.

So even if I learn all this I wouldn't ever be able to sing [very good]

-ends little talking-about-self-time. sorry its super early in the morning and i need to go to bed and im unfocused and easily distracted by radiant points when tired-

However I couldn't understand your post because I didn't know what any of those words meant, but it did look like there was some geometry to it.

 

[apophenia]

I'm right-brain hemisphere dominant, if that means anything. Visual representations might work good because of that, but I don't know.

I'm also tone deaf. I can differentiate different tones in other people's voices (as well as Music but I probably can't identify specifically what parts are what), but not my own. Some weird thing about how the sound waves from my voice-box vibrates in the bones of my skull to my ears and my brain can't figure it out... or something. That's just what my brother told me (he's been in his HighSchool Choir for ages so he probably knows) though, he also says he learned that it's (Tone Deafness) common with people who have Aspergers, which I do.

So even if I learn all this I wouldn't ever be able to sing [very good]

Being Aspergers, you would probably have no problem getting into making synthetic music. Though I don't have any reason to think that except that Aspies are often pretty smart AFAIK. Do you know of any Asperger musicians ? I would be interested to check that out.

(A little later...) Check this out - Classical music notes: Mozart had Asperger’s, says expert, Beethoven maybe « The Well-Tempered Ear

Just thought you may find that interesting.

 

[Billy goatee]

Lack of understanding does not equal chaos. I bet everything follows patterns, just ones more complex than the golden ratio and such.

I mean the definition of chaos where little unpreventable manipulations of the initial conditions produce an unpredictable or damaged outcome.

 

[Billy goatee]

Cool story bro, but obviously I know that, but there substances such as crystals that have definite patterns in their structures. I was just saying that in general they bond in certain "shapes" that change how the react to other substances. This just seems like splitting hairs imo

Actually they don't. only in theory.

 

[1137]

Apophenia, you blow my mind. That post was not well made (mine). As said in the previous one (I think) I was simply talking about the golden ratio. My thoughts were definitely scattered. I understand music is follows patterns that are not man made, sound in general.

 

[crossfire]

Now I want to pull my old guitar and tape measure out to figure out if phi makes an overtone.

 

[Eni Alihm]

Not to let Apophenia have all the fun!

In order to know what is NOT the natural order of music we need to know first what the natural order IS.

We have basically two sounds; they are either Harmonious or Chaotic. Examples of Harmonious sounds include the human voice, vibrating strings, lawn mowers, jet engines, jack hammers, cars and fans. Examples of Chaotic sounds include crumpling paper, blowing leaves, sneezes, the background conversational din in a restaurant and firecrackers.

Each and every sound we hear, whether musical or noise this sound is surrounded by a series of harmonic overtones which vibrate and gives the sound its texture or timber in addition to its fundamental note or tone.

The cleaner and purer the sound/tone the fewer harmonic overtones are being produced. Think of the clean tone of a bell when first struck, the fundamental tone can be heard loudest and as the bell swells from resonating frequencies you hear deeper as well as higher ringing sounds, these are our harmonic overtones. When you hit a rock with a stick it produces hardly any resonating harmonic overtones.

Lord Rayleigh from his Theory of Sound of 1896: "the highly composite, and often discordant, character of the sounds of bells tend to explain the discrepancies sometimes manifested in estimations of pitch".

Italian music theorist and composer of the 16th Century, Gioseffo Zarlino called musical intervals "inventions . . . of nature herself".

The Fibonacci sequence is a mathematical ratio which generates the classic spiral found in Nature / Ordered Universe. It is evident in many things such as, nautilus shells, the growth pattern of thorns on a rose, DaVinci's paintings and drawings, the pyramids and even sound. The distances between harmonic overtones of any sound, progress and change within the same ratio as that of the Fibonacci sequence. The Harmonic Overtone Series unfolds exactly like the Fibonacci sequence also known as the Golden Mean, and Phi (1 2 3 5 8 13 21 etc.).

This can be experienced on any string instrument, where if your finger is lightly placed at any one of the ratios a high harmonic tone can be plucked. These harmonics do not occur just anywhere but are in relation to these exact ratios that subdivide the string. This may be seen as the Natural Ordering of Sound being manifest into the Objective Universe for us to hear.

Johannes Avianius offered this viewpoint: "The harmonic, simple, and direct triad is the true and unitrisonic root of all the most perfect and most complete harmonies that exist in the world. It is the root of even thousands and millions of sounds, because each of them should ultimately be reduces to the parts of the triad, either by unison or by octave.[The Isagoge 1581].

Christiaan Huygens in his ‘The Celestial Worlds Discover'd' 1698 states "the Laws of Musick are unchangeably fix'd by Nature, and thus must not only apply for western cultures, the earth, and our solar system, but the rest of the universe too"

So, is there an opposite of this ordered sound? And if so, what could it be? Why would it be?
There is and it is called The Harmonic Undertone Series

Our ear is said to be ‘naturally wired' to hear the Overtone Series, anything else is heard as ‘unnatural'. This brings me to what theorists call The Undertone Series. The Undertone Series is a series of notes that result from inverting the intervals of the overtone series. The undertone series is a series of notes that results from inverting the intervals of the overtone series. The undertone series does not sound simultaneously with its fundamental tone, as the overtone series does. It is, rather, opposite in every way. There is no undertone series in the physical world.

In Graham H. Jackson’s 2006 book ‘The Spiritual Basis of Musical Harmony' he states that the over/under tone series' represent on the one hand the outer, material world, and on the other hand, our subjective, inner world. The overtone series can be explained by materialistic science but the undertone series is only achieved by our subjective experience.

 

[1137]

The Fibonacci sequence is a mathematical ratio which generates the classic spiral found in Nature / Ordered Universe.

A spiral, not the spiral. There are many natural spirals.

It is evident in many things such as, nautilus shells,

Over exaggerated / false.

the growth pattern of thorns on a rose,

Exaggerated / false.

DaVinci's paintings and drawings,

Exaggerated / false.

the pyramids

Plain false.

and even sound.

Hmm, I am not sure whether it occurs naturally or not. An octave is 13 noted, but that is 1, 2, 3, 4 , 5 , 6, 7, 8, 9, 10, 11, 12, 13, not 1, 1, 2, 3, 5, 8, 13. However, look at a piano. From C to C there are 8 white notes and 5 black notes. The black are split into a group of 2 and a group of 3. It needs to be noted that the piano is not natural, it is a man made instrument we created to mess around with sound. So yes, fib numbers may apply to it but it implies very little. Remember, we started making such instruments after discovering the golden ratio, which directly relates to the fib sequence.

The Fib sequence / golden ratio does occur in nature, yes. However it is greatly exaggerated. While it occurs in many spiraling type designs, it does not apply to even close to all of them, not always apply. It may appear but does not stay. For example, the nautilis shell does not make a golden spiral. Also, the use of it in DaVinci's work is not only exaggeraged but also irrelevant. He was a man who used a certain ratio that he found beautiful. The golden ratio does not occur in the human body as often as suggested, and it definitely does not make a person objectively more beautiful.

 

[1137]

An example of the New Age touch to sacred geometry: we are all familiar with the human being inside of the pentagram, that is very cool. However, if the man in the pentagram changes his stance, he no longer fits. We have 5 fingers, toes, parts (2 arms, 2 legs, 1 head), senses, etc sure. And the pentagram appears in sacred geometry, just not a golden one.

You can easily see this by spending a few minutes with sacred geometrical designs in your computer's basic paint program. I have nothing against the golden pentagram, Fibonacci sequence, and golden ratio. I find them all relatively beautiful, especially the direct use of the Fib sequence in one of my favorite songs. But it is not fundamental. We can use it to create beauty, but it's not our there in all reality creating all the beauty. It's natural occurrence is greatly exaggerated.

 

[Eni Alihm]

Fibonacci sequence Shell . . . . looks like it to me?

You're refuting with hundreds of scholars and scientists, not me. A rudimentary read into this will reveal that science is on my side with all of this.

A spiral, not the spiral. There are many natural spirals.

Nit picking?

Hmm, I am not sure whether it occurs naturally or not. An octave is 13 noted, but that is 1, 2, 3, 4 , 5 , 6, 7, 8, 9, 10, 11, 12, 13, not 1, 1, 2, 3, 5, 8, 13. However, look at a piano. From C to C there are 8 white notes and 5 black notes. The black are split into a group of 2 and a group of 3. It needs to be noted that the piano is not natural, it is a man made instrument we created to mess around with sound. So yes, fib numbers may apply to it but it implies very little. Remember, we started making such instruments after discovering the golden ratio, which directly relates to the fib sequence.

How the overtone series and harmonics unfolds naturally is by the sequence 1 then 1+1=2 then 2+1=3 then 3+2=5 etc. This is very spiritual for those who can see the relation.
An octave is merely the same frequency either higher or lower in pitch. There are many theories regarding Octaves. Only in Western music theory, where equal temperament is used do we have such abominations as 8 white notes and 5 black notes. The rest of the world uses quarter tonal temperaments and utilize 22 note scales (22 also is magickal for those with the insight).

[/quote]The Fib sequence / golden ratio does occur in nature, yes. However it is greatly exaggerated. While it occurs in many spiraling type designs, it does not apply to even close to all of them, not always apply. It may appear but does not stay. For example, the nautilis shell does not make a golden spiral. Also, the use of it in DaVinci's work is not only exaggeraged but also irrelevant. He was a man who used a certain ratio that he found beautiful. The golden ratio does not occur in the human body as often as suggested, and it definitely does not make a person objectively more beautiful.[/quote]Of course feel free to back up any of what you say with evidences ("exaggerated/false" just won't cut it :slap

I've been studying music theories for decades, applying them in my music compositions as well. The correlations between number, metaphysics, and music is just amazing and many of these ideas I am covering in my (some day to be finished :sad book "Tarkhem: music and the black arts"

 

[1137]

Fibonacci sequence Shell . . . . looks like it to me?

You're refuting with hundreds of scholars and scientists, not me. A rudimentary read into this will reveal that science is on my side with all of this.

Lol, is that first one not even a fibanocci / golden spiral?

How the overtone series and harmonics unfolds naturally is by the sequence 1 then 1+1=2 then 2+1=3 then 3+2=5 etc. This is very spiritual for those who can see the relation.
An octave is merely the same frequency either higher or lower in pitch. There are many theories regarding Octaves. Only in Western music theory, where equal temperament is used do we have such abominations as 8 white notes and 5 black notes. The rest of the world uses quarter tonal temperaments and utilize 22 note scales (22 also is magickal for those with the insight).

Can you send me some links on the fib sequence in music? I understand it fits into music, but music is not fundamental. It is not all sound, and we cannot even hear all sound to my knowledge. It is a way we manipulate sound to sound pleasing.

course feel free to back up any of what you say with evidences ("exaggerated/false" just won't cut it :slap

Hahaha ok.
Golden Ratio -- from Wolfram MathWorld
The Myth That Will Not Go Away
http://www.sonoma.edu/math/faculty/falbo/cmj123-134
Golden ratio - Wikipedia, the free encyclopedia
Fibonacci Flim-Flam.
The Myth*of the Golden Ratio - Home (I have not read fully through this one yet)

Let me know if you want more. I'm sad to see that this nonsense is reaching into the path specifically about seeking truth, though I was guilty of it as well.

 

[crossfire]

OK, we have geometry as mathematics in space, and we have music as mathematics in time. There are problems manifesting each in perfection in the physical world. {Dang those quantum fluxuations!} Is this a message to us that perfection is boring? Beauty is found in the imperfections?

 

[1137]

Hmmm, I was incorrect. Not about it's occurrence in nature and art being completely over exaggerated or false, but the golden ratio appears in the Platonic solids which come from sacred geometrical patterns. Very interesting. And yes, they do occur in nature and music, but not nearly as commonly as believed and widely accepted. In fact, the most common references to where this ratio supposedly appears are false. The golden ratio can specifically be found in the dodecahedron, which if I remember correctly is the "spirit" / ether platonic solid. Interesting that the pattern can be found in music.

 

[Eni Alihm]

I'm certainly no mathematician, fortunately Ms. DeWhitt is one and a music theorist.

The distance “across” each rectangular “diamond” in the figure above calculates to be 32/27, the minor 3rd (Major Whole Tone plus Limma, or 9/8 x 256/243]. This pink “diagonal” multiplied by the other green “diagonal” of 25/24 (Just-Chromatic-Semitone) equals 1.2345679. [32/27 x 25/24 = 1.2345679, a repeating decimal]. When inverted, the number becomes 0.81 i.e. the One divided by the parts [1 ÷ 1.2345679 = 0.81].

There are five rectangular diamonds in all, each divided vertically in half, making a total of ten triangles. The perimeter of each triangle also sums to 1.2345679, or inverted, to 0.81. [10/9 x 16/15 x 25/24 = 1.2345679]. The whole thus divided within by the ten triangles, each division equals 10 x 0.81 = 8.1. The length of the pipe of the the huang-chung, 8.1 ts’un, was the fundamental measure of ancient China. (The ‘ts’un” is also discussed in prior writings).

(This is 90/81. Mathematicians and engineers may find it interesting to follow through with an investigation of “Fibonacci Ladders” and “power of 10 attenuators,” the latter which divides the input voltage by successive powers of 10 such that m2 = 81/10 when series arm resistance, r = 81ohms; parallel arm resistance, 1/p = 10ohms; terminal impedance, 9ohms; input impedance, 90ohms. I have drawn freely from the illuminating book, Gnomon: From Pharoahs To Fractals, by Midhat Gazale, Princeton Univ. Press, 1999. Any misinterpretations of the scientific material are my own.)

A decent read on Phi and the Fibonacci sequence - GreenSage E-zine11/2007

 

[Eni Alihm]

OK, we have geometry as mathematics in space, and we have music as mathematics in time. There are problems manifesting each in perfection in the physical world. {Dang those quantum fluxuations!} Is this a message to us that perfection is boring? Beauty is found in the imperfections?

Music is really organized sound. I find that Rhythm plays the deciding factor with whether 'we' accept or reject what is musical or not.

One of my recent experiments is with this Undertone Series and its chaotic timber, if I leave it Rubato, it is just noise, but when I give it rhythm it is musical.

 

[1137]

I'm certainly no mathematician, fortunately Ms. DeWhitt is one and a music theorist.

The distance “across” each rectangular “diamond” in the figure above calculates to be 32/27, the minor 3rd (Major Whole Tone plus Limma, or 9/8 x 256/243]. This pink “diagonal” multiplied by the other green “diagonal” of 25/24 (Just-Chromatic-Semitone) equals 1.2345679. [32/27 x 25/24 = 1.2345679, a repeating decimal]. When inverted, the number becomes 0.81 i.e. the One divided by the parts [1 ÷ 1.2345679 = 0.81].

There are five rectangular diamonds in all, each divided vertically in half, making a total of ten triangles. The perimeter of each triangle also sums to 1.2345679, or inverted, to 0.81. [10/9 x 16/15 x 25/24 = 1.2345679]. The whole thus divided within by the ten triangles, each division equals 10 x 0.81 = 8.1. The length of the pipe of the the huang-chung, 8.1 ts’un, was the fundamental measure of ancient China. (The ‘ts’un” is also discussed in prior writings).

(This is 90/81. Mathematicians and engineers may find it interesting to follow through with an investigation of “Fibonacci Ladders” and “power of 10 attenuators,” the latter which divides the input voltage by successive powers of 10 such that m2 = 81/10 when series arm resistance, r = 81ohms; parallel arm resistance, 1/p = 10ohms; terminal impedance, 9ohms; input impedance, 90ohms. I have drawn freely from the illuminating book, Gnomon: From Pharoahs To Fractals, by Midhat Gazale, Princeton Univ. Press, 1999. Any misinterpretations of the scientific material are my own.)

A decent read on Phi and the Fibonacci sequence - GreenSage E-zine11/2007

None of this has Fibonacci numbers or the golden ratio... Not one single time.