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Originally posted by UncleV
If we're going to take this route, dismissing simple, easily understood words like 'second' and 'hertz' and turning them into complicated and unclear concepts just for the sake of it then I'm going to have to insist that 90% of the words you use are null and void. Ratios can no longer be used, neither can 'phase' or 'amplitude' because nearly everything you utter can be broken down into some complicated blather. How can one measure anything if we don't set some simple standards? Mention harmonics? Nope sorry, why? Because how do you define harmonics without using frequency or time standards? You can vaguely allude to them but you can not define them otherwise.
Through natural overtones we do not get every note in our western scale but using it for one root note gives us major thirds, fifths, octaves from which to build the next batch. This is neither western or eastern. It just is and unfortunately for you, it uses hertz/seconds to provide us with this information.
Professor Michael Hudson concurs: “The worst problem in tuning occurs in the interval of three whole tones, e.g., between C and F#/Gb in the “natural” untempered methods of tuning. If the ratio of the octave is 2:1, then the ratio of C to F# represents the square root of two — an irrational number. (Burkert [1972:441] notes that the harmonic mean discovered in the context of Pythagorean music theory has a major use precisely in approximating the square root.)”
The figures for the thirds are most easily derived by the arithmetic or harmonic means of the fifth, just as a harmonic framework is derived from means within the octave.213
When it's contended that the Pythagoreans recognized the harmonic mean (2AB)/A + B, the geometric mean (a square root) and the arithmetic mean (A + B)/2 there must be the correction that in fact these means were the innovation of Archytas to create the Greek Miracle. “Similarly, in Fragment 2, Archytas is clearly taking over the three means from his predecessors, although he renames one of them and adds his own additional characterization of each mean.”228 Or as Professor Luigi Borzacchini describes it in the Greek ratios: “the arithmetic mean, a-b=b-c, the geometric a:b=b:c, and the harmonic or subcontrary a-b:a = b-c:c.”229
12:6 as the octave with 9 as the arithmetic mean or 12:9:6, giving the perfect fourth music interval or 12:9 as 4:3 and the perfect fifth music interval as 9:6 or 3:2.
Dr. Alan C. Bowen reveals how Archytas developed these means from Pythagorean harmonics in his article “The Minor Sixth (8:5) in Early Greek Harmonic Science,” The American Journal of Philology, 1978: “For it was during this time that scales of a double octave magnitude, i.e. the Greater Perfect System, were constructed to facilitate the analysis of melody.”
Any who doubt that the musical ratios are all of greater inequality, i.e., that the antecedent or first term in each is greater than the consequent or second term, should consult Archytas DK 47 B 2. This Fragment requires that the ratios be of this form if the assertions about the three means [arithmetic, harmonic and geometric] are to be true. Accordingly, the ratios assigned to the octave, fifth, fourth and minor sixth, must be 2:1, 3:2, 4:3 and 8:5, and not 1:2, 2:3, 3:4 and 5:8, respectively, as Mosshammer and others would have them. Indeed, there is early proof deriving from the Pythagorean school that intervals, such as the fifths, which are represented by superparticular [n + 1 : n] ratios cannot be partitioned into any number of equal subintervals because the terms of these ratios admit no number of geometric means….There is reason to believe that these were supplied by Archytas in the early fourth century B.C.233
Although the later Pythagoreans used the ratio 9/8 for tuning it must be emphasized the Orthodox Pythagoreans did not use 9/8, not in the sense of Archytas. Why? Because the ratio 9/4, reduced to 9/8, is not of the Pythagorean Tetrad based on the “orthodox” perfect fifth “Great Dragon Tuning.” As Professor Andre Barbera exposes: Orthodox Pythagorean theory recognizes five consonances: fourth, fifth, octave, twelfth, and double octave; and these are represented by the multiple and superparticular ratios [n + 1 : n] from the tetrad. The number 8 obviously does not belong to the tetrad.235
Barbera does note that Archytas used the Babylonian tetrachord, an extension of the tetrad, 6:8::9:12 whereby 8 is the harmonic mean and 9 is the arithmetic mean between 6 and 12 with the above changed meanings as discussed.236 So 1, 4/3, 3/2, 2 were converted to 6:8:9:12. So 8 x 9 = 72 (harmonic mean x arithmetic mean = geometric mean squared) and the square root of 72 in simplified radical form is 6 times the square root of 2 – or the equal-tempered logarithmic tritone music interval, the 6th semitone of the 12 note scale aka the Devil’s Interval. In other words 9/8, the major 2nd music interval, cubed, is the square root of two as the most dissonant music interval of the Western logarithmic scale.
Originally posted by BASSPLYR
also don't get too hung up on cathedrals having sonic properties to eliminate certain frequencies. at every sound check the engineer is doing the same thing but electronically. all rooms and shapes have acoustic qualities both good and bad. their dimensions are mathematical fractions of certain sound frequencies. you get a standing wave which makes the music sound muddy or overbearing on one frequency. for some instruments it augments either it's good or bad sound qualities. SO the engineer finds those frequencies and dials them back so the mix will sound OK. I'm sure some churches have been built to eliminate the offending frequencies in respect to the instruments likely to be played in them (organs, human voices etc...) No conspiracy they were just doing a good job building a church.
ALso. don't get hung up on the math regarding temperings of the scales we use. westerners use a less exact (mathematically) ratio between one note to the next in the diatonic system because it sounds better to our western ears. the folks from india and that region have a much more mathematically precise scale tempering but we don't use it over here as much because we think it sounds like crap. so not using certain frequencies is just speculation and opinion and probably most likely not some conspiracy to control humanities consciousness. some of us don't even listen to music so hows it supposed to take over the worlds conciousness. it's a crappy tool there are more direct ways to control people than through music alone. Yes music can help to manipulate people but so can news stories, movies, books, poems, religion, etc...
Now, Vedral and colleagues have shown otherwise. The UK-Portugal-Austria team have calculated that an entangled state formed between the photons in a laser pulse and the phonons -- quantum mechanical vibrations of the crystal lattice -- in a mirror can persist at arbitrarily high temperatures. The physicists obtained their results by treating both the laser light and the mirror as simple quantum-mechanical harmonic oscillators. The photons and phonons interact via the so-called light pressure mechanism, in which photons bombarding the mirror exert a pressure on it because of mutual interactions. The pressure exerted on the mirror depends on the number of photons hitting it: the more photons in the laser, the more pressure they exert on the mirror and the more the mirror vibrates. Vedral and co-workers calculated that if they were to measure five photons in the light field, then there would be five phonons in the motion of the mirror; and if they measured ten photons, then that meant ten phonons, and so forth. This is typical of an entangled state but the difference in the new calculation is that it works for large systems too -- there are millions of photons in the laser beam and more than a billion atoms in the mirror.364
As Vlatko Vedral states: “In the modern point of view, the world looks classical because the complex interactions that an object has with its surroundings conspire to conceal quantum effects from our view.”365
Originally posted by rwfresh
reply to post by fulllotusqigong
You need to listen to this in it's entirety if you truly want to liberate yourself. It is the ultimate expression of Truth through music and has been responsible for a number of well documented spontaneous enlightenings.
vimeo.com...
The ultimate secret is revealed around 2:08 . I've said enough. But listen and you will understand. Those with ears will hear.
Peace!
Yeah as I mentioned earlier it is not proven that the Pythagoreans ever used a monochord string to determine their harmonics.
So then I was shown by my other music teacher -- the U of MN professor -- that if you silently press a higher harmonic and then strike the lower harmonic then the higher harmonic will ring out "magically" on its own. So this is about the one note having inherent subharmonics and higher harmonics and how this is an eternal process that is nonlinear.
Listen through these 75 audio music examples -- they are all based on the intuitive 1-4-5 overtones without the need of Hertz
we can still find beautiful music with no Hertz and also the amazing secret of how to create healing light energy from music
Originally posted by fulllotusqigong
Truth is not put in words -- only through silence in meditation. Listening to the source of sound.
So, for the third time - do you agree that an octave is an exact doubling or halving of a root note?: YES/NO
Originally posted by UncleV
AHA! I figured it out! You don't know what hertz means! Music without hertz??? Silence. Were those audio samples silent? No? Every sound we hear contains hertz (clumsy but that's how you phrased it). Hertz, being the measurement of sound accepted by the entire world except for you. Please do some research, you are obviously a smart fella, but this takes the cake. Whether we hear it or not, it 'contains' hertz.
Analogy - here's a beautiful picture with no color. Unless it's clear, it has some color (please no quibbles about black/white being colors).
By the way, the fourth is not contain in the overtone series, oddly enough. Root, octave, fifth, major third, second, flat seventh.
The sound of square roots
Take two strings, one sounding an octave higher than the other, so that their lengths are in the ratio 2:1. Then find the geometric ratio (also called the mean proportional) between these strings, the length x at which 2:x is the same proportion as x:1. This means that 2:x = x:1; cross-multiplying this gives x2 = 2. Thus, the “ratio” needed is √ 2:1 ≈ 1.414, in modern decimals. This is close to the dissonant interval called the tritone, which later was called the “devil in music,” namely the interval composed of three equal whole steps each of ratio 9:8. The tritone is thus 9:8 × 9:8 × 9:8 = 93:83 = 729:512 ≈ 1.424.
Originally posted by UncleV
Also, for the fourth (4th) time you have failed to answer this question. So I'll recap. PS, I'm not asking this to be a turd, I'm trying to sift through the woo woo to see where you are coming from.
So, for the third time - do you agree that an octave is an exact doubling or halving of a root note?: YES/NO
PS. RWFRESH, that was just mean (the video link - Shine)
Frequency - Wikipedia, the free encyclopedia en.wikipedia.org/wiki/Frequency In SI units, the unit of frequency is the hertz (Hz), named after the German physicist Heinrich .... The wavelength is inversely proportional to the frequency, s
Right -- the fourth is created through a mathematical "divide and average" geometric means -- sound is not contained by geometry. the Just Third is also created through the same symmetric "divide and average" geometric means process -- using phonetic numbers and the commutative property. O.K. so the subharmonic of the Fifth is converted to the Fourth in violation of the Inverse of frequency as Time -- the time-frequency uncertainty principle.
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Originally posted by UncleV
Hertz relied on symmetry....of course! Have you ever looked at a sound wave on an oscilloscope? Pretty symmetrical. You dance all around the issue. Hertz is a simple measurement of sound, please refrain from cluttering it up. It is a great tool to work with sound because it is tied to sound.
What you are doing is applying math, which you moan about is so bad in western music. But all I see are ratios. If you stopped cluttering up simple concepts you could use a tool like hertz to show us what you mean, instead of formulas!
Right -- the fourth is created through a mathematical "divide and average" geometric means -- sound is not contained by geometry. the Just Third is also created through the same symmetric "divide and average" geometric means process -- using phonetic numbers and the commutative property. O.K. so the subharmonic of the Fifth is converted to the Fourth in violation of the Inverse of frequency as Time -- the time-frequency uncertainty principle.
See, this is where your choosing to ignore what I've been trying to convey is getting us nowhere. Is it because, when faced with the natural proof I've offered your theory fails? Hell, couldn't say, 46 pages and most of us are still confused! The major third is not 'created through the same symmetric "divide and average" geometric means process -- using phonetic numbers and the commutative property', it is created in nature as the fourth order harmonic. The fifth is the second, the octave the first. It is so simple, I guess your tendency to overthink/complicate is getting in the way.
Now, I can prove this. When you say zero frequency is not silence but reversed time....well, not sure how you prove that. If a tree falls in the forest and makes no sound, is he a sapling?
DenyO, the feeling I get is that the issue has to do more with how we name our notes/general music theory, which I could totally get behind understanding if it were something so simple as "I figured out that G# should now be called Fred and that there are two more notes, W# and U"
Now, fifth time asking.....is an octave the exact doubling or halving of a given note?
Additional question for clarification (hahahaha, clarification) - when you say a note has subharmonics, are you suggesting there a frequencies below the fundamental that occur? Not cosmically but in the physical world you and I occupy?
The figures for the thirds are most easily derived by the arithmetic or harmonic means of the fifth, just as a harmonic framework is derived from means within the octave.213
When Pythagoras divided the octave he discovered the ratios for fourth and fifth; and these, 3/2 and 4/3, are superparticular.
From Archytas' writings this might well be expected, for it was he who renamed the subcontrary mean harmonic because of its use in music, and he is responsible for the proof that no supraparticular ratio can be divided into equal rational parts. (9
But wait shouldn't it be an OCTAVE if Denyobfuscation is correct? haha.
If it is commutative then it has to be G to G as the subharmonic of G -- as the octave. In other words -- as Denyobfuscation has repeated over and over.
3:2 is C to G and 2:3 is G to C. -- Same C. But NO -- not for the "Doe a Deer" Solfeggio scale. O.K. if you state they are just ratios - but we are talking about a subharmonic as a fraction -- 2/3 is the lower frequency -- it's not just the same interval as an inversion as DenyObfuscation wants to claim.
Originally posted by DenyObfuscation
reply to post by fulllotusqigong
But wait shouldn't it be an OCTAVE if Denyobfuscation is correct? haha.
Not based on anything I've said.
If it is commutative then it has to be G to G as the subharmonic of G -- as the octave. In other words -- as Denyobfuscation has repeated over and over.
Show the quote.
3:2 is C to G and 2:3 is G to C. -- Same C. But NO -- not for the "Doe a Deer" Solfeggio scale. O.K. if you state they are just ratios - but we are talking about a subharmonic as a fraction -- 2/3 is the lower frequency -- it's not just the same interval as an inversion as DenyObfuscation wants to claim.
You obviously don't get my very simple point.
As already pointed out in the context of HFQPOs (Abramowicz & Klu´zniak, 2003), a subharmonic (at half the fundamental frequency) is a hallmark of non-linear interactions. The presence of subharmonics is a frequency domain manifestation of period doubling.
In most cases, more than one subharmonic is present. This is a result of the strong nonlinearity of oscillations, which generates harmonics of the main frequency (at 2 f , 3 f , etc.), but also odd multiples of the subharmonic (at 3/2 f , 5/2 f , etc.).
1. An example is 4/3, which defines the interval we call the fourth, DO-FA. 1/3 is the third subharmonic of a series projected downward from the 1. Since 3 is an odd number, it is the 1 that is transposed by octaves, to 4.
The musical distances are identical, and of course the intervals are inverted (3/1 gives SOL, while 1/3, its inverse, gives FA). The two sets of harmonics are complementary, and the multiplication of any harmonic interval by the corresponding subharmonic intervals always gives 1/1 (3/2 x 2/3 = 3/3= 1/1, for example).
All musical intervals, a higher note with a lower note, come about in one of the following three ways: 1. As the relationship between an ascending harmonic and the nearest 1 below as the lower note. Examples are 2/1 (the octave), 3/2 (the fifth), 5/4 (the perfect third). Mathematically, this can be expressed simply as h/1, where h is any positive whole number, and where the denominator is 1 or any of its octaves--2,4,8, etc. 2. As the relationship between a higher note corresponding to 1 or one of its octaves and descending harmonic of this1 above. Mathematically, this can be expressed as 1/h, where a note corresponding to 1 is the higher note, and the lower note corresponds to a harmonic projected downward from this 1. An example is 4/3, which defines the interval we call the fourth, DO-FA. 1/3 is the third subharmonic of a series projected downward from the 1. Since 3 is an odd number, it is the 1 that is transposed by octaves, to 4.
and the nearest 1 below as the lower note.
Bring it down an octave (multiply by 1/2) so you can keep building your scale. Well … (3/2)*(1/2) = 3/4 is the inverse of 4/3, an interval with a great deal of consonance. When you completely build the scale, the ratio 4/3 turns out to be the fourth interval in the series of eight that make up an octave. Thus the name fourth. The fifth and the fourth are inversions of one another in an octave. They are the only intervals that work out this way. That makes them special, in my mind, but the adjective that was ascibed to them was perfect. Thus the intervals 4/3 and 3/2 are called the perfect fourth and perfect fifth, respectively.
Did I say music was based on notes? That's not true. Real music is based on intervals (the ratio of two notes) with high degrees of consonance (shared harmonics).
Originally posted by DenyObfuscation
reply to post by fulllotusqigong
But wait shouldn't it be an OCTAVE if Denyobfuscation is correct? haha.
Not based on anything I've said.
If it is commutative then it has to be G to G as the subharmonic of G -- as the octave. In other words -- as Denyobfuscation has repeated over and over.
Show the quote.
3:2 is C to G and 2:3 is G to C. -- Same C. But NO -- not for the "Doe a Deer" Solfeggio scale. O.K. if you state they are just ratios - but we are talking about a subharmonic as a fraction -- 2/3 is the lower frequency -- it's not just the same interval as an inversion as DenyObfuscation wants to claim.
You obviously don't get my very simple point.
If octaves are important for reasons that extend beyond just overlap of harmonics, then the doubleoctave should sound more similar than the twelfth.
This argument suggests there should exist a measurable asymmetry in octave perception: a note should sound more like its subharmonics than like its harmonics.
The interpretation is that a note an octave above the interfering tone sounds like the interfering tone itself — which is the real note’s subharmonic octave — and thus serves to interfere; a note an octave below the interfering tone sounds less like the interfering tone — it is distinguished by having more harmonics present — and interferes less. Furthermore, a single frequency can elicit a subharmonic percept if noise is present (Houtgast 1976), which the current hypothesis explains as noise tending to increase the random neural firing background and increasing the probability of superthreshold coincidence detection of subharmonic periodicities.
We want to examine whether notes of a double-octave are perceptually more or less similar than those of a twelfth.
Similarly, it is a central assumption in music theory that all octaves function equivalently in harmony; it is a supposedly innate attribute of a frequency ratio of 2:1, the simplest possible nontrivial relationship. Beyond such numerical mysticism, no satisfactory theoretical reason for all-octave equivalence has ever been given. I directly challenge this assumption. Instead, I propose that octave equivalence, in the strong alloctave sense required by music theory, is only a by-product of tradition and training but does have its solid foundation in a weaker near-octave equivalence, which may be caused by stochastic subharmonic mistakes in the firings of periodicity detectors in the laminae of our brainstem inferior colliculus.