Discussion concerning the first major re-evaluation of Dewey B. Larson's Reciprocal System of theory, updated to include counterspace (Etheric spaces), projective geometry, and the non-local aspects of time/space.
bperet wrote:
There are harmonics present--but the wrong series (computer-generated waves being a square-wave approximation). Now if you use analog components, such as tubes or transistors operating in the analog range (not saturated), then you get "real" waves.
"(not saturated)" does this saturation = distortion{?} introduce "noise or an artificial harmonic" to the wave purity {if thats the right term}?
thanks.
tymeflyz wrote:"(not saturated)" does this saturation = distortion{?} introduce "noise or an artificial harmonic" to the wave purity {if thats the right term}?
thanks.
Saturation means that you have "maxed out," with the consequence that components then only have two states, "on" or "off." Any wave shape that was there gets squashed in a "ceiling-floor" relationship to a square wave. Good for digital computers, but bad for wave processing.
There's a lot more to musical relationships than I realized. Turns out that it is impossible to produce "unison" from any instrument, because it requires three conditions: same frequency, same phase, and originating from the same location. Of course, when a location coincides, all that changes is the amplitude for the unison. And you cannot even determine if it is a single or multiple sources.
Phase relationships in music appear very complex, as it is determined by the timing of hitting two or more notes and the spatial distance between the components generating the sound. Computer-generated music tends to lose this phase aspect, because the notes of a chord are timed to exactly coincide to a nanosecond (unlike the fingers of a musician), and usually the strings, reeds, holes or other source of vibration have some physical distance--not the same, physical electronic speaker vibrating the "net" wave pattern.
It is becoming fairly obvious that the rules of "equivalent" or "yin" motion (space or time) rely on frequency (as rotational speed) and phase, that bears a striking resemblance to "turns" and "shift" of projective geometry. Now this makes sense, because equivalent space is 2D and based on orbital (not linear) velocity.
When you apply projective geometry concepts (as harmonics) to atomic equivalent space, something interesting arises: you get patterns of attraction and repulsion that look exactly like chemical bonds. It has nothing to do with "charge," but matching speed and phase in equivalent space. Molecules are a "natural consequence" to bring the harmonics of atoms into unison (1:1). This also explains why there are SO MANY oxidation states and different bond types associated with atoms to explain existing chemical bonds... I always wondered about that in chemistry class.
I mean, look at carbon, a very simple atom: +4, +3, +2, +1, 0, −1, −2, −3, −4. In the early days when the bonding concept was just conceived, it just had +4, -4. Now there are 9 states, depending on what it is bonding with. And that's the key--what you are bonding with is one of the "notes" that an atom is trying to come into harmony with, so if an atom can resonate at a harmonic ratio that brings the molecular "song" back to unison, it bonds--and stays bonded. If it cannot, then dissonance sets in and the atom is pushed away.
Larson's concept of bonding is closer than the conventional as it deals with rotational speeds (frequencies), but omits the shear between frequencies (the harmonic ratio) and the phase relationships.
Question for those with a musical background: how do phase relationships, the spacing between strings and the tiny pauses between hitting notes, affect the music being played?
bperet wrote:
Question for those with a musical background: how do phase relationships, the spacing between strings and the tiny pauses between hitting notes, affect the music being played?
I am no music expert, but I have been thinking and reading about these questions a lot the past few years. My first post on this website was me asking you, Bruce, to help me think through what implications phase relations in acoustics meant for projection in general. I sent you this link among others:http://www.thedaobums.com/topic/5295-the-hempel-effect/, which I think deals with your question if you can tolerate this guy's schitzo-style. Basically altering the phase doesn't matter because the mind does its own transform. In the book he references, The Magic of the Senses, the author shows the combined curves for a fundamental and its overtones in different phase relationships. One would think we would hear a difference, but our ear always separates out the tones in the same way. Some would say the mind does its own Fourier analysis, but it must go beyond simple analysis, since humans can beat the Fourier uncertainty principle:http://phys.org/news/2013-02-human-four ... ciple.html
The book author relates it to the structure of the human ear, and indeed we do look for, recognize and match pure ratios partly because we are built of them. This guy Richard Merrick has built an entire Theory of Everything out of matching temporal and spatial ratios. Check out his free ebook Interference:http://www.interferencetheory.com/
I had for a while, following Dan Winter, thought of it as does Drew in the article above, in terms of phase being relative to consciousness, of the phase-conjugating, attractive and organizing dynamics of gravity and perception. But I think RS theory has filled out and altered some of the content of this problem for me, though I look forward to hearing more of your exploration into harmonics. There is a reason esoteric thinkers have so often been obsessed with it. Just thinking about the yin yang nature of the dominant and subdominant:http://www.newmusicbox.org/articles/IV- ... tom-Tonic/, helps me see so many connections that suggest reasons why your model works so well and connects with so many things at the cutting edge of Theory.
I did a simulation of the waveform of a 2D atomic rotation, where the A and B components were in a harmonic ratio. Basically, if you put a mark on a sphere, this is the path that mark would follow as the two rotating systems interact. If that point coincides with the real axis, this is what the resulting waveform looks like:
1:1 Unison
c-rotation1.png (76.68 KiB) Viewed 38198 times
2:1 Octave
c-rotation2.png (87.51 KiB) Viewed 38198 times
3:2 Perfect Fifth
c-rotation3.png (103.26 KiB) Viewed 38198 times
4:3 Perfect Fourth
c-rotation4.png (112.88 KiB) Viewed 38198 times
5:4 Third
c-rotation5.png (122.15 KiB) Viewed 38198 times
The color indicates the path of motion, from black (start) to white (rotation completed).
Thanks for posting these pictures, they're quite helpful for visualization and seeing how the harmonic ratios as rotational operations translate to geometry. Also, thank you Adam for the links you shared. These are going to be quite helpful for my understanding of harmonies the inverse relationship between music and geometry.
JoeyV wrote:Thanks for posting these pictures, they're quite helpful for visualization and seeing how the harmonic ratios as rotational operations translate to geometry. Also, thank you Adam for the links you shared. These are going to be quite helpful for my understanding of harmonies the inverse relationship between music and geometry.
Bruce's diagrams are very similar to what can be created with a harmonograph, a pendulum-based instrument used to view harmonic relationships. Wooden Books has a fun little book on the figures that can be made. Though my favorite book on music is Dane Rudhyar's "The Magic of Tone and The Art of Music". Rudhyar was an important esotericist and composer and in that book he gets at some deep truths behind the evolution of music and our understanding of the harmonic series, though he wasn't much for geometry. My other favorite,"Homage to Pythagoras" by various authors gets deep into the geometry of harmonics. I highly recommend it. What Bruce has elsewhere discussed as the reciprocal relationship between an ascending arithmetic progression and a descending harmonic progression, are key to musical proportion and I think are symbolic of an underlying topological process present in all morphogenesis. Just as an arithmetic mean and harmonic mean between the geometric ratio of the octave double produce the yin/yang subdominant and dominant as traces of the infinite series that gave rise to them, so do the coupling of any ordinal series in the right ratios give rise to phenomenon emerging out of a purely ordinal topology into not just a metric/euclidean space but a metric time as well. GIlles Deleuze explored the details of this process (though I am speculating on the music connections), putting the hierarchy of geometries first developed by Felix Klein which Bruce uses partially in his projective strata into a full ontology that I believe greatly supports, helps explain and extends many of the ideas of the reciprocal system.
Deleuze is still the biggest name in European philosophy, but his texts are difficult to penetrate, so I highly recommend Manuel Delanda's clear interpretations. Delanda's Intensive Science and Virtual Philosophy should be of interest to anyone here. He fills in so many philosophical details that I (and it has seemed also a few others) have been wondering about since discovering Larson and Bruce's ideas.
I've been slowly going through Richard Merrick's book, Interference, and finding it quite fascinating--particularly how he identifies so many "reciprocal relationships" in music theory (when done the right way).
Of particular interest is that his theory is based on the TriTone (the "devil's tone"), which appears to be the "natural unit" of music, behaving much like a natural unit of space or time.
Blavatky said that Keely's engine would only work in his presence since he was like a magician who interacted with the etheric plane and the same I think of Wilhelm Reich, since both the organic accumulator as well as the cloudbuster even the experiment ORanur, it seems that they only worked in their surroundings.
Blavatky, dijo que el motor de Keely, solo funcionaria en su presencia ya que el era como un mago que interactuaba con el plano eterico y lo mismo opino yo de Wilhelm Reich, ya que tanto el acumulador orgonico,como también el cloudbuster incluso el experimento ORanur, parece que solo funcionaban en su entorno.
