http://www.egroups.com/files/tuning/monz/solarsystem/Solar2.mid This post may seem off-topic to many List members. Skip it if not interested, but see my footnote at the bottom. ====== >> [Paul Erlich] >> http://www.egroups.com/message/tuning/11956 >> >> A Google search on "Orbital Resonances" reveals the following (at >http://www.google.com/search?q=cache:gbms01.uwgb.edu/~dutchs/planets/resonan >c.htm+orbital+resonances&hl=en: > >>Resonances result when two celestial objects interact with each other >>gravitationally at regular intervals. The regularity of the interaction can >do >one of two things: > >>Lock the two objects in step so they repeat the same patterns of movement. >>Perturb one or both bodies enough to break up the resonance. > >So Monz and Kraig/Banashphu are both right! But Monz would do well to heed >Kraig/Banashphu's warning, that it's possible to find a simple ratio close >to any proportion, and that alone does not prove that resonance is at work. Right - see what I wrote about how comparing the orbital periods (which is what I did in my 'chord') is equivalent to using a *mean* constant velocity, as opposed to mapping the true velocity, which changes over the duration of the period: http://www.egroups.com/message/tuning/11943 Mapping changing velocities over time would also sound more like a typical musical piece (_pace_ La Monte Young fans), because it would be a lot less static than what I did. As I also pointed out in that post, there are other variables that also change periodically and that could be mapped somehow into sound, things such as rotation, nutation, precession, etc. I've looked and outside of rotation, haven't even been able to find this data for planets other than Earth, and even finding accurate values for Earth was difficult. Additional complexity could be included by also mapping the movements of satellites, ring particles, etc. - perhaps even atmospheric and magnetic data. I used the same amplitude (volume level) for all 9 planets, but perhaps this value could be mapped as a function of the planet's mass - that would make sense to me. Imagine the soft buzzing that would occur in the background as a result of including a mapping of the asteroids and comets with the planets! Another interesting idea that I had would be to allow the listener to choose his point of reference, on the surface of any one of the orbiting objects, and hear the music that results from mapping the celestial distances from that reference. So we'd hear one piece by listening from Earth, but an entirely different one by listening from Venus, etc. Planetarium software computes this data and maps it visually to the computer screen; there's no reason why it can't be mapped aurally instead - my piece represents a first tentative step towards that. >Also see: > >http://www.treasure-troves.com/physics/OrbitalResonances.html Also, from http://www.britannica.com/bcom/eb/article/printable/5/0,5722,119065,00.html: There are stable configurations in the restricted three-body problem that are not stationary in the rotating frame. If, for example, Jupiter and the Sun are the two massive bodies, these stable configurations occur when the mean motions of Jupiter and the small particle--here an asteroid--are near a ratio of small integers. The orbital mean motions are then said to be nearly commensurate, and an asteroid that is trapped near such a mean motion commensurability is said to be in an orbital resonance with Jupiter. For example, the Trojan asteroids librate (oscillate) around the 1:1 orbital resonance (i.e., the orbital period of Jupiter is in a 1:1 ratio with the orbital period of the Trojan asteroids); the asteroid Thule librates around the 4:3 orbital resonance; and several asteroids in the Hilda group librate around the 3:2 orbital resonance. There are several such stable orbital resonances among the satellites of the major planets and one involving the planets Pluto and Neptune. The analysis based on the restricted three-body problem cannot be used for the satellite resonances, however, except for the 4:3 resonance between Saturn's satellites Titan and Hyperion, since the participants in the satellite resonances usually have comparable masses. Although the asteroid Griqua librates around the 2:1 resonance with Jupiter, and Alinda librates around the 3:1 resonance, the orbital commensurabilities 2:1, 7:3, 5:2, and 3:1 are characterized by an absence of asteroids in an otherwise rather highly populated, uniform distribution spanning all of the commensurabilities. These are the Kirkwood gaps in the distribution of asteroids, and the recent understanding of their creation and maintenance has introduced into celestial mechanics an entirely new concept of irregular, or chaotic, orbits in a system whose equations of motion are entirely deterministic. http://www.google.com/search?q=cache:gbms01.uwgb.edu/~dutchs/planets/resonan c.htm+orbital+resonances&hl=en: Certain resonances seem to enhance orbital stability by locking bodies in step in such a way they avoid conflict. 3:2 resonances seem to be especially effective. Pluto crosses Neptune's orbit, but its period is 3/2 that of Neptune, so the two objects never approach closely. Of the 40-plus objects discovered orbiting beyond Neptune since 1992, an astounding 40% have periods very close to Pluto's and are also in 3:2 resonance with Neptune. These objects have been dubbed "plutinos". > AHA! - so *that's* a big part of the reason why there's such debate right now over whether Pluto should really be classified as a planet, because it has lots of little 'siblings'. Paul! (As announced earlier I am back and banaphshu is gone for the moment.) Hi Kraig, welcome back. Glad to have you involved in this discussion. > That 365.26 divided by 13 then times 8 is 224.77 is as close > as one can get i would imagine to matching the rotation of Venus. > a little over an hour an a half. PHI is over a day off. But this value for an Earth-year is a rounded one! This will have an effect on your calculations. I know this is the figure I gave in my chart, but we can be more accurate. According to an essay I read recently by Isaac Asimov [in _Of Time, Space, and Other Things_, p 79], the 'second' is defined as 1/31,556,925,9747 of the 'tropical (= solar) year'; this gives a value for the tropical year of 365 days, 5 hours, 48 minutes, 45.9747 seconds, which translates to ~365.2421988 days. (For this last figure, minutes become significant at the second decimal-place, and seconds become significant at the fourth decimal place.) (The essay is called 'Round and Round...'. In other essays in this book where Asimov actually gives the figure for the year, he rounds the seconds to an integer, either up to 46 or down to 45.) Asimov's value for the sidereal year is 365 days, 6 hours, 9 minutes, 10 seconds, which equals 365.2563657 days. The rounded figure you quoted from my chart is the sidereal year, and is 5 minutes, 14 seconds longer than the one given by Asimov. There are several different ways to measure the length of a year on Earth, the two most common being the sidereal, which is based on the positions of the starts, and the 'tropical', based on the position of the sun and the one you used here. - that's the one we ordinarily mean by 'year'. I think you meant to go one digit below 365.25 rather than above; 365.24 is a more accurate value. If the value was exactly 365.25 days, then we would always have a leap year every 4 years: ((365*3)+(366*1))/4. (This was how the Julian calendar worked. It was invented by Julius Caesar and his Egyptian astronomer Sisogenes, and in general use from 45 BC until the Gregorian reform. The latter was adopted by most cultures between 1582 (the Christian Church) and 1752 (America). The variance in dates is mostly due to religious affiliation; the Orthodox church still uses the Julian calendar, while the Jews and Muslims also retain their own reckonings.) 'Century' years are always divisible by 4, but 3/4 of them are not leap years - this year was one of the exceptional '1 out of 4'. This makes our calendar more accurate: our current 'Gregorian' value is ((365*303)+(366*97))/400 = 365.2425 days over the long haul - i.e., the average over 400 years. The error of the Gregorian calendar from the accurate solar-year figure given by Asimov is thus 26.0253 seconds every 400 years, or just under 2/3 second per decade, or 1 second every ~15&1/3 years. In my original post about my 'Solar System' piece, http://www.egroups.com/message/tuning/11923 I gave the orbital period of Venus as 224.7 Earth-days. A slightly more exact figure for the orbital period of Venus is given at http://www.solarviews.com/eng/venus.htm as 224.701 Earth-days. ************ > I believe for the ancients the relationships that were more > interested in were of repeated conjunctions as opposed to > a sidereal measure of rotation. Yes, Kraig, my recent research into ancient astronomy suggest that you're correct about this. In fact, I believe that I've figured why the Mayans began their current cycle of time in 3114 BC, why it will end soon in 2012, and why a cycle lasts ~5125 years: There was a triple conjunction in 3114 BC, and there will be another one in 2012, of the Moon, Venus, and Jupiter at sunrise. These are the three brightest objects in the night sky, and a triple conjunction of them would truly be a sight to behold. The Mayans based their calendar on the movements of Venus, so to them this would have been an especially significant celestial event. MONZ! do you know how to compute these, I do not but could use them in deciphering some features of the Anaphorian calendar. How to compute planetary positions http://hotel04.ausys.se/pausch/comp/ppcomp.html SLALIB -- Positional Astronomy Library [software library] http://star-www.rl.ac.uk/star/docs/sun67.htx/sun67.html International Earth Rotation Service - Sub-bureau for Rapid Service and Predictions of Earth Orientation Parameters http://maia.usno.navy.mil/ Many of you may feel that this thread is too far off-topic for this List, but researchers who study tuning often get involved in these ancient ideas connecting music and cosmology. As I've noted here before, tuning has to do with much more than just music. And since my project is to map the celestial motions into sound, it's all relevant here anyway. If the musicians on the List are too impatient to bypass this stuff, perhaps there should be a separate 'celestial harmonics' list. REFERENCE --------- Asimov, Isaac. [<1965]. 'The Days of Our Years', from _The Magazine of Fantasy and Science Fiction_. Reprinted in _Of Time, Space, and Other Things_, Discus/Avon. ISBN 0-380-00325-2. **** IMO, tempered tunings suit modern life better, as JI apparently suited ancient life better. Before the invention of electric lighting, people generally followed a more periodic lifestyle, going to bed when it was dark and living out their conscious lives during the daylight hours. While this daily rhythm has not entirely faded, many more people today adjust their personal time to suit their own needs, while ignoring the 'natural' solar rhythm to a large extent.