Rhythm and Harmony can be in Tune

Rhythm or tempo can be considered as slow vibrations compared to normal sound vibrations, but that nevertheless may be in tune with the frequencies of the notes in the music. This is a novel idea and requires some explanation. Suppose that we have a piano tuned so that middle C is 256 Hz (256 vibrations per second). Then as we go down octaves, the next C will be 128 Hz, then 64 Hz, 32 Hz, 16 Hz and so on. When we reach 16 Hz it falls off the piano keyboard and out of the human hearing range. However we can imagine more C octaves at 8Hz, 4 Hz and 2 Hz. Well 2 Hz is 2 vibrations per second, or 120 per minute. As it happens, pieces of music written in C are often played at 120 bpm (beats per minute), and we see that this rhythm is really a very low octave of the note C also.

OK, that is the basic idea. Now John Townley has asked some questions about this here. So this post is a reply to those questions. But first a little background. There is a long discussion that occurred in the Alexandria City forum in August 1996, which includes a discussion of this topic and others.

In answer to the question “Have you given any consideration to rhythmic ratios and what significance they may hold, since music is also proportion in time?”

Ah yes, another whole rich field of study. It occurred to me that rhythm can be considered as slow vibrations and could be in tune with the key. For example, if a piece of music is in A then as A=440 Hz it is also 220, 110, 55, 27.5, 13.75, 6.88, 3.44, 1.72 Hz. But 1.72 Hz is 1.72/sec*60sec/min = 103 beats/minute. Therefore if a piece is played at 103 bpm then its rhythm is in A.

My guess was that good music should have a match between the music key and the rhythm with possibly one ratio of 3 among the ratios of 2 used to get down from the note frequencies to the rhythm. It is only possible to compare when the tempo is accurately stated, although I suppose that it would be possible to time recordings. In fact the great composers such as Beethoven and Mozart did do this right most of the time.

Not all composers get it right, but some modern composers such as Billy Joel do also. He is an especially interesting case because many pieces have accurately stated tempo and I found that he played them about 2 to 3% faster than would be expected. But adding this percentage to the standard A of 440 gives 450 Hz. I regard this as another good piece of evidence that the true and correct A is 450 Hz. This was in fact the extra evidence that I mentioned earlier.

I explained the above by email to a friend who is into drumming with others and was investigating putting different ratio rhythms together. He sent me an email about a week later saying “Check out this web page; someone else has been thinking your thoughts! http://arts.usf.edu/music/wtm/art-sj.html”. [link no longer working]

This is a description of rhythms as chords reduced in frequency by octaves until we hear the oscillations as rhythm. The writer describes how many of the common rhythms are in fact simple chords played in slow motion.

From here on, the indented text in italics is by John, and the following plain text bits are my replies.

Ray, you have noted elsewhere (as I also independently happened upon) that different tempos become different pitches when raised high enough by octave. I have made some observations on the scaled generality of that as a principle in regard to planetary cycles (which serve as a kind of deep bass track, by comparison) at http://www.astrococktail.com/windowpanes.html and http://www.astrococktail.com/rainbows.html .

It needs to be said right away, that once you start thinking about these relationships, you begin to look at the whole world in a different way. The human centered time frame is no longer some absolute reference point, but much faster and much slower cyclical movements are considered each in their own perspective. So you start to listen to the sound that the lights of the aurora make, or the sound of planetary radio or solar x-ray emissions make, or think about “the music of the spheres”. This is a disclaimer – let the readers consider themselves warned that their world view might change from reading this stuff.  😉

John, on the first page linked to above you state “The universe was once seen as a large, resonant musical entity right after Pythagoras discovered the fundamental relationships of temporal acoustic cycles, which determine musical pitch” and I have to say in reply “it still is”. Not only me, but even big bang believers look at sound waves in the early universe. Actually the largest scale waves, which are around a billion light years wavelength can be shown to be electromagnetic rather than sound, but the principle is just the same.

The idea of a fractal universe has certainly become more popular over the last few decades. In the harmonics theory the Universe is is not actually fractal, but nearly so, with scales at ratios of around 1:34560 being most noticeable. This explains why a galaxy is a bit different to a solar system or an atom, even though they all have lighter stuff orbiting a central mass.

It is worth noting that in the Harmonics theory (as well as in common cycles reported by Dewey and others) there are ratios of 3 as well as 2 between the frequencies. My examination of the great composers show that this is true in music also. I know that it is common to calculate the planetary periods in pure ratios of 2 keeping to one key, but I consider this to be not accurate. In music for example we often find chords in which the bass plays C-E-G while the treble plays G-B-D but not the other way around – that is because there is a ratio 3 present.

I wonder, since 60 beats per second and 80 beats per second become a perfect fifth if doubled enough, do not syncopated tracks, where 4s and 3s overlap for instance, paint a musical melodic/harmonic tapestry when so raised? Anyone have software to do this, or have done it already? Similarly, in the higher, single octave of color, the equivalent of the “tritone” makes for some of the greates color clashes, opposites. Any more on this anywhere?

As regards colour (we non-Americans spell it that way) you might have noticed the 3 coloured sine waves at the top of my web site main page which are blue-green-red and also in the frequency proportion 5:4:3. As near as I can get the colours that is their true frequency ratios. It is of course a major chord and a wee wink at Pythagoras as well. I hope that you might enjoy that one.

Each perceived window of cycle scaling, from planetary cycles to light, is a repeat of both proportion and associated meaning. Even on the planetary level, what we experience as a single birthday-year of growth may be experienced at a different scale by a longer-scale superorganism such as a nation, see http://www.astrococktail.com/adolescent.html for example. Is there software one can use to plug in and visualize/audialize these differing scales? I have seen a nice planetary-to-pitch animation recently out of Europe, but not much else… — John Townley

Couldn’t agree more with these sentiments. This is how I view the Universe too.

Regarding software, many sound software programs allow sounds to be played faster and slower. Try Audacity or something similar. You may need to change the speed of a sound and then save and recombine with the original to get 3:4 ratio etc.

John, I look forward to further thoughts from you here.

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About Ray Tomes

Ray's career was in computer software development including system software design, economic modeling, investments. He spent 15 years full time on cycles research and has spoken on cycles and related topics at conferences and seminars around the world. He retired at age 42 to study cycles full time and work out “The Formula for the Universe” and as a result developed the Harmonics Theory as an explanation for observed patterns of cycles and structure of the Universe. His current project is the development of CATS (Cycles Analysis & Time Series) software, and collecting and organizing large quantities of time series data and analyzing this data to test and confirm Dewey's findings in an organized way. Interested in all aspects of cycles especially climate change and causes.
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One Response to Rhythm and Harmony can be in Tune

  1. John Townley says:

    Thanks, Ray, for the link to Audacity, will go see what that can do, and thanks for all the other things to think about in harmonics, a subject that has been an integral part of some kinds of modern astrology since John Addey introduced them in the ‘60s and ‘70s. I myself also published early in the cycles division of that field, being a fan of Dewey and the cycles foundation. And, the Alexandria discussion is where I found you when looking to see if others had also discovered the rhythm/pitch equivalencies, which proportions extend way above and below beats per minute or Hz. Each window/scaling seems to repeat the others, in a self-similar but not necessarily fractal way. It’s all cycles and their similar proportioning, whether in sound waves, electromagnetic, or in astrology orbit repeats which are physically gravitational cycles, cyclical pulls that perturb each planet (and its entire set of subsystems) on a regular basis, integrating downward into shorter cycles in the surface environment and eventually to the individual creatures at their own, shorter, but entrained harmonic rhythms.

    In astrology, it’s important as backdrop to try to find a physical mechanism to explain astrology’s apparent manifestations. Suggestions how that happens at http://www.astrococktail.com/moonondeck.html and http://www.astrococktail.com/articles/basis.html where the principles of entrainment of shorter, faster, weaker cycles by longer, slower, stronger ones is a step-down mechanism from out there to down here, but one in which the effects don’t happen to us directly, one-on-one from above (an egotistical and anthropomorphic conceit) but through the enveloping, entrained cycles which surround and maintain us, and with which we synchronize for survival.

    The numbers 2 and 3 which you mention as prime musical proportions are the same in gravitational ones, depicted by the Lagrange points (with 2 manifested in L points 1-3, and 3 in L points 4 and 5). That’s the key structure of orbital resonance, and it’s not surprisingly the basis for astrological aspects, though astrologers don’t really know that, but might if they looked at http://www.astrococktail.com/Lagrangepoints.html .
    What would be of great help to all might be more extensive observations and listings of parallels between the windows of big, slower cycles that manifest at lifetime or even long-term cultural or evolutionary levels, and those faster ones like sound and light, where in each we seem to be finding the same type of relative meanings, effects, and operations. Much of our talents as humans in being able to spot things that are meaningful is just through this cross-metaphor recognition. And, the more we are aware of the parallels, the more we can dig out of each scale by pushing the quite literal metaphors we find applicable from others.

    As to how all this condenses in the structure of matter and time, that’s yet another story I’m feeling for, with some clear speculations that seem very explanatory, but for later on. Three dimensions of time to balance three dimensions of space, inversely proportionate, with the speed of light as a pivot has lots of promise, immediately establishing an already-cast multiverse with specifics becoming only delineated voyages within it. But, later…

    Regardless, and back to the earlier threads, it appears to be all of a piece, with the same sets of mutual proportions in play wherever, whenever you go, from hugely big to vanishingly small… establishing usable details so you can jump from one set to the other, using parts of one to predict parts of another, is what we (or at least I) need more of…

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