Now, disclaimers and trigger warnings up front ... any time a type of music or sound claims "infinite universe consciousness revealed," you just need to know: Shepard's Tones are POWERFUL, and can literally change the way you feel and think. If you are having one of those days, or trying to avoid one of those days, maybe come back, because I can't guarantee how Roger Shepard's idea of music is going to affect you...
Of course, before Roger Shepard, and even independently afterward, composers had figured out how to create a melody that seemed endlessly recurring ... one might say the entire Baroque period, with its four and five-part fugues, had figured that out at least with fragments of a melody ... Bach shocked me as a student ... this version has all the places this melody comes in ...
Rumor has it that Beethoven, somewhere in his Eighth Symphony, also figured this out in ascending style ... I don't have that clip, but given that Mozart also seems to be aiming that way in the finale of his 41st and last symphony...
... I don't doubt it!
... but then THIS HAPPENED in 2014, and although it is called "Nightmare," I feel like could groove to it for hours...
HOWEVER, there is a HUGE GAP ... I can tell a difference in my perception between Bach, Mozart, and that last one, and then that LAST ONE and the sound of the whole rest of the world afterwards. If Bach makes you look, and Mozart gently wakes one up (and we might guess Beethoven's version points even more firmly in that direction), then with the passage of time since 2014, we might expect that this idea can jump out and take us hostage ... and the reason in between is Roger Shepard, who worked out one thing that computers help us with and added it to something Bach, Beethoven, and Mozart surely knew.
The German classical composers knew that a note made with three or more instruments or voices could be endlessly sustained by giving individuals staggered breaks so the sound itself never seems to end. Mr. Shepard worked out that if you tuned three or more sets of voices octaves apart, tuned them to an ascending chromatic scale, and were subtle about where the top notes end, the lower set would pick up and be ascending again right where the higher ones started and the stopping of the higher tones would go unnoticed by most.
Later, with more computing, other people came along and realized that with synthesized sounds, one can take the leading set of tones and let it run off the human range of hearing either ascending or descending -- thus disappearing -- as the next set of tones takes its place. Either way, what one gets is the auditory illusion of a constantly rising or falling tone, without end.
Again, we have known for a long time that sounds that do not resolve have an effect on the human mind --- it has long been that same Bach had a unique alarm clock if his children needed him. They knew to go play seven notes of a C major scale, ascending -- C, D, E, F, G, A, B -- on the family's clavichord, and he would get right up and play that last C note to complete the octave. That is, an ascending scale, incomplete, could disrupt the mind of Bach -- all the alpha, delta, and theta waves, all the grand music he surely was dreaming up -- and cause a change in his behavior his children could count on whether he knew it or not.
Now, of course, this is Bach we are talking about ... his music is the EPITOME of resolution and order. I listen to Bach to add sanity back to my world! We would expect that he would be disturbed by incompleteness ... but as it turns out, Shepard's Tones are broadly effective in mass media online and off for providing tension and unrest to scenes of suspense and horror, and, I have read enough YouTube comments that converge to a view: these tones can tear your mind and emotions and even your body up. They have been compared to forms of auditory torture...
... but then there are people like me who LOVE THEM. Welcome to the mind of a very strange person ... maybe...
Shepard's Tones are often paired with their infinite visual analogs, fractal art, and in a world in which many people cannot listen to them for ten minutes, I sometimes put on this ten-hour descending version with an infinite fractal to get ready for sleep, and sometimes just leave it on ...
... but then again, I can hear the change over in tones, I am a composer who composes quite a bit for choir and sometimes for orchestra. I'm also a fractal artist ... count the miniatures of this flower in this flower if you can ...
"Garden 8," fractal art by the author, Deeann D. Mathews
... so the math Roger Shepard used to calculate how his auditory illusion works is not beyond my thinking; it's not EXACTLY the same math, but it's in the family of iteration and recurrence. The first video in this post is of a zoom and un-zoom into the famous Mandelbrot set, and the match is beautiful because the math FITS.
But there's also that deep connection of what makes a Shepard's Tone work to the classical music that I love, and you all also know: I LOVE bass, so descending Shepard's Tones, visiting those low regions, sound to me like my beloved Kurt Möll warming up his vast basso profundo with an echo ... and, as it happens, there IS a recording of him with orchestra that plays around with the same principles ... Richard Strauss contributed to the development of the endless descent in music by getting the lead character in "Der Einsame" from a dark room into the bottomless pit ... the first two lines begin from a low place, rise a bit, and then descend unspeakably, with the orchestra hinting already at Herr Möll's first long pause on his lowest note that there is a LOT further down to go...
Over and over again ... even the bright portions spend most of their time in descent, and even though there are some tremendous leaps upward throughout the piece, they are just there to set up further unspeakable drops.
Now as it happens, there IS a limit to how low any orchestra can go: the double bass's lowest note is a contrabass E, and I think the contrabassoon can go a third or so lower ... yet by means of approach, infinite depth can be suggested ... and, sure enough, Herr Möll's approach to his last and lowest note is backed up by a big drop in key and all those wandering low strings and horns and winds to suggest that infinity of depth -- those notes STOP, indeed, and go out of hearing, but there is no end to that bottom. Herr Möll has walked off into the bottomless pit in front of us, courtesy of Strauss ... and many, many people have been loving every moment of it for a long time! "Der Einsame" is from 1902 ... so, for 121 years, goodly numbers of us have been enjoying this descent!
But THEN AGAIN, the reason this came to mind is because of a good conversation with 
... or, descending into chaos (or hell) with a few deceptive hopes popping up from time to time, but getting dragged right back down ...
The difference between gospel and blues, in African American music, can also be thought of in this way... are you singing "Come Sunday" ...
... "or Stormy Monday"?
And even in "Der Einsame," there is a moment in which Herr Möll's voice trembles and suggests that it could break ... he gets across the despair of lost love quite well, and it may be because he could imagine the unthinkable, the loss of his beloved wife Ursula ... he could empathize ... but also could in the song before in that set put out all the unspeakable joy of his life --
-- because losing Frau Möll would not be his reality! His biography suggests that although his formative childhood years were marked by the destruction of Germany in World War II, there was only one way Herr Möll's life ever went from there, bumps and setbacks notwithstanding as all humans must experience -- the testimony of everyone who remembers him (at least in English and as far as my much-forgotten German will go) was that in light and love and joy, in beauty of character as in voice, as close to the end as the public and his friends could know, Kurt Moll only knew of one direction: UP. So he could visit "Der Einsame" convincingly -- he could step right off into that pit and convince us he had gone in -- and then step right out the other side, for it could not hold him. His one bad habit, reputedly, was that he messed over every major villain he ever played in opera! He simply could not find a way to stay down that low in character -- he lifted his villains to noble and sometimes even show-stealing comic favorites!
I wish I had Herr Möll's characteristics ... I wish I had the luxury of having Herr Möll's characteristics! There are people on the other side of me at work and in the community who mean no good that have found out: I can out-villain them, with ease. My stone face and thundering contralto comes out at need to reduce the enemies of my community (ESPECIALLY elders and children) to silence, and where I don't show up in person, I use my communication, knowledge of government and law, and note-taking skills to project my power far and wide. I am that "villainness" who can mess your whole life up ... but only in defense.
I also have known terrible grief ... this early spring going into this early summer ... so much loss ... I have sat in that dark room with Herr Möll and contemplated the abyss, and even at moments felt as though I could step off into it ... but I also know it is not meant for me, nor me for it.
One thing about being a devout, well-studied Christian ... one knows that even death can be experienced, and transcended. Because my Savior did it, I will also, and everlastingly, at some point. So will everyone I love Who believes on Him. So, at my lowest point, when everything is going wrong, I end up with Bach again, a man who also visited the depths ... he lost a wife and TEN children, but wrote this ... "I have enough ... I have my Savior ... I have seen Him through the eyes of faith ... I HAVE ENOUGH -- let death come even, and I am only freed of this world of pain to rise and be with Him -- I HAVE ENOUGH!"
It is just hard to stay down when so much beauty, faith, and hope is part of one's life ... so, the ever-ascending nature of a Shepard's Tone is just not that disruptive an idea to me, and even the descending tones ... that's somewhere I can visit without fear.
Now, DON'T GET ME WRONG ... notice the depths of reasons that Shepard's Tones do not bother me as much as average! They do have certain psychological and auditory effects on me -- gently made descending tones absolutely knock me out, and the "Nightmare" groove up there, love it though I do, is not something I would dare listen to for hours because after hearing it even once or twice, I do have a certain amount of disorientation relative to the rest of the world! I can listen sometimes to Shepard's Tones for hours without getting the "torture" effects, but depending on how they are made, there is a "pressure" element I can feel in my head sometimes as well.
So, with even deep and powerful musical, psychological, and spiritual foundations, I recognize Shepard's Tones are not to be fooled around with ... they can change even our physical states by virtue of what they are. Roger Shepard, like every other musician and auditory specialist who understood how sound works on and in the human mind, knew what he was doing. His contribution to the long journey of the "endless melody" is to be approached with great, deep, and careful respect ... but, once you know how, you too can love them ... maybe ... it depends on where they find you, in your life.