Podcast Six- Better Know Time is a short show & tell that will help connect small time values with what they sound like. Special Guest: 400 Milliseconds
There is a follow-up piece to this podcast here
Here is an ongoing thread of auditory amusement.
Music and mysticism have always gone together. It’s not suprising. I might be a lot more mystical about music myself if I hadn’t spent many years staring at an oscilloscope. The glowy green line on the little screen can show you what you are hearing. Seeing pure tones, music signals, resonances, and summing and cancelling changed the way I think of music.
For drama, let’s start with the theme from 2001 A Space Odyssey (once known only as the opening bit of Also Sprach Zarathustra).
The 2001 theme has Strauss’s solo horn play a root note, then a fifth up, then an octave up from the root. The last note makes the air wiggle exactly two times as fast as the first note. It’s wavelength is exactly half the length of the first. That’s an octave interval. Any string of a guitar will sound one octave up at the fret that lines up with the exact middle of the string's length.
If you heard the first and last note at the same time, they would blend together into a single voice with a simple harmonic structure, like a flute. Here, science and music are in complete agreement. An octave interval is always twice or half the frequency you started wirh. So far, this has nothing to do with scale. Except that you could call it a one tone scale with one note per octave.
The middle note is less simple to explain. It is not the exact halfway point between octaves. In fact, the halfway point is considered the ugliest sounding interval of them all by everyone. It is known as the Flat Fifth or the Augmented Fourth in regular music scale. It is used to express digust, alarm, war, conflict, darkness, and sinisterness.
A fifth is found by dividing the guitar string into thirds. Find the fret that is at exactly one third the length of the string and there (pluck the other two thirds of the string) is the middle note of 2001's opening horn.
If you heard the first two notes together, they would blend into a voice with a raspy, reedy quailty like a sax. A fifth is so familiar and comfortable to hear that most musical newbies can find the interval simply by hearing it. Imagine tuning a second string to be a fifth up from the first. As the pitch closes in, it gains a purity and rhythm to its resonance that just sounds right.
Back to the 2001 theme…
If you have a subwoofer, you may have noticed that someone has laid a pipe wrench on the low C pedal of the pipe organ just a moment before the horn starts. The horn plays root-fith-octave (C-G-C) and then a whole bunch of people with various instruments blast out a “chord”. Everyone is playing C’s and G’s and one other note- the Third of the scale –which comes in two flavors and we hear them both… one, then the other. The Major Third and the Minor Third.
The top note goes E then Eb or, “Da-dum”. That makes the C major chord quickly turn into a C minor chord. Major chords sound happy. Minor chords sound sad. So, here the orchestra goes “happy-sad” and then the tuned kettle drums beat out C G C G C G C! Then, a somewhat larger horn sounds the solo line again followed by a loud “sad-happy” chord from everybody. That means the top note goes Eb then E. Just that one change of pitch gives us “happy-sad” then “sad-happy”.
Another happy sound can be the way one chord is followed by another. Following a C major with another major chord based on the fourth note of the scale, in this case F major (with its own root, major third and fifth), is a very pleasing change of notes.
After more kettles and a final and deeper horn spelling out C-G-C, the orchestra blasts out “happy-very happy”. More chords come along and trigger some drama. The drama is mustered by some chords that create tension. By themselves, these chords are not tense but if they follow a string of C major and F major chords, look out. They are a musical crisis that wants to be resolved. Happy is followed by “tense” then “tenser”, then “really, really happy” with horns sounding the notes of the chord one by one. More chords make things “a little tense” then “very tense” and finally, everything lands back on C major and sounding “orgasm happy”. At the last moment, the organist who was stuck in traffic arrives just in time to almost participate.
All this emotion triggering works not because of the chosen notes like C and G but because of the harmonic relationships that all the notes have to the first note no matter what it is.
If the horn player decided to start the line with a different note, like A#, then as long as all the following notes maintained the A# scale with the same harmonic intervals relative to that first note, the result will be the same. Globally changing all the pitches preserves the intended musicality. Aging singers will transpose their songs to a lower pitch to make them easier to sing. Same melody and intervals, just a lower starting note. The chosen scale is what matters with music.
All a musical scale is, is a nearly arbritrary decision about how many equal-intervaled segments to divide the octave into. A two-tone scale would go, root, flat fifth, octave. We don’t hear that a lot except on hard rock radio. The do-re-mi-fa-so-la-tee-do scale is a twelve tone scale. An octave must be divide into twelve parts in order to place the seven notes of do-re-mi in their order.
Pianos are friendly to the key of C. If C is your root note, than do-re-etc is all the white keys. The other five of the twelve spaces not involved in do-re-mi are the sinister-looking black keys. The middle horn note shows up at G or four white keys to the right of C.
Other cultures around the world have developed music based on dividing an octave into other interesting numbers of notes, like five, seven or nine. Melodies and chords are played involving only those intervals. Avant garde artist use them at their tiny and infrequent gigs. Bach, Pink Floyd and Taylor Swift all use the twelve-tone scale and do-re-mi. A lot of thought went into do-re-mi.
There is real science behind the do-re-mi scale that makes it the least abritrary of all. But it’s an example of being scientific up to a point then saying frack it and carrying on subjectively.
Do-re-mi is based on the way things in the universe resonate and make harmonic structures. Each note of the scale has a harmonic relationship to Do that has discernable mathematical properties. The frets on the neck of a guitar are based on sub-dividing the length of the string to find the exact position at which certain notes will sound relative to the pitch of the whole string. Other scales have mathematical propeties too, but do-re-mi uses naturally occuring intervals.
The space between any two notes of a scale is an interval of some kind. The first and second notes of 2001 are a fifth interval apart. The second and third notes are a fourth interval apart. The first and third notes are an octave or eighth interval apart. All the gaps in the do-re-mi scale have an interval name like major third or minor sixth.
My aunt had Perfect Pitch and could do that palor game where someone hits a note on the piano and she names it. I say parlor game because you don’t need to actually have Perfect Pitch to do it. Any good musical training will emphasize learning the perception of intervals. Specifically, do-re-mi intervals.
Uncle Vladimir is drunk and showing off again. Little Nancy has pounded a note on the white keys. Vlad stands with his back turned to the piano. Nancy’s puffy shoulders obscure the view provided by the reflection in the shiny china on the hutch but then… the cups did wiggle and ring that certain way when exposed to B flat. “It’s B flat.” Nancy laughs at him. “No, it’s an A. You’re a drunken a-hole!” Vlad is undetered. “But I was so close! Try it again, quickly!” Nancy pounds out more notes. Vlad nails their identity in quick succession. Vlad knows his intervals and now armed with an identified starting note, then any other note will be the starting note plus the perceived interval. Nancy is amazed. “Now go get me another highball you little…”
It is a bit complicated and, from a novice’s view, it seems arbritrary. Why 12 steps and not some other number? What can 12 steps do that 9 cannot? Twelve steps puts us in close correspondence with the way things actually resonate and how different vibration rates (pitches) relate to each other. Do-re-mi is very clever in organizing actual pitch interval science and subjective musical experience. But only up to a point. This is where science and music go their separate ways.
The fifth interval of the do-re-mi scale, so, can also have a fifth interval at re of the next octave of do-re-mi. Re's fifth interval is la and la's fifth interval is mi of the next octave. Mi's fifth interval is si and si's fifth interval is fa# of the next octave. This progression can continue until all twelve notes of the twelve-stepped octave are hit and the next fifth up is do, now seven octaves up from the first do. It's called the Circle of Fifths. If carried out with so-called perfect fifth intervals, it should land on the same exact frequency found by doubling the first do's frequency seven times. It doesn't. This can cast doubt on the Order of the Universe. The fifths must be slightly imperfect intervals in order to achieve the desired Perfect Order. The universe requires some fudge. That is why we have well-tempered scales and even-tempered scales. They are differing applications of fudge. They make cosmic order a matter of opinion. If that is disappointing, it is best not to think about it.
It gets worse. Why are the twelve steps always called half steps? The half-step or half-tone is the quirky name given to the interval between mi and fa. Do and re are a whole step apart even though it is two steps of the twelve. It takes twelve half-steps in total to provide the seven spaces of do-re-mi. That’s all. The # sharp sign raises a note a half-step and the b flat sign denotes a drop of a half-step. A “whole-tone scale” would go, do-re-mi-fa#-so#-la#-do, and have only six notes per octave and a small audience. Step is more of a musical talking point than a scientific parameter.
On the other hand, the half step is smallest practical gap to put between two notes that is musically discerned as this note and that note. Any less than a half-step sounds like two variations of the same note or two notes that are out of tune with each other.
If you start with two sounds with the same pitch and start raising one of them a bit and then stop, the result is unmusical. Raise it a bit more and it get worse, musically. If the second pitch keeps rising, there will be a point at which it begins to sound like it has a vaguely discernable musical relationship with the steady pitch. is whole-step interval. But that’s two notes alone without a backup band. Half-steps are easily discernable within the context of a scale like do-re-mi.
However. OUR EARDRUMS are sensitive to every and all frequencies between the lowest and highest pitch of our hearing range. Since there are an infinite number of points on a line, there are an inifinite number of possible frequencies that we can hear. Like, 440.0000013 Hz. That’s a whole different frequency than 440.0000012 Hz. Is that the same as an infinite number of musical notes? Not exactly.
If you had a 500’ long slide whistle and slid from deep whale song notes all the way to high tinny notes there would be no gap in audibility. If the slide stopped anywhere along the way, we would hear a pitch of that frequency. But it would have to stop, and stay there for a moment at least before it is technically a pitch. A sliding pitch or changing frequency is not perceived as a “note”.
A frequency of 20 wiggles per second is the lowest note anyone can detect. When air is wiggling loudly at 20 hertz you can feel it with your hand. The highest note will range from 10,000 to 20,000 wiggles per second. That might seem like a lot of frequencies (10,000 of them) but if you remember how octaves work (x½ = octave down, x2 = octave up), it is only one octave of do-re-mi. Many can hear nothing of the top octave. Many speakers do not try to reproduce it or do so only faintly. Likewise, most speakers cannot produce the lowest octave of 20 to 40 wiggles per second.
That still gives us eight octaves of hearable range. And not just the do-re-mi’s, but all the possible pitches in-between them.
A more obvious perceptual threshold is time- how long a pitch is held steady and how close to truly steady it is. All musical notes quiver and vary a bit in pitch or they are not musical. Back to 2001… When HAL murders the hybernated crewmen, alarm screens flash and there is an unpleasant beeping noise that is unmusical and nearly painful in 5.1. It is the sound of perfection.
Those beeping alarms are single unvarying and unquivering pitches. Science may suggest that these are perfect musical notes but they sound awful. The reason is because they overstay their welcome.
If a note is continuously sliding up or down like a old siren, it has no discernable pitch. The note must linger near a single frequency long enough to be heard by us as a pitch. It’s a perceptual threshold- close enough and for long enough and OUR EARDRUMS will call it a note. And there is the difference in a musical tone and an alarm tone.
Musical tones quiver and shift and fall in and out of our note-threshold and in doing so, make an unfolding articulated voice that resounds a pitch over and over again like renewing a frame of a flow. Alarm tones do not unfold or articulate or express. They nail the note threshold and leave it on. There is no discernable flow except the frequency itself. It is not a sound nature prepared us to hear. A continuous perfect pitch is an unnatural sound.
Imagine the sonic horror of the 2001 theme played entirely by test and alarm tones. Even if played at the proper octaves and for the proper durations, it won’t sound like music or even bad music. We will perceive it as sounds that won’t stop.
Musicality comes from pitches quivering or, stepping in and out of our perceptual threshold of pitch. Even if the voice is continous, there is a flowing renewal of pitch that makes us perceive a note that is sounding over and over again within the voice. This caters to how we hear things, which is from the perspective of a moving flow. Pure and steady tones provide only the horror of the actual frequency to correspond to.
While the tape machine is out, record a newborn’s hunger cry and slow it down until you hear Mom’s voice. Then slow it down some more until you hear Dad’s. Music? Or science?
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