The Relative Nature of Time: Calculating for the Speed of Music in Space-Time

Music theory is boring. Music language is fun! Learn to talk good.

The Relative Nature of Time: Calculating for the Speed of Music in Space-Time
Break out the reading glasses, bring the iPad to the bathroom, it's story time! A short story, long, about the importance of clear oral communication when speaking the language of music. Music theory is boring. Music language is fun! Learn to talk good! Music as linguistics! Then later on in the article, we take a look at the formula for calculating the relative speed of music in space-time! Mathematics is a language too!:)

Behind The Music: Language for Communicating Language

The language of music is a fascinating topic - not just the music itself, but also the words themselves that we use to communicate our thoughts to one another in the language of music - when you stop for a moment to smell the flowers.

Firstly, it is old, older than Latin. It is at least 4000 years old, but its true origins, shrouded in mystery. Much as we will never know what the first word spoken was, and what it meant, we will never know the true origins of music. Flutes, over 40,000 years old, discovered at archeology sites, play a pentatonic scale. They are definitely from way back in the day because they are made of materials like, Woolly Mammoth ivory.

Philosophers have long asked the question: did mathematics, and numbers, always exist? Did humans invent them? You could ask the same thing of music. A chiselled tablet, dating back to 2000 BC, contains instructions for playing music using the diatonic scale. Who then, taught that dude about the diatonic scale?! It might be the oldest language in the world still in active use.

Right now, and in every corner of the globe, there is someone using music to communicate effectively. Unlike many other ancient languages, it is stronger than ever, and it gets only stronger over time. There is no preservation effort going around cataloguing it and sounding the alarm over its disappearance, despite its cultural importance; it is unnecessary to do so. The language of music is here to stay, and it is going nowhere except into the future, and beyond.

Music might be the only language which is communicated orally (i.e., not playing an instrument, melody, or rhythm) by speaking another language. The only real way to communicate in the language of music is to play music; so when there is a need to communicate music without playing music, we must then use words to describe what the music sounds like, or, what the intent or application of the music is, put into specific practical applications and environments. This might be one reason why music is considered difficult to understand, or hard to be fluent in.

To understand the language of music, you first must understand the use of language itself; and, the historical context of the words in relation to music; and of course, what the words actually meant before applied to music. The musical vocabulary is peppered with words and phrases stolen from various languages, and branches of language, such as: Latin, Arabic, Bantu, Russian, Mandarin, Japanese, Italian, German, Spanish, French, and English - just to name a few - and then there's the amalgamation of math, physics, science, numerology and religion. That is a huge base for only one language to expand on. No wonder it is not as easy as it is from the outside listening in.

The words incorporated through history, are a mix picked up from the dominant languages of that specific period's music. Almost all of them have stuck around, because they were important. They meant something, and nothing else could say it so well. If there was only one word, which could describe something perfectly - a concept not easily explained quickly - someone brought it along for the ride. Now by learning a new word, the next time there was a need to explain that particular musical concept; it became much simpler to communicate effectively.

As the word catches on, it becomes a part of the vernacular. If there is not a need, or there is already a perfectly good word, no need to change it. There are no metaphors, no double entendre, nor creative nuances like 2000 different words for "snow." The words are adapted purposefully. Eloquence, grace and class, are not adequate purpose. They must be succinct, fulfilling a specific need cast by an inherent problem with written or oral communication.

The written music language has evolved in a way to garner the most possible information on a single piece of paper. Green way ahead of its time, Maestros were trying to go paperless well before anyone knew deforestation was a thing. Papers, and page-turners alike, have faced shortages throughout history. Simple economics might have led to the condensation of the written language by Maestros looking to save a few bucks. We must eliminate three page-turners from the orchestra to ensure profits! By evolving this way, very little is redundant, thereby discarded. Even the oldest words from the language of music are still taught, and with purpose, by classical academics.

However, with the advancement of modern spoken language, many of the traditional words cast aside by the youth, in favour of English and English slang, are now lost. A similar kind of degradation has happened to the English language in the last 25 years, however, from an historical context, this spill over into music has happened at a much more rapid pace. The last 25 years of English, in an evolutionary context, are more like 5 years for music. Dog years, but for the evolution of language. In other words, it has been a fast decline for music.

Like how we blame the Internet for our lack of communication skills today - and for the general degradation of the English language by way of slang and shorthand - musicologists, or other scholarly blowhards, will one day blame the electric guitar for, "the beginning of the end for the romance language of music."

To a certain extent, they may have a point. It was not until the electric guitar became popular that music became an accessible thing. It was not just for wealthy, arrogant, upper-crust types anymore. It was now something found in a second-hand store, at a dime-a-dozen; and, you did not need to go a fancy prep school just to learn how to play it. All you needed was a little patience and a record player so you could rewind your favourite songs over, and over, again to figure out what was going on. Music had not seen anything like it since the piano sales boom of the early 1900s, only now you could take a guitar along wherever you went.

All of a sudden there were a bunch of poor, uneducated, people running around playing "music" with these "instruments" called, "electric guitars." It was not long before the uneducated outnumbered the educated. A few decades pass, the uneducated have kids, and of course, this leads to them teaching the next generation how to play guitar. The cycle perpetuates. Many people got truly great at playing, taking the music world by storm, all while not knowing a single thing about the language of music. Many famous bands, founded on the very basis that they were not good enough to play other people's music, started out this way. They did not have that music background to pull it off, but what they could do, was make some sh-t up; or steal something from someone nobody were paying attention to. The classic style of language, the one that had worked so well for thousands of years, was not working the same way anymore. A new group of musicians, refusing to play ball like everyone else, were shaking up the establishment.

In one corner, academics were crying, "... It must be so!"

While in the other corner, guitarists were all replying, "... Take a hike, old-timer, you're system sucks and we're doing just fine without it."

They were right. They, and the music, were doing just fine exploring the new possibilities, unsaddled by antiquated ways for thinking about music that had nothing to do with a guitar anyways. It is not as though they received an invitation to the party either. People were figuring out the magic of the electric guitar long after classical theory was established. This was a new instrument, the players also. They had no idea what they were doing. They could just go out there and kick everyone's a-s with a big, dumb grin on their face while people with monocles spat out their tea in disgust. They never had any problems communicating through their own music to an audience, but the communication of their music to the other musicians - like when they are telling their band about this new jam they've got going on - challenged those around them with new problems. No prep school in the world could prepare you for the fly-by-night approach of interpretive music communication.

The James Brown Band had to figure out how to take a series of grunts, and translate them into music that a band could play. The members would recount that it was a difficult task, and there might have been easier ways for James to communicate with the band, but he just did not know any other way. They made it work, and in the end, the world was a better place for it. By listening to their instincts, drawing on what they knew of the similar problems already solved, they worked it on out, like a sex machine.

After decades on the road, many of these "savants" went on to become instructors at various institutions, which began popping up to capitalize on the popularity of the guitar as a specialized, lead instrument. The new instructors, unfamiliar with the formal language of music and its communication, started teaching from their own experiences with trial-by-fire, and the second-hand knowledge gleaned from various interactions members having formal training like keys, horns, drums, and bass. This is a great thing. Real world instruction is invaluable; never compromising, however, this would best incorporate with traditional methods to develop new levels of understanding far into the future.

The complete separation of guitar from the classical classroom led to the development of contemporary theories based on real word scenarios on the fly. Cities like, Nashville, were at the forefront; dominating. At many modern schools of music with a guitar-heavy focus, instructors are encouraged to develop their own methods, which introduce their own terminology. More schools, more students, more instructors. By the numbers, there are now many more people, attempting to introduce many different systems, introducing many different slang words to accompany many different systems.

While the general gist of it all might be the same, the differences in the use of language can bring evolution to a grinding halt in the real world. When two musicians, who went to two different schools, have two different words for exactly the same thing, chaos arrives. Better yet, one person may be using a word correctly, while the other person taught an antonym by the same name. When either attempts to use that same word, neither knows to what the other is referring. Both will be adamant in the acceptance of their way, or the highway. Those are just artistic differences... Eventually, the enlightened of the two will likely agree with the other, if only just to stop the nonsense, making a mental note of a predictable translation error in the event this same problem arises again.

This only helps to perpetuate the problem, however, because the enlightened few "knows what they mean," but the vocal majority are still happily going about their day using the word entirely wrong. It is astonishingly ironic how many people use irony incorrectly. If this happens enough times, eventually the wrong meaning of the right word gets inscribed in the collective consciousness forever, much to the bewilderment of those bearing common sense.

English, being the dominant mainstream language, is now the root for most new words adapted to the language of music. A high percentage of English speakers spoke another language first, creating prime conditions for errors in translation across several languages when introduced to music. Thankfully, most of the verbal diarrhea spat on today's vernacular, will be eventually be weeded out of use. Thousands of years from now, scars left from present-times, in the form of a few great words music has chosen to borrow from English, carry on. Slang trends with the times. Trends come and go. Music, and the language, is here to stay.

Sometimes though, a bad word perpetuates. It lingers for so long that when we come to our senses, we do not know how we ended up making a word mean not at all, what the word meant. Some people have a large audience, making it easier to spread the truth of your-word-versus-mine. Sometimes the truth spread is not the whole truth. Sometimes, it is only true within their, little, world. Nobody teaches their kid, that the word for knife, is actually fork, so why would we do that to people just learning the language of music?

When English is not their first language, it only makes for more confusion. Let us not make it more difficult for all of us to understand each other. We can make better choices than to teach a word in English to mean one thing, but then applied to music, while still speaking English, warping it to mean something completely counter-intuitive. If some of you are asking yourselves, "Why did they do that to me?" it is not your fault. The hardest part is to recognize where you led astray. Once you can identify that, you can then attempt to correct the habit. Who is right, and who is wrong, is not important. What is important, is for everyone to be on the same page.

The instruction of half time, is a prime example. I cannot speak for the entire world yet, but over in this corner of the globe, there is rampant misuse of the term. When somebody barks at you in the middle of a jam, "... Now go half-time!" what do you imagine as happening?

If your answer was "slowing down," you are not alone.

It is probably not your fault. A large percentage of people will come to this conclusion instantly. Many are taught this way, and have never really thought about it. It is not because they are bad musicians. It is not because they are dumb. They know exactly what you mean when you explain at a fundamental level; and, they know how to play it instinctively, but taught the wrong meaning, applications become incorrect, misguided by the use of language. Maybe they were passing down lessons received. Maybe they were just following the drummer, making up their own terms in their heads. Regardless, they failed to communicate effectively in the language of music.

Half time means exactly what it says: half the amount of time. It is faster! Imagine 4 quarter notes. You play them in X amount of seconds, now play 4 quarter notes in X/2 seconds. You play the same thing, in less time.

What is being illogically concluded when half time is interpreted to be slower, is that time = speed, when in reality, speed = distance/time. The BPM, or tempo, is not the complete picture of speed. Speed is a ratio, and tempo is only one of the input variables in the equation. What we should have said, to have said what we really wanted, is "half tempo."

Have a look at the diagram below. Given the tempo remains the same, which time signature is fastest?

If the beat has a length of one quarter note in common time, and there is one beat every second, and one whole note has four quarters, then we can conclude that a whole note lasts for exactly 4 seconds at 60 BPM, or, 1 Hz. If a whole note is 4 seconds in length, then an eighth note lasts for 0.5 seconds, and a dotted quarter note lasts for 1.5 seconds. If one measure of 4/4 is exactly one whole note in length, then one measure in a 4/4 time signature at 60 BPM lasts for exactly 4 seconds.

If we then want to play half time, while maintaining 60 BPM, we would play one measure of 6/8. Three quarter notes of distance in 2 seconds makes a speed ratio of 1.5. 3/2 = 1.5. Playing three quarter notes in a 6/8 time signature, at 60 BPM takes 2 seconds. If we compared 4 seconds of time at 4/4 to 4 seconds of time at 6/8, we find that there are 50% more quarter notes per second in a measure of 6/8 than there are in a measure of 4/4. Cutting half time to a 2/4 time signature would not accomplish a change in speed, because 4 quarter notes would still take 4 seconds to play. 4/4 = 1. 2/2 = 1. At the same tempo, 2/4 and 4/4 are the same speed.

So if we can go faster without moving away from 4 beats per measure at 60 BPM, what would the equivalent shift in BPM be to play a measure of 4/4 at the same speed as a measure of 6/8 at 60 BPM?

Instead of changing the beat value from a quarter to a dotted quarter note, we can manipulate the tempo to achieve the same effect. To put it another way, 1 second of time now is worth one dotted quarter note. 4 beats per measure of 12/8 makes 4 seconds of time, or a relative speed of 1. Speed is proportional to the number of quarter notes per measure, divided by the number of seconds per measure. Halfing the BPM, makes 50% more time. 50% more BPM reduces the distance of one quarter note by 33%. 1/1 is 50% more than 2/3. 2/3 is 33% less than 1. If a quarter note is 2/3 of a second at 90 BPM, then 50% more time is a dotted quarter note, one second. 4/4 at 90 BPM is the same speed as 12/8 at 60 BPM.

Click here to view a cross-analysis chart of proportional speeds in musical space-time, relative to 1 Hz. Aside from the obvious applications, the math here becomes useful while programming delays, oscilators, virtual drums, click tracks, MIDI, various effects and studio tasks.

Stay tuned for upcoming chapters, including: "Help! I'm Lost in a C of Scales!," and, "The Pentatonic Scale: vi for I, or a Half-Dozen of the Other."

About the Author:
Dealey is a Vancouver, Canada based guitarist, songwriter, recording engineer and producer. He is the author of the forthcoming independent book, "The Relative Nature Of Chords: A Street-Smart Field Guide for Guitar." Watch for exclusive excerpts on Ultimate-Guitar! You can support his ventures by buying his music here or talk to him about collaborating on your project by email to: info(a.t.)

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    Like most of your other articles... You are overly complicating something that is fundamentally basic and much simpler than you are trying to portray it. By adding in all this unnecessary math and unnecessarily convoluted terminology, you're doing the complete opposite of what you set out to do, stated by the first few lines in your article. "A short story, long, about the importance of clear oral communication when speaking the language of music. Music theory is boring. Music language is fun! " Leading into some of the most overly complicated mess of unnecessary equation to describe a change in meter. "If we then want to play half time, while maintaining 60 BPM, we would play one measure of 6/8. Three quarter notes of distance in 2 seconds makes a speed ratio of 1.5. 3/2 = 1.5. Playing three quarter notes in a 6/8 time signature, at 60 BPM takes 2 seconds. If we compared 4 seconds of time at 4/4 to 4 seconds of time at 6/8, we find that there are 50% more quarter notes per second in a measure of 6/8 than there are in a measure of 4/4. Cutting half time to a 2/4 time signature would not accomplish a change in speed, because 4 quarter notes would still take 4 seconds to play. 4/4 = 1. 2/2 = 1. At the same tempo, 2/4 and 4/4 are the same speed." What a complicated way to say "There are half as many notes in 2/4 as there are in 4/4 because of the BPM/Note Value relationship of a time signature."
    Just like the other articles, there is also no scholarly basis to this information whatsoever. Here's a highlight (of which there are too many to count), "a chiselled tablet, dating back to 2000 BC, contains instructions for playing music using the diatonic scale." The word "diatonic" (as well as its musical application) is believed to have originated in Ancient Greece: this civilization existed over a thousand years later than what this author is suggesting. Further, in Ancient Greece, they had books and scrolls - it was the late bronze/early iron age, not the stone age lol
    No. Half-time means half-time - it means that in a 4/4 times signature, should the drummer plays the downbeat on 2 and 4, he will then displace the downbeat on 3. This gives the impression that the tempo is cut in half : twice as slow. What you meant was *double-time : We say double-time for going twice as fast - in fact, for counting one quarter on two, at 300bpm and faster. Yes, you're mathematically right. But, your definition is wrong in the langage of musicians (sorry) and it is plainly counter-intuitive : half-time means you want the time to cut in half; does that means slowing down?? Absolutely NOT. It's an illusion. Check out some half-time shuffles like in Rosanna by Toto. If goes *tch-k-tch-k-TA-k-tch-k* (repeat) in 4/4 (I think anyone here can figure this out). That is half-time.