Most of us react viscerally when we listen to music: You either like/love what you’re hearing, or you dislike/hate it — or perhaps you’re just neutral about it.

It’s mostly just musicians or technicians (such as audio engineers) who tend to take a more analytical approach, but however you look at things, the fact remains that, at its essence, music is a numbers game.

What do I mean by that? Well, as every music student learns early on, each octave represents a doubling of pitch, and each note (in Western music) is roughly a twelfth of an octave. Each song consists of a fixed number of bars, and each bar consists of a fixed number of beats, played at a certain tempo (described by the number of beats per second). Even tonal quality — something called timbre — is determined by the number and type of overtones, which are whole (harmonic) and non-whole (inharmonic) multiples of a sound’s fundamental frequency (the predominant component that gives a musical sound a discernible pitch). Most instruments also produce resonant undertones, which are whole and non-whole number divisions of its fundamental, adding low-end heft to their sound.

Producer Tony Visconti, who worked with David Bowie for many decades (including Bowie’s 2016 farewell album Blackstar), described in an interview I did with him how he uses numbers to improve the sonics of the recordings he makes. Knowing that Tony is himself a bass player, I asked him to talk about his general approach to shaping the tonality of the instrument through the use of equalization. His answer?

“I don’t do anything especially radical,” he said, “except that I look up the frequency of the key that the song is in. Say if it’s in the key of F, I know that the low F on the bass string is something like 48 cycles, so I’ll pinpoint that frequency and boost it. In fact, you can often get more clarity — you can make the low end seem more apparent — if you boost it again an octave higher. So if I’m boosting it at 60 cycles, I’ll also do a slight tweak at 120, and I might even go to 240. Sometimes that’s where the definition lies — it’s not just in the low end. When I discovered this principle, I found that if you go a little higher up, you can actually hear not just the warmth of the note, but the clarity of the note.”

Visconti takes the same approach to other instruments as well. As an example, he pointed to bass drum, which typically has a fundamental down at around 50 cycles (Hz). “That’s a frequency you’re not really going to hear,” he explained. “In fact, it’ll wreck most speakers — it will rip a car speaker apart if you boost it too much. So I’ll find the octave of it — which will be 100 or 200 Hz — and by boosting that frequency instead, the sound of the kick [bass drum] is both fat and clear.

“In opera,” Tony added, “a voice has its tessatura — the range where it sounds most pleasant. A singer might have a four-octave range, but there’s maybe one octave that’s golden, and you want to [have them] sing things in that register. The same thing with instruments. Technically, with its undertones, a guitar will go down to 40 Hz because that’s an octave lower than the low E string. But does it sound good down there? Do you really want to boost those frequencies, or do you want to go where the guitar sounds most pleasant, to the area it was built for? Every instrument has got its range that’s beautiful, and that’s what you want to find.”

The importance of mathematics to music was underscored further still when I had the opportunity to interview Nashville engineer Clarke Schleicher, who revealed that prime numbers (that is, numbers which can be divided only by 1 or by themselves) play an important role in how we respond to music, at least when it comes to delay times.

“Regardless of tempo, prime number delays always work especially well,” Clarke told me, as he reminisced about an analog delay unit popular in the 1970s and 1980s called a Prime Time, which would spit out delays of 31 ms, 37 ms, 41 ms, etc. — but not 32, 36, or 42 ms. “It was always interesting to me how those delays added an extra dimension to the music,” he said.

“Like all other engineers,” Schleicher added, “I use a lot of delay times that are in time with the tempo: eighth notes, sixteenth notes, triplets, and the like. Those help underlay and reinforce the groove. But I also use prime number delay times. I always put a 29 or 31 ms delay on a vocal, for example: I just like the way it gives the vocal depth, regardless of what the tempo is. Similarly, I use 61 or 71 ms delays on guitars a lot.”

“Why do you think that is?” I asked him. “Why would a 31 ms delay sound better than a 32 ms delay? Is there a physical explanation?”

His refreshingly honest answer: “I don’t know. All I know is that it sounds a lot better to me, and I can hear a big difference between a 31 ms delay and a 32 ms one.”

When I returned to my home studio, I tried it out for myself, and you know what? He was absolutely right. I’ve since learned that this is a secret “trick of the trade” employed by many pro recording engineers … albeit one that they are sometimes reluctant to share with outsiders.

I personally was never good at math in school. (In fact, calculus completely baffled me. It was the first college course that I flunked with flying colors.) Yet I was always pretty good at comprehending what goes into making music; in fact, it was my passion, and remains so to this very day.

I’m sure I’m not the only musician who has such a limited affinity for mathematics, despite numbers being at the heart of all music and musical sound. And I’m equally certain there are plenty of people out there who excelled in algebra and geometry yet are tone-deaf and can’t play an instrument. Why this disparity? Perhaps it comes down to genetics, or perhaps it’s just a matter of instinct: the blessing of being able to take pleasure from even those things we don’t understand.

Check out Howard’s other postings.

I recently came across a video on YouTube that made me laugh.

Nothing unusual there, I know, but this one also did something else: It made me think.

The imagery was the famous high school gymnasium promo video that was made back in the early 1990s for Nirvana’s classic hit “Smells Like Teen Spirit,” but the accompanying audio was a very cleverly redone version of the music played in a major key.

What you hear is a well-crafted pop song (Kurt Cobain was nothing if not a skilled songwriter) in the vein of a Weezer or a Goldfinger … but, despite the familiar visuals, it has absolutely none of the emotional impact of the original.

I quickly discovered that both YouTube and Vimeo offer dozens of such videos — familiar songs like “House of the Rising Sun,” “Losing My Religion,” “Sweet Dreams,” even the theme from The Godfather, transformed (in some cases by humans, in other cases by computer algorithm) from a minor to a major key.

What an eye-opener! In every instance, the original intent of the song — to make the listener feel a certain way — had been rendered impotent. Not that you necessarily get a wash of good vibes when you hear these reworked versions … but you certainly don’t experience the same sense of connection, either.

Something even more striking occurs when you take a familiar song written in a major key and convert it to minor: The “sadness” of the minor scale manifests itself with an overly heavy hand. John Lennon’s normally inspirational “Imagine” becomes a dreary exercise in doom and gloom; Bobby McFarrin’s endlessly cheerful “Don’t Worry, Be Happy” turns into a dirge; “Wonderful World” will have you in tears … for all the wrong reasons. And once you hear “Happy Birthday” in a minor key, well, let’s just you may never want to celebrate another one.

Switching between major and minor keys within a song can be used to tremendous effect. The Beatles were masters of that trick, even in their early days. In their song “We Can Work It Out,” the verses (written by Paul, with optimistic lyrics) are in a major key, while the bridge (written by John, with a distinctly pessimistic slant) is in a minor key. Another great example is Paul’s “And I Love Her,” which moves between major and minor throughout its duration, creating tension and ambiguity … until it ends on a triumphant major chord that leaves the listener with a distinct sense that there is hope after all.

Clearly the decision to compose a song in a major or minor key has a big impact on how it is perceived by the listener, but the specific choice of key in which it is played (i.e., C versus B♭, etc.) can play a large role too. Over the centuries, certain keys have become to be associated with subjective terminology. For example, C major is described as “open and noble”; E♭ major “solemn and imperial,” etc. Whether or not this is objectively true, there is little doubt that the choice of key has an impact on the listener’s response to the music being performed.

There are several reasons why. For one thing, certain keys will naturally sound better on particular acoustic instruments due to their physical construction. As an example, the keys of E, A, D, and G work especially well for pop songs since they conform to the open strings of guitar and electric bass, which tend to “ring” and therefore cut through better than fretted notes. Similarly, violinists usually prefer playing in the key of C, which has maximum open strings. Playing in other keys — even in D♭, just a half-step away, not only makes it harder to play in tune, but the most important notes do not resonate as well. The same is the case for other instruments — even, surprisingly, digital keyboards, where you can easily change keys at any time simply by pressing the transposition button.

In addition, most musicians have better improvisational chops in some keys than they do in others — only the most advanced players have equal facility in all keys. Irving Berlin, who wrote standards like “White Christmas” and “Alexander’s Ragtime Band” back at the turn of the 20th century, composed on piano despite the fact that he could only play in the key of F♯, where the black notes predominate. (He got around this limitation by using a transposing piano that employed a mechanism to physically move the hammers over the strings. This allowed him to hear his music in a variety of different keys while continuing to play solely in F♯.)

Perhaps the people most affected by the choice of key are vocalists, who may not even be able to reach the highest or lowest note of a song (think about some of the horrendous renditions of “Star Spangled Banner” you’ve heard) if it is not played in the optimum key.

This was brought home to me by none other than iconic producer Arif Mardin (Aretha Franklin, Chaka Khan, Bee Gees), whom I interviewed a few years before his untimely passing in 2006. During our conversation I asked him what advice he would give an artist making their first commercial recording in a professional studio. I thought he might respond by talking about the importance of choosing the right songs, or avoiding common mixing pitfalls. But his answer — especially the second part of it — surprised me.

“First, read the lyrics of the song you’re recording,” he said. “Ask yourself, what is the song about? What kind of musical setting is required by the melody? Secondly, the producer must get together with the singer and find out how he or she sounds when performing that song. The selection of the key is very important. A song may sound fantastic in a key that forces the singer to strain, but it may sound terribly unimportant when the singer is very comfortable in a lower register — or vice versa. Barry White songs, for example, may sound awful in a high key. For me, a record is almost like a mini-film: you have to invoke imagery.”

Imagery. That’s really what it all boils down to when making music, or even when just listening to it. And there, more than anything, the key really is key.

Photo by Julie Mardin, courtesy of Joe Mardin.

Check out Howard’s other postings.

Lately I’ve been reflecting on just how important timing is.

Rhythm is, in fact, one of the cornerstones of music. Look up the Merriam-Webster dictionary definition of “music” and here’s what you’ll find:

“the science or art of ordering tones or sounds in succession, in combination, and in temporal relationships to produce a composition having unity and continuity”

This is just a fancy way of saying that music consists of a specific series of tonalities (timbre) and pitches (melody), combined together in a certain way (harmony) and played in a certain fixed order (rhythm). In future postings, I’ll be talking more about timbre, melody and harmony, but let’s take a closer look here at rhythm.

First of all, with some exceptions, the tempo of most music — both classical and popular — falls into the 60 – 168 bpm (beats per minute) range, which roughly corresponds to the rate of our heartbeats. A typical normal resting heartbeat for most individuals is 60 to 70 beats per minute, while some moderate activity like a brisk walk can elevate the heart rate to 110 to 120 beats per minute; a strenuous workout can easily push your heart rate up into the 160+ beats range. That’s almost certainly the reason why we find these tempos to be the most “natural” and appealing when composing or listening to music, especially when you consider that we all spent the first nine months of our lives in our mother’s womb listening to her heart beating.

Secondly, as none other than the late, great producer George Martin observed during an interview I did with him some years ago, music is a unique art form in that it needs time to develop. Think about it: music requires someone at the other end to listen to it. Here’s what he had to say on the subject:

“You can’t look at it and say, “What a nice piece of music that is.” You’ve got to spend a bit of your life in order to appreciate it. Every time you listen to a symphony, you invest forty minutes of your life. You’ve only got a finite amount of time on this earth, and you’ve just spent forty minutes of it listening to a symphony, or to an album.

“The fact is that music doesn’t exist at all without time; time is the dimension which makes it work. [That’s why] music is the most sublime of all the arts. It’s the most intangible, it’s a mystery, and it’s been with us since we were primeval. Human beings were making music tens of thousands of years ago, before they could talk. I think it’s the most fundamental part of our lives; without rhythm, we wouldn’t exist. Your heart is pumping out a rhythm, and when it stops, you don’t live anymore, so rhythm is actually the difference between life and death.”

Everything, as Sir George pointed out in the conclusion of the interview, has a rhythm — not just we humans, but the sun, the moon, the stars, everything. And that’s probably the reason why music is indeed the universal language!

Photo by Robert Essel, courtesy C A Management.

Check out Howard’s other postings.