Electrical hum

If you hear electrical equipment humming, it’s probably at a pitch of about 60 Hz since that’s the frequency of AC power, at least in North America. In Europe and most of Asia it’s a little lower at 50 Hz. Here’s an audio clip in a couple formats: wav, mp3.

The screen shot above comes from a tuner app taken when I was around some electrical equipment. The pitch sometimes registered at A# and sometimes as B, and for good reason. In a previous post I derived the formula for converting frequencies to musical pitches:

h = 12 log(P / C) / log 2.

Here C is the pitch of middle C, 261.626 Hz, P is the frequency of your tone, and h is the number of half steps your tone is above middle C. When we stick P = 60 Hz into this formula, we get h = -25.49, so our electrical hum is half way between 25 and 26 half-steps below middle C. So that’s between a A# and a B two octaves below middle C.

For 50 Hz hum, h = -28.65. That would be between a G and a G#, a little closer to G.

Update: So why would the frequency of the sound match the frequency of the electricity? The magnetic fields generated by the current would push and pull parts, driving mechanical vibrations at the same frequency.

What key has 30 sharps?

Musical keys typically have 0 to 7 sharps or flats, but we can imagine adding any number of sharps or flats.

When you go up a fifth (seven half steps) you add a sharp. For example, the key of C has no sharps or flats, G has one sharp, D has two, etc. Starting from C and adding 30 sharps means going up 30*7 half-steps. Musical notes operate modulo 12 since there are 12 half-steps in an octave. 30*7 is congruent to 6 modulo 12, and six half-steps up from C is F#. So the key with 30 sharps would be the same pitches as F#.

But the key wouldn’t be called F#. It would be D quadruple sharp! I’ll explain below.

Sharps are added in the order F, C, G, D, A, E, B, and the name of key is a half step higher than the last sharp. For example, the key with three sharps is A, and the notes that are sharp are F#, C#, and G#.

In the key of C#, all seven notes are sharp. Now what happens if we add one more sharp? We start over and start adding more sharps in the same order. F was already sharp, and now it would be double sharp. So the key with eight sharps is G#. Everything is sharp except F, which is double sharp.

In a key with 28 sharps, we’ve cycled through F, C, G, D, A, E, and B four times. Everything is quadruple sharp. To add two more sharps, we sharpen F and C one more time, making them quintuple sharp. The note one half-step higher than C quintuple sharp is D quadruple sharp, which is enharmonic with F#.

You could repeat this exercise with flats. Going up a forth (five half-steps) adds a flat. Or you could think of a flat as a negative sharp.

Related posts:

How to convert frequency to pitch

I saw somewhere that James Earl Jones’ speaking voice is around 85 Hz. What musical pitch is that?

Let P be the frequency of some pitch you’re interested in and let C = 261.626 be the frequency of middle C. If h is the number of half steps from C to P then

P / C = 2h/12.

Taking logs,

h = 12 log(P / C) / log 2.

If P = 85, then h = -19.46. That is, James Earl Jones’ voice is about 19 half-steps below middle C, around the F an octave and a half below middle C.

More details on the derivation above here.

 

Photo credit Wikipedia
Music image created using Lilypod.

New Twitter accounts for DSP and music theory

I’ve started two new Twitter accounts this week: @DSP_fact and @MusicTheoryTip.

DSP_fact is for DSP, digital signal processing: filters, Fourier analysis, convolution, sampling, wavelets, etc.

MusicTheoryTip is for basic music theory with a little bias toward jazz. It’ll tweet about harmony, scales, tuning, notation, etc.

Here’s a full list of my 15 daily tip twitter accounts.

If you’re interested in one of these accounts but don’t use Twitter, you can subscribe to a Twitter account via RSS just as you’d subscribe to a blog.

If you’re using Google Reader to subscribe to RSS feeds, you’ll need to switch to something else by July 1. Here are 18 alternatives.

Mars, magic squares, and music

About a year ago I wrote about Jupiter’s magic square. Then yesterday I was listening to the New Sounds podcast that mentioned a magic square associated with Mars. I hadn’t heard of this, so I looked into it and found there were magic squares associated with each of solar system bodies known to antiquity (i.e. Sun, Mercury, Venus, Moon, Mars, Jupiter, and Saturn).

Here is the magic square of Mars:

The podcast featured Secret Pulse by Zack Browning. From the liner notes:

Magic squares provide structure to the music. Structure provides direction to the composer. Direction provides restrictions for the focused inspiration and interpretation of musical materials. The effect of this process? Freedom to compose.

The compositions on this CD use the 5×5 Magic Square of Mars (Secret Pulse), the 9×9 Magic Square of the Moon (Moon Thrust), and the ancient Chinese 3×3 Lo Shu Square found in the Flying Star System of Feng Shui (Hakka Fusion, String Quartet, Flying Tones, and Moon Thrust) as compositional models.  The musical structure created from these magic squares is dramatically articulated by the collision of different musical worlds …

I don’t know how the composer used these magic squares, but you can listen to the title track (Secret Pulse) on the podcast.

Related posts:

All day long I'd bidi-bidi-bum

This evening I watched my daughter in Fiddler on the Roof. I thought I knew the play pretty well, but I learned something tonight.

Before the play started, someone told me that the phrase “bidi-bidi-bum” in “If I Were a Rich Man” is a Yiddish term for prayer. I thought “All day long I’d bidi-bidi-bum” was a way of saying “All day long I’d piddle around.” That completely changes the meaning of that part of the song.

When I got home I did a quick search to see whether what I’d heard was correct. According to Wikipedia,

A repeated phrase throughout the song, “all day long I’d bidi-bidi-bum,” is often misunderstood to refer to Tevye’s desire not to have to work. However, the phrase “bidi-bidi-bum” is a reference to the practice of Jewish prayer, in particular davening.

Unfortunately, Wikipedia adds a footnote saying “citation needed,” so I still have some doubt whether this explanation is correct. I searched a little more, but haven’t found anything more authoritative.

Now I wonder whether there’s any significance to other parts of the song that I thought were just a form of Klezmer scat singing, e.g. “yubba dibby dibby dibby dibby dibby dibby dum.” I assumed those were nonsense syllables, but is there some significance to them?

Update: At Jason Fruit’s suggestion in the comments, I asked about this on judaism.stackexchange.com. Isaac Moses replied that the answer is somewhere in between. The specific syllables are not meaningful, but they are intended to be reminiscent of the kind of improvisation a cantor might do in singing a prayer.

John Coltrane versus Kenny G

My previous post began with a story about a performance by John Coltrane. Douglas Groothuis left a comment saying that he used the same story in his book Truth Decay. Before telling the Coltrane story, Groothuis compares the philosophies of Kenny G and John Coltrane.

Kenny G’s philosophy is as shallow as his music.

I just play for myself, the way I want to play, and it comes out sounding like me.

Coltrane’s philosophy, like his music, is more ambitious.

Overall, I think the main thing a musician would like to do is give a picture to the listener of the many wonderful things he knows and senses in the universe. That’s what music is to me — it’s just another way of saying this is a big, wonderful universe we live in, that’s been given to us, and here’s an example of just how magnificent and encompassing it is. That’s what I would like to do. I think that’s one of the greatest things you can do in life, and we all try to do it in some way. The musician’s is through his music.

As Groothuis comments, Kenny G only spoke of expressing himself, while Coltrane “expressed a yearning to represent objective realities musically.”

Nunc dimittis

In his book The Call, Os Guinness tells the following story of John Coltrane.

After one utterly extraordinary rendition of “A Love Supreme,” Coltrane stepped off the stage, put down his saxophone, and said simply “Nunc dimittis.” … Coltrane felt he could never play the piece more perfectly. If his whole life had been lived for that passionate thirty-two minute jazz prayer, it would have been worth it. He was ready to go.

Nunc dimittis is Latin for “Now dismiss.” These are the opening words of the Vulgate translation of the Song of Simeon, Luke 2:29–32. Simeon says he is ready to die because he has seen what he was waiting for, the promised Messiah.

Lord, now lettest thou thy servant depart in peace, according to thy word:
For mine eyes have seen thy salvation,
Which thou hast prepared before the face of all people;
A light to lighten the Gentiles, and the glory of thy people Israel.

Coltrane’s story brings several things to mind. First, it is awe-inspiring to imagine an accomplishment so fulfilling that you would say “That was it. I’m ready to die.”

Next, it’s interesting to ponder Coltrane’s eclectic spirituality. I knew Christianity was part of his spiritual gumbo, but I was surprised to hear that he made a spontaneous reference to Latin liturgy.

Coltrane was canonized by the African Orthodox Church in 1982. Truth is stranger than fiction.

Finally, I was interested in the name Nunc dimittis itself. I hadn’t heard it before. (I’ve only been part of non-liturgical churches.) I thought the name might only be familiar to Catholics, being a Latin term. But an Episcopalian friend informed me that the Anglican mass preserves many Latin titles even though the liturgy itself is in English. I suppose Coltrane encountered this Anglican name via the Episcopalian influence on the African Methodist Episcopalian Zion Church.

Closely related post:

John Coltrane versus Kenny G

Less related posts:

Software sins of omission (Software and the Book of Common Prayer)
Doing good work with bad tools (Charlie Parker story)
Dave Brubeck mass (Mass composed by a jazz icon)

Accelerated learning

Derek Sivers tells how a mentor was able to teach him a semester’s worth of music theory in three hours. His mentor also prepared him to place out of four more classes in four sessions. He gives the details in his blog post There’s no speed limit. It’s an inspiring story.

However, Sivers didn’t go through his entire education this way. He finished his degree in 2.5 years, but at the rate he started he could have finished in under a semester. Obviously he wasn’t able to blow through everything as fast as music theory.

Some classes compress better than others. Theoretical classes condense better than others. A highly motivated student could learn a semester of music theory or physics in a short amount of time. But it would take longer to learn a semester of French or biology no matter how motivated you are because these courses can’t be summarized by a small number of general principles. And while Sivers learned basic music theory in three hours, he says it took him 15 years to learn how to sing.

Did Sivers’ mentor expose him to everything students taking music theory classes are exposed to? Probably not. But apparently Sivers did learn the most important material, both in the opinion of his mentor and in the opinion of the people who created the placement exams. His mentor not only taught him a lot of ideas in a short amount of time, he also told him when it was time to move on to something else.

It’s hard to say when you’ve learned something. Any subject can be explored in infinite detail. But there comes a point when you’ve learned a subject well enough. Maybe you’ve learned it to your personal satisfaction or you’ve learned it well enough for an exam. Maybe you’ve reached diminishing return on your efforts or you’ve learned as much as you need to for now.

One way to greatly speed up learning is to realize when you’ve learned enough. A mentor can say something like “You don’t know everything, but you’ve learned about as much as you’re going to until you get more experience.”

Occasionally I’ll go from feeling I don’t understand something to feeling I do understand it in a moment, and not because I’ve learned anything new. I just realize that maybe I do understand it after all. It’s a feeling like eating a meal quickly and stopping before you feel full. A few minutes later you feel full, not because you’ve eaten any more, but only because your body realizes you’re full.

Related posts:

Casablanca and Einstein

Humphrey Bogart and Ingrid Bergman in Casablanca

If you’ve ever seen Casablanca, you’ve heard the song As Time Goes By, but only the chorus.

You must remember this
A kiss is just a kiss, a sigh is just a sigh.
The fundamental things apply
As time goes by.

Did you know the song includes references to relativity and four-dimensional geometry?

Here’s the first verse.

This day and age we’re living in
Gives cause for apprehension
With speed and new invention
And things like fourth dimension.

Yet we get a trifle weary
With Mr. Einstein’s theory.
So we must get down to earth at times
Relax relieve the tension.

And no matter what the progress
Or what may yet be proved
The simple facts of life are such
They cannot be removed.

Here are the full lyrics.

Via Math Mutation podcast #134.