Showing posts with label music. Show all posts
Showing posts with label music. Show all posts
14 August 2011
867-5309
The number 8,675,309 is the title of a song. It is also a prime number, and as far as I can tell, it's the largest prime number to appear in a song title. According to this list of songs with numbers in the title from Wikipedia (which is currently in the "Wikilists" space because it was deleted from mainstream Wikipedia, larger numbers in song titles are: 9 million, 30 million, 93 million, 100 million, 1 billion, 1 trillion, 1 quadrillion, 1 googolplex, infinity minus one, and infinity.
I'm not surprised to see that most of these are "round numbers", simply because they're easier to say; in particular by inspection they are not prime, since they're all multiples of large powers of 10. But I'm wondering if anybody out there has written a song titled, say, "six billion and one".
(No fair going out and writing such a song.)
I'm not surprised to see that most of these are "round numbers", simply because they're easier to say; in particular by inspection they are not prime, since they're all multiples of large powers of 10. But I'm wondering if anybody out there has written a song titled, say, "six billion and one".
(No fair going out and writing such a song.)
08 May 2009
The physics of singing in the shower
I was singing in the shower, as I do.
I noticed that certain notes seemed to resonate with the shower more than others.
These were, in ascending order, Eb2, G2, C3, and G3, where C4 is middle C. (These may not be exactly right; I don't have perfect pitch. The intervals are right, though.)
Exercise for the reader: how large is my shower?
I noticed that certain notes seemed to resonate with the shower more than others.
These were, in ascending order, Eb2, G2, C3, and G3, where C4 is middle C. (These may not be exactly right; I don't have perfect pitch. The intervals are right, though.)
Exercise for the reader: how large is my shower?
13 March 2009
Three songs about circles
WXPN is a radio station of the University of Pennsylvania. This statement is a bit ambiguous; they're not a "college radio station", in that they're not student-run, but rather a professionally-run, public (i. e. non-commercial, and every so often they come on the air and beg for money) radio station. WQHS is the student radio station. I've been working from home this week, since it's our Spring Break, so I've been listening a lot.
Every weekday morning at nine they have a "select-a-set": listeners call or e-mail and suggest three songs, which are perhaps somehow related. Somebody suggested the following three songs today, which got played:
Sarah McLachlan, Circle
Edie Brickell & New Bohemians, Circle
Joni Mitchell, Circle Games
Why? (Hint: the select-a-set feature does not exist on Saturdays.)
Every weekday morning at nine they have a "select-a-set": listeners call or e-mail and suggest three songs, which are perhaps somehow related. Somebody suggested the following three songs today, which got played:
Sarah McLachlan, Circle
Edie Brickell & New Bohemians, Circle
Joni Mitchell, Circle Games
Why? (Hint: the select-a-set feature does not exist on Saturdays.)
11 July 2008
Good's "singing logarithms"
I've previously mentioned Sanjoy Mahajan's Street Fighting Mathematics. (Yes, that's right, almost the entire sentence is links, deal with it.)
One thing I didn't mention is approximating logarithms using musical intervals, from that course. We all know 210 and 103 are roughly equal; this is the approximation that leads people to use the metric prefixes kilo-, mega-, giga-, tera- for 210, 220, 230, and 240 in computing contexts. Take 120th roots; you get 21/12 ≈ 101/40.
Now, 21/12 is the ratio corresponding to a semitone in twelve-tone equal temperament. So, for example, we know that 27/12 is approximately 3/2, because seven semitones make a perfect fifth. So log10 3/2 ≈ 7/40 = 0.175; the correct value is 0.17609... Some more complicated examples are in Mahajan's handout.
You might think "yeah, but when do I ever need to know the logarithm of something?" And that may be true; they're no longer particularly useful as an aid for calculation, except when you don't have a computer around. But I often find myself doing approximate calculations while walking, and I can't pull out a calculator or a computer! (To be honest I don't use this trick, but that's only because I have an arsenal of others.)
Is this pointless? For the most part, yes. But amusingly so.
The method is supposedly due to I. J. Good, who is annoyingly difficult to Google.
Oh, and a few facts I find myself using quite often -- (2π)1/2 ≈ 2.5, e3 ≈ 20.
One thing I didn't mention is approximating logarithms using musical intervals, from that course. We all know 210 and 103 are roughly equal; this is the approximation that leads people to use the metric prefixes kilo-, mega-, giga-, tera- for 210, 220, 230, and 240 in computing contexts. Take 120th roots; you get 21/12 ≈ 101/40.
Now, 21/12 is the ratio corresponding to a semitone in twelve-tone equal temperament. So, for example, we know that 27/12 is approximately 3/2, because seven semitones make a perfect fifth. So log10 3/2 ≈ 7/40 = 0.175; the correct value is 0.17609... Some more complicated examples are in Mahajan's handout.
You might think "yeah, but when do I ever need to know the logarithm of something?" And that may be true; they're no longer particularly useful as an aid for calculation, except when you don't have a computer around. But I often find myself doing approximate calculations while walking, and I can't pull out a calculator or a computer! (To be honest I don't use this trick, but that's only because I have an arsenal of others.)
Is this pointless? For the most part, yes. But amusingly so.
The method is supposedly due to I. J. Good, who is annoyingly difficult to Google.
Oh, and a few facts I find myself using quite often -- (2π)1/2 ≈ 2.5, e3 ≈ 20.
27 September 2007
Fun with fugues
At Science after Sunclipse, Blake Stacey links to some videos from Stephen Malinowski's Music Animation Machine. The Music Animation Machine animates music; the basic idea is that notes are represented by rectangles, the length of which corresponds to the length of the note. What I found particularly interesting was that the videos use color to represent either:
Johann Sebastian Bach, Toccata and Fugue in D Minor:
[埋込みオブジェクト:http://www.youtube.com/v/ipzR9bhei_o]
Frederic Chopin, Etude, opus 10 #7:
[埋込みオブジェクト:http://www.youtube.com/v/vMyg9CJxWNA]
The harmonic coloration is based on the circle of fifths, which is an interesting solution to the problem that notes which are close together in pitch are not close together in some sort of "harmonic space".
I find myself wondering if the coloring based on voice could be automated. This would be trivial for things written entirely in, say, standard four-part voice leading as taught in an introductory music theory class, because there are always exactly four notes at any given time and the voices don't cross; it would be very nontrivial for actual music. (This isn't just a musical problem, believe it or not. A related problem is as follows: a baseball team has five starting pitchers, which it uses in a pitching rotation: ideally pitcher n pitches on days n, n+5, n+10, ... But there are off days, people get hurt, and so on. How do you decide when one pitcher has "replaced" another in the rotation? The people at Baseball Prospectus have thought about this -- sorry I can't find the link -- but their solutions basically involve just staring at a list of who pitched what day and writing numbers next to them kind of arbitrarily. It's not quite the same thing, though, because there's only one starting pitcher per game (relief pitchers are used in a much more ad hoc manner) but notes are played simultaneously. I suspect there are other problems of this sort where there are logical ways to sort some sequence of things into bins -- musical voices, rotation slots, and so on -- but none come to mind.)
The sort of notation they're using here seems like a logical historical antecedent of present-day musical notation (though I don't know enough about the history to know if it is); the main differences are that in modern notation we decide that seven of the notes in each octave are more important than the other five (and enshrine this in the notation) and we don't write a whole note as being, say, sixteen times as long as a sixteenth note. This is probably a good thing from the point of view of readability. It also resembles a player piano roll (modulo coloring) which I doubt is a coincidence.
Oh, and you have to watch the "Oops, I Did It Again" fugue, which I found from Good Math, Bad Math:
[埋込みオブジェクト:http://www.youtube.com/v/tgDcC2LOJhQ]
- the "voices" in the score, as in the first video below (Bach), and
- harmonic information, as in the second video below (Chopin)
Johann Sebastian Bach, Toccata and Fugue in D Minor:
[埋込みオブジェクト:http://www.youtube.com/v/ipzR9bhei_o]
Frederic Chopin, Etude, opus 10 #7:
[埋込みオブジェクト:http://www.youtube.com/v/vMyg9CJxWNA]
The harmonic coloration is based on the circle of fifths, which is an interesting solution to the problem that notes which are close together in pitch are not close together in some sort of "harmonic space".
I find myself wondering if the coloring based on voice could be automated. This would be trivial for things written entirely in, say, standard four-part voice leading as taught in an introductory music theory class, because there are always exactly four notes at any given time and the voices don't cross; it would be very nontrivial for actual music. (This isn't just a musical problem, believe it or not. A related problem is as follows: a baseball team has five starting pitchers, which it uses in a pitching rotation: ideally pitcher n pitches on days n, n+5, n+10, ... But there are off days, people get hurt, and so on. How do you decide when one pitcher has "replaced" another in the rotation? The people at Baseball Prospectus have thought about this -- sorry I can't find the link -- but their solutions basically involve just staring at a list of who pitched what day and writing numbers next to them kind of arbitrarily. It's not quite the same thing, though, because there's only one starting pitcher per game (relief pitchers are used in a much more ad hoc manner) but notes are played simultaneously. I suspect there are other problems of this sort where there are logical ways to sort some sequence of things into bins -- musical voices, rotation slots, and so on -- but none come to mind.)
The sort of notation they're using here seems like a logical historical antecedent of present-day musical notation (though I don't know enough about the history to know if it is); the main differences are that in modern notation we decide that seven of the notes in each octave are more important than the other five (and enshrine this in the notation) and we don't write a whole note as being, say, sixteen times as long as a sixteenth note. This is probably a good thing from the point of view of readability. It also resembles a player piano roll (modulo coloring) which I doubt is a coincidence.
Oh, and you have to watch the "Oops, I Did It Again" fugue, which I found from Good Math, Bad Math:
[埋込みオブジェクト:http://www.youtube.com/v/tgDcC2LOJhQ]
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