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The Mathematics of Music [pdf]

210 点作者 kondor将近 5 年前

11 条评论

082349872349872将近 5 年前
C, E-flat, and G go into a bar. The bartender says, "Sorry, but we don't serve minors." So E-flat leaves, and C and G have an open fifth between them. After a few drinks, the fifth is diminished, and G is out flat. F comes in and tries to augment the situation, but is not sharp enough. D comes in and heads for the bathroom, saying, "Excuse me; I'll just be a second." Then A comes in, but the bartender is not convinced that this relative of C is not a minor. Then the bartender notices B-flat hiding at the end of the bar and says, "Get out! You're the seventh minor I've found in this bar tonight." E-flat comes back the next night in a three-piece suit with nicely shined shoes. The bartender says, "You're looking sharp tonight. Come on in, this could be a major development." Sure enough, E-flat soon takes off his suit and everything else, and is au natural. Eventually C sobers up and realizes in horror that he's under a rest. C is brought to trial, found guilty of contributing to the diminution of a minor, and is sentenced to 10 years of D.S. without Coda at an upscale correctional facility.
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OscarCunningham将近 5 年前
Another good book in the same vein is Dave Benson&#x27;s &#x27;Music: a Mathematical Offering&#x27;.<p><a href="https:&#x2F;&#x2F;homepages.abdn.ac.uk&#x2F;d.j.benson&#x2F;pages&#x2F;html&#x2F;maths-music.html" rel="nofollow">https:&#x2F;&#x2F;homepages.abdn.ac.uk&#x2F;d.j.benson&#x2F;pages&#x2F;html&#x2F;maths-mus...</a>
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addictedcs将近 5 年前
Musimathics is great [1].<p>If you want a more interactive source you can play with python notebooks from the music information retrieval site [2]. I&#x27;ve found it helpful, as you try some of the described music theory concepts in a programming environment.<p>Shameless plug, I&#x27;ve also written about how audio fingerprinting works [3], which touches on some of the topics regarding music theory.<p>[1] <a href="http:&#x2F;&#x2F;www.musimathics.com" rel="nofollow">http:&#x2F;&#x2F;www.musimathics.com</a><p>[2] <a href="https:&#x2F;&#x2F;musicinformationretrieval.com" rel="nofollow">https:&#x2F;&#x2F;musicinformationretrieval.com</a><p>[3] <a href="https:&#x2F;&#x2F;emysound.com&#x2F;blog&#x2F;open-source&#x2F;2020&#x2F;06&#x2F;12&#x2F;how-audio-fingerprinting-works.html" rel="nofollow">https:&#x2F;&#x2F;emysound.com&#x2F;blog&#x2F;open-source&#x2F;2020&#x2F;06&#x2F;12&#x2F;how-audio-f...</a>
lioeters将近 5 年前
Recommended:<p>A Geometry of Music by Dmitri Tymoczko - <a href="http:&#x2F;&#x2F;dmitri.mycpanel.princeton.edu&#x2F;geometry-of-music.html" rel="nofollow">http:&#x2F;&#x2F;dmitri.mycpanel.princeton.edu&#x2F;geometry-of-music.html</a><p>The Geometry of Musical Rhythm by Godfried Toussaint<p>- Original paper - <a href="http:&#x2F;&#x2F;cgm.cs.mcgill.ca&#x2F;~godfried&#x2F;publications&#x2F;geometry-of-rhythm.pdf" rel="nofollow">http:&#x2F;&#x2F;cgm.cs.mcgill.ca&#x2F;~godfried&#x2F;publications&#x2F;geometry-of-r...</a> (PDF)<p>- Book - Review <a href="https:&#x2F;&#x2F;mtosmt.org&#x2F;issues&#x2F;mto.13.19.2&#x2F;mto.13.19.2.gotham.php" rel="nofollow">https:&#x2F;&#x2F;mtosmt.org&#x2F;issues&#x2F;mto.13.19.2&#x2F;mto.13.19.2.gotham.php</a>
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siraben将近 5 年前
In a similar vein, there&#x27;s the Topos of Music book[0], which, according to Wikipedia, has been somewhat controversial among mathematicians and musicians alike.<p>[0] <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Topos-Music-Geometric-Concepts-Performance&#x2F;dp&#x2F;3764357312" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Topos-Music-Geometric-Concepts-Perfor...</a>
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motohagiography将近 5 年前
Have posted this link before, but so relevant to the discussion: <a href="https:&#x2F;&#x2F;softwareengineering.stackexchange.com&#x2F;questions&#x2F;136085&#x2F;is-musical-notation-turing-complete" rel="nofollow">https:&#x2F;&#x2F;softwareengineering.stackexchange.com&#x2F;questions&#x2F;1360...</a><p>If music were Turing complete, it could imply we&#x27;ve been developing the ability to derive theorems in it as a species forever, which has some speculatively interesting philosophical implications as well. :)
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brudgers将近 5 年前
the software can be found here, <a href="https:&#x2F;&#x2F;imaginary.org&#x2F;programs" rel="nofollow">https:&#x2F;&#x2F;imaginary.org&#x2F;programs</a>
kevindeasis将近 5 年前
I started learning music recently, and another type that I would like to see, is mathematics for music genres, mathematics for music effects and mathematics for music theory
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aaron-santos将近 5 年前
Absolutely fascinating section on Lissajous figures. I had only been exposed to the concept through orbits.[1]<p>[1] - <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Lissajous_orbit" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Lissajous_orbit</a>
TheOtherHobbes将近 5 年前
I&#x27;m not sure whom this is aimed at. The name &quot;La La Lab&quot; and the interactivity suggests kids, but there&#x27;s a Fourier integral on Page 7 which immediately suggests undergraduates.
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kian将近 5 年前
I highly recommend Drew Nobile&#x27;s book or papers on functional circuits as an adjunct to this on how to recursively generate songs from an initial seed progression.