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Welcome to the Vault Network
forum archive.
This is not a complete archive, time didn't allot us the
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Topic: New algorithm may make professional instrument tuners obsolete
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-Accident-
Title: Waiting to happen
Posts:
16,541
Registered:
Aug 24, '00
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Real Post Cnt: 16,161
User ID: 41,169
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Subject:
New algorithm may make professional instrument tuners obsolete
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I really think it's fascinating how mathematical music is, and how our brains have learned to perform a fairly sophisticated optimization without our sitting down and explicitly doing the math. It will be interesting, too, to see what other applications they may be able to find for this kind of algorithm.
http://www.technologyreview.com/blog/arxiv/27673/
[snip]
At first glance, tuning a musical instrument seems a straightforward task. However, any professional tuner will tell you that the reality is rather different.
Pluck a string and the sound it produces is the result of its fundamental frequency and its harmonics at frequencies that are whole number multiples of the fundamental. Clearly, harmonics have a simple linear relationship with the fundamental.
The problem arises because music consists of repeating patterns of notes based on octaves. Since the frequency of a note doubles from octave to octave, the frequencies grow exponentially as the octaves increase.
And therein lies the problem. The linear increase in the frequency of harmonics can never exactly match the exponential increase required when the notes are arranged in octaves. So there is always a compromise.
Western musical scales consists of notes that differ by a constant frequency ratio of 2^1/12, a system known as equal temperament. These notes are equidistant on a logarithmic scale but not on a linear scale.
In this system, notes that are an octave apart can all be in tune but other intervals, such as perfect fourths or fifths, are always slightly out of tune.
To get around this, a professional tuner 'stretches' the interval between some notes to correct these intervals. And that's where things get tricky.
The amount and type of stretching differs depending on the type of instrument (and even between instruments of the same type) and so cannot be calculated by electronic tuners, which have otherwise revolutionised tuning.
[snip]
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I realize now I do not fear death. I fear my daughter will not be free when I die.
- NR, #iranelection
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winga
Title: Canadian
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Subject:
New algorithm may make professional instrument tuners obsolete
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Interesting... will read more later.
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Gaevren
Title: Wat do?
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Subject:
New algorithm may make professional instrument tuners obsolete
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We are a pretty musical family so I find this quite fascinating. Thank you!
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There are no automatic doors, just very polite ninjas
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Jezza_Belle
Title: =^.^=
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Subject:
New algorithm may make professional instrument tuners obsolete
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Well, at least they're only putting a tiny amount of people out of work (potentially).
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Arc_DT
Title: Mithan said I am smart
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Subject:
New algorithm may make professional instrument tuners obsolete
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So the new method is to measure the entropy of the system, apply a small random change to the frequency of a note and measure the entropy again. If it has dropped, the system is considered to be more in tune and another random change is applied until the process finds a minimum value for the entropy.
Either the author is a non-mathematician or he recognizes that most of his audience isn't, but he buried the lead... this employs a non-deterministic turing machine, which I find to be the most fascinating part. It says something about ourselves, that a non-deterministic algorithm employed subconsciously by the tuner would result in a more pleasant sound to the average and untrained listener.
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MICHIGAN - Where the trees are the right height!
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-Accident-
Title: Waiting to happen
Posts:
16,541
Registered:
Aug 24, '00
Extended Info (if available)
Real Post Cnt: 16,161
User ID: 41,169
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Subject:
New algorithm may make professional instrument tuners obsolete
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Arc_DT posted:
So the new method is to measure the entropy of the system, apply a small random change to the frequency of a note and measure the entropy again. If it has dropped, the system is considered to be more in tune and another random change is applied until the process finds a minimum value for the entropy.
Either the author is a non-mathematician or he recognizes that most of his audience isn't, but he buried the lead... this employs a non-deterministic turing machine, which I find to be the most fascinating part. It says something about ourselves, that a non-deterministic algorithm employed subconsciously by the tuner would result in a more pleasant sound to the average and untrained listener.
yeah, I admit I was surprised that they started the algorithm with a small random step, but I guess the end of the loop will see whether you walked in the right direction so you can converge on a minimum. but it could still be possible to accidentally wander away from an optimum solution if there is a small local minimum in the way. sorry if I'm putting it badly, it's been a long time since I took any math classes.
-----signature-----
I realize now I do not fear death. I fear my daughter will not be free when I die.
- NR, #iranelection
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