With the return of The X Factor to TV screens, we look at the physics behind pitch correction.
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Auto-Tune software in action.
Back on the TV schedule for the autumn, the singing competition programme The X Factor was criticised last year after it emerged that the contestants’ voices were being altered via Auto-Tune.
Producer Simon Cowell subsequently banned any further use of the technology on the show.
But how does audio signal processing help to make singers’ voices sound better?
What would you do if I sang out of tune?
Few singers are perfect. Sometimes, the pitch of their vocal slightly misses the exact note they’re trying to hit.
If they are a little out of tune, the vocal track can still be rescued – or ruined, depending on your point of view – with a little help from the science of signal processing.
The pitch of a note is dependent on the frequency of the sound wave produced – the A above middle C is usually defined as 440 Hz. Therefore manipulating the frequency can produce a different note, or hit an exact note from a noise that is slightly off-key.
Musical scales are divided into 12 pitches each separated by a semitone – the difference in note between two adjacent keys on a piano or frets on a guitar neck. The goal of pitch correction is to retune a slightly high or low note to the nearest semitone.
In the system usually used by MIDI instruments in which pitch is assigned a number, with the 440-Hz A being 69 and each semitone increasing or decreasing the pitch number by 1, it is related to frequency f by a simple formula.
If an attempt at singing that A note actually came out at, say, 445 Hz instead, then using a computer to correct the frequency back down would ensure that the recording sounds in tune.
Sound engineers can’t simply change the frequency by itself, however.
Because the frequency of a wave is related to its speed via its wavelength, the duration of the sound would change too – this is why sped-up tapes sound chipmunk-like.
The frequency can be altered without changing the speed by going digital.
Music by numbers
Although it is possible to alter analogue signals – those based directly on the electrical signal generated by a microphone, or by a guitar pickup – a wider range of effects is possible when working with digital signals.
A digital signal uses discrete values rather than continuous ones, so converting an analogue signal requires taking sets of discrete points or samples. (Higher sampling rates more closely approximate the original sound).
The green line is the continuous analogue signal. The blue dots are the points at which it is sampled.
These digital signals can be altered so that a sound produces the correct musical note by using a phase vocoder.
This works by first changing the duration of the sound without altering its frequency, and then changing the frequency to both hit the correct pitch and restore the original duration.
The name comes from its use of the signal’s phase information to manipulate the signal in the desired way.
It breaks an audio signal down into many small, overlapping frames and then changes the spacing of those frames to change the total duration of the sound. In practice, this is a complicated task that requires the use of the advanced maths of Fourier transforms to convert the signal into a form that can be manipulated in this way.
The sound is then resampled to take it back to its original duration and hit the desired note.
As guitarpitchshifter.com explains, if the aim was to double the frequency then this would be as easy as picking one out of every two samples and constructing a waveform from those. But to fit the signal back into its original length when not scaling by an integer, interpolation is used to determine which bits of the sample should go at which points.
Auto-tune
For imperfect singers to remain perfectly in key, we have this piece of maths and physics to thank – or to blame.
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Updated 4:27 AM EST Dec 11, 2019
NEW YORK – Michael D'Alessio, a White Plains developer who pleaded guilty to a federal charge of defrauding investors out of about $58 million, was sentenced Friday to six years in prison.
D'Alessio, 53, once a successful developer who had an office on Water Street in White Plains, was arrested in August on a federal wire-fraud charge in connection with an alleged years-long scheme to defraud investors in luxury real estate development projects in Westchester County, Manhattan and the Hamptons.
D'Alessio promised investors that he would develop and build luxury homes and condominiums that would yield big returns, but when the real estate market took a downturn, he resorted to fraud, said Manhattan U.S. Attorney Geoffrey S. Berman.
'In the end, all he built was a Ponzi scheme that he used to rip off his investors of their hard-earned life savings to the tune of $58 million,' Berman said in a statement. 'Others who would consider funding a life of luxury with the proceeds of fraud should take heed. We will continue to work with our law enforcement partners to see that such fraud is met with justice, and that those who would commit such crimes understand that crime doesn’t pay.”
In addition to the prison term, D'Alessio was sentenced to three years of supervised release and ordered to pay forfeiture in the amount of $58 million.
In November, D'Alessio pleaded guilty before U.S. District Judge Jesse Furman to one count of committing wire fraud, as well as one count of concealing assets from a bankruptcy court.
The government recommended the court impose a sentence of 97 to 121 months in prison, along with $57.9 million in restitution, arguing that D'Alessio's criminal conduct was 'brazen, predatory and calculated to avoid detection,' according to Berman's sentencing memorandum.
'He victimized hundreds of people through outright lies, and he corrupted the bankruptcy proceeding (that he was forced into) with more lies when his Ponzi scheme fell apart,' he said.
D'Alessio's lawyer, Benjamin Brafman, petitioned the court, saying that D'Alessio is a 'fundamentally decent man who unfortunately committed serious crimes' as he suffered from the 'vicious grip of a compulsive gambling disorder' that Brafman said was further intensified by D'Alessio's use of a prescription medication.
Brafman suggested to the court a sentence of 36 months — or three years — in prison followed by three years of supervised release would be 'sufficient, but not greater than necessary' to accomplish the goal of the sentencing.
The wire fraud charge carried a maximum sentence of 20 years in prison and a maximum fine of $250,000, or twice the gross gain or loss from the offense; and the charge of hiding assets from a bankruptcy court carried a maximum sentence of five years in prison and a maximum fine of $250,000, or twice the gross gain or loss from the offense.
Last year, nearly 20 investors, including some with ties to Westchester, filed several lawsuits in state Supreme Court against D'Alessio and Michael Paul Enterprises, as well as several other entities under D'Alessio's control, claiming that he and his companies lured investors into seven development projects by promising 9 to 16 percent annual returns.
And after receiving hundreds of thousands of dollars of investments for a specific project, D'Alessio 'began siphoning the investor funds for personal use,' commingling funds earmarked for a certain project with his other projects, while misinforming investors about the projects' progress and their costs, according to the complaints.
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The investors included Rella Fogliano and Joseph Breda with The MacQuesten Cos., a Pelham-based developer; Attis Properties of Harrison; and Stacey Gendels, Bonni Stanley and Marilyn Shendell, who are associated with Cornell Pace, a New Rochelle-based property-management and investment company.
Twitter: @AskAkiko
Craig Cartoon Auto Tune Machine Heads
GUILTY PLEA: Michael D'Alessio, White Plains developer, faces prison
CHARGED: Feds arrest White Plains developer Michael D'Alessio for wire fraud
SUED: White Plains developer accused of siphoning millions from investors
Craig Cartoon Auto Tune Machines
CREDITORS: Banks seek to force White Plains developer into bankruptcy
CRAIG CARTON: New Rochelle native and former WFAN radio host, sentenced in ticket scam
Auto-tune Microphone
Updated 4:27 AM EST Dec 11, 2019
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