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Semitones, Octaves and Note Frequency


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What's that G doing in there?

I just threw it in there to give the sample a more "musical" feel, I felt it helped establish the key.

 

Oh, and the top C sounds a tiny bit flat.

 

The top note sounds maybe slightly flat

 

High note flat

 

Well, see, to me too, that note sounds flat. Problem is, it's perfectly in tune, according to the "octave up is 2x the frequency" paradigm. But to hear it in tune, we'd have to sharpen that top note a bit, therefore stretching the tuning so a note an octave higher is a little over 2x the frequency of the octave lower.

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Well, see, to me too, that note sounds flat. Problem is, it's perfectly in tune, according to the "octave up is 2x the frequency" paradigm. But to hear it in tune, we'd have to sharpen that top note a bit, therefore stretching the tuning so a note an octave higher is a little over 2x the frequency of the octave lower.

 

But you have to go to the absolute top of any normal musical range to get even the slightest effect of this. Plus it was an electric piano sound. When I used the test oscillator with a sine wave, I had to go into 8-9kHz range to hear any of this effect. Otherwise, 2:1 is, in most musical scenarios, the most consonant ratio.

 

I'm not disagreeing that at very high pitches this effect takes place, I'm just disputing that we generally hear all octaves as being a larger ratio than 2:1.

 

...Except on pianos, which, as we've all now read, due to the physics of wire tension have to be tuned to second or fourth harmonics rather than the fundamental, to greater or lesser degrees, according to taste.

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The effect is more pronounced in very low and very high frequencies, but in my experience it is still present in medium frequencies - although less obvious.

 

I almost always tune bass guitars a bit lower than what the tuner says. Electronic-tuner-tuned bass guitars sound out of tune to me. I usually drive the bass players crazy in the studio!

 

Years ago as I was studying sound engineering, I performed an experiment overseen by a psychoacoustic researcher at the CNAM. The experiment was performed onto 20 students of the Conservatoire National Superieur de Musique de Paris - high caliber musicians destined to be some of the best professional working musicians in national orchestras.

 

I gave them an analog sine wave generator. The generator was plugged into an oscilloscope to measure its frequency. I set the generator to several frequencies, like 1,000Hz, and asked them to turn the frequency button until they found the perfect octave. The results were different for each individual (the tests were performed several times to account for errors and aberrations), however not a single student found 2,000Hz to be a perfect octave up from 1,000Hz. The generator was systematically set higher than that. Maybe 2,015Hz or something like that (honestly I don't remember the exact numbers).

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I almost always tune bass guitars a bit lower than what the tuner says. Electronic-tuner-tuned bass guitars sound out of tune to me. I usually drive the bass players crazy in the studio!

 

I can understand that, I was going to say before, when I mentioned lower pitches sounding better flat than sharp and higher pitches sounding better sharp than flat, that I learnt early on as a bassist that you can get away with playing slack but playing sharp will make everything sound awful. But I must say that bass tuned to an electronic tuner sounds fine to me.

 

Years ago as I was studying sound engineering, I performed an experiment overseen by a psychoacoustic researcher at the CNAM. The experiment was performed onto 20 students of the Conservatoire National Superieur de Musique de Paris - high caliber musicians destined to be some of the best professional working musicians in national orchestras.

 

I gave them an analog sine wave generator. The generator was plugged into an oscilloscope to measure its frequency. I set the generator to several frequencies, like 1,000Hz, and asked them to turn the frequency button until they found the perfect octave. The results were different for each individual (the tests were performed several times to account for errors and aberrations), however not a single student found 2,000Hz to be a perfect octave up from 1,000Hz. The generator was systematically set higher than that. Maybe 2,015Hz or something like that (honestly I don't remember the exact numbers).

 

Shame you don't remember the numbers. It would have been interesting to try lower frequencies too.

 

I wonder if the results would differ with Indian or Chinese classical musicians.

 

Maybe it's my relatively recent (last 1/3rd of my life to date) introduction to pianos and/or big exposure to music not of the fretted variety, but the oscillators sound perfectly in tune to me up to 8-9kHz (or maybe I'm tone-deaf in a backward kind of way? :? )

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Years ago as I was studying sound engineering, I performed an experiment overseen by a psychoacoustic researcher at the CNAM........

 

Fascinating!

Truly!

 

I just did my own test.

 

Two audio tracks

One with a Test Oscillator set to 1K

The other with a Test Oscillator set to 2K

I soloed the 1K track for about 10 seconds to get a fix on it.

Then, I Option+soloed the 2K track and it indeed sounded flat to me! :shock:

 

I did it again.

This time, when I Option+soloed the 2K track, I clicked on the Frequency knob, closed my eyes and hit the "+" key on the numeric key pad to increment up until I thought the 2K tone was a perfect octave.

(Hearing just the 2K tone and trying to match the octave by memory of the 1K tone)

I ended up stopping at 2057 Hz. :shock: :shock:

 

I did it again.

This time, I stopped incrementing the 2K tone at 2063 Hz. :shock: :shock: :shock:

 

I did it again.

This time, I stopped incrementing the 2K tone at 2060 Hz :shock: :shock: :shock: :shock:

 

WTF!

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I'm not noticing this effect at all with 50Hz > 100Hz > 200Hz > 400Hz > 800Hz > 1600Hz. Once I get to 3200Hz, I have to add about 50Hz. But no flattening of notes in the lower register.

[EDIT: These were all referenced to 200Hz.]

 

I'm really wondering if this is completely physical, or whether our tuning systems have conditioned the expectations of people who experience the full octave-stretch effect (which would make conservatoire students the worst people to be testing this on, then presuming a physical cause).

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I just noticed that everyone else has been talking about just using one oscillator. I was using two simultaneously and comparing.

 

I tried with one, upping the pitch with my eyes closed, as redlogic did. This time I didn't even add the 50Hz to 3200Hz, they were all right on the money :?

Edited by Rev. Juda$ Sleaze
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I wonder: is this octave stretching incorporated in most piano/grand piano sample libraries? It would make sense to me that they do... I can't test it right now, as my WD disk with my sample libraries has "collapsed" this weekend :( :(

 

If the library is made of individual key samples and not just middle C pitch-shifted, then yes I would imagine so. It wouldn't make sense to sample a nice piano then change the pitch of the notes.

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Pianos are tuned that way to make them "sing", and as Ski pointed out, this is not a fixed formula but up to pesonal preference. It also doesn't hold for other types of Western instruments, each class of which have their own tuning peculiarities according to their inherent structure.

 

That's true. A piano is unique in several elements; it's hammered as opposed to plucked or strummed, and it has more than one string for most notes. Tuning a piano is much about making the harmonic partials and intermodulation products consonant, and voicing the attack which is mostly noise. You can't really discuss perceived pitch and intervals of a piano in the same context as doing the same with sine tones played back over a loudspeaker.

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You can't really discuss perceived pitch and intervals of a piano in the same context as doing the same with sine tones played back over a loudspeaker.

 

Agreed. Different beasts, each with their own inherent sonic peculiarities.

 

...And we haven't even mentioned any brass or woodwind instruments yet!

 

The Mel scale, and the others with formulae "borrowed" from work on comb-filters, seem totally out-of-whack with my experience.

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