* Envelope fit: A spectral envelope is a curve which envelopes the magnitude spectrum, i.e. it wraps tightly around it, linking the peaks of sinusoidal partials or passing close to the maxima of non-sinusoidal spectra.

* Smoothness: Smoothness of the curve is required: it should not oscillate erratically (fluctuate too wildly over frequency), but give a general idea of the distribution of energy of the signal over frequency.

* Adaptation to fast spectrum variations: A spectral envelope is defined relative to a short segment of sound (typically between 10 and 50 ms). When the spectrum varies rapidly from one analysis frame to the next, the spectral envelope should follow precisely.

Here is an example of a spectrum and various ways people have devised to calculate the envelope:

Leo, based on these materials, am I correct in assuming that you’ve created a spreadsheet that calculates note values in Hz from whatever your starting reference tone is (in most cases A440) as compounded by 1.0595 for the number of steps required to reach the note’s position above or below your reference tone?

For example, if I wanted to know the frequency for the C above A on the 5th string, I would start at A440, count up three chromatic steps from A to C and use that as my compounding multiplier with the rate of 1.0595 to get the end result of 523.2 as follows:

(((440*(1.0595))*1.0595)*1.0595)

This seems to work against the materials provided by Adrian.

Does the envelope concept described above correspond to the Q setting a reasonably equipped Parametric EQ processor will have? This allows you to adjust the number of frequencies that will be included (enveloped) in whatever EQ adjustments you are making to a selected frequency. The width of the open end of the envelope bell shape will vary depending on how many neighboring frequencies you choose to include in the envelope. Q envelopes look similar to the envelopes pictured above.

There is another envelope described in one of Adrian's links. It maps resonance (gain) over time rather than against surrounding frequencies.

Great stuff !

Thanks for the suggestion. The combo tuner looks interesting but I don't think the tuner component tells you the frequency of the pitch it hears. The picture on the website illustrates this. It shows the tuner hearing E with a 440 meaning that it has determined that it's an E when heard against an A440 starting reference pitch. If it were telling you the frequency, it would display E with either 82.4, 164.8, 329.6, or 659.2, if the E was a multiple off of A440, depending on what octave it's hearing.

It seems to work the same way for the frequencies of pitches it generates.

Have I discerned its features correctly or am I missing something on its tuner capabilities? I checked what my Korg GT-12 tuner does. It works the same way.

Interesting question though. Is there a small, battery operated, and affordable frequency analysis tool? There's probably something in the telephony or computer networking market but I'll bet its expensive.

I also seem to have in the back of my mind a piece of freeware software that allows you to use your computer's microphone to bring a sound in and analize its frequency. Hmmmm. I sort of remember playing with something like this awhile back.

Whoops, you're right. My mistake.
Check this one out; http://www.sigview.com/

It's free (shareware) but you 'may' have to look at already recorded audio. I don't know if it will work for live or acoustic signals. I suppose that has more to do with the sound card and software/recording capabilities of your computer.

Yep, that's the software. I'll have to look at it again and maybe run some of my Cakewalk recorded files through it. When I looked at it before, I really had no idea what I was looking at. Now, armed with the very helpful info here, I should be able to assess its capabilities better. I'll bet the demo is still on my PC somewhere. Thanks for finding it again.

Mr. Mando:

Thanks for the offer. Just send the "non-understandable english/german mix-language" sh*t along in its current form when you have a minute. I may be be able to make sense of it with my smattering of college German. I don't want to be responsible for taking any of your time away from your new family member. I was wondering whether you were using the 12th root of 2 or the 1.0595 value. Do you work from Alain Danielou's "Comparative Table of Musical Intervals" for your cents and natural interval adjustments?

Note that wound guitar string partials are not harmonic. The higher frequency partials are stretched higher than where you would expect. This raises the question of what pitch is and a number of practically important complications. The ear relies on several partials to decide what pitch a sound is at. We know this because we still hear a strong pitch even if the fundemental frequency partial is completely missing. So if the partials are not harmonic what pitch does the ear decide on? Some kind of average perhaps? Why might all this matter? Because an electronic guitar tuner will lock onto the frequency of the lowest partial which might not correspend to what you here the pitch of the string to be.

Consider tuning a wound guitar string by listening for beats. The beats from the upper partials will have a different structure to the lower ones. When you tune by the method of harmonics you surpress the upper partials. You also don't displace the string. That's now a total of three ways to tune a string that can give different results.

I mention all this because I think these practical things often deserve more attention than how many digits you calculate the 12th root of 2 to.