I'm not sure if this is the right place to post this, so feel free to move this or delete it.

I'm working on this application and I've run into a little roadblock. I noticed that as I play higher notes on my guitar, the sound intensity decreases (like the difference between a low E and a high E string). I noticed this before when I was learning that it would be harder to tune higher notes just because they're harder to hear.

Is there a name for this occurrence and is there some formula that I could use to normalize this, like a function where I can input a frequency and multiply the result by the intensity?

  • How does the application relate to what you're doing on the guitar? Might be relevant. Also note that lower frequencies naturally have less power and therefore tend to be quieter, but this is partly countered by using larger instruments, heavier strings, etc for the bass parts. Thus there won't be a simple, single formula to predict it on a guitar. Apr 30, 2014 at 5:24
  • Define "harder to hear". Maybe you have a high-frequency hearing loss? Or do you mean it's harder (for you) to "sense" the frequency in high ranges? Apr 30, 2014 at 11:48

3 Answers 3


This is actually completely normal. In orchestration, we call it a dynamic response envelope which illustrates the dynamic responsiveness of instruments throughout their registers. Composers, orchestrators, and arrangers all must have knowledge of these envelopes in order to effectively balance textures.

Normalizing dynamic response for all register seems enticing, but it makes the sound less realistic, and people become accustomed to listening to music / sounds that do not contain nuance or subtleties (one of the many current issues that pervade the contemporary popular musical landscape). Therefore, I would caution against it. Instead, I would recommend finding a guitar that naturally contains the response you are looking for (a better dynamic response envelope) that will give a clearer, more authentic overall picture of the guitar sound.

Yes, dynamic envelopes are generally the same for each type of instrument, however, better quality instruments can allow for more control and the extreme ends of the ranges.

  • 1
    This so-called 60 song mashup demonstrates pretty effectively how this lack of nuance and subtlety pervades the popular musical landscape. They all sound like one song! You'll notice that there is pretty much no dynamic variation at all; if there were, the songs wouldn't blend so seamlessly.
    – BobRodes
    Apr 30, 2014 at 21:45

A place to start with theoretically modelling the decay of a note is with a damped harmonic oscillator. The key point is that, in a linear model, the oscillator, i.e. the string, looses a fixed fraction of its energy per cycle; higher notes => shorter cycle => less time for the note to decay. In this model, the amplitude of the note should decay like exp(- K*f*t) where K is a dimensionless constant (proportional to the zeta in the wikipedia article), f is the frequency and t is the time.

For a real instrument, there are various factors that will affect this, these include:

  • the differences between the different strings, which amount to each string having a different dimensionless decay constant,
  • the differing impact of fretting a given string at different locations, different frets induce different changes in the tension of the string, and affect the ratio of the length of the string to its diameter and thus influence how it vibrates.

If it were the light, the perceived loudness would be inversely proportional to the frequency, but also depending of the sound sensitivity curve of the human ear and any resonances in the body of the instrument.

The energy of the light particle (photon) is proportional to its frequency (colour), and human eye counts them by number.

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