The smallest interval

Research has established that under certain favorable conditions (Anechoic chamber, excellent listening, strong attention), it is possible to hear frequency modulations on the order of 5 cents, or even up to one twentieth of a semitone!

Melodic or harmonic interval?

Thank you TheSimon

Zedef wrote:

Melodic or harmonic interval?

Interesting question, I was actually imagining 2 sounds in succession; indeed, probably 2 simultaneous sounds can change many things. What do you think?

Why if it were harmonic, with beats one hears truly minimal intervals (a 1 Hz difference, at least in the "middle" zone of the hearing range, entails 1 amplitude oscillation per second; 2 every half second and so on.. )

And harmonically, what would be the minimum audible interval?

It depends on the pitch (and the auditory characteristics of individuals). Frequencies are logarithmic, so a 1 Hz difference between two sounds results in different "intervals". 440 Hz is the central A; Bb is located at approximately 466 (a 26 Hz difference); an octave below the difference is 13, and an octave above it is 52. It is self-evident that the lower you go, the less you hear, whereas towards the treble, at a certain point, pitches can no longer be distinguished (they become "whistles").

Still regarding a melodic discussion, one can also apply Weber's law, which associates parameters of the physical domain with parameters of the psychoacoustic domain. Delta S = k*S. The parameter k is approximately 0.0023 regarding pitch; consequently, to know the minimum perceptible differential knowing a starting frequency, one must multiply the reference frequency by the tonal k. In the case of 440 Hz, the differential is 1.012 Hz, so I will recognize a subsequent sound with a melodic progression if its frequency is greater than or at most equal to 441.012 Hz. Obviously, the differential varies depending on the frequency range being considered. Regarding the harmonic progression, Zedef has already answered you excellently by speaking about the harmonic ratios found below the limit of what is defined as the critical band.

TheSimon wrote:

Still regarding a melodic discussion, one can also apply Weber's law, which associates parameters of the physical domain with parameters of the psychoacoustic domain. Delta S = k*S. The parameter k is approximately 0.0023 regarding pitch; consequently, to know the minimum perceptible differential knowing a starting frequency, one must multiply the reference frequency by the tonal k. In the case of 440 Hz, the differential is 1.012 Hz, so I will recognize a subsequent sound with a melodic progression if its frequency is greater than or at most equal to 441.012 Hz. Obviously, the differential varies depending on the frequency range being considered. As for the harmonic progression, Zedef has already answered you excellently by talking about the harmonic ratios found below the limit of what is defined as the critical band.

Think about it, The Simon: organs were tuned (and some people still tune them) without knowing anything about Weber's law! Even temperaments (mesotonic docet) were discovered by ear centuries ago: a certain number of beats between notes x-y = a quarter comma"}

Zedef wrote:

Think, Simon, that organs were tuned (and some are still being tuned) without knowing anything about Weber's law! Even temperaments (mesotonic docet) were discovered by ear centuries ago: a certain number of beats between notes x-y = a sixteenth note

Great Zedef

Zedef wrote:

Think, Simon, that organs were tuned (and some are still being tuned) without knowing anything about Weber's law! Even temperaments (mesotonic docet) were discovered by ear centuries ago: a certain number of beats between notes x-y = a sixteenth note

And I would like to see it! In fact, it is not clear to me why you mixed organ tuning with Weber's law. Weber's law associates subjective sensations with a mathematical law based on empirical results. In other words, it tries to mathematically motivate the limitations of the ear and does not intend to be useful for practical application in the field of instrument tuning. Honestly, I do not know well what the method for tuning organs is; I imagine, however, that beats are used in relation to a reference frequency... (Diapason or some other reference instrument, I don't know).

One day I will take you there: a beautiful mix of science and craftsmanship

Kappa wrote:

In your opinion, what is the smallest interval that the human ear can distinguish?

Given that auditory perception possesses the ability to place pitches in successive order in relation to their frequencies, from an acoustical point of view, the question falls within the scope of the ear's perceptual resolution in the pitch domain; specifically, it is the frequency difference between two successive pure tones such that these tones are perceived as distinct or different in pitch—that is, when a quantitative difference in the physical stimulus results in a perceived difference, and below such a difference, the two physical stimuli are perceived as equal.

I believe it is also important to know that there exists the JND (Just Noticeable Difference), which is the numerically expressed measure of the physical variation of the stimulus required to achieve a variation in perception.

The JND in the pitch domain, or frequency resolution of auditory perception, depends on frequency, intensity, duration, and the transition speed between the two tones.

Zedef wrote:

One day I'll take you there: a beautiful mix of science and craftsmanship

Sorry, I hadn't read it. Maybe!!

if you pass by Crema, give a whistle

Minimum, but you must make your famous cakes!

it would be really nice to organize a meetup, but we are all scattered across Italy...

TheSimon wrote:

At least, but you have to make your famous cakes!

thallo wrote:

it would be really nice to organize a meetup, but we are all scattered across Italy...

In fact Simone, the last time we spoke about it I gave up on the mega Jam Session to get behind the stove with Thallo

Maybe I'll pick up some trade secrets

Crema is 2 hours from here.. I'm coming.

Zedef wrote:

Crema is 2 hours from here.. I'm coming.

Well... I'll keep quiet