Encyclopedia/All topics/Acoustics

Acoustics

Articles 1–44 of 44. Alphabetical by title.

• Acoustics Harmonic Distortion Rs

  A machine-checked module about sound distortion proves only generic facts about a cost function, not facts about acoustics.

• Acoustics Harmonic Distortion Rs Canonical Threshold

  A machine-checked library defines a number meant to mark the edge of audible distortion, but proves only that the number is positive.

• Acoustics Harmonic Distortion Rs Canonical Threshold Pos

  A machine-checked proof shows a proposed audibility threshold is positive, but the number itself is a research note, not a derived result.

• Acoustics Harmonic Distortion Rs Cert

  A machine-checked certificate records three simple mathematical facts about a cost function; it does not prove anything about hearing.

• Acoustics Harmonic Distortion Rs Cert Inhabited

  A machine-checked proof shows that a certain abstract certification structure is not empty, but the proof itself says nothing about real acoustic distortion.

• Acoustics Harmonic Distortion Rs Domain Cost

  A machine-checked library proves three general facts about a cost function, but its acoustic meaning remains an unproven research note.

• Acoustics Harmonic Distortion Rs Domain Cost At Eq

  A machine-checked theorem proves one small fact about a cost function; the acoustics meaning it was built for remains unproved.

• Acoustics Harmonic Distortion Rs Harmonic Dist Cert

  A machine-checked certificate in the Recognition Science library proves three general facts about a cost function, but says nothing specific about harmonic distortion.

• Acoustics Middle C Frequency Rs

  Middle C is the note at 261.63 Hz; a framework called Recognition Science tries to reach that number from a single scaling constant.

• Acoustics Middle C Frequency Rs Middle Cfreq Rs

  A machine-checked file about middle C proves only general facts about a cost function, not that the note's frequency is 261.63 Hz.

• Acoustics Music Consonance From Jcost

  A single cost function ranks musical intervals from the most consonant to the most dissonant, with the octave and fifth near the top and the tritone at the bottom.

• Acoustics Music Consonance From Jcost Domain Cost At Equilibrium

  A machine-checked theorem states that when two frequencies are equal, the recognition cost between them is exactly zero, a fact that anchors a proposed ranking of musical consonanc

• Acoustics Music Consonance From Jcost Music Consonance Cert

  A machine-checked certificate records three general facts about a cost function, but says nothing yet about music itself.

• Acoustics Music Pitch Jndfrom Jcost

  The smallest pitch change a trained ear can hear is a fixed fraction of an octave, and one framework derives that fraction from a single cost function.

• Acoustics Music Pitch Jndfrom Jcost Pitch Cost

  A single formula from a recognition framework converts frequency ratios into a cost, and its smallest meaningful step lands inside the range where trained musicians detect a differ

• Acoustics Music Pitch Jndfrom Jcost Pitch Cost At Unison

  When two tones match exactly, the Recognition Science framework assigns them a recognition cost of zero, a small theorem with a clear boundary.

• Acoustics Music Pitch Jndfrom Jcost Pitch Cost Nonneg

  A theorem about a cost function guarantees that comparing two sounds never yields a negative price, a small but load-bearing fact for a theory of pitch perception.

• Acoustics Music Pitch Jndfrom Jcost Pitch Jndcert

  A machine-checked certificate packages the just-noticeable difference of pitch as a fraction of the octave, and proves that fraction is positive and less than one.

• Acoustics Music Pitch Jndfrom Jcost Pitch Jndfraction

  A machine-checked definition pins the smallest noticeable pitch change to a specific fraction of an octave, then the claim stops at the edge of what hearing tests can confirm.

• Acoustics Music Pitch Jndfrom Jcost Pitch Jndfraction Lt One

  A theorem about a fraction of an octave, and what it does and does not say about the limits of human hearing.

• Acoustics Music Pitch Jndfrom Jcost Pitch Jndfraction Pos

  A machine-checked theorem proves the framework's proposed pitch discrimination step is a positive fraction of an octave, but the link to human hearing remains a prediction.

• Acoustics Musical Note A4 Exact Rs

  The note A4 is defined as 440 Hz, but what does that mean for a theory of recognition costs?

• Acoustics Musical Note A4 Exact Rs A4 Exact Rs

  The declaration A4ExactRS bundles three general facts about a cost function, but it does not derive the 440 Hz tuning standard.

• Acoustics Room Acoustics From Phi Ladder

  Room acoustics classifies five acoustic environments, from anechoic to echoic, and the golden ratio governs the scaling between them.

• Acoustics Room Acoustics From Phi Ladder Room Acoustic Regime

  A machine-checked library of formal theorems defines five room-acoustic regimes and ties their reverberation times to the golden ratio.

• Acoustics Room Acoustics From Phi Ladder Room Acoustic Regime Count

  A machine-checked theorem counts five canonical room-acoustic regimes, and a companion proof shows their reverberation times climb by the golden ratio.

• Acoustics Room Acoustics From Phi Ladder Rt60

  In room acoustics, RT60 is the time for a sound to decay by 60 decibels; the framework's rt60 builds that familiar quantity from a single scaling ratio.

• Acoustics Room Acoustics From Phi Ladder Rt60 Pos

  In room acoustics, a simple theorem proves that reverberation time, scaled in golden-ratio steps, is always a positive number.

• Acoustics Room Acoustics From Phi Ladder Rt60 Ratio

  A machine-checked theorem says that in one framework's model of room acoustics, reverberation time rises by the golden ratio from one regime to the next.

• Acoustics Room Acoustics Rt60 Rs

  Reverberation time RT60 measures how long a room's sound takes to decay by 60 decibels, and a framework called Recognition Science models its ideal values with a golden-ratio

• Acoustics Room Acoustics Rt60 Rs Rt60 Cert

  A formal certificate about reverberation time that proves only general facts about cost, not the acoustic values it names.

• Acoustics Room Acoustics Sabine From Jcost

  A century-old formula for how long sound lingers in a hall, and a modern proof that the ideal concert hall obeys the golden ratio.

• Acoustics Room Acoustics Sabine From Jcost Optimal T60

  In room acoustics, the Sabine formula T60 = 0.161 V/A sets the standard for how long sound lingers, and one framework derives an optimal value from a single cost function.

• Acoustics Room Acoustics Sabine From Jcost Optimal T60 Band

  A machine-checked theorem pins the ideal concert-hall reverberation time to a narrow band around 1.618 seconds, the golden ratio.

• Acoustics Room Acoustics Sabine From Jcost Over Damped Below One

  A machine-checked theorem pins the optimal concert-hall reverberation time above one second, matching the golden ratio.

• Acoustics Room Acoustics Sabine From Jcost Room Acoustics Cert

  A machine-checked certificate pins the optimal concert-hall reverberation time to the golden ratio, within a narrow band.

• Acoustics Room Impulse Response From Jcost

  A room's acoustic fingerprint, called its impulse response, measures how sound decays after a clap, and Recognition Science models that decay with a single cost function.

• Acoustics Room Impulse Response From Jcost Room Impulse Cert

  A formal certificate in the Recognition Science library proves three general properties of a cost function, but it does not yet connect them to any specific room or sound.

• Acoustics Speech Intelligibility From Jcost

  Speech intelligibility, the fraction of words a listener catches, can be described by a single cost function on the signal-to-noise ratio.

• Acoustics Speech Intelligibility From Jcost Hearing Loss Penalty Zero

  A machine-checked theorem pins down the one point where hearing loss costs nothing: when the signal exactly meets the noise threshold.

• Acoustics Speech Intelligibility From Jcost Speech Intelligibility Cert

  Speech intelligibility depends on the signal-to-noise ratio, and a machine-checked certificate pins down the exact cost of a mismatch.

• Acoustics Speech Intelligibility From Jcost Sr Cost Nonneg

  A machine-checked proof shows that the cost of recognizing speech never goes negative, but it does not by itself prove that any particular listener will understand any particular s

• Acoustics Speech Intelligibility From Jcost Sr Cost Reciprocal Symm

  The cost of recognizing speech follows a strict symmetry: a signal twice as strong as noise costs the same to recognize as one half as strong.

• Acoustics Speech Intelligibility From Jcost Sr Cost Zero At Threshold

  Speech intelligibility drops as background noise rises; the Recognition Science framework pins the exact point where recognition becomes effortless.