For more information on SINAD and why it’s not important, here’s the article, along with the test tones if you want to try it for yourself: https://www.headphones.com/community/reviews-learning-and-news/evaluating-sinad-why-its-not-important
Check out this calculator to see how much or how little a piece of equipment would add: http://www.sengpielaudio.com/calculator-thd.htm
Use this calculator to check if an amplifier would result in audible noise for your headphones: https://www.headphones.com/pages/headphone-amplifier-noise-calculator
Not all distortion is equal (Julian Krause): https://youtu.be/DZ4IGAR7iio

References & Further reading on THD+N, distortion, and audibility:

D. Shorter, “The Influence of High Order Products on Nonlinear Distortion”, Electron. Eng. vol 22, pp.152-153, 1950

Vanderkooy & Krauel, “Another View of Distortion Perception”, JAES, 2012 https://www.aes.org/e-lib/browse.cfm?elib=16631

Louis Fielder, “Dynamic-Range Issues in the Modern Digital Audio Environment”, JAES,1995 https://www.aes.org/e-lib/online/browse.cfm?elib=7948

Louis Fielder, “Perceptual Assessment of Headphone Distortion”, JAES, 2017, https://www.aes.org/e-lib/browse.cfm?elib=19238

Mikhail Pahomov & Yong Hyuk Na Sr., “Method for Objective Evaluation of Nonlinear Distortion”, JAES, 2015, https://www.aes.org/e-lib/browse.cfm?elib=17995

Alex Voishvillo, “Measurements and Perception of Nonlinear Distortion – Comparing Numbers and Sound Quality”, JAES, 2007, https://www.aes.org/e-lib/browse.cfm?elib=17995

Alex Voishvillo, “Assessment of Nonlinearity in Transducers and Sound Systems – From THD to Perceptual Models”, JAES, 2006, https://www.aes.org/e-lib/browse.cfm?elib=13744

Voishvillo, Terekhov, Czerwinski, & Alexandrov, “Graphing, Interpretation, and Comparison of Results of Loudspeaker Nonlinear Distortion Measurements”, JAES, 2004, https://www.aes.org/e-lib/browse.cfm?elib=12996

Lidia Lee & Earl Geddes, “Auditory Perception of Nonlinear Distortion”, JAES, 2003, http://www.gedlee.com/Papers/Distortion_AES_II.pdf , https://www.aes.org/e-lib/browse.cfm?elib=12465

Phillip Minnick, “Nonlinear Distortion Measurement in Audio Amplifiers: The Perceptual Nonlinear Response”, JAES, 2012, https://www.aes.org/e-lib/browse.cfm?elib=16624

Temme, Brunet, & Qarabaqi, “Measurement of Harmonic Distortion Audibility Using a Simplified Psychoacoustic Model – Updated”, JAES, 2013, https://www.aes.org/e-lib/browse.cfm?elib=16885

Temme, Olive, Welti, & McMullin, “The Correlation between Distortion Audibility and Listener Preference in Headphones”, JAES, 2014, https://www.aes.org/e-lib/browse.cfm?elib=17441

00:00 – Overview of SINAD
04:01 – Distortion
11:47 – Audible Threshold?
13:15 – Noise
15:07 – Conclusion – is there a ‘safe’ SINAD score?

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