Amplitude Reference for Sound Synthesis

Overview

This page provides a table of amplitudes for note lists. When working with amplitudes the relevant unit of measurement is the decibel.

Table of Amplitudes

This table is based on the following premises.

To use this graph, determine the maximum number of simultaneous notes in your note list, then use the row of the table with the smallest voice count that equals or exceeds your maximum.

Voicesfff   ff   f   mf   mp   p   pp   ppp
1327672827724403210601817515685135361168110081870075086479559148254164359431012676231019931720148412811105954823710613529
216383141381220110530908778426768584050404350375432392795241220821797155013381155996860742640552477411355306264
3109229425813470206058522845123893336029002502215918631608138811981033892770664573494427368318274236204176
56553565548804212363531372707233620161740150112951118965832718620535462398344296256221190164142122105
84095353430502632227119601692146012601087938809698603520449387334288249215185160138119102887666
13252021751877162013981206104189877566957749843037132027623820517715313211498857363544740
21156013461162100286574664455648041435730826622919817114712711094817061524539332925
3593680769760151944838633328824821418515913711810288766656494236312723201715
56585504435376324280241208180155134115998674645547413530262219171412109

Table 1: Amplitudes by voice count with zero-to-peak maximum 32767.

Frequency-Dependent Amplitudes

Pyschoacoustic research indicates that sensitivity to changes in amplitude vary with frequency according to the “equal-loudness contours” derived through experiment by Fletcher and Munson. A graph of these contours is presented in Wikipedia. Roughly summarizing, sensitivity at the low range of hearing (around 20 Hz.) ranges from 90 to 130 decibels. This region gradually widens while shifting downwards until around 3,500 Hz. where sensitivity ranges from -10 to 100 decibels. From that point the region narrows, shifting back upwards. At the upper limit of hearing (around 15,000 Hz.), sensitivity ranges from 10 to 110 decibels.

The catch is that equal-loudness contours were probably derived using sine tones, while the loudness of a complex tone with a low fundamental has more to do with the strength of the tone's harmonics in the more sensitive frequency regions. My recommendation therefore is to use the values given in Table 1 for your initial realization, then adjust amplitudes “by ear” to obtain the most favorable mix of highs and lows. If a low-fundamental voice speaks badly, you should consider using a waveform with stronger mid-range harmonics.

© Charles Ames Page created: 2013-02-20 Last updated: 2017-08-15