3 ms·

The ear does not care about ratios. Dissonance can be modeled using Plomp and Levelt's curve, which predicts the perceived dissonance of a pair of sine waves. D

by mrob 5y ago

The ear does not care about ratios. Dissonance can be modeled using Plomp and Levelt's curve, which predicts the perceived dissonance of a pair of sine waves. Dissonance is minimum at unison, smoothly increases to a maximum at a narrow interval (dependent on absolute frequency), and smoothly decreases again as the interval increases. Sethares extended this model to arbitrary sounds by decomposing them into their sine-wave partials with a Fourier transform and then taking an amplitude-weighted average of the predicted dissonance of each pair of partials. If you apply this procedure to intervals using harmonic timbres (timbres composed of partials with frequency an integer multiple of the fundamental frequency), the dissonance curve has minima that happen to be at small integer frequency ratios. Harmonic timbres are most common in music, but there is an important class of musical instruments that are naturally inharmonic: tuned percussion. Unless substantial effort is put into designing them to approximate harmonic timbres, these sound most consonant when tuned outside small integer ratios. Indonesian gamelan music is a well known example of this. And with synthesized timbres you can have whatever inharmonicity you like, so timbres can be designed to suit any arbitrary tuning system. Non-technical explanation of Sethares' model: https://sethares.engr.wisc.edu/consemi.html https://sethares.engr.wisc.edu/consemi.html Full mathematical details: https://sethares.engr.wisc.edu/paperspdf/consonance.pdf https://sethares.engr.wisc.edu/paperspdf/consonance.pdf

notahacker 5y ago
> If you apply this procedure to intervals using harmonic timbres (timbres composed of partials with frequency an integer multiple of the fundamental frequency), the dissonance curve has minima that happen to be at small integer frequency ratios. In practice that's pretty much "the ear cares about ratios" isn't it? Sure, it's caring about the ratios because they align with harmonic timbres in non-percussive instruments, but various human cultures do listen to a wide variety of instruments and voice with harmonic timbres, and perceive melody and chords based around [reasonably close approxiaations] of simple integer ratios sounding more consonant. The implications for creating chordal music with synthesised inharmonic timbres designed to be consonant are interesting, but not widely applicable to what we actually listen to as music; and much of what we hear that goes outside simple ratios with the express intent of sounding dissonant...
whycombs 5y ago
Take one minute and try to sing a perfect 5th over a drone note. You'll waver around that beautiful sturdy 3:2. And if you're lucky, or if you practice you'll eventually lock in to that resonance/ratio and feel a universal truth as important as the right triangle. All of music is based on resonance. And resonance is a ratio
- mrob 5y ago
  Voice is a harmonic timbre. If you could sing with inharmonic partials that perfect 5th would not sound so consonant. And this is relevant even in Western music. The piano is technically tuned percussion, and although it's very close to harmonic, it's inharmonic enough that you have to deviate from small integer ratios (beyond any deviation required for tempered scales) if you want the most consonant sound: https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning
  - jacquesm 5y ago
    Some people can do that all by themselves: https://www.youtube.com/watch?v=vC9Qh709gas https://www.youtube.com/watch?v=vC9Qh709gas
PaulDavisThe1st 5y ago
> Sethares extended this model to arbitrary sounds by decomposing them into their sine-wave partials with a Fourier transform and then taking an amplitude-weighted average of the predicted dissonance of each pair of partials. This is not entirely fair to Plomp & Levelt: they were the first to consider a timbre as a set of sine-wave partials and do the pair-wise partial average. Sethares' extension was to consider inharmonic sine wave series and reason about the implied relationship between timbre and consonance. As others have noted, I think that that "The ear does not care about ratios" is pushing the implications of Plomp & Levelt's and Sethares' work a little too far. They have made a convincing case that our experience of dissonance and consonance is based on a more complicated set of relationships that just the harmonic series, but it's still fundamentally all about ratios (just more of them, and they cannot be considered independent of each other). Even the P&L dissonance curve is in some senses a ratio plot.

by mrob 5y ago

notahacker 5y ago

> If you apply this procedure to intervals using harmonic timbres (timbres composed of partials with frequency an integer multiple of the fundamental frequency), the dissonance curve has minima that happen to be at small integer frequency ratios. In practice that's pretty much "the ear cares about ratios" isn't it? Sure, it's caring about the ratios because they align with harmonic timbres in non-percussive instruments, but various human cultures do listen to a wide variety of instruments and voice with harmonic timbres, and perceive melody and chords based around [reasonably close approxiaations] of simple integer ratios sounding more consonant. The implications for creating chordal music with synthesised inharmonic timbres designed to be consonant are interesting, but not widely applicable to what we actually listen to as music; and much of what we hear that goes outside simple ratios with the express intent of sounding dissonant...

whycombs 5y ago

Take one minute and try to sing a perfect 5th over a drone note. You'll waver around that beautiful sturdy 3:2. And if you're lucky, or if you practice you'll eventually lock in to that resonance/ratio and feel a universal truth as important as the right triangle. All of music is based on resonance. And resonance is a ratio

mrob 5y ago
Voice is a harmonic timbre. If you could sing with inharmonic partials that perfect 5th would not sound so consonant. And this is relevant even in Western music. The piano is technically tuned percussion, and although it's very close to harmonic, it's inharmonic enough that you have to deviate from small integer ratios (beyond any deviation required for tempered scales) if you want the most consonant sound: https://en.wikipedia.org/wiki/Stretched_tuning https://en.wikipedia.org/wiki/Stretched_tuning
- jacquesm 5y ago
  Some people can do that all by themselves: https://www.youtube.com/watch?v=vC9Qh709gas https://www.youtube.com/watch?v=vC9Qh709gas

PaulDavisThe1st 5y ago

> Sethares extended this model to arbitrary sounds by decomposing them into their sine-wave partials with a Fourier transform and then taking an amplitude-weighted average of the predicted dissonance of each pair of partials. This is not entirely fair to Plomp & Levelt: they were the first to consider a timbre as a set of sine-wave partials and do the pair-wise partial average. Sethares' extension was to consider inharmonic sine wave series and reason about the implied relationship between timbre and consonance. As others have noted, I think that that "The ear does not care about ratios" is pushing the implications of Plomp & Levelt's and Sethares' work a little too far. They have made a convincing case that our experience of dissonance and consonance is based on a more complicated set of relationships that just the harmonic series, but it's still fundamentally all about ratios (just more of them, and they cannot be considered independent of each other). Even the P&L dissonance curve is in some senses a ratio plot.