Wanted: A mathematical definition for consonant...
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From: Jay Bala on 6 Jun 2010 08:41 Who can give me a mathematical definition for consonant, possibly tied to even order harmonics. I don't words, I want an equation. I have something, but I think its not the best. I wanted to see whats out there before I put anymore time into it. Thanks, Jay Bala.
From: rabid_fan on 6 Jun 2010 12:16 On Sun, 06 Jun 2010 05:41:40 -0700, Jay Bala wrote: > Who can give me a mathematical definition for consonant, possibly tied > to even order harmonics. I don't words, I want an equation. > There can be no purely mathematical definition of "consonant" because the phenomenon derives entirely from human perception and the properties of the human basilar membrane (i.e. cochlea). Consonance (or lack thereof) arises from the overlapping of partial frequencies of two or more separate tones. See any reference work on psychoacoustics for a more in-depth analysis. Ultimately, consonance is a highly relative concept because higher cortical areas of the brain are the final arbiter. What may sound pleasing to some individual or cultures may sound dissonant to others.
From: Cwatters on 6 Jun 2010 13:18 "Jay Bala" <jay1bala(a)gmail.com> wrote in message news:2abb25ee-7925-4d66-a5e4-62dce7d8293d(a)d37g2000yqm.googlegroups.com... > Who can give me a mathematical definition for consonant, possibly tied > to even order harmonics. I don't words, I want an equation. > > I have something, but I think its not the best. I wanted to see whats > out there before I put anymore time into it. > > Thanks, > Jay Bala. I'm no expert on music but it appears to be impossible.Whole papers are written on the subject. Not even clear that it would be the same for all cultures.
From: Androcles on 6 Jun 2010 14:24 "Jay Bala" <jay1bala(a)gmail.com> wrote in message news:2abb25ee-7925-4d66-a5e4-62dce7d8293d(a)d37g2000yqm.googlegroups.com... | Who can give me a mathematical definition for consonant, possibly tied | to even order harmonics. I don't words, I want an equation. | | I have something, but I think its not the best. I wanted to see whats | out there before I put anymore time into it. | | Thanks, | Jay Bala. | http://www.merriam-webster.com/dictionary/consonant 1 : being in agreement or harmony : free from elements making for discord 2 : marked by musical consonances 3 : having similar sounds <consonant words> 4 : relating to or exhibiting consonance : resonant consonant = integer ratio Where a = x/y and a belongs to the set of natural numbers {1,2,3,...}, x and y are consonant. In music, F# = 1480 Hz and G = 1568 Hz are dissonant (and sound it), 1480/1568 = 0.943877551 which is not an integer. However, for F# = 185 Hz and G = 18,130 Hz (185*98) can be mathematically consonant if G is taken from a different and much higher octave; but 18,130 Hz is a higher frequency than most people can hear and we don't have 98 * 12 = 1176 keys on a piano, most have only 88 keys or less. Therefore we can in practice limit the set of consonant natural numbers to those we can hear which have the ratio x/y that belong to the set {1,2,3,4,5,6,7} in music, but not in mathematics. There is no limitation to even or odd numbers being consonant in music or mathematics.
From: Uncle Al on 6 Jun 2010 15:17
Jay Bala wrote: > > Who can give me a mathematical definition for consonant, possibly tied > to even order harmonics. I don't words, I want an equation. > > I have something, but I think its not the best. I wanted to see whats > out there before I put anymore time into it. We can handle discrete consonants and the five vowels, but what about the letter Y? Syzygy at the nodes eclipes philosophical dialetic and critique. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz4.htm |