6 ms·

If I open 2 tabs of https://www.szynalski.com/tone-generator/ https://www.szynalski.com/tone-generator/ and then listen to 440+880, and then change 880 to 850 i

If I open 2 tabs of https://www.szynalski.com/tone-generator/ https://www.szynalski.com/tone-generator/ and then listen to 440+880, and then change 880 to 850 it is a world of difference. I would definitely describe that difference as dissonance and consonance. Now the overtone series IS important and is not always 'simple ratios', a good example in a real instrument is the strong minor third overtone of a carillon, and as expected writing in major for that instrument is hard.

cousin_it 7y ago
That sine wave sounds a bit "fuzzy" to me, maybe the generator adds a small amount of overtones or aliasing. I tried another generator (http://onlinetonegenerator.com/ http://onlinetonegenerator.com/) and the consonance feels weaker.
- onnodigcomplex 7y ago
  Interesting, I still hear it the same, dissonant and consonant, perhaps western music ruined me. Thanks for sharing. Edit: Didn't see the url, makes my old reply obsolete: Interesting. I tried to avoid clipping/aliasing by using audacity with as high quality audio as my system allows and I can still reproduce pretty much exactly what you hear on those websites. https://vocaroo.com/i/s0Be5CexLgVs https://vocaroo.com/i/s0Be5CexLgVs is 440hz, then 440hz+880hz, then 440hz+850hz. But I would be interested in any repeatable signal that does not harmonize at all so do share!
  - cousin_it 7y ago
    You're right and I was overconfident. I tried some more, and the sense of consonance is weak but still there. Amended the comment.
geofft 7y ago
I'm not sure if this is the same thing as consonance/dissonance, but the graph of sin(x) + sin(2x), an octave, is regular and pretty and the graph of sin(x) + sin(sqrt(2)x), a tritone, is much less so. https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%282x%29+from+-100+to+100 https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%282... https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28sqrt%282%29x%29+from+-100+to+100 https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28s...
- etatoby 7y ago
  If you plot them as XY it's even more obvious which one is perfect consonance and which one dissonance: https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3B+y+%3D+sin%282t%29+%7D+t+%3D+0+to+100 https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3... https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3B+y+%3D+sin%28sqrt%282%29t%29+%7D+t+%3D+0+to+1000 https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3...
  - tripzilch 7y ago
    Except that if you use a frequency ratio of sin(x)+sin(2.01 x), which is really very close to an octave and really sounds just as consonant as an octave to almost all people, you almost the same "dissonant" picture: https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3B+y+%3D+sin%282.01+*+t%29+%7D+t+%3D+0+to+1000 https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3... The strange thing is, none of these "simple ratio" theories account for the fact that our brains allow a lot of "fuzziness" around these simple ratios, so much that you can't really call them simple ratios as they encompass a whole bunch of not-simple ratios as well.
jacquesm 7y ago
Thank you for that link. I never thought of my browser as a test bench before. (Of course, now I want a DVM, function generator, scope, logic analyser, spectrum analyzer and all the other goodies ;) ).

cousin_it 7y ago

That sine wave sounds a bit "fuzzy" to me, maybe the generator adds a small amount of overtones or aliasing. I tried another generator (http://onlinetonegenerator.com/ http://onlinetonegenerator.com/) and the consonance feels weaker.

onnodigcomplex 7y ago
Interesting, I still hear it the same, dissonant and consonant, perhaps western music ruined me. Thanks for sharing. Edit: Didn't see the url, makes my old reply obsolete: Interesting. I tried to avoid clipping/aliasing by using audacity with as high quality audio as my system allows and I can still reproduce pretty much exactly what you hear on those websites. https://vocaroo.com/i/s0Be5CexLgVs https://vocaroo.com/i/s0Be5CexLgVs is 440hz, then 440hz+880hz, then 440hz+850hz. But I would be interested in any repeatable signal that does not harmonize at all so do share!
- cousin_it 7y ago
  You're right and I was overconfident. I tried some more, and the sense of consonance is weak but still there. Amended the comment.

geofft 7y ago

I'm not sure if this is the same thing as consonance/dissonance, but the graph of sin(x) + sin(2x), an octave, is regular and pretty and the graph of sin(x) + sin(sqrt(2)x), a tritone, is much less so. https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%282x%29+from+-100+to+100 https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%282... https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28sqrt%282%29x%29+from+-100+to+100 https://www.wolframalpha.com/input/?i=sin%28x%29+%2B+sin%28s...

etatoby 7y ago
If you plot them as XY it's even more obvious which one is perfect consonance and which one dissonance: https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3B+y+%3D+sin%282t%29+%7D+t+%3D+0+to+100 https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3... https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3B+y+%3D+sin%28sqrt%282%29t%29+%7D+t+%3D+0+to+1000 https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3...
- tripzilch 7y ago
  Except that if you use a frequency ratio of sin(x)+sin(2.01 x), which is really very close to an octave and really sounds just as consonant as an octave to almost all people, you almost the same "dissonant" picture: https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3B+y+%3D+sin%282.01+*+t%29+%7D+t+%3D+0+to+1000 https://www.wolframalpha.com/input/?i=%7B+x+%3D+sin%28t%29%3... The strange thing is, none of these "simple ratio" theories account for the fact that our brains allow a lot of "fuzziness" around these simple ratios, so much that you can't really call them simple ratios as they encompass a whole bunch of not-simple ratios as well.

jacquesm 7y ago

Thank you for that link. I never thought of my browser as a test bench before. (Of course, now I want a DVM, function generator, scope, logic analyser, spectrum analyzer and all the other goodies ;) ).