The problem is, in reality you can multiply the whole thingy, but it is not the same as to multiply each it's member.
If to rectify by a bridge sinewave you will get new function with frequency an octave higher, and lots of harmonics, odd and even, but who will agree to listen to such a rectified music?
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Sorry, you are right. I did a mistake. Triangle has odd harmonics but in different phase with respect to the squeare. The sawtooth is who has all even harmonics when symmetric around 0V.
You can try a frequency doubler: get a signal symmetrical around gnd, and then rectify it in full wave. It´s a common frequency doubler used in RF.
Hz: 1000, 2000, 3000, 4000, 5000 (1,2,3,4,5 Harmonics of 1000 Hz)
now consider 500 Hz as the fundamental.
Hz: 1000, 2000, 3000, 4000, 5000 (2nd, 4th, 6th, 8th, 10th Harmonic)
Same waveform.
Or: 1000, 3000, 5000, 7000, 9000 Hz (1,3,5,7,9 Harmonic of 1000 Hz)
or for 500 Hz fundamental (2,6,10,14,18 Harmonic)
Odd = Even (sound of last pillar of math empire falling over)
now consider 500 Hz as the fundamental.
Hz: 1000, 2000, 3000, 4000, 5000 (2nd, 4th, 6th, 8th, 10th Harmonic)
Same waveform.
Or: 1000, 3000, 5000, 7000, 9000 Hz (1,3,5,7,9 Harmonic of 1000 Hz)
or for 500 Hz fundamental (2,6,10,14,18 Harmonic)
Odd = Even (sound of last pillar of math empire falling over)
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Not only for RF, I did that for lead guitar. In late 70'th I explored all possibilities of creating sounds by generation and transformation of signals using analog electronics, designing synthesizer and guitar effects. The side effect from that work is, I calibrated perception of sounds, imagining waveforms and FFT plots corresponding to this sounds.
Why? Knowledge how to recognize source of dirt helps me to eliminate it.
I think this is where I must side with the subjectivists. It's where simple sine wave testing is misleading.
Music signals are more than harmonically related frequencies so trying to split 'harmonics' and intermodulation products into good and bad has meaning for a musical instrument but is bad for high fidelity reproduction.
Total harmonic distortion measurements and analysis of the relative levels of the harmonics is some way to quantify performance but all distortion is bad.
Music signals are more than harmonically related frequencies so trying to split 'harmonics' and intermodulation products into good and bad has meaning for a musical instrument but is bad for high fidelity reproduction.
Total harmonic distortion measurements and analysis of the relative levels of the harmonics is some way to quantify performance but all distortion is bad.
Here is the beauty of tube distortions (in synthesis! For reproduction all distortions are bad!):
Novachord video - YouTube
Novachord video - YouTube
Are people who understand maths and Fourier analysis supposed to now be quaking in their boots as you have shown, to your own satisfaction only, that Odd=Even? If the fundamental of a waveform was a matter of choice then you would be right. It is not, so you are not. The fundamental is given by the periodicity, so not a matter of choice.smoking-amp said:
I once made a thingy, a little box with mic and linear ins, and one out. It contained 4 - quadrant multiplier. I could sing an octave below my physical abilities aiding by keyboard.
DJs are wannabe musicians. They create own kind of music from records. I prefer raw one, though.
Wavebourn:
I like electronic music very much, specially from DJ´s like Tiësto, Armin van Buuren, Mauro Picotto, Westbam, and many more, and my compatriot Hernán Cattáneo, and DJ Deró. In fact I have more than 1400 hour of live electronic music in my HD´s.
Some time ago in a TV program called "Sábado Bus" (Saturday bus) there were a discussion between DJ (Ezequiel) Deró and a blues artist called Pappo (Died), and where Pappo accused to Deró that DJ´s doesn´t do music, only play music recorded by another music, and that making music from pure noise like electronic one, is not music. And since this moment, I hate this Pappo guy, although never listen him.
On purpose, where can I listen some your´s?
I like electronic music very much, specially from DJ´s like Tiësto, Armin van Buuren, Mauro Picotto, Westbam, and many more, and my compatriot Hernán Cattáneo, and DJ Deró. In fact I have more than 1400 hour of live electronic music in my HD´s.
Some time ago in a TV program called "Sábado Bus" (Saturday bus) there were a discussion between DJ (Ezequiel) Deró and a blues artist called Pappo (Died), and where Pappo accused to Deró that DJ´s doesn´t do music, only play music recorded by another music, and that making music from pure noise like electronic one, is not music. And since this moment, I hate this Pappo guy, although never listen him.
On purpose, where can I listen some your´s?
Here I "re-engineered" one famous song making my own text about an audio engineer that wants to sing on a stage.
http://wavebourn.com/music/alisovskiy/SebeNaBis.mp3
No worries. Pot-shots from the hip don't help anyone, anyway.
Instead, you can devote some attention to understanding what I wrote.
Sorry, I did not have any intention to shoot you. I just did not want to go to debris of details of your remarks on selected phrases in my post you quoted. As DF96 said, you did not understand what you were arguing against. I agree with him.
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