these are called Automatic Negative Thoughts by NLD specialists. They are created by the amygdala, which in people like us is more active than in most people. Therapy and medication can work wonders with this.
what if the Messiah came to earth and was executed in the electric chair. Many years from now, would His followers decorate themselves with electric chairs the way people do with crosses?
what if the Messiah came to earth and was executed in the electric chair. Many years from now, would His followers decorate themselves with electric chairs the way people do with crosses?
maybe
but it is hard to make a 2D abstraction of an electric chair
The electric chair is a perverse and disgusting invention, and when people still used it that weren't Texas or whatever, people used it incorrectly a lot of the time, which could have really gruesome results.
Frequency Modulation (or FM) synthesis is a simple and powerful method for creating and controlling complex spectra, introduced by John Chowning of Stanford University around 1973. In its simplest form it involves a sine wave carrier whose instantaneous frequency is varied, i.e. modulated, according to the waveform (assumed here to be another sine wave) of the so-called modulator. This model then is often called simple FM or sine-wave FM. Other forms of FM are extensions of the basic model. The systematic properties of FM were used to compose Barry Truax's tape solo works Arras, Androgyny, Wave Edge, Solar Ellipse, Sonic Landscape No. 3, and Tape VII from Gilgamesh, as well as those involving live performers or graphics (Aerial, Love Songs, Divan, Sonic Landscape No. 4 ).
When the frequency of the modulator (which we'll call M) is in the sub-audio range (1-20 Hz), we can hear siren-like changes in pitch of the carrier. However, when we raise M to the audio range (above 30 Hz) then we hear a new timbre composed of frequencies called SIDEBANDS. To determine which sidebands are present, we have to control the ratio between the carrier frequency (C) and the modulating frequency (M). Instead of dealing with these frequencies in Hz, we'll refer to this relationship as the C : M RATIO, keeping C and M as integers.
The so-called upper sidebands are those lying above the carrier. Their frequencies are:
C+M C+2M C+3M C+4M C+5M ....
For example, if C:M is 1:2, that is, the modulator is twice the frequency of the carrier, then the first upper sideband is: C+M = 1+2 = 3. The second upper sideband is: C+2M = 1+(2x2) = 1+4 = 5. Another way to get the second sideband is to add M=2 to the value of the first sideband which is 3; i.e. (C+M) + M = 3+2 = 5. It quickly becomes clear that the upper sidebands in this example are all the odd numbers, and since the carrier is 1, the upper sidebands are all the odd harmonics, with the carrier as the fundamental (i.e. the lowest frequency in the spectrum).
However, if our C:M were 2:5, the first upper sideband would be 2+5 = 7. Since 7 is not a multiple of 2, it would be termed inharmonic. But the second upper sideband would be 7+5 = 12, and that is the 6th harmonic. Therefore, we can see that sidebands can be harmonic or inharmonic.
The lower sidebands are: C-M C-2M C-3M C-4M C-5M ...
When the sideband is a positive number it will lie below the carrier, but at some point, its value will become negative. It is then said to be reflected because we simply drop the minus sign and treat it as a positive number, e.g. the sideband -3 appears in the spectrum as 3. Acoustically, however, this reflected process involves a phase inversion, i.e. the spectral component is 180 degrees out of phase. Mathematically, we express this reflection by using absolute value signs around the expression: /C-M/ to indicate that we drop the minus and treat the number as positive.
For example, for 1:2, the 1st lower sideband is: /C-M/ = /1-2/ = /-1/ =1.
The second lower sideband is: /C-2M/ = /1-(2x2)/ = /1-4/ = /-3/ = 3. However, to make things easier, we could have added 2 to the first lower sideband (1), which is already reflected, and have obtained 3.
For the ratio 1:1, the 1st lower sideband is 0 (inaudible) and the 2nd, 3rd and 4th lower sidebands are 1, 2, 3, respectively.
For 7:5, the lower sidebands are: 2 3 8 13 where 3 is the 1st reflected one. One concern we have in using a given C:M ratio is whether the carrier frequency is the lowest frequency in the spectrum, i.e. is it the fundamental? If it is, we can treat the carrier frequency as the principal pitch that will be heard in the resulting timbre.
First we have the case of the 1:1 ratio whose upper sidebands are 2,3,4,... and whose lower sidebands are 0,1,2,3,... Clearly the carrier is the lowest non-zero component, and all the sidebands are harmonics, i.e. multiples. Because 1:1 is the only ratio with a zero lower sideband, it is a special case. It is also the only ratio producing the entire harmonic series. For other ratios, we could work out their sidebands and decide if any of them were lower than the carrier. That is fine, but tedious, and we'd like to know in advance what to expect. First, we might note that in the 1:2 case the 1st lower sideband is /-1/ = 1; therefore it fell against the carrier. Further, if M is larger than twice C, e.g. 2:5, then the 1st reflected sideband will always be greater than the carrier.
Work out a few examples and you'll find that the rule is:
FOR THE CARRIER TO BE THE FUNDAMENTAL: M MUST BE GREATER THAN OR EQUAL TO TWICE C, OR ELSE BE THE 1:1 RATIO.
Another useful property to be familiar with is the occurrence, as you may have noticed already, of lower sidebands coinciding with the upper set. They are said to 'fall against' them.
What this means acoustically is that the amplitudes of the two sidebands will add together, influenced as well by the phase inversion of the reflected sideband. Since the amplitude of each sideband varies according to the strength of the modulation, as expressed by the Modulation Index, the sum of the contributions of each sideband becomes quite complex!
You've probably noticed that the sidebands of the 1:1 ratio have this property of falling against each other. You'll find a very similar pattern with all of the N:1 ratios, i.e. 2:1, 3:1, 4:1, 5:1 ...
The second type of ratio showing the same property is that like 1:2. The odd harmonics are found in both the upper and lower sidebands. Therefore we can extrapolate the second case, namely odd N:2, that is, the ratios 1:2, 3:2, 5:2, 7:2 ...
No other ratios except N:1 and odd N:2 have this property. All ratios other than N:1 and odd N:2 have an asymmetrical spacing of their sidebands. That is, the distance in frequency between adjacent sidebands is unequal. For instance, the ratio 2:5 with its sidebands 2 3 7 8 12 .... However, there is still a pattern to the spacing.
We want the distance between the first upper sideband (C + M) and the first reflected lower sideband (C - M) which is negative by definition and therefore can be made positive to give the expression (M - C). Subtract these two frequencies to get: (C + M) - (M - C) = 2C We find that the answer is 2C. Since the spacing of all upper or lower sidebands is M, then the remaining spacing is M - 2C.
Therefore the rule is:
WHEN C IS THE LOWEST FREQUENCY IN THE SPECTRUM, THE SPACING OF SIDEBANDS ABOVE IT (EXCEPT FOR 1:1) WILL BE: M - 2.C & 2.C
For the above example (2:5), the spacing is 2x2=4 and 5-4=1. Note that we have to start with C as the fundamental. This will be referred to in the next section as the Normal Form of the Ratio.
The electric chair is a perverse and disgusting invention, and when people still used it that weren't Texas or whatever, people used it incorrectly a lot of the time, which could have really gruesome results.
Edison invented the electric chair in one of his worst sleazebag moves. Look at William kemmler. Edison new darn well that was a broken machine he was using. He knew damg well what pain it would out Kemmler in, and how it would discredit AC electricity.
Frequency Modulation (or FM) synthesis is a simple and powerful method for creating and controlling complex spectra, introduced by John Chowning of Stanford University around 1973. In its simplest form it involves a sine wave carrier whose instantaneous frequency is varied, i.e. modulated, according to the waveform (assumed here to be another sine wave) of the so-called modulator. This model then is often called simple FM or sine-wave FM. Other forms of FM are extensions of the basic model. The systematic properties of FM were used to compose Barry Truax's tape solo works Arras, Androgyny, Wave Edge, Solar Ellipse, Sonic Landscape No. 3, and Tape VII from Gilgamesh, as well as those involving live performers or graphics (Aerial, Love Songs, Divan, Sonic Landscape No. 4 ).
When the frequency of the modulator (which we'll call M) is in the sub-audio range (1-20 Hz), we can hear siren-like changes in pitch of the carrier. However, when we raise M to the audio range (above 30 Hz) then we hear a new timbre composed of frequencies called SIDEBANDS. To determine which sidebands are present, we have to control the ratio between the carrier frequency (C) and the modulating frequency (M). Instead of dealing with these frequencies in Hz, we'll refer to this relationship as the C : M RATIO, keeping C and M as integers.
Speaking of FM Synthesis, here's the paper John Chowning published back in '73:
I mostly use FM only for percussion now, i tend to find that the analogue/subtractive emulation VSTs i have on hand sound nicer than the FM synths i have
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http://www.acuteaday.com/blog/wp-content/uploads/2012/07/sleeping-baby-cow-calf.jpg
that is natural. If we never second guessed, we would go with our first whims, like eating dirt or sticking a fork in the electric socket.
But we must decide. Just choose something and end the mental torment of indecision.
these are called Automatic Negative Thoughts by NLD specialists. They are created by the amygdala, which in people like us is more active than in most people. Therapy and medication can work wonders with this.
you've forgotten a lot of bad memories. You don't realize it because you forgot all about them.
Well, I still recommend therapy, it can't hurt, even though you don't have NLD.
-psst, I'm just jealous that there's no Aliroz.jpeg- that's the joke.
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Please try to be more thoughtful when discussing that most important of all subjects.
The electric chair is a perverse and disgusting invention, and when people still used it that weren't Texas or whatever, people used it incorrectly a lot of the time, which could have really gruesome results.
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The so-called upper sidebands are those lying above the carrier. Their frequencies are:
For example, if C:M is 1:2, that is, the modulator is twice the frequency of the carrier, then the first upper sideband is: C+M = 1+2 = 3. The second upper sideband is: C+2M = 1+(2x2) = 1+4 = 5. Another way to get the second sideband is to add M=2 to the value of the first sideband which is 3; i.e. (C+M) + M = 3+2 = 5. It quickly becomes clear that the upper sidebands in this example are all the odd numbers, and since the carrier is 1, the upper sidebands are all the odd harmonics, with the carrier as the fundamental (i.e. the lowest frequency in the spectrum).
However, if our C:M were 2:5, the first upper sideband would be 2+5 = 7. Since 7 is not a multiple of 2, it would be termed inharmonic. But the second upper sideband would be 7+5 = 12, and that is the 6th harmonic. Therefore, we can see that sidebands can be harmonic or inharmonic.
The lower sidebands are: C-M C-2M C-3M C-4M C-5M ...
When the sideband is a positive number it will lie below the carrier, but at some point, its value will become negative. It is then said to be reflected because we simply drop the minus sign and treat it as a positive number, e.g. the sideband -3 appears in the spectrum as 3. Acoustically, however, this reflected process involves a phase inversion, i.e. the spectral component is 180 degrees out of phase. Mathematically, we express this reflection by using absolute value signs around the expression: /C-M/ to indicate that we drop the minus and treat the number as positive.
For example, for 1:2, the 1st lower sideband is: /C-M/ = /1-2/ = /-1/ =1.
The second lower sideband is: /C-2M/ = /1-(2x2)/ = /1-4/ = /-3/ = 3. However, to make things easier, we could have added 2 to the first lower sideband (1), which is already reflected, and have obtained 3.
For the ratio 1:1, the 1st lower sideband is 0 (inaudible) and the 2nd, 3rd and 4th lower sidebands are 1, 2, 3, respectively.
For 7:5, the lower sidebands are: 2 3 8 13 where 3 is the 1st reflected one. One concern we have in using a given C:M ratio is whether the carrier frequency is the lowest frequency in the spectrum, i.e. is it the fundamental? If it is, we can treat the carrier frequency as the principal pitch that will be heard in the resulting timbre.
First we have the case of the 1:1 ratio whose upper sidebands are 2,3,4,... and whose lower sidebands are 0,1,2,3,... Clearly the carrier is the lowest non-zero component, and all the sidebands are harmonics, i.e. multiples. Because 1:1 is the only ratio with a zero lower sideband, it is a special case. It is also the only ratio producing the entire harmonic series. For other ratios, we could work out their sidebands and decide if any of them were lower than the carrier. That is fine, but tedious, and we'd like to know in advance what to expect. First, we might note that in the 1:2 case the 1st lower sideband is /-1/ = 1; therefore it fell against the carrier. Further, if M is larger than twice C, e.g. 2:5, then the 1st reflected sideband will always be greater than the carrier.
Work out a few examples and you'll find that the rule is:
Another useful property to be familiar with is the occurrence, as you may have noticed already, of lower sidebands coinciding with the upper set. They are said to 'fall against' them.
What this means acoustically is that the amplitudes of the two sidebands will add together, influenced as well by the phase inversion of the reflected sideband. Since the amplitude of each sideband varies according to the strength of the modulation, as expressed by the Modulation Index, the sum of the contributions of each sideband becomes quite complex!
You've probably noticed that the sidebands of the 1:1 ratio have this property of falling against each other. You'll find a very similar pattern with all of the N:1 ratios, i.e. 2:1, 3:1, 4:1, 5:1 ...
The second type of ratio showing the same property is that like 1:2. The odd harmonics are found in both the upper and lower sidebands. Therefore we can extrapolate the second case, namely odd N:2, that is, the ratios 1:2, 3:2, 5:2, 7:2 ...
No other ratios except N:1 and odd N:2 have this property. All ratios other than N:1 and odd N:2 have an asymmetrical spacing of their sidebands. That is, the distance in frequency between adjacent sidebands is unequal. For instance, the ratio 2:5 with its sidebands 2 3 7 8 12 .... However, there is still a pattern to the spacing.
We want the distance between the first upper sideband (C + M) and the first reflected lower sideband (C - M) which is negative by definition and therefore can be made positive to give the expression (M - C). Subtract these two frequencies to get: (C + M) - (M - C) = 2C We find that the answer is 2C. Since the spacing of all upper or lower sidebands is M, then the remaining spacing is M - 2C.
Therefore the rule is:
For the above example (2:5), the spacing is 2x2=4 and 5-4=1. Note that we have to start with C as the fundamental. This will be referred to in the next section as the Normal Form of the Ratio.
Edison invented the electric chair in one of his worst sleazebag moves. Look at William kemmler. Edison new darn well that was a broken machine he was using. He knew damg well what pain it would out Kemmler in, and how it would discredit AC electricity.
https://ccrma.stanford.edu/sites/default/files/user/jc/fmsynthesispaperfinal_1.pdf
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