Before I go on, there is more than one right way to do most anything, and there might even be a better way than the way I do it.
I play 7 instruments and voice but sax is my primary. We are always more critical on the instruments we play so if I am going to emulate a sax, flute, guitar, bass, or drums I am more critical than if I'm emulating a trombone or harmonica. In the wind synth community we call it Home Instrument Bias. Keyboards are easier with keyboard controllers as you can't help but play them like a keyboard.
On the sax there is pitch shift done with the reed (vibrato) and volume shift done with the diaphragm (tremolo). Many sax and wind synth players use those two terms to differentiate the two.
For vibrato I use good old pitch bend, for tremolo I prefer cc2 (breath) for wind instruments, if the synth doesn't recognize cc2, I'll go with cc11 (expression) as a second choice.
As far as a sine wave or U shaped wave is concerned, when playing the sax, the shape, insensitivity and speed of the vibrato depends on the song and can change drastically during the hold of a single note. I'd do it with a wind controller, or a joystick (set for less than a half step total travel) to get more realistic changes as the time goes by. On an EWI I'd use the pitch bend plates.
If you are wanting to do a faithful emulation of an instrument, you need to understand its limitations and it's capabilities. These are controlled by both the player and the construction of the instrument.
Some things about saxophone (in no particular order, or simply in the order I think of them - thinking out loud here)
One note at a time and the timbre gets brighter as the notes get higher and also with increasing volume
Vibrato is usually done with the reed, and it's much easier to relax and let the pitch to flat than to bite harder and make the pitch go higher. Plus the pitch bend is not linear, the same amount of lip movement makes more pitch bend as you go lower in pitch. So vibrato goes below pitch and back. If you do that LFO thing where it goes over and under by the same degree, it won't sound sax-like
Vibrato is hardly ever constant like a LFO but is done in context with the music and up to the player's vision, and it often changes in real time during the duration of the note
Tone changes with vibrato, darker when the note is flatter and brighter when it moves sharper
Sax players often like to scoop up to the note. A little like a guitarist might by playing a not one fret lower and bending it up to pitch, but not as much as a half step flat.
Sax players can change the tone and the vowel sound by both changing their embouchure and the shape of their oral cavity to get tones that resemble ooh and aah. Sometimes in a run I'll ooh-aah-ooh-aah... all the way up or down.
Sax players can change their breath support and embouchure to get mellow, airy subtones to overblowing the horn for some bright distortion. The tone is rarely constant throughout any phrase
Sax players can add distortion with their throat or more severely flutter tongue
Sax players can attack the note in very different ways from slurs (no articulation) to lightly touching the reed (legato) through slapping the reed
Breath force can be changed at will, making the attack a severe accent or a slow rise. You can make it yell "Hey!" "Mmm" or anything in between
Every note is not attacked the same way. Using one sample sometimes will kill sax expression if it attacks the note the same way every time.
Breath force can make the volume rise and fall for expressiveness as a note is being held, and the timbre changes with those volume changes
As the sax changes register (C# to D in the saxes key - tenor is a Bb instrument, alto Eb) it changes tone
there is a lot more, and they will come after I hit submit but that's enough to get started.
Each instrument has it's quirks, and that's what makes it sound like that instrument. Tone is secondary to making the nuances of the instrument come out. After all when a comedian does an impression of the President or other famous person, he or she doesn't have the same voice, but relies on copping their expressive patterns. This is what you need to do when doing a good emulation of another instrument. If you want a sax, you need to give the part "true sax nature" or it won't sound right no matter what patch and how good the tone is.
You lean on the things your synth can do that emulate the instrument in question, and you avoid the things it cannot do. That is unless you don't want a faithful emulation and want something different, which is OK too.
All this goes to other instruments.
One very different example. MIDI drum rolls often sound like machine guns. When I do a single stroke roll on a drum, my right hand hits a bit harder than the left because it's stronger. That makes that hand brighter and louder. The left hand being weaker often lags an almost imperceptible bit (perhaps a clock tic or two in MIDI @196). Plus both sticks do not hit the drum in the exact same place, and as you move around the drum the tone changes. You can do something that approaches a single stroke roll that doesn't sound like a machine gun by detuning every other note a tiny bit, lowing it's volume a bit, and delaying that note a clock tic or two.
The great sax player, Charlie Parker once said, "You don't play the sax, you let the sax play you."
That goes for every instrument, you can't play a piano like a guitar or a trombone like a sax. So you have to figure out how the instrument you want to emulate plays the player, and that's your starting point.
Insights and incites by Notes
Before I go on, there is more than one right way to do most anything, and there might even be a better way than the way I do it. I play 7 instruments and voice but sax is my primary. We are always more critical on the instruments we play so if I am going to emulate a sax, flute, guitar, bass, or drums I am more critical than if I'm emulating a trombone or harmonica. In the wind synth community we call it Home Instrument Bias. Keyboards are easier with keyboard controllers as you can't help but play them like a keyboard. On the sax there is pitch shift done with the reed (vibrato) and volume shift done with the diaphragm (tremolo). Many sax and wind synth players use those two terms to differentiate the two. For vibrato I use good old pitch bend, for tremolo I prefer cc2 (breath) for wind instruments, if the synth doesn't recognize cc2, I'll go with cc11 (expression) as a second choice. As far as a sine wave or U shaped wave is concerned, when playing the sax, the shape, insensitivity and speed of the vibrato depends on the song and can change drastically during the hold of a single note. I'd do it with a wind controller, or a joystick (set for less than a half step total travel) to get more realistic changes as the time goes by. On an EWI I'd use the pitch bend plates. If you are wanting to do a faithful emulation of an instrument, you need to understand its limitations and it's capabilities. These are controlled by both the player and the construction of the instrument. Some things about saxophone (in no particular order, or simply in the order I think of them - thinking out loud here) One note at a time and the timbre gets brighter as the notes get higher and also with increasing volume Vibrato is usually done with the reed, and it's much easier to relax and let the pitch to flat than to bite harder and make the pitch go higher. Plus the pitch bend is not linear, the same amount of lip movement makes more pitch bend as you go lower in pitch. So vibrato goes below pitch and back. If you do that LFO thing where it goes over and under by the same degree, it won't sound sax-like Vibrato is hardly ever constant like a LFO but is done in context with the music and up to the player's vision, and it often changes in real time during the duration of the note Tone changes with vibrato, darker when the note is flatter and brighter when it moves sharper Sax players often like to scoop up to the note. A little like a guitarist might by playing a not one fret lower and bending it up to pitch, but not as much as a half step flat. Sax players can change the tone and the vowel sound by both changing their embouchure and the shape of their oral cavity to get tones that resemble ooh and aah. Sometimes in a run I'll ooh-aah-ooh-aah... all the way up or down. Sax players can change their breath support and embouchure to get mellow, airy subtones to overblowing the horn for some bright distortion. The tone is rarely constant throughout any phrase Sax players can add distortion with their throat or more severely flutter tongue Sax players can attack the note in very different ways from slurs (no articulation) to lightly touching the reed (legato) through slapping the reed Breath force can be changed at will, making the attack a severe accent or a slow rise. You can make it yell "Hey!" "Mmm" or anything in between Every note is not attacked the same way. Using one sample sometimes will kill sax expression if it attacks the note the same way every time. Breath force can make the volume rise and fall for expressiveness as a note is being held, and the timbre changes with those volume changes As the sax changes register (C# to D in the saxes key - tenor is a Bb instrument, alto Eb) it changes tone there is a lot more, and they will come after I hit submit but that's enough to get started. Each instrument has it's quirks, and that's what makes it sound like that instrument. Tone is secondary to making the nuances of the instrument come out. After all when a comedian does an impression of the President or other famous person, he or she doesn't have the same voice, but relies on copping their expressive patterns. This is what you need to do when doing a good emulation of another instrument. If you want a sax, you need to give the part "true sax nature" or it won't sound right no matter what patch and how good the tone is. You lean on the things your synth can do that emulate the instrument in question, and you avoid the things it cannot do. That is unless you don't want a faithful emulation and want something different, which is OK too. All this goes to other instruments. One very different example. MIDI drum rolls often sound like machine guns. When I do a single stroke roll on a drum, my right hand hits a bit harder than the left because it's stronger. That makes that hand brighter and louder. The left hand being weaker often lags an almost imperceptible bit (perhaps a clock tic or two in MIDI @196). Plus both sticks do not hit the drum in the exact same place, and as you move around the drum the tone changes. You can do something that approaches a single stroke roll that doesn't sound like a machine gun by detuning every other note a tiny bit, lowing it's volume a bit, and delaying that note a clock tic or two. The great sax player, Charlie Parker once said, "You don't play the sax, you let the sax play you." That goes for every instrument, you can't play a piano like a guitar or a trombone like a sax. So you have to figure out how the instrument you want to emulate plays the player, and that's your starting point. Insights and incites by Notes
