The kids are back at school, so I have some time to myself during the day again. (If you're just joining this thread I have ME - it's in wikipedia.) I've got a bunch of paperwork to do to finish up Hands Off, but I'm having a bit of me-time first. It's not helping that the builder has been tearing up my patio and drive with a jack-hammer, but the unceasing din is somewhat offset by knowing that [i]finally[/i] we are getting our house extended. It has been a loooong time coming.
Enough of me. Me-time for the last couple of mornings has been drawing graphs. It's kind of Hands Off tidy-up work in a sense - it's the guts of the paper I would have presented at Hands Off if I hadn't been busy organising it, and had the time to really do it properly. This is the Cliffs Notes.
It's a flickr slideshow (http://www.flickr.com/photos/8666613@N04/sets/72157601954673258/show/). I suggest you open it, pause it on the first frame and then rearrange your windows if you can so that you can read the notes below at the same time.
[b]Slide 1. A Simple Gliding Note[/b]
"Gliding note" indicated a note of variable pitch. A glissando is a simple gliding note. The one in the illustration is not terribly musical - it's a sine wave, and sounds like a police siren, if you live in a part of the world where police sirens sound like that. We're quite deliberately taking a simple but not completely trivial example, and will look at some ways of deriving new notes from it in interesting ways. Note that, in the interests of simplicity I am assuming this is a mid-section of a longer gliding note - thereby avoiding talking about the start and end of a note. In short - delays take time to get up and running, and tend to linger on at the end, which isn't always desirable.
[b]Slide 2. Pitch Shift[/b]
This is an obvious, but not very exciting way of adapting it. Fixed interval pitch shifters are good but a bit limited - whatever you do they're pretty much going to sound the same. However, we can develop the idea into something more exciting.
[b]Slide 3. Time Shift[/b]
Delay, echo - I prefer "time shift" to highlight its similarity to pitch shifting. They are implemented totally differently, but they both do the same thing - translate a curve on a graph along either the x or the y axis. We can see that this is more interesting than the pitch shift, as it allows a strong relationship between the length of the delay and the tempo of the music being played. It is musically more appealing than the pitch shifter as the intervals between notes varies, but has weaknesses as noted above, and if not used carefully can become overly complicated.
[b]Slide 4. Pitch And Time Shift.[/b]
Wow! Op Art! I've matched the delay to the tempo in a simple relationship and look what happens. You know that is going to sound interesting. This has a ton of potential for further investigation.
[b]Slide 5. Exaggeration[/b]
This is an obvious adaptation of a pitch shift. As noted on the slide it can be implemented by measuring the interval between the current pitch and a predetermined pitch and multiplying. It can also be achieved by observing the current rate of change of pitch and exaggerating it - the "dead reckoning" approach. Each would behave differently with other gliding notes than the one illustrated, so there is room for investigation there.
[b]Slide 6. Acceleration[/b]
This and the final slide are more "artist's impression" than the previous slides. It's been a long time since I could do the maths required to derive the actual equations I was looking for, but these give some sort of idea. The point is, that there is a progression that goes distance, velocity, acceleration, jolt, jounce... (the last two are terms used by, amongst others, roller coaster designers - to make the rides as thrilling as possible they consider jolt - rate of change of acceleration, and jounce - rate of change
Enough of me. Me-time for the last couple of mornings has been drawing graphs. It's kind of Hands Off tidy-up work in a sense - it's the guts of the paper I would have presented at Hands Off if I hadn't been busy organising it, and had the time to really do it properly. This is the Cliffs Notes.
It's a flickr slideshow (http://www.flickr.com/photos/8666613@N04/sets/72157601954673258/show/). I suggest you open it, pause it on the first frame and then rearrange your windows if you can so that you can read the notes below at the same time.
[b]Slide 1. A Simple Gliding Note[/b]
"Gliding note" indicated a note of variable pitch. A glissando is a simple gliding note. The one in the illustration is not terribly musical - it's a sine wave, and sounds like a police siren, if you live in a part of the world where police sirens sound like that. We're quite deliberately taking a simple but not completely trivial example, and will look at some ways of deriving new notes from it in interesting ways. Note that, in the interests of simplicity I am assuming this is a mid-section of a longer gliding note - thereby avoiding talking about the start and end of a note. In short - delays take time to get up and running, and tend to linger on at the end, which isn't always desirable.
[b]Slide 2. Pitch Shift[/b]
This is an obvious, but not very exciting way of adapting it. Fixed interval pitch shifters are good but a bit limited - whatever you do they're pretty much going to sound the same. However, we can develop the idea into something more exciting.
[b]Slide 3. Time Shift[/b]
Delay, echo - I prefer "time shift" to highlight its similarity to pitch shifting. They are implemented totally differently, but they both do the same thing - translate a curve on a graph along either the x or the y axis. We can see that this is more interesting than the pitch shift, as it allows a strong relationship between the length of the delay and the tempo of the music being played. It is musically more appealing than the pitch shifter as the intervals between notes varies, but has weaknesses as noted above, and if not used carefully can become overly complicated.
[b]Slide 4. Pitch And Time Shift.[/b]
Wow! Op Art! I've matched the delay to the tempo in a simple relationship and look what happens. You know that is going to sound interesting. This has a ton of potential for further investigation.
[b]Slide 5. Exaggeration[/b]
This is an obvious adaptation of a pitch shift. As noted on the slide it can be implemented by measuring the interval between the current pitch and a predetermined pitch and multiplying. It can also be achieved by observing the current rate of change of pitch and exaggerating it - the "dead reckoning" approach. Each would behave differently with other gliding notes than the one illustrated, so there is room for investigation there.
[b]Slide 6. Acceleration[/b]
This and the final slide are more "artist's impression" than the previous slides. It's been a long time since I could do the maths required to derive the actual equations I was looking for, but these give some sort of idea. The point is, that there is a progression that goes distance, velocity, acceleration, jolt, jounce... (the last two are terms used by, amongst others, roller coaster designers - to make the rides as thrilling as possible they consider jolt - rate of change of acceleration, and jounce - rate of change