If you map one audio sample in Logic's EXS24 from C1 to C4 not only will you be able to create a pitched instrument, you will also notice the duration of the sample will be altered. The higher the pitch, the shorter and duration, the lower the pitch the longer the original sample will be stretched out. Now, while this may be what you wish to achieve, there will be times you want to create a pitched instrument without the speed up/slow down effect. There are 3rd party Samplers and applications that can do this, but here's one way to get this working in Logic 9.
For this example I'm using a short sound of a crow from the Apple Loops library that comes with Logic studio. In order to create a pitched sounds without affecting duration, we're going to create multiple samples that are already pitched and import these into the EXS24.
Position your audio region on Bar 1 1 1 1 and choose Region > Repeat Regions
Because my region is so short I've chosen to repeat the region on every Beat. (Choose the correct Adjustment according to the length of your audio region). I've also chosen to create a one octave (12 note pitches) sampler instrument, again, create as many as you need.
Insert the Pitch Shifter II plugin on an Insert slot. Set it's Mix to 100% and the Semi Tones to 0.
You can experiment with the Pitch Shift type (Drum, Speech and Vocals). I find Vocals works pretty well for most monophonic sounds.
The idea here is for every region to be one Semi Tone higher than the previous one. Using Automation will make this easy to achieve.
Draw in the Automation for the Semi Tones parameter as shown in the image above. Click to create two nodes at the beginning of each region and drag the automation line up one step. It should resemble a staircase. If you need to create more than one octave, you can start from -12 Semi Tones up to +12. If you need more octaves, you can insert a second Pitch Shifter II on the channel strip.
You may find using the Marquee Tool a quicker way to create automation as explained in this article.
Once you're finished creating the automation hide Automation view "A" and listen to the results. Now we need to render the effects to audio before importing these regions into the EXS24 Sampler. The easiest way is to click on the Track Header and then choose: Track > Bounce Track in Place
Make sure to disable the checkbox "bypass effects plugins" as we do want the pitch plugin automation rendered to the audio file.
Now we have a single audio file. We need to divide the audio region into multiple regions, one for each pitched sound sample. Using the Scissor tool could take a long time to go through and split the regions. Alternatively, to divide it into multiple regions of the same length, Option-click where you'd like the first cut to be as shown in the image below:
Select all the regions you have just created. (A quick way to do this is to click on the Track Header - all regions on the track, or within an active Cycle range, will be selected).
Next choose: Audio > Convert Regions to New Sampler Track
From the New Sampler Track dialogue window you'll need to set Create Zones From: Regions and set the Trigger Note Range as desired.
Click OK when you're done.
The audio regions will be muted and a new Software Instrument Track is created with the samples already loaded into an EXS24 Sampler Instrument. As an additional bonus there is a MIDI region which corresponds to the Audio we converted on the above track. In this case, I'm not going to keep the region.
Test out your Sampler Instrument and you'll find the duration of the notes is constant. They are also pitched across the Note range you specified and even better, as a Sampler instrument it's easier to play and program sequences.