I suspect there are many parts to your question, and I'm not sure I understand exactly what you are asking.
First of all you can't display raw analog values on a display. I.e. the Teensy is not an oscilliscope directly (though you can run programs that make it act as a scope).
You have to read the audio into digital format. Then you do what ever transformation you want on the digital form. To print out the value on to the display, you have to use a library that takes the digital signal and plots it on the display. You will need to dive into the display library to get more information about this.
To hook up a display there several different ways to connect the display. The two most common methods are I2C and SPI.
In the Teensy 4.1 environment, the main I2C and SPI use certain pins:
- The main I2C bus uses pins 18 (SDA) and 19 (SCL), plus ground and 3.3v;
- The main SPI bus uses pins 11 (MOSI), 12 (MISO), and 13 (SCLK), plus possibly several other pins (CS, D/C, and possibly reset);
- Note for older Teensy 3.x boards, the audio adapter forces you to use alternate pins for SPI, but the Teensy 4.x uses the standard pins.
In general, I2C is slower than SPI. One advantage of I2C is it is a shared bus that doesn't need additional pins to add more devices. Each device has an address, and as long as you don't have devices with the same address, things should work. Note, the audio shield has 2 I2C devices on it that allows the audio library to control the SGTL5000 on the audio adapter.
SPI uses a separate pin (CS) that says you are talking to one particular device (rather than having an address like I2C). That means to add 2 SPI devices, you need to have at least 2 CS pins. SPI devices often have 2 other pins (D/C that speeds up switching between data and command modes, and a reset pin). This can mean you would need to allocate 3 fixed pins plus 3 pins per device on the SPI bus (i.e. 2 devices might need 9 pins).
Note, some of the cheaper 128x128 displays do not have a CS pin. This means that device must be the only SPI device. This might be problematical on the audio shield since the audio shield has 2 other SPI devices (the SD card reader and the flash memory port). Now, you probably won't be using either of these on the 4.1, since the 4.1 has a faster micro SD card reader and pads for soldering the flash memory, but I don't know if the existence of the other SPI devices would cause problems for those cheap displays without a CS pin.
If you are trying to use several SPI devices at the same time on the same SPI bus, there are some details you probably need to look at. For your example, it does not sound like you might have multiple SPI devices.
In terms of speed, since the Teensy 4.1 is rather fast, you can sometimes drive a slow display faster than its specs, and in your code, you may need to slow down the bus. For example, I found in the past with the the Teensy 3.5/3.6 that I needed to limit the SPI display speed to 19Mhz, as the devices just code not keep up if I pushed the speed faster.
Obviously for your example, you would worry about correctness first, and then if it is correct worry about pushing the speed up. I was using a program called uncanny eyes that was trying to drive two OLED displays as fast as possible, with each display displaying an eye pattern. Generally the TFT LCD displays would run faster than the OLED displays (but the OLED displays look better and you can see the image at a wider angle).
I would break down your program into two parts. The first part is to get the audio input, and just print it to the USB serial port. The second part is with the audio input, then graph it to your display.
Note, there is an audio example (Part_3_03_TFT_Display) that reads an audio WAV file and displays it on the ILI9341 display that PJRC sells. Unfortunately, I looked at it, and it looks like it needs some changes for the Teensy 4.1 (it was written for the Teensy 3.2, and unfortunately the pin assignments are different between the 3.x and 4.x series in terms of audio stuff).