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Hi patrickjones, because the issue has occurred after doing an update I reccommend running a software repair on your handset to see whether that helps - it is quite likely to.
To do this you just need access to a computer with an internet connection.
You will need to download either PC Companion or Bridge for Mac.
Note: a software repair will delete all user data, to back up your phone:
using PC Companion
1. Go to Support to install PC Companion on a Windows computer.
2. When installed, start PC Companion on the computer.
3. Connect your phone to the computer using a USB cable.
4. Click Start under Backup & Restore.
5. Follow the on-screen instructions.
(Exactly what contents will be backed up may differ depending on phone model.
You can view detailed information about this as you follow the steps in the Backup & Restore wizard).
using Bridge for Mac
1. Launch Bridge For MAC.
2. Select "Back up your Xperia device".
3. Select the data you wish to back up from your device (the windows can be expanded for more detail as below; then select "Next".
4. The backup will now be in process, do not disconnect the phone while this runs.
Running the software repair on PC Companion:
1. Install and open PC Companion then select Support Zone.
2. Phone Software Update.
3. Start.
4. Repair Phone
5. Continue
6. Accept data removal
7. Next
8. Wait for prepare
9. Select Phone
10. Follow the connection steps
Running the software repair on Bridge for Mac:
1. Launch Bridge for MAC without the handset connected.
2. On the Main Window select "Xperia > Repair Xperia Device".
3. Ensure the phone is charged and select "Ok" in the following window.
4. Select Continue on the following page.
5. Wait until the initialising step is finished the continue as below.
6 . Select your model of phone from the list that appears
7. Follow the connection steps that appear, ensuring that you are holding the relevant button down before during and after the connection phase until the update/repair begins.
Hope this helps, keep us updated 
Do you experience this with the walkman app or a third-party app?
If you look here,you might find the same issues:
/t5/Xperia-Z1-Compact/Lollipop-update-is-a-mixed-bag/m-p/968018#M14527
/t5/Xperia-Z1-Z1s/Z1-issues-after-5-0-update/td-p/968554/page/16
Which software version do you have in your Xperia Z1?
Check under Settings > About phone > Software version
Best regards,
Have you check the Settings via the Music/Walkman app - Settings then Sound effects then Sound enhancements unless you are on LP then these are as far as I'm aware incorporated or maybe found in Settings then Sound and notifications then Audio settings