The downtime activity ‘Training’ states that receiving training in a language or tool typically takes at least 10-INT modifier workweeks, although negative intelligence modifier has not effect. Training also costs 25gp per week.
Players may occasionally wish to try to learn on the go, picking up new skills as part of applied trial and error, or by devoting a few hours to studying the craft each long rest.
Without the benefit of a teacher, a player must have a sufficiently detailed manual in lieu of instruction, which are typically very hard to come by. Guilds and learning institutions typically jealously guard their trade secrets. Such a manual will be worth at least 250gp if purchased at market price, if it cannot be stolen or found amongst encounter loot.
Practice requires sustained dedication. Each long rest, while not exhausted or ill, or doing other tasks such as keeping watch, or otherwise distracted, a PC may make an intelligence check and expend at least 5gp worth of materials. The PC keeps a running total of the sum of all their intelligence checks.
When the PC reaches a total of 200, they can be considered conversant in a language but not literate enough to read or write more than a sentence or eloquent enough to make convincing persuasion or deception checks, or capable enough with a tool or instrument to attempt to use it under pressure without disadvantage but not strictly proficient. For most PC, this level of aptitude will be sufficiently accomplished, and will enable them to complete their training faster using less downtime when the opportunity arises.
When the PC reaches a total of 500, they can be considered proficient in the language or tool, and gain all the usual benefits thereof.
Expertise in an ability skill or tool is usually the purview of specific classes, namely the Rogue. However, certain players may be dissatisfied with the idea that a Rogue may be able to achieve a higher ability check on Arcana compared to a Wizard who has dedicated their life to understanding its intricacies.
Typically, if a player gains access to proficiency in a skill or tool from two or more sources, for example a racial feature and a background feature, they are prevented from ‘doubling up’. However, I allow players to double up on skills as a way of gaining expertise in that skill.
I also allow, and would encourage players to take expertise in tools, instruments, and languages that they otherwise would not.
The rules for adding and multiplying proficiency bonuses say:
<aside> 🗒️ Occasionally, your proficiency bonus might be multiplied or divided (doubled or halved, for example) before you apply it. For example, the rogue's Expertise feature doubles the proficiency bonus for certain ability checks. If a circumstance suggests that your proficiency bonus applies more than once to the same roll, you still add it only once and multiply or divide it only once.
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Since I allow adding Proficiency from multiple sources to gain the equivalent effect as Expertise (which the PHB describes as doubling the proficiency bonus), I also allow instruments, tools, and languages to have a similar effect, with similar limitations.
The rules for proficiency in musical instruments say:
<aside> 🎵 If you have proficiency with a given musical instrument, you can add your proficiency bonus to any ability checks you make to play music with the instrument.
Performance: Your ability to put on a good show is improved when you incorporate an instrument into your act.
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Therefore, if you are proficient in Performance make a Performance check with a musical instrument that you are proficient in, you can add your proficiency bonus again to that roll - you effectively have ‘expertise’ for this roll. However, as implied by the proficiency rules above, you can only add or multiply once. If you have expertise in Performance AND proficiency/expertise with a musical instrument, you still only add your proficiency bonus twice.