The double letters are:

They each have two sounds, hard[1] and soft. They are also unions of opposing principles:[2]

• Beth (ב) is wisdom [חכמה] and folly [אולת].
• Gimel (ג) is wealth [עושר] (riches) and poverty [עוני].
• Daleth (ד) is seed [זרע] (fertility) and desolation [שממה].
• Kaph (כ or ך) is life [חיים] and death [מות].
• Peh (פ or ף) is dominance [ממשלה] (rule) and servitude [עבדות].
• Resh (ר) is peace [שלום] and war [מלחמה] (evil).
• Tau (ת) is grace [וחן] and ugliness [כיעור].

In the Gra and Ari Trees, the double letters are vertical paths communicating between Sephiroth in adjacent Pillars.

Please note that the assignations above are those taught by the Gra. That system assigns their correspondences by matching their order in the Alef-Bet to the order in which they are named in chapter 4 of Sefer Yetzirah. Hermetic Qabalah assigns them differently, saying that:

• Beth is life and death
• Gimel is wisdom and folly
• Daleth is peace and war
• Kaph is riches and poverty
• Peh is grace and ugliness
• Resh is fertility and barrenness
• Tau is rule and servitude

The double letters change their pronunciation based on how they are written. With a dot (called a dagesh) in them, they are hard -- B or T -- and without it they are soft -- V or Th. … Or at least this was true of them all in Biblical times. We know there was a hard Resh (ר) because it appears in the Bible, but today no one knows how it was pronounced. Modern Hebrew treats Resh like a laryngeal, not a double. Similarly, modern Hebrew is in the process of losing the soft Tau (ת), no longer distinguishing between the T and Th sounds as it once did.

Read more about:

Alef-Bet | Sefer Yetzirah | letter classes | Gra | Ari