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What is the significance (if any) of a repeated radical in a Kanji character?

I have been learning Kanji for almost a year now. In the early days my
assumption would have been that repeating a radical would emphasise
quantity/intensity/scale in an intuitive way such as with the following
characters:

> # 木 林 森

Now I am starting to come across Kanji with repeated radicals where the
meaning (at least to me) isn't as obvious. I notice they almost always appear
as adjacent pairs.

> # 談 態 曜 歌
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question
kanji etymology radicals
What is the significance of a repeated radical in a Kanji character?
What you are referring to are called 理義字. Radicals containing more strokes are
more likely to emphasize quantity/intensity/scale as you have mentioned: 轟
(roaring), the sound of many carriages. 昌(clear) and 晶(crystal) follow a
similar pattern.

For 談, the two 火 together indicate burning. Together with 言 they would
indicate 'hot conversation' or 'discourse'.

Some 理義字 are merely simplified from the original kanji to repeat the same
radical with no further meaning. Others, such as 曜, used to mean something
else (a flying bird next to the sun = bright), and later came to represent the
contemporary meaning.

This might be a bit above my ability to explain properly. I would just suggest
that sometimes they can be read more literally, sometimes they have evolved
from more literal meanings, and sometimes they are simple representations of
more complex Chinese characters.
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answer
In general, don't overinterpret repeated components. It's inconsistent and
largely a hit-and-miss exercise.

Sometimes they just mean "lots of" the single repeated component, or some
extended meaning from that. For example, in addition to 「木」->「林」->「森」, there
is

  * 「火」( _fire_ ) ->「炎」( _blaze_ )
  * 「屮」( _sprouting plant_ , not used as an individual character) ->「艸」(full character form of 艹, _grass radical_ )
  * 「人」( _person_ ) ->「衆」( _crowd_ ; the bottom was actually originally 3「人」, as can be seen in the Taiwan variant「眾」)
  * 「」( _right hand_ , top left component of「右」) ->「友」( _friend_ , two right hands) 
    * Note that「又」was also originally a picture of a right hand; the meaning _again/also_ is a phonetic loan, and had nothing to do with the character itself.)
  * 「一」->「二」->「三」(trivial example)
  * There are also plenty of Chinese-only examples that I won't mention here.

Other times, they don't have anything in particular to do with the whole
character, like all the rest of your examples.

  * 「[談]{だん}」is just a word meaning _to discuss_ that has a semantic component「言」and a phonetic component「[炎]{えん}」. 
    * There was an ancient variant「譚」that meant and was pronounced exactly the same as「談」; neither「譚」nor「談」, nor other characters which use「炎」as a phonetic component, such as「[淡]{だん}」( _dilute_ ) or「[毯]{たん}」( _carpet_ ), have anything to do with _fire_.
  * 「[態]{た​い}」( _manner_ ; c.f. [態度]{た​いど}, _attitude_ ) has a semantic component「心」and a phonetic component「能」, which had a very ancient alternative pronunciation of「ない」. 
    * The repeated component「匕」doesn't actually contribute to the meaning of「能」at all, because「能」( _ability_ ) was originally a phonetic loan, and cannot be broken down; the original character was a full-fledged picture of a type of bear, where「匕」was the bear's legs:  
[![enter image description
here](https://i.stack.imgur.com/N6bZV.png)](https://i.stack.imgur.com/N6bZV.png)

    * _Bear_ is now written「熊」to differentiate the character from the meaning of _ability_.
  * 「曜」just has a semantic component「日」and a phonetic component「翟」. 
    * 「翟」had an Old Chinese pronunciation ***lˤewk** , while for「曜」, The pronunciation evolved in accordance to **/*lewk-s/** (Old Chinese) -> **/jiᴇuʰ/** (Middle Chinese) -> **よう** (Japanese On'yomi).
    * The repeated component「习」cannot be separated from「羽」, which was originally a picture of _feathers_.
    * 「翟」originally referred to a type of bird:  
[![enter image description
here](https://i.stack.imgur.com/OA8k9.png)](https://i.stack.imgur.com/OA8k9.png)

  * 「[歌]{か}」just has a semantic component「欠」and phonetic component「[哥]{か}」. 
    * 「欠」was originally a depiction of a person with an open mouth:  
[![enter image description
here](https://i.stack.imgur.com/Z8qJI.png)](https://i.stack.imgur.com/Z8qJI.png)  
The meaning _to lack_ is an extension from the original meaning. Other
characters which feature「欠」as a semantic component include 吹 ( _to blow_ ) and
歎 ( _to sigh_ , variant of 嘆).

    * 「哥」itself is an ancient variant of「歌」and is no longer used for the meaning _song_. It is a reduplication of「[可]{か}」, which also originally meant _song_ , but very early on shed this meaning and took on the role of a phonetic loan for _can, be able to, permissible_. These original meanings of「哥」and「可」were entirely lost through the course of history, and you shouldn't view「哥」as "lots of 可".
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answer