If you want to avoid some of the jiggery pokery you could do something like:
%%%%%%%%%%%%%%%%%%%%
\version "2.25.12"

#(define ((time-alternate-time upa downa upb downb) grob)
   (grob-interpret-markup grob
                          (markup #:override '(baseline-skip . 0) #:number
                                  (#:line (
                                            (#:center-column (upa downa))
                                            (#:center-column (upb downb)))))))

global = { 
  \override Score.TimeSignature.stencil = 
  #(time-alternate-time "6" "8" "3" "4")
  \time 6/8 s2. 
  \omit Score.TimeSignature
  \repeat unfold 5 { 
    \time 3/4 
    \set Timing.beamExceptions = #'() %so 3/4 isn't beamed in whole measures
    s2.
    \time 6/8 s2.
}}

\score {
  \new Staff <<
    \global
    { \repeat unfold 66 a'8 }
  >>
}
%%%%%%%%%%%%%%%%%%%%%%%%%

> 1 feb. 2024 kl. 23:52 skrev Raphael Mankin <[email protected]>:
> 
> Thank you, that worked a treat. Though I also had to add a "\time 6/8" in 
> order to get automatic bar lines inserted. "\time 3/4" produced wrong beaming 
> in the 6/8 bars, and I can see that I may have to do some jiggery pokery to 
> the beaming in 3/4 bars if, for example, I have 4 or more quavers.
> 
> On 01/02/2024 20:10, Knute Snortum wrote:
>> On Thu, Feb 1, 2024 at 10:50 AM Raphael Mankin <[email protected] 
>> <mailto:[email protected]>> wrote:
>>    I have music with alternate bars in 3/4 and 6/8. The usual way to
>>    indicate this is to  put both  time signatures at the start, but  I can
>>    find  no way to do this.
>>    I have tried "\time 3/4 <> \time 6/8", but I only get the last one.
>>    Note, this  is not a compound time of 3/4+6/8, but alternating time
>>    signatures.
>> I think this is what you are looking for.  I'm not sure where I found the 
>> code so I can't give credit to its author:
>> %%%
>> #(define ((time-alternate-time upa downa upb downb) grob)
>>    (grob-interpret-markup grob
>>      (markup #:override '(baseline-skip . 0) #:number
>>        (#:line (
>>            (#:center-column (upa downa))
>>            (#:center-column (upb downb)))))))
>> % and use it like this (5/8, 4/8 in this case):
>>   \override Score.TimeSignature.stencil =
>>     #(time-alternate-time "5" "8" "4" "8")
>> %%%
>> --
>> Knute Snortum
> 
> -- 
> https://saturday-october-seven.com/


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