How to determine which type of transposition cipher I have? I have some ciphertext that I have determined using frequency analysis to be most likely encrypted using a transposition cipher, as the letter frequencies are similar to plain English language text. I believe the next step should be to determine which transposition cipher it is, but I don't know how to do that.
Am I right to assume that what I have is definitely a transposition cipher? And if so, how do I determine which transposition cipher it is?
For what it's worth, here is the ciphertext I have. But (as asking for decryption of a specific ciphertext would be off-topic here) I'm interested in general techniques that could be applied to any ciphertext.
CTCRAL TYNIH ORFLN NLONH LTOWH SLINI IIEER NOENT AHRNE NWAAM CTEAK ERDHH
DMIOD AEINA YTFEI IEINM FSTGI UOVED GLMEI YINEE EYNGS BSCRA TUVGU UEIEV
OHIDA TISRO IEEEA TETMG RSFHD DHARA ICSEU EVHNS WIYII YIRND TFVCX GSMVL
IUELH RETRG NNREC ONEYI OTLUN SBRSH AIIEE TTOOI ESCLS KWSLE ETGHN EOTNU
STGIM EEACR TAEEN LAPEH RHNHE GWIEH EWRNN UETHT EPREN SDNFW YUFGI TUEAY
ETLMR TBIPW UPANI OEFUS RSEAT NRTDP RENOA EETIL HNNAD HECWD TTILI UECDT
DTLAM RQERS MVVTR HYTYO UFOAM ONCNS NFSST EEVHA YHERE OEONM RE- GAO HCVLO
COIYT HSENZ FAHHL LYRII USBAS IEHEO IOSOT TILAI EOGOT ETEHL DEENP AEISP
IDDMT RHNBI EEEMO NTIOE ISGZE SEAEE IDLNI TRTTD RIDUT PTNIY NIYNQ MMMIR
BDAOI AYDOT DTELG HAIHO BDESA RSYLN HNWCN TRLRE NTAMN AESEI EHAEY NHGMO
REFOT TFTUP AEREE HTONG OISHT TVEHO MSEFO OLINE TOLET SOATR AERTC TGEGT
STTNA ONNTG OHAIA TYUOT IIARN TENCO TKGAU TSEHH EIBWO SDTUW INDTR UECHC
RSEAT DEOEW ENWFA ELGKM
However how do I determine which transposition cipher I would need to use? Am I right to assume this is definitely a transposition cipher also?

As you found out that the ciphertext has a similar frequency to the English letter frequency. This can lead to lots of possibilities

It can be a shift cipher, that is the generalization of the Caesar cipher $$c = m + k \bmod 26.$$ In the Caesar cipher, the $k=3$ is fixed. There are at most 26 candidates to test, not so far.

It can be a permutation cipher, that is there is a permutation $\pi$ on the alphabet that permutes the letters. The 1000 years old frequency attack work on this. You need to swap the top three letters and try to reveal some other. Since you have a long message this should be working very well. Actually, the substitution cipher is also a permutation cipher.

It can be any of the transposition ciphers since they are keeping the letter frequency, too.

Rail fence cipher
Try some possible rail lengths. It is a very weak cipher. The below is the Rail Fence histogram with rail size 3. This is exactly the same as Moby Dick's frequency since the letters are not permuted, just the positions changed. The same applies other transposition ciphers since they just transpose.






Scytale
The cylinder size cannot be too long. try some possible sizes.

Route cipher
Row size and route to read the letters are required. Don't expect the road to be too complex. Set a row size and test for well-known routes. spiral inwards.outwards, clockwise/anticlockwise, starting from the top right/top left, bottom right/ bottom left, etc.

Columnar transposition


 Guess the column size and look for digrams to determines the permutation on the columns.


Double transposition
This is hard to attack, it takes the result of the column transposition and applies another transposition. Still, we have computers, and once can test all values up to some limit and check for the string in the decrypted text. Linux's strings command can be helpful to distinguish those.

Myszkowski transposition
Just a modification of the Columnar transposition that deals with the reoccurrence of a letter in the key. Increases the key space a little bit.

Disrupted transposition

Grilles
This is one of the hardest ones in this series since the attacker needs to form the grille. Gaines book's chapter is advised. It has some variants.


We don't expect combinations since the combinations can hide the frequency.

Vigenère cipher
It is not expected to be Vigenère cipher, however, the Kasiski test can be used to test.


Online Tools

Crypto Tools 2
dCode.xyz
boxentriq


I also did;

The light gray is from the Moby Dick text, the medium grey is your text.
In a bar, a light grey on the top means that moby dick has a higher frequency, a medium grey on the top means that your text higher frequency, a sample Python code, and Moby Dick is here.
From here we can simply say that it cannot be Caesar or Shift Cipher since the frequency is very close to the real English frequency!.