Contain complex query date_format and between - cakephp

Question

Code Update 2017/07/20
I followed the recommendations of #Arcesilas (here) with the use of date_format of MySQL.
I upgraded my data structure by merging start_month and start_day (ex 2017-01-16 = 0116)
[...]
->contain([
'Bookings',
'Amenities',
'Periodicities' => function ($q) use ($check_in, $check_out) {
$start = $q->func()->date_format([
'Periodicities.start' => $check_in->format('Ymd'),
"'%m%d'" => 'literal'
]);
$end = $q->func()->date_format([
'Periodicities.end' => $check_out->format('Ymd'),
"'%m%d'" => 'literal'
]);
return $q
->where(function ($exp) use ($start) {
$exp->between($start, 'Periodicities.start', 'Periodicities.end');
return $exp;
})
->orWhere(function ($exp) use ($end) {
$exp->between($end, 'Periodicities.start', 'Periodicities.end');
return $exp;
});
}
])
[...]
Cakephp SQL Log
SELECT
PeriodicitiesRooms.id AS `Periodicities_CJoin__id`,
PeriodicitiesRooms.periodicity_id AS `Periodicities_CJoin__periodicity_id`,
PeriodicitiesRooms.room_id AS `Periodicities_CJoin__room_id`,
PeriodicitiesRooms.price AS `Periodicities_CJoin__price`,
Periodicities.id AS `Periodicities__id`,
Periodicities.name AS `Periodicities__name`,
Periodicities.start AS `Periodicities__start`,
Periodicities.end AS `Periodicities__end`,
Periodicities.price AS `Periodicities__price`,
Periodicities.modified AS `Periodicities__modified`
FROM
periodicities Periodicities
INNER JOIN periodicities_rooms PeriodicitiesRooms ON Periodicities.id = (
PeriodicitiesRooms.periodicity_id
)
WHERE
(
date_format('20170726', '%m%d') BETWEEN 'Periodicities.start'
AND 'Periodicities.end'
OR (
PeriodicitiesRooms.room_id in ('1', '2', '3')
AND date_format('20170720', '%m%d') BETWEEN 'Periodicities.start'
AND 'Periodicities.end'
)
)
This does not give me any more result because ORM of CakePHP adds apostrophes (') to the end of BETWEEN' Periodicities.start 'AND' Periodicities.end'
If in my database I paste the CakePHP query without the apostrophes (') it works. Do you have any idea what changes to make to the end of my query so that it looks like this: BETWEEN 'Periodicities.start' AND 'Periodicities.end' to BETWEEN Periodicities.start AND Periodicities.end ?
'SELECT * FROM periodicities WHERE date_format(' . $check_in->format('Ymd') . ', '%m%d') BETWEEN start AND end'

Answer 1

EDIT
From your comment I see you don't want to store years because the year is not relevant.
In that case, you can still store all your dates as a specific year and then hard code that year into the query. I have modified the query to use year 2000.
ORIGINAL
The conversation is unclear to me but I will attempt to answer the question I believe you are asking.
It appears you want to know how to find Periodicities between the checkin time or Periodicities between the checkout time.
It also appears you want to know the best way to store the dates.
Just store the dates as dates. No need to make it complicated
Between is also overly complicated.
This will do what you need it to do without being confusing.
[...]
->contain([
'Bookings',
'Amenities',
'Periodicities' => function ($q) use ($check_in, $check_out) {
$q->where([
'Periodicities.start >' => $check_in->format('2000-m-d'),
'Periodicities.end <' => $check_in->format('2000-m-d')
]);
$q->orWhere([
'Periodicities.start >' => $check_out->format('2000-m-d'),
'Periodicities.end <' => $check_out->format('2000-m-d')
]);
return $q;
}
])
[...]

Answer 2

I solved my problem with this query :
->contain([
'Bookings',
'Amenities',
'Periodicities' => function ($q) use ($check_in, $check_out) {
$q->where(function ($exp) use ($check_in, $check_out) {
$exp->gte('Periodicities.start', $check_in->format('md'));
$exp->lte('Periodicities.end', $check_out->format('md'));
});
return $q;
}
])
I keep storing in database dates with the month and day md format
Ex: 0901 < 1030
01 September < 30 October