What is the fewest cycles to clear Majora's Mask, without exploiting glitches?

This is the glitchless speedrun, which appears to use 2 cycles (counting the prologue cycle):

Less cycles should not be possible since you have to get the Ocarina on the first.

The first cycle (to get the ocarina) is completely necessary.

Using the song of inverted time, I've been able to get Temples 1-2 in a single cycle, Great bay as well as the Elegy of Emptiness in another. Stone tower temple still took most of the last cycle, though.

The downside of this is you only have 7 hearts for the final battle (3 to start, and one from each boss)

I died to majora's wrath during the final battle, triggering a GO, and the start of a new day, which means my best run ever clocks in at 5 cycles.

1. Getting the Ocarina
2. Woodfall & Snowhead
3. Pirates Fortress/Great Bay & Ikana Valley/Castle
4. Stone Tower Temple + First attack on Majora
5. Majora take 2.

Assuming you can manage to not die to Majora with only 7 hearts an no faries (no time to go get them) , you could pull it off in 4 cycles.

The things that you do when the save flash has gone bad...

Without any glitches, I beat the game at least once every few years with 100% completion, meaning all stray fairies, all heart pieces, all masks including the Fierce Deity's Mask and having completed all other "missable" events like reading Lulu's journal within six cycles, not including the "Prologue" and the second round with Majora, just to be sure I keep all my masks. This is possible in both the N64 version and the 3DS version, but the speeding up of time with the ISoT in effect makes reliance on the saving functionality in the 3DS version optional, although I won't truly count myself a master until I can do it without needing to soft reset even once. As for beating the game in one cycle, regrettably, it's no longer possible. Even if you manage to take a perfect route, avoid every enemy, leave the Woodfall Temple until a later time and never pause for even a second (and yes, I grinded until I got to that point), you still can't get the Fire Arrow before 8 pm on the First Night, which is the cut-off for being able to get Epona. The biggest problem as I see it is having to traverse the Mysterious Woods twice and then having to wait forever and a day for the boat tour to reach the Deku Palace, although the floating platforms in the Inner Garden, the sluggish speed of the Deku's flight, the omnipresence of those annoying Dragonfly monsters and a few other little gimmicks slow you down just a little too much, even for someone talented enough to defeat the Dinolfos mini-boss in six seconds.

I had to say that using the save state feature on the Switch I have managed to 100% Majora's Mask in 4 cycles.

Cycle 1 - 500 rupees in bank and 4 heart pieces

Cycle 2 - beat all temples, Anju and Kafei, gilded sword (yes, it can be done) and every collectible mask except Blast and All Night

Cycle 3 - get the fairies in all temples and do the last two masks

Cycle 4 - do Anju/Kafei again to get the last bottle

In cycles 3 and 4 there's actually quite a bit of spare time to pick up those heart pieces, biggest bomb bag and quiver and buy all the maps.

So the answer is actually 2 cycles to beat the game, or 4 cycles for 100% completion, both including the Deku intro.

There was one thing that tripped me up on of my attempts though: it was cycle 4 and I hadn't got the heart piece in Ikana graveyard on night 2. I was doing the Anju/Kafei quest so I couldn't get the second all night mask heart piece without missing either the meeting with Anju or the trip to the graveyard. So annoying.

I just completed it in three cycles, 2 uses of the song of time, not including the Deku reset, no glitches were used and I finished with 14 hearts. This was the 3DS version and requires rushing everywhere and using any extra time between resets to get heart pieces.

It's fairly trivial to beat the game, glitchless, in one cycle (excluding the prologue cycle, which is normally not counted) and even do it before the end of the second day. The only time-sensitive obstacles are Epona (powder keg license by end of first day) and the Song of Storms (Ikana Graveyard on first night). The key is understanding that you only need the dungeon items to progress to the next dungeon (glitchless): the bow is used as normal, and you can use the fire arrows to get into the powder keg workshop in winter.

100% requires three cycles. On the first, you must rush to Great Bay and clear the Ocean Spider House on the first day, while also stopping Sakon's robbery at night, so you can buy the All-Night Mask on the first cycle. On the second, you complete the entire Anju and Kafei side quest for the Couple's Mask and also deliver the Special Delivery to Mama to one of the two possible recipients. The third cycle requires you to deliver the Special Delivery to Mama to the other recipient, along with using the All-Night Mask and Couple's Mask to get their respective heart pieces. An alternate path would be to get the Couple's Mask on the first cycle and All-Night on the second, which despite the frequent returns to Clock Town may actually be easier than getting all the way to the Hookshot and then clearing the Ocean Spider House on day 1. Nothing else in the game is mutually exclusive to anything else, so it's just a matter of being fast and knowing the game well.

It is technically possible in all versions of the game to beat it in a single cycle not including the deku one where all you do is get back your ocarina. It is very hard to pull off as you must have the game known and its location known like the back of your hand.

N64, Gamecube, Wii Versions

Day 1
Your objective is to get epona before night 1
Play inverted song of time immediately 6 am
Song of Healing
Buy a bomb bag and several deku sticks
Southern Swamp
Get red potion
Boat tour
Deku palace 8:15 am
Sonata
Woodfall Owl statue 10:30 am
Hero's Bow 12 pm
Mountain Village
Lens of truth (I also highly recommend you go talk to the goron baby in goron shrine. 
  Trust me it saves time)
Goron Mask 2 pm
Snowhead owl statue 3 pm (Note you must be in snowhead temple before 3:30 pm otherwise 
  it is very unlikely you will get to romani ranch before night 1.)
Fire Arrows 4 pm
Powder Keg
Epona (MUST BE OBTAINED BEFORE NIGHT 1)
Garo Mask (Only if it isn't night 1 yet after you obtain epona otherwise this can wait 
  till day 2)
Night 1
From here is basically won as long as you know the rest of the game like the back of 
  your hand so congratulations
Song of storms
Day 2
Day 3 Complete the game normally
Final hours Wreck MAJORA

3DS

This one involves a few glitches to be possible plus the inverted song of time is nerfed making this one even harder to single cycle.

You must get red potion, sneak into mountain village with a precise sidehop, do everything normally to get goron mask, grab hot spring water and thaw the water hole in mountain village, Goron chuchu boost to great bay get the zora mask and activate the owl, go back to mountain village collect hot spring water from the watering hole you thawed and go to the powder keg certification place in goron village it is frozen but zora link has a couple of frames to get the hot spring water to melt the ice. go to romani ranch get epona you can't complete the mini game because you don't have the bow but it does not matter because she teaches you epona's song anyway after you get epona link will be swordless untill you do one of 2 things figt skull keeta that resets the story back on track or simply go fishing at a fishing hole.

After that the game is yours to conquer but just remember that you don't have a lot of time.