What meditation practice(s) are encompassed by 'asubha' (non-beautiful)? What meditation practice(s) are encompassed by 'asubha' (non-beautiful)?
I've heard one teacher say that in the EBT (early buddhist texts), asubha practice only refers to 31 body parts, and later Theravada expanded it to include 9 cemetary corpse decay, and perhaps other practices as well?

Does anyone know for sure? In the pali suttas, most of the references to asubha do not specify a specific meditation practice(s). 

Is AN 10.60 the only place where asubha is specifically assigned to 31 body parts?

I'd prefer to believe asubha meditation encompasses more practices than just the 31asb, unless there is conclusive evidence. Simply because in an oral tradition where memory of teachings is mandatory, it's helpful when a label, 'asubha' in this case, covers all the practices that could qualify for doing that job.

We know that the purpose of asubha (ugly or non-beautful), is to counter the effects of subha (beautiful) have in inducing lust/passion/desire for sensual pleasure, especially for sex.

Clearly the stages of decomposition of corpses, the discharge from the 9 orifices of the body, all qualify in accomplishing that goal.

AN 10.60 defines the practice of asubha as 31 body parts contemplation:


  Katamā cānanda, asubhasaññā?
  And what is the perception of ugliness?
  Idhānanda, bhikkhu imameva kāyaṃ uddhaṃ pādatalā adho kesamatthakā tacapariyantaṃ pūraṃ nānāppakārassa asucino paccavekkhati:
  It’s when a monk examines their own body up from the soles of the feet and down from the tips of the hairs, wrapped in skin and full of many kinds of filth.
  ‘atthi imasmiṃ kāye kesā lomā nakhā dantā taco, maṃsaṃ nhāru aṭṭhi aṭṭhimiñjaṃ vakkaṃ, hadayaṃ yakanaṃ kilomakaṃ pihakaṃ papphāsaṃ, antaṃ antaguṇaṃ udariyaṃ karīsaṃ, pittaṃ semhaṃ pubbo lohitaṃ sedo medo, assu vasā kheḷo siṅghāṇikā lasikā muttan’ti.
  ‘In this body there is head hair, body hair, nails, teeth, skin, flesh, sinews, bones, bone marrow, kidneys, heart, liver, diaphragm, spleen, lungs, intestines, mesentery, undigested food, feces, bile, phlegm, pus, blood, sweat, fat, tears, grease, saliva, snot, synovial fluid, urine.’
  Iti imasmiṃ kāye asubhānupassī viharati.
  And so they meditate observing ugliness in this body.
  Ayaṃ vuccatānanda, asubhasaññā.
  This is called the perception of ugliness.


summary of my research on this so far:
(lots of hyperlinks embedded within source link)
http://lucid24.org/tped/a/asubha/index.html

a-subha ‍ = un-attractive
✅in EBT meditation, it refers to 31asb‍ body parts contemplation. See AN 10.60, AN 6.29.
⚠️300+ years after EBT, in Vimt. and Vism., Theravada re-defines asubha meditation to refer to 10 stages of corpse decay, and they reclassify 31asb‍ under kāya-gatā-sati ‍. It's important to know this, because in EBT suttas, an instruction to "develop asubha" is frequently mentioned, but without detail (examples: SN 8.4, SN 54.9). 31asb is immediately accessible, corpse contemplation considerably more complex.
• What's the purpose of asubha meditation? To counter perversions of our inverted perception AN 4.49, SN 8.4.
• But be careful, this is an advanced practice. Best to first have foundation in breath meditation SN 54.9.
• SN 12.61 and SN 12.62 is the more general case of seeing 4 elements via dependent origination 12ps as not being worth clinging to.
The core buddhism's meditation is not about body parts or anything related to outer world. It's always about the dependent co-arising. 

Below is about the uninstructed run-of-the-mill person from Assutava Sutta


  "Monks, an uninstructed run-of-the-mill person might grow disenchanted
  with this body composed of the four great elements, might grow
  dispassionate toward it, might gain release from it. Why is that?
  Because the growth &amp; decline, the taking up &amp; putting down of this
  body composed of the four great elements are apparent. Thus the
  uninstructed run-of-the-mill person might grow disenchanted, might
  grow dispassionate, might gain release there.


And below is about instructed disciple of the noble ones from same Assutava Sutta


  "The instructed disciple of the noble ones, [however,] attends
  carefully &amp; appropriately right there at the dependent co-arising:


Therefore based on above, the famous asubha meditation conflicts with that sutta. So the reason should be asubha is misinterpreted. 
Explained detailed on Asubha meditation is in Kuddaka Nikaya-1 -&gt; Asubhanupassi Sutta (If anyone found an english reference please add). This says that sabba sankharesu aniccanupassino viharathi That's the abstracted meaning of asubha meditation. (I'm referring to sinhala - pali cannon, sorry I can't translate this to english)

There's another sutta which clearly says that, Noble meditation should not be based on air, fire, water etc. I'll try to find the reference to that as well.

With this you might be confused by now. Yes, most of the meanings are mis-interpreted. The real dhamma is out there now, It will come famous but will take sometime to accept by people.

With Metta...!