1. This I would call "Scientific system" because it comes from Physics. Overtone Analyzer (OA) uses it. Each number means "the number of times the frequency is higher than the base freq.". So, the 1st "overtone" is actually the fundamental tone, because it is "one times the base". We probably all know this physics of overtones.
a) Computer programm OA uses it and some composers too.
b) Every octave (from fundamental) is seen on the first sight, because TWO times anything = anything just octave higher. Octaves from fundamental: 2, 4, 8, 16. Also octaves between overtones are obvious, for example: 3, 6 , 12 (perfect fifths) or 5, 10, 20 (major thirds).
a) Not so "friendly" for Musicians to learn and to read them. I can see in those numbers the intervals - fifths and thirds etc... on first sight because I was no musician when I have learned them. But I know other people having problems during learning it comming from interchanging (perfetc) fifth with 5th overtone, sixth with 6th overtone etc... But we still have some that are "the same" in interval: 7th overtone = (minor) seventh, 8, 9, 10, 11, 12th ovt.have pretty much the same interval as their numbers are.
2. This I would call "Basic System" (or "Emergency System" - this would be good if we would have no other to choose from. Thats why I call it also "Emergency System").
The numbers are nearly the same (like "Scientific Sys.") BUT they are shifted by one. 1st overtone starts with first "real overtone / higher tone" which means one octave higher from fundamental. So, 1st is 2nd(in Sci.S.), 2nd = 3rd (Sci.S.), 3rd ovt. = 4th ovt.(Sci.S.) etc...
I have first met with it in Czech Republic. One well know professor and university teacher (and ethno-musicologist) used it in reply to my message with composition (so we did misunderstood each other about which ovt.is which). Second time I have seen it (short time ago) used by one singer from this OM-Network ;) . This alarmed me, because of that misunderstanding experience from the past:
Thats why I have created this discussion. To help to prevent those "possible conflicts between Ovt.numbering systems" in the future.
If anyone finds another system, please post it here so we can discuss it.
Also we can create a NEW system, which would combine PROS of all available systems ;)
We will see.
Let the discussion begin.