Talk:IFDO: Difference between revisions

Line 367:

--[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:52, 8 April 2023 (UTC)

'''Additional thoughts'''

Okay, sorry for how lengthy my side of this thread is getting. But I had some further thoughts overnight. I'll try to keep it brief.

The page I created for [[Arithmetic tuning]]s is like the first ''row'' of the tables I shared above. Like this:

{| class="wikitable"

|+

!

!frequency

!pitch

!length

|-

!arithmetic (''p'' = 1)

|style="background-color: #9fc5e8;" |AFS, OS, EFD, OD

|style="background-color: #ea9999;" |APS, AS, E(P)D

|style="background-color: #ffd966;" |ALS, US, ELD, UD

|}

While your system is like the first ''column''. If you created a central page for them, it'd be called [[Frequency sequence]]s. Again, we overlap on the top-left cell, for AFS. Like this:

{| class="wikitable"

|+

!

!frequency

|-

!super-arithmetic (''p'' > 1)

|''p''FS, ''p''FD

|-

!arithmetic (''p'' = 1)

|style="background-color: #9fc5e8;" |AFS, AFD

|-

!super-geometric (1 > ''p'' > 0)

|''p''FS, ''p''FD

|-

!geometric (''p'' = 0)

|style="background-color: #ea9999;" |GFS

|-

!sub-geometric (0 > ''p'' > -1)

|''p''FS, ''p''FD

|-

!harmonic → "inverse-arithmetic" (''p'' = -1)

|style="background-color: #ffd966;" |IFS, IFD

|-

!sub-inverse-arithmetic (-1 > ''p'')

|''p''FS, ''p''FD

|}

There's no reason to worry about the middle of the table, i.e. where I had "GPS" for "geometric pitch sequence". Because of the diagonal equivalence pattern, it's only necessary to think in terms of possible arithmetic sequences (our system), or possible frequency sequences (your system).

These two systems have reason to coexist. For some people, our system may make more sense. For others, yours may make more sense. Though I repeat, that I think our system is more natural for actual musicians, while yours may be more natural for mathematicians or engineers.

'''A vs E'''

But what my system calls an "EFD", for "equal frequency division", yours calls an "AFD", for "arithmetic frequency division". Per [[Talk:Arithmetic tuning]], Paul, Mike, and I find "arithmetic division" incorrect and prefer "equal division".

But it's not a simple fix for your system, because you're not really speaking about dividing arithmetically, which doesn't make grammatical sense, and that's our concern; you're talking about dividing with respect to the arithmetic mean/progression. Before I understood the relationship between means and progressions, I had suggested "arithmetic-mean-based division", but you noted that your system is as much about progressions as it is about means, and I see that now.

But I do have an observation which might help with this. Since the main new value for your system is how it can fill in between and beyond the values of p = 1, 0, and -1, it's really about power ''means''. And I don't find that "power progressions" are written about much, so I believe that "mean" should take precedence over "progression" here. In other words, I suggest that your system might even better be thought of as the "frequency power mean sequence" system, and indeed AFD would stand for "arithmetic-mean-based frequency division".

Nonetheless, perhaps "frequency power progression tunings" or something like that, with AFD standing for "arithmetic-progression-based frequency division". Not sure. Just suggestions.

--[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:15, 9 April 2023 (UTC)

@@ Line 367: / Line 367: @@
 --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:52, 8 April 2023 (UTC)
+'''Additional thoughts'''
+Okay, sorry for how lengthy my side of this thread is getting. But I had some further thoughts overnight. I'll try to keep it brief.
+The page I created for [[Arithmetic tuning]]s is like the first ''row'' of the tables I shared above. Like this:
+{| class="wikitable"
+|+
+!
+!frequency
+!pitch
+!length
+|-
+!arithmetic (''p'' = 1)
+|style="background-color: #9fc5e8;" |AFS, OS, EFD, OD
+|style="background-color: #ea9999;" |APS, AS, E(P)D
+|style="background-color: #ffd966;" |ALS, US, ELD, UD
+|}
+While your system is like the first ''column''. If you created a central page for them, it'd be called [[Frequency sequence]]s. Again, we overlap on the top-left cell, for AFS. Like this:
+{| class="wikitable"
+|+
+!
+!frequency
+|-
+!super-arithmetic (''p'' > 1)
+|''p''FS, ''p''FD
+|-
+!arithmetic (''p'' = 1)
+|style="background-color: #9fc5e8;" |AFS, AFD
+|-
+!super-geometric (1 > ''p'' > 0)
+|''p''FS, ''p''FD
+|-
+!geometric (''p'' = 0)
+|style="background-color: #ea9999;" |GFS
+|-
+!sub-geometric (0 > ''p'' > -1)
+|''p''FS, ''p''FD
+|-
+!harmonic → "inverse-arithmetic" (''p'' = -1)
+|style="background-color: #ffd966;" |IFS, IFD
+|-
+!sub-inverse-arithmetic (-1 > ''p'')
+|''p''FS, ''p''FD
+|}
+There's no reason to worry about the middle of the table, i.e. where I had "GPS" for "geometric pitch sequence". Because of the diagonal equivalence pattern, it's only necessary to think in terms of possible arithmetic sequences (our system), or possible frequency sequences (your system).
+These two systems have reason to coexist. For some people, our system may make more sense. For others, yours may make more sense. Though I repeat, that I think our system is more natural for actual musicians, while yours may be more natural for mathematicians or engineers.
+'''A vs E'''
+But what my system calls an "EFD", for "equal frequency division", yours calls an "AFD", for "arithmetic frequency division". Per [[Talk:Arithmetic tuning]], Paul, Mike, and I find "arithmetic division" incorrect and prefer "equal division".
+But it's not a simple fix for your system, because you're not really speaking about dividing arithmetically, which doesn't make grammatical sense, and that's our concern; you're talking about dividing with respect to the arithmetic mean/progression. Before I understood the relationship between means and progressions, I had suggested "arithmetic-mean-based division", but you noted that your system is as much about progressions as it is about means, and I see that now.
+But I do have an observation which might help with this. Since the main new value for your system is how it can fill in between and beyond the values of p = 1, 0, and -1, it's really about power ''means''. And I don't find that "power progressions" are written about much, so I believe that "mean" should take precedence over "progression" here. In other words, I suggest that your system might even better be thought of as the "frequency power mean sequence" system, and indeed AFD would stand for "arithmetic-mean-based frequency division".
+Nonetheless, perhaps "frequency power progression tunings" or something like that, with AFD standing for "arithmetic-progression-based frequency division". Not sure. Just suggestions.
+--[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 18:15, 9 April 2023 (UTC)