Talk:IFDO: Difference between revisions

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:::::: Per Fredg999's suggestion, I have started a discussion for GPS on the Discord server: https://discord.com/channels/332357996569034752/1096541142167846962 --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 21:45, 14 April 2023 (UTC)

:::::: Okay, I have a few updates from Dave, who asked for a link to this discussion and then emailed me about it:

:::::: "The equivalences in this table are strictly by reflection across the main diagonal, not by merely being on the same anti-diagonal." I think that's an excellent generalization, and it explains why I got the color wrong for the GPS cell.

:::::: He also noted that in my tables, I should have had "p → 0", not "p = 0" for geometric sequences.

:::::: He also notes that "quadratic" would be a preferable way to refer to the case of p = 2, rather than RMS, as in "quadratic mean" and "quadratic progression", for better parallelism.

:::::: He also notes that "reciprocal-arithmetic mean" would have been better than "inverse-arithmetic mean". In other words, he thinks RFDO would be clearer than IFDO. For example, if we introduce CompactStar's p=2 scale as a QFDO (quadratic frequency division of the octave), then the "inverse-quadratic mean" would be square-root (p = ½) while "reciprocal-quadratic" would be λx.1/x² (p = -2). But I hesitate even to bring this up, since there's been so much critique of this new naming system already.

:::::: --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:13, 19 April 2023 (UTC)

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 :::::: Per Fredg999's suggestion, I have started a discussion for GPS on the Discord server: https://discord.com/channels/332357996569034752/1096541142167846962 --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 21:45, 14 April 2023 (UTC)
+:::::: Okay, I have a few updates from Dave, who asked for a link to this discussion and then emailed me about it:
+:::::: "The equivalences in this table are strictly by reflection across the main diagonal, not by merely being on the same anti-diagonal." I think that's an excellent generalization, and it explains why I got the color wrong for the GPS cell.
+:::::: He also noted that in my tables, I should have had "p → 0", not "p = 0" for geometric sequences.
+:::::: He also notes that "quadratic" would be a preferable way to refer to the case of p = 2, rather than RMS, as in "quadratic mean" and "quadratic progression", for better parallelism.
+:::::: He also notes that "reciprocal-arithmetic mean" would have been better than "inverse-arithmetic mean". In other words, he thinks RFDO would be clearer than IFDO. For example, if we introduce CompactStar's p=2 scale as a QFDO (quadratic frequency division of the octave), then the "inverse-quadratic mean" would be square-root (p = ½) while "reciprocal-quadratic" would be λx.1/x² (p = -2). But I hesitate even to bring this up, since there's been so much critique of this new naming system already.
+:::::: --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 19:13, 19 April 2023 (UTC)