Xenharmonic Wiki:Cross-platform dialogue: Difference between revisions

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:I wrote some of the headings at the top wrong. I uploaded new versions of the files with this fixed, but it might take a few hours for the file pages to start showing the new versions. Specifically, the columns that say "CTE vs KE" are supposed to say "POTE vs CTE". Sorry for the confusion --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 07:17, 19 March 2024 (UTC)

=== Mike is Done For Now ===

Hi all

This has been fun but I need to be done with this for a while, so I leave it with you all.

So some parting words for POTE vs KE:

# Thanks for putting POTE back and making the charts.

# I've added a bunch of theory, history and Python to the constrained tunings page, so it's easy to compute any arbitrary the CTE/KE/whatever in closed form. Since it looks like you have Lua code for the pseudoinverse you'll be able to use this to easily compute the KE tuning without needing nonlinear optimization.

# When comparing these things it's best to compare the tuning maps, not the generators. It's hard to know how much difference a cent makes just looking at the generator map.

# I would just subtract the two tuning maps and take an RMS of the differences.

# It looks like the biggest differences involve temperaments where the period is some fraction of an octave: Augmented, Diminished, Blackwood, etc.

# The differences should also be pretty small for stuff like magic, porcupine, etc, and also for 5-limit temperaments. It's the things that are a bit further out error-wise and in higher limits that I'm curious about: superpyth, machine, semaphore, pajara, modus, mohajira, etc.

# I think there are some errors - Porcupine doesn't look right; I think it should be 164.0621.

# In general I'm fairly impressed with KE though.

For organizing this stuff:

# I agree having one or two "default" tunings shown prominently is good, and then the rest below it. Maybe one pure-octave and one stretched-octave, if you like.

# Yes, please do put a pure-octave tuning up there. Nobody wants to grab a calculator to derive POTE from TE!

# The above results for POTE vs KE look fairly good to me. If they look this good after checking with higher-limit temperaments and ones a bit less accurate, I'd be alright with making KE the standard and POTE secondary.

# If you like CTE then add it but I don't think it should be standard. It's awful, really.

For the math:

# I don't know how I always end up in this position of defending the "old guard" - I spent the last 15 years arguing with people about changing stuff and now suddenly I'm defending it.

# If you really want my view, I don't really think any of these optimal tunings are ideal. I think log-weighting in general is ridiculous. All of these higher primes end up weighted ridiculously strongly. The "best" EDOs (http://x31eq.com/cgi-bin/more.cgi?r=1&limit=2_3_5_7_11_13_17_19_23_29_31_37_41_43_47_53&error=5) in very high limits with log-weighting are always very strange things like 26, 29, etc, because higher primes just pop up faster than they roll off.

# There is a version of the zeta function which weights things as 1/log(nd) instead of 1/(nd)^s, and the results just seem very silly compared to the real one.

# I came up with the "BOP" and "BE" tunings for this reason, which weight ratios inversely proportional to the exponential of their norm (i.e. 1/(nd)) instead. FWIW I think they're better, the BE tuning in particular. It would not be that hard to figure out some kind of Weil version of this.

# The subgroup version of these is a little bit less easy to do, as you need to check the convex hull of all intervals divided by the exponential of their norm.

# I think this is a much more radical change though and I'd say to go with POTE/KE for now and do this later.

That's it for now, thanks. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 09:27, 19 March 2024 (UTC)

@@ Line 205: / Line 205: @@
 :I wrote some of the headings at the top wrong. I uploaded new versions of the files with this fixed, but it might take a few hours for the file pages to start showing the new versions. Specifically, the columns that say "CTE vs KE" are supposed to say "POTE vs CTE". Sorry for the confusion --[[User:BudjarnLambeth|BudjarnLambeth]] ([[User talk:BudjarnLambeth|talk]]) 07:17, 19 March 2024 (UTC)
+=== Mike is Done For Now ===
+Hi all
+This has been fun but I need to be done with this for a while, so I leave it with you all.
+So some parting words for POTE vs KE:
+# Thanks for putting POTE back and making the charts.
+# I've added a bunch of theory, history and Python to the constrained tunings page, so it's easy to compute any arbitrary the CTE/KE/whatever in closed form. Since it looks like you have Lua code for the pseudoinverse you'll be able to use this to easily compute the KE tuning without needing nonlinear optimization.
+# When comparing these things it's best to compare the tuning maps, not the generators. It's hard to know how much difference a cent makes just looking at the generator map.
+# I would just subtract the two tuning maps and take an RMS of the differences.
+# It looks like the biggest differences involve temperaments where the period is some fraction of an octave: Augmented, Diminished, Blackwood, etc.
+# The differences should also be pretty small for stuff like magic, porcupine, etc, and also for 5-limit temperaments. It's the things that are a bit further out error-wise and in higher limits that I'm curious about: superpyth, machine, semaphore, pajara, modus, mohajira, etc.
+# I think there are some errors - Porcupine doesn't look right; I think it should be 164.0621.
+# In general I'm fairly impressed with KE though.
+For organizing this stuff:
+# I agree having one or two "default" tunings shown prominently is good, and then the rest below it. Maybe one pure-octave and one stretched-octave, if you like.
+# Yes, please do put a pure-octave tuning up there. Nobody wants to grab a calculator to derive POTE from TE!
+# The above results for POTE vs KE look fairly good to me. If they look this good after checking with higher-limit temperaments and ones a bit less accurate, I'd be alright with making KE the standard and POTE secondary.
+# If you like CTE then add it but I don't think it should be standard. It's awful, really.
+For the math:
+# I don't know how I always end up in this position of defending the "old guard" - I spent the last 15 years arguing with people about changing stuff and now suddenly I'm defending it.
+# If you really want my view, I don't really think any of these optimal tunings are ideal. I think log-weighting in general is ridiculous. All of these higher primes end up weighted ridiculously strongly. The "best" EDOs (http://x31eq.com/cgi-bin/more.cgi?r=1&limit=2_3_5_7_11_13_17_19_23_29_31_37_41_43_47_53&error=5) in very high limits with log-weighting are always very strange things like 26, 29, etc, because higher primes just pop up faster than they roll off.
+# There is a version of the zeta function which weights things as 1/log(nd) instead of 1/(nd)^s, and the results just seem very silly compared to the real one.
+# I came up with the "BOP" and "BE" tunings for this reason, which weight ratios inversely proportional to the exponential of their norm (i.e. 1/(nd)) instead. FWIW I think they're better, the BE tuning in particular. It would not be that hard to figure out some kind of Weil version of this.
+# The subgroup version of these is a little bit less easy to do, as you need to check the convex hull of all intervals divided by the exponential of their norm.
+# I think this is a much more radical change though and I'd say to go with POTE/KE for now and do this later.
+That's it for now, thanks. [[User:Mike Battaglia|Mike Battaglia]] ([[User talk:Mike Battaglia|talk]]) 09:27, 19 March 2024 (UTC)