User:Eufalesio/Ultimate: Difference between revisions

Line 141:

The chain of fifths is a very important framework historically. It's been in Western music THE way to think about everything all the way from plainchant to Renaissance meantone temperaments to the modern day; where the 12-pitch-class circle of fifths is taught; 12edo, a massively over-represented tuning. It has a bit of a bad reputation in the xen circles, but the more I researched, the more I realized it is a '''paragon''', and that its position nowadays is very much well earned.

My main aim is to expand tonality with JI, and there is no better way to do so than to also extend the fundamental tuning framework to its logical conclusion.

My main aim is to expand tonality with JI, and there is no better way to do so than to also extend the fundamental tuning framework to its logical conclusion. Behold, the ''sequence''.

12edo introduces the [[compton]] framework, which closes the chain of fifths with 12 flat, but proportionally very good fifths. Compton ''sensu stricto'' uses an independent generator to each all the different primes, and is generally a very good temperament. However, if the fifths are tuned sharper to become closer to just, the chain goes on for longer...

* '''12edo''' introduces the [[compton]] framework, which closes the chain of fifths with 12 flat, but proportionally very good fifths. Compton ''sensu stricto'' uses an independent generator to each all the different primes, and is generally a very good temperament. However, if the fifths are tuned sharper to become closer to just, the chain goes on for longer...

* '''41edo''' introduces the [[cassandra]] framework, which thanks to its incredibly accurate fifths, introduces the poma as an accidental. In cassandra, the poma acts as 81/80~64/63 at around ~29c, and two of them add to 1053/1024~33/32~36/35. 41edo is a bit overtempered but notable as a proportionally coarse but good system. 53edo has practically pure fifths and very good p5 (prime 5) and p13 (prime 13), but p7 and p11 are tuned worse.

41edo introduces the [[cassandra]] framework, which thanks to its incredibly accurate fifths, introduces the poma as an accidental. In cassandra, the poma acts as 81/80~64/63 at around ~29c, and two of them add to 1053/1024~33/32~36/35. 41edo is a bit overtempered but notable as a proportionally coarse but good system. 53edo has practically pure fifths and very good p5 (prime 5) and p13 (prime 13), but p7 and p11 are tuned worse.

* '''94edo''' is in my opinion the optimal cassandra equal tuning with a poma of 25.5c, tempered just enough for the 13-limit to reach <4 cents of error and very easy to use.

94edo is in my opinion the optimal cassandra equal tuning with a poma of 25.5c, tempered just enough for the 13-limit to reach <4 cents of error and very easy to use.

However, if you forgo p5 and p13 for the chain of fifths, you end up with [[gary]]. Gary is a serendipitous temperament, the same as cassandra but optimized for the [[zala]]. 135edo is an essentially perfect tuning, reaching sub-cent levels of error in the subgroup, with a poma of 26.{{Overline|6}} c.

Ultimate is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent "minicomma" generator for p5 and p13, which acts as 385/384, ~352/351, ~5120/5103, layoma, ... etc, being around 4.4c. It doesn't begin to be fully useful up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo.

* '''Ultimate''' is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent "minicomma" generator for p5 and p13, which acts as 385/384, ~352/351, ~5120/5103, layoma, ... etc, being around 4.4c. It doesn't begin to be fully useful up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo. [[176edo]] also supports it earlier at full structure, but it kinda blows as an equal tuning because the MC is too wide.

[[176edo]] also supports it earlier at full structure, but it kinda blows as an equal tuning because the MC is too wide.

'''The key reasons''' on why Ultimate is ultimate, is ultimately due to the fact that 270edo and 311edo are inside the supported equal tunings, because going any further would make the edosteps not discernible, and because no other edo in their vicinity is as good as them. Beyond that, I see no reason to use edos.

Line 205:

Line 201:

94edo and 270edo have the key property of being even, tempering out the [[kalisma]] and allowing the poma to be halved. Using them this way is reminiscent of [[Gariwizmic]], a very similar subset of Ultimate, but with the MC found deep in the generator chain, not independent. This is useful for easier navigation within a DAW. It's possible to use Gariwizmic wholesale, though it only slightly improves 270edo in precision, Newt is a much better choice for accuracy's sake, though 94edo does ''not'' support it. Gariwizmic provides structure, not the tuning.

== Ultimate ~~still not enough?~~ ==

== Beyond Ultimate ==

There's a reason why I deem Ultimate ultimate. You're supposed to end there and go no further, because Ultimate is right at the limit of practicality. If you're stubborn enough to ignore my warnings and venture into the land of impossible... I still know how you can continue ~~following~~ the ~~same path of reasoning,~~ and add extra pairs of accidentals that are fully retrocompatible.

There's a reason why I deem Ultimate ultimate. You're supposed to end there and go no further, because Ultimate is right at the limit of practicality. If you're stubborn enough to ignore my warnings and venture into the land of impossible... I still know how you can continue the sequence and add extra pairs of accidentals that are fully retrocompatible.

=== Olympic ===

[[Olympic|This]]. The best course of action for detempering Ultimate is to observe the garischisma, resulting in rank-4 olympic, which is just {S64, S65}. Notationwise, this results in spliting the saruyoma being observed. Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller.

[[Olympic|This]]. The best course of action for detempering Ultimate is to observe the garischisma, resulting in rank-4 olympic, which is just {S64, S65}. Notationwise, this results in spliting the saruyoma being observed. Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller. A [[10241/10240|tina]] is required to reach prime 17 and 19.

Olympic decouples 64/63 from the chain of fifths; 64/63 is now its own thing, and the poma is \|↑. (\| is a garischisma down)

Everything else is the same:

* ↑ is 64/63.

* v↑ is 81/80.

* ⇈ is 33/32.

* v⇈ is 1053/1024.

~~Olympic decouples 64/63 from the chain of fifths; 64/63~~ is ~~now its own thing~~, ~~and the poma~~ is ◸↑.

t's something I don't think I'll ever see myself doing because this accuracy is enough to represent highly fine edos such as 494, 764, or 935edo, which is already too much for me.

~~Everything else is~~ the ~~same. v↑ for 81~~/80, ~~⇈ for 33/32~~, ~~v⇈ for 1053/1024. It~~'s ~~something I don't think I'll ever see myself doing because this accuracy is enough~~ to ~~represent highly fine edos such as 494, 764, or 935edo, which is already too much~~ for me.

Extensions to the 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, [[Catalog of rank-4 temperaments#Metaolympic|Metaolympic]] works, and though it's a weak extension; it can still be written retrocompatibly. Acknowledgements to [[Flora Canou]] for this insight.

Extensions to the 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, and a decent but weak one adding 5776/5775 and 4200/4199 needs you to split the septimal comma in halves, which is not ideal and also breaks the sequence. Acknowledgements to [[Flora Canou]] for this insight. This means, 19/16 is ~~still ^~~m3. 17/16 is vv\'''⇊⇊'''M2.

Here, 19/16 is †|\m3. 17/16 is 𐕣^|\'''⇊⇊'''M2. (|\ is a schisma up, † is a heavily inflated tina; 10241/10240)

=== Insanic ===

Olympic STILL not enough? Split your losses and use [[5767168/5767125|{S64/S65}]]. Now you observe the olympia and get a schismina accidental. An olympia is 3 of these schisminas. You could write this as dots above or below the accidentals but this is possibly getting a tad crowded. ↑ is 64/63 ~~and~~ 81/80 ~~is v↑~~. ⇈̱ is 33/32 whilst ⇈ is 4096/3969. v⇈̇ is 1053/1024 whilst v⇈ is 36/35. {S64/S65} is at a level of precision comparable to 8539edo and much finer. The people at sagittal.org had already declared its own version of this notation to be of "Insane" precision, so if you need anything finer, you are ''beyond insane''. Or, to be more crude... '''batshit''' insane.

Olympic STILL not enough? Split your losses and use [[5767168/5767125|{S64/S65}]]. Now you observe the olympia and get a schismina accidental.

An olympia is 3 of these schisminas. You could write this as dots above or below the accidentals but this is possibly getting a tad crowded.

* ↑ is 64/63.

* v↑ is 81/80.

* ⇈̱ is 33/32 whilst ⇈ is 4096/3969.

* v⇈̇ is 1053/1024 whilst v⇈ is 36/35.

{S64/S65} is at a level of precision comparable to 8539edo and much finer. The people at sagittal.org had already declared its own version of this notation to be of "Insane" precision, so if you need anything finer, you are ''beyond insane''. Or, to be more crude... '''batshit''' insane.

Unlike Olympic, this one is undeniably '''WAY''' more accurate, at least 100 times more accurate. It can be extended to the whole 19-limit by adding S76/S77 and S2431 to the comma list, however, a tina is required to reach prime 17 and 19, which is close, but not equal to a third of a schismina. The tina is 10241/10240. 19/16 is †|̈\m3. 17/16 is 𐕣^^'''⇊⇊̱'''M2.

Unlike Olympic, this one is undeniably '''WAY''' more accurate, at least 100 times more accurate. It can be extended to the whole 19-limit by adding S76/S77 and S2431 (or the [[devicisma]]) to the comma list, however, a tina is required to reach prime 17 and 19, which is close, but not equal to a third of a schismina. The tina is 10241/10240. 19/16 is †|̈\m3. 17/16 is 𐕣^^'''⇊⇊̱'''M2.

Look how goddamn accurate this temp is! Look, I even made a technical temp data section!

=== Batshit AKA Batshit-Insanic or simply call it Insanic if profanity is not allowed ===

[[Subgroup]]: 2.3.5.7.11.13.17.19

[[Subgroup]]: 2.3.5.7.11.13

[[Comma list]]: [[5767168/5767125|S64/S65]]

[[Mapping]]:

{| class="right-all"

|[⟨

|1

|0

|2

|7

|],

|-

|⟨

|0

|1

|0

|],

|-

|⟨

|0

|1

|0

| -1

|],

|-

|⟨

|0

|1

|0

|],

|-

|⟨

|0

| -3

| -1

|]]

|}

Mapping generators: ~2, ~3, ~5, ~7, ~128/65

[[Optimal tuning|Optimal tunings]]? (the calculator isn't very helpful here...)

: [[CWE]]: ~2 = 1200.000 ¢, ~3/2 = 701.956 ¢, ~5/4 = 386.315 ¢, ~7/4 = 968.827 ¢, ~608/385 = 1173.154¢

: error map: -0.000, 0.001, 0.001, 0.001, 0.001, 0.003

Optimal ET sequence: {{EDOs|7, 10e, 12e, 30b, 31e, 34, 36, 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1609, 1696, 1920, 2190, 2684, 3395, 5144, 5585, 6079, 8269, 8539, 11664, 14124, 14348, 14618, 20203}}

Badness (Flora): 0.241077 [Sintel Badness gives me NA]

[[Comma list]]: ~~[[5767168/5767125|~~S64/S65]], [[11413376/11413325|S76/S77]], [[633556/633555]]

==== Subgroup: 2.3.5.7.11.13.17.19 ====

[[Comma list]]: S64/S65, [[11413376/11413325|S76/S77]], [[633556/633555]]

[[Mapping]]:

Line 291:

Line 367:

: [[CWE]]: ~2 = 1200.000 ¢, ~3/2 = 701.956 ¢, ~5/4 = 386.316 ¢, ~7/4 = 968.828 ¢, ~608/385 = 791.052¢

: error map 0.000, 0.001, 0.002, 0.002, 0.001, 0.002, 0.001, 0.001

~~'''Optimal''' ET sequence~~: ~~{{EDOs|53,94,270,???,3395,???,8539,16808,20203}} (I have no idea what follows.)~~

:

~~CWE errors~~: ~~0.000~~, ~~0.001~~, ~~0.002~~, ~~0.002~~, ~~0.001~~, ~~0.002~~, ~~0.001~~, ~~0.001 (the calculator isn't very helpful here..~~.)

'''Optimal''' ET sequence: {{EDOs|41g, 53, 94, 176g, 217, 270, 311, 487, 581, 1115g, 1385, 1696, 1966, 2597, 2814, 3084, 3178, 3395, 5144, 6573, 7958, 8269, 8539, 11934, 16808, 20203}}.

Badness (Sintel): 0.279

@@ Line 141: / Line 141: @@
 The chain of fifths is a very important framework historically. It's been in Western music THE way to think about everything all the way from plainchant to Renaissance meantone temperaments to the modern day; where the 12-pitch-class circle of fifths is taught; 12edo, a massively over-represented tuning. It has a bit of a bad reputation in the xen circles, but the more I researched, the more I realized it is a '''paragon''', and that its position nowadays is very much well earned.
-My main aim is to expand tonality with JI, and there is no better way to do so than to also extend the fundamental tuning framework to its logical conclusion.
+My main aim is to expand tonality with JI, and there is no better way to do so than to also extend the fundamental tuning framework to its logical conclusion. Behold, the ''sequence''.
-edo introduces the [[compton]] framework, which closes the chain of fifths with 12 flat, but proportionally very good fifths. Compton ''sensu stricto'' uses an independent generator to each all the different primes, and is generally a very good temperament. However, if the fifths are tuned sharper to become closer to just, the chain goes on for longer...
+* '''12edo''' introduces the [[compton]] framework, which closes the chain of fifths with 12 flat, but proportionally very good fifths. Compton ''sensu stricto'' uses an independent generator to each all the different primes, and is generally a very good temperament. However, if the fifths are tuned sharper to become closer to just, the chain goes on for longer...
+* '''41edo''' introduces the [[cassandra]] framework, which thanks to its incredibly accurate fifths, introduces the poma as an accidental. In cassandra, the poma acts as 81/80~64/63 at around ~29c, and two of them add to 1053/1024~33/32~36/35. 41edo is a bit overtempered but notable as a proportionally coarse but good system. 53edo has practically pure fifths and very good p5 (prime 5) and p13 (prime 13), but p7 and p11 are tuned worse.
-edo introduces the [[cassandra]] framework, which thanks to its incredibly accurate fifths, introduces the poma as an accidental. In cassandra, the poma acts as 81/80~64/63 at around ~29c, and two of them add to 1053/1024~33/32~36/35. 41edo is a bit overtempered but notable as a proportionally coarse but good system. 53edo has practically pure fifths and very good p5 (prime 5) and p13 (prime 13), but p7 and p11 are tuned worse.
+* '''94edo''' is in my opinion the optimal cassandra equal tuning with a poma of 25.5c, tempered just enough for the 13-limit to reach <4 cents of error and very easy to use.
-edo is in my opinion the optimal cassandra equal tuning with a poma of 25.5c, tempered just enough for the 13-limit to reach <4 cents of error and very easy to use.
 However, if you forgo p5 and p13 for the chain of fifths, you end up with [[gary]]. Gary is a serendipitous temperament, the same as cassandra but optimized for the [[zala]]. 135edo is an essentially perfect tuning,  reaching sub-cent levels of error in the subgroup, with a poma of 26.{{Overline|6}} c.
-Ultimate is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent "minicomma" generator for p5 and p13, which acts as 385/384, ~352/351, ~5120/5103, layoma, ... etc, being around 4.4c. It doesn't begin to be fully useful up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo.
+* '''Ultimate''' is not just an extension of the concept, but what I believe to be the '''end''' of that extension. Ultimate adds an independent "minicomma" generator for p5 and p13, which acts as 385/384, ~352/351, ~5120/5103, layoma, ... etc, being around 4.4c. It doesn't begin to be fully useful up until 217edo, but 270edo and 311edo are arguably the best tunings. 217edo is alright, but not the best, which would make it a waste of time if it weren't a multiple of 31edo. [[176edo]] also supports it earlier at full structure, but it kinda blows as an equal tuning because the MC is too wide.
-[[176edo]] also supports it earlier at full structure, but it kinda blows as an equal tuning because the MC is too wide.
 '''The key reasons''' on why Ultimate is ultimate, is ultimately due to the fact that 270edo and 311edo are inside the supported equal tunings, because going any further would make the edosteps not discernible, and because no other edo in their vicinity is as good as them. Beyond that, I see no reason to use edos.
@@ Line 205: / Line 201: @@
 edo and 270edo have the key property of being even, tempering out the [[kalisma]] and allowing the poma to be halved. Using them this way is reminiscent of [[Gariwizmic]], a very similar subset of Ultimate, but with the MC found deep in the generator chain, not independent. This is useful for easier navigation within a DAW. It's possible to use Gariwizmic wholesale, though it only slightly improves 270edo in precision, Newt is a much better choice for accuracy's sake, though 94edo does ''not'' support it. Gariwizmic provides structure, not the tuning.
-== Ultimate still not enough? ==
+== Beyond Ultimate ==
-There's a reason why I deem Ultimate ultimate. You're supposed to end there and go no further, because Ultimate is right at the limit of practicality. If you're stubborn enough to ignore my warnings and venture into the land of impossible... I still know how you can continue following the same path of reasoning, and add extra pairs of accidentals that are fully retrocompatible.
+There's a reason why I deem Ultimate ultimate. You're supposed to end there and go no further, because Ultimate is right at the limit of practicality. If you're stubborn enough to ignore my warnings and venture into the land of impossible... I still know how you can continue the sequence and add extra pairs of accidentals that are fully retrocompatible.
 === Olympic ===
-[[Olympic|This]]. The best course of action for detempering Ultimate is to observe the garischisma, resulting in rank-4 olympic, which is just {S64, S65}. Notationwise, this results in spliting the saruyoma being observed. Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller.
+[[Olympic|This]]. The best course of action for detempering Ultimate is to observe the garischisma, resulting in rank-4 olympic, which is just {S64, S65}. Notationwise, this results in spliting the saruyoma being observed. Unlike in JI, where the schisma is around half the garischisma, here the schisma is ~1.6x LARGER, not smaller. A [[10241/10240|tina]] is required to reach prime 17 and 19.
+Olympic decouples 64/63 from the chain of fifths; 64/63 is now its own thing, and the poma is \|↑. (\| is a garischisma down)
+Everything else is the same:
+* ↑ is 64/63.
+* v↑ is 81/80.
+* ⇈ is 33/32.
+* v⇈ is 1053/1024.
-Olympic decouples 64/63 from the chain of fifths; 64/63 is now its own thing, and the poma is ◸↑.
+t's something I don't think I'll ever see myself doing because this accuracy is enough to represent highly fine edos such as 494, 764, or 935edo, which is already too much for me.
-Everything else is the same. v↑ for 81/80, ⇈ for 33/32, v⇈ for 1053/1024. It's something I don't think I'll ever see myself doing because this accuracy is enough to represent highly fine edos such as 494, 764, or 935edo, which is already too much for me.
+Extensions to the 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, [[Catalog of rank-4 temperaments#Metaolympic|Metaolympic]] works, and though it's a weak extension; it can still be written retrocompatibly. Acknowledgements to [[Flora Canou]] for this insight.
-Extensions to the 19-limit are bad: the strong one keeps 1729/1728 and 1216/1215, and a decent but weak one adding 5776/5775 and 4200/4199 needs you to split the septimal comma in halves, which is not ideal and also breaks the sequence. Acknowledgements to [[Flora Canou]] for this insight. This means, 19/16 is still ^m3. 17/16 is vv\'''⇊⇊'''M2.
+Here, 19/16 is †|\m3. 17/16 is 𐕣^|\'''⇊⇊'''M2. (|\ is a schisma up, † is a heavily inflated tina; 10241/10240)
 === Insanic ===
-Olympic STILL not enough? Split your losses and use [[5767168/5767125|{S64/S65}]]. Now you observe the olympia and get a schismina accidental. An olympia is 3 of these schisminas. You could write this as dots above or below the accidentals but this is possibly getting a tad crowded. ↑ is 64/63 and 81/80 is v↑. ⇈̱ is 33/32 whilst ⇈ is 4096/3969. v⇈̇ is 1053/1024 whilst v⇈ is 36/35. {S64/S65} is at a level of precision comparable to 8539edo and much finer. The people at sagittal.org had already declared its own version of this notation to be of "Insane" precision, so if you need anything finer, you are ''beyond insane''. Or, to be more crude... '''batshit''' insane.
+Olympic STILL not enough? Split your losses and use [[5767168/5767125|{S64/S65}]]. Now you observe the olympia and get a schismina accidental.
+An olympia is 3 of these schisminas. You could write this as dots above or below the accidentals but this is possibly getting a tad crowded.
+* ↑ is 64/63.
+* v↑ is 81/80.
+* ⇈̱ is 33/32 whilst ⇈ is 4096/3969.
+* v⇈̇ is 1053/1024 whilst v⇈ is 36/35.
+{S64/S65} is at a level of precision comparable to 8539edo and much finer. The people at sagittal.org had already declared its own version of this notation to be of "Insane" precision, so if you need anything finer, you are ''beyond insane''. Or, to be more crude... '''batshit''' insane.
-Unlike Olympic, this one is undeniably '''WAY''' more accurate, at least 100 times more accurate. It can be extended to the whole 19-limit by adding S76/S77 and S2431 to the comma list, however, a tina is required to reach prime 17 and 19, which is close, but not equal to a third of a schismina. The tina is 10241/10240. 19/16 is †|̈\m3. 17/16 is 𐕣^^'''⇊⇊̱'''M2.
+Unlike Olympic, this one is undeniably '''WAY''' more accurate, at least 100 times more accurate. It can be extended to the whole 19-limit by adding S76/S77 and S2431 (or the [[devicisma]]) to the comma list, however, a tina is required to reach prime 17 and 19, which is close, but not equal to a third of a schismina. The tina is 10241/10240. 19/16 is †|̈\m3. 17/16 is 𐕣^^'''⇊⇊̱'''M2.
 Look how goddamn accurate this temp is! Look, I even made a technical temp data section!
 === Batshit AKA Batshit-Insanic <small><small><small><small><small>or simply call it</small></small></small></small></small> Insanic<small><small><small><small><small> if profanity is not allowed</small></small></small></small></small> ===
-[[Subgroup]]: 2.3.5.7.11.13.17.19
+[[Subgroup]]: 2.3.5.7.11.13
+[[Comma list]]: [[5767168/5767125|S64/S65]]
+[[Mapping]]:
+{| class="right-all"
+|[⟨
+|1
+|0
+|0
+|0
+|2
+|7
+|],
+|-
+|⟨
+|0
+|1
+|0
+|0
+|0
+|0
+|],
+|-
+|⟨
+|0
+|0
+|1
+|0
+|0
+| -1
+|],
+|-
+|⟨
+|0
+|0
+|0
+|1
+|1
+|0
+|],
+|-
+|⟨
+|0
+|0
+|0
+|0
+| -3
+| -1
+|]]
+|}
+Mapping generators: ~2, ~3, ~5, ~7, ~128/65
+[[Optimal tuning|Optimal tunings]]? (the calculator isn't very helpful here...)
+: [[CWE]]: ~2 = 1200.000 ¢, ~3/2 = 701.956 ¢, ~5/4 = 386.315 ¢, ~7/4 = 968.827 ¢, ~608/385 = 1173.154¢
+: error map: -0.000, 0.001, 0.001, 0.001, 0.001, 0.003
+Optimal ET sequence: {{EDOs|7, 10e, 12e, 30b, 31e, 34, 36, 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1609, 1696, 1920, 2190, 2684, 3395, 5144, 5585, 6079, 8269, 8539, 11664, 14124, 14348, 14618, 20203}}
+Badness (Flora): 0.241077 [Sintel Badness gives me NA]
-[[Comma list]]: [[5767168/5767125|S64/S65]], [[11413376/11413325|S76/S77]], [[633556/633555]]
+==== Subgroup: 2.3.5.7.11.13.17.19 ====
+[[Comma list]]: S64/S65, [[11413376/11413325|S76/S77]], [[633556/633555]]
 [[Mapping]]:
@@ Line 291: / Line 367: @@
 : [[CWE]]: ~2 = 1200.000 ¢, ~3/2 = 701.956 ¢, ~5/4 = 386.316 ¢, ~7/4 = 968.828 ¢, ~608/385 = 791.052¢
+: error map 0.000, 0.001, 0.002, 0.002, 0.001, 0.002, 0.001, 0.001
-'''Optimal''' ET sequence: {{EDOs|53,94,270,???,3395,???,8539,16808,20203}} (I have no idea what follows.)
+:
-CWE errors: 0.000, 0.001, 0.002, 0.002, 0.001, 0.002, 0.001, 0.001 (the calculator isn't very helpful here...)
+'''Optimal''' ET sequence: {{EDOs|41g, 53, 94, 176g, 217, 270, 311, 487, 581, 1115g, 1385, 1696, 1966, 2597, 2814, 3084, 3178, 3395, 5144, 6573, 7958, 8269, 8539, 11934, 16808, 20203}}.
 Badness (Sintel): 0.279