My Criteria For Art - Music Diaries - Forums : Best Ever Albums

DelBocaVista

Rhyner wrote:

I'll need to digest and ruminate more fully on the giant wall of text above to contribute more to this conversation, but I do have one observation off the top of my head that could potentially be of value. It's something I've always wondered about ever since I first saw your "rating by halves" math, and has always kinda rubbed me the wrong way. Your ten-point scale seems to me to be logarithmic, and I'm pretty sure you confirmed to me, in some previous conversation, that it basically is. In which case traditional arithmetic operations don't apply, at least not in a uniform and simplistic way. Which means something like this...

AfterHours wrote:

9.0/10 = Combined total of both halves equaling 15.2 or 15.3. Examples: 7.6/10 + 7.6/10; 8.3/10 + 7.0/10

...is no bueno. In logarithmic terms, two 7.6es do not add the same as some other combination that adds up to 15.2. If 7.6 + 7.6 = 9, then 8.3 + 7.0 (or even 8.3 + 6.9) should be higher, more like 9.1. The more disparate the numbers, the bigger the difference would be. For example, 9.5 + 5.7 should, on the face of it, be something like 9.7 or 9.8. This example is helpful in getting the point across because if the 5.7 is purely additive to the quality of the piece as a whole, then you should certainly expect the resulting score to be higher than the 9.5 on its own. Yet 9.5 and 5.7 combine to the 15.2 that should equal a score of just 9.0 according to your stated rule.

If you compare a 9.5+5.7 to a 7.6+7.6
- yes the first track is an improvement to a greater extent than the second track is lowered (jump 7.6 to 9.5 is greater than drop from 7.6 to 57)
- but the inconsistency of the two parts (9.5 v. 5.7) is detrimental
- and these two factors cancel each other out

Also 5.7 is not inherently additive. At the 9.5 level, it takes more than a 5.7 from the second half for the score to maintain

AfterHours

Gender: Male
Location: originally from scaruffi.com ;-)

Rhyner wrote:

Oooh, dry nerdy math talk about ratings systems! One of my favorite subjects!

I'll need to digest and ruminate more fully on the giant wall of text above to contribute more to this conversation, but I do have one observation off the top of my head that could potentially be of value. It's something I've always wondered about ever since I first saw your "rating by halves" math, and has always kinda rubbed me the wrong way. Your ten-point scale seems to me to be logarithmic, and I'm pretty sure you confirmed to me, in some previous conversation, that it basically is. In which case traditional arithmetic operations don't apply, at least not in a uniform and simplistic way. Which means something like this...

AfterHours wrote:

9.0/10 = Combined total of both halves equaling 15.2 or 15.3. Examples: 7.6/10 + 7.6/10; 8.3/10 + 7.0/10

...is no bueno. In logarithmic terms, two 7.6es do not add the same as some other combination that adds up to 15.2. If 7.6 + 7.6 = 9, then 8.3 + 7.0 (or even 8.3 + 6.9) should be higher, more like 9.1. The more disparate the numbers, the bigger the difference would be. For example, 9.5 + 5.7 should, on the face of it, be something like 9.7 or 9.8. This example is helpful in getting the point across because if the 5.7 is purely additive to the quality of the piece as a whole, then you should certainly expect the resulting score to be higher than the 9.5 on its own. Yet 9.5 and 5.7 combine to the 15.2 that should equal a score of just 9.0 according to your stated rule.

Of course this is all ignores confounding factors, like how your the logarithmic base of your scale seems to fluctuate as you go up and down the scale itself, or whether there is some threshold that the second half of an album needs to cross before its contributions begin factoring positively into the final score, or whether the scale is not simply logarithmic but something more complicated (for instance, it might factor in the "consistency per unit of time" and thus the length of an album is nontrivial).

Or this could all be futile because it's a matter of trying to quantify and compare proverbial Wittgensteinian beetles in Wittgensteinian boxes. Although that shouldn't affect the math.

I do have more thoughts, but I think they'll need to congeal a bit more to be coherent and of any use to anyone.

Thanks for your input Rhyner and feel free to keep it coming.

As you've correctly observed, the scale itself (even if it were still "correct") is...

1. Overly simplistic.

2. some shifts in upward or downward surge seem "unnatural", and some combos seem illogical

1: is mostly intentional for user friendly purposes. I simply wanted to provide a general guide to how others could verify and figure out the ratings quickly and easily without a lot of calculation and additional math beyond judging the scores of each half. It has long been known that this was an overly simplistic version of it and that a more detailed or advanced math would probably be necessary to truly illustrate the "qualitative curve" or "logarithm" of it.

2: knowing that it is overly simplistic pretty much guaranteed some minor discrepancies and imperfect "combos". It was not totally clear at the time if a very low half + a very high half (such as your 5.7 + 9.5 example for "15.2") would equal the same as two high halves that have the same combined total (such as 7.6 + 7.6 for 15.2). Mainly because this is so difficult to find examples of and verify (Sun Ra's Atlantis is the only potential suitor that approaches such, off the top of my head). It is extremely rare (perhaps non-existent) for an artist operating at the level of a 9.5 to -- within the same work and time of inspiration -- produce another half of said work on the order of a 5.5 or so. This is because it is practically impossible for these to be of the "same" work. Beethoven's 9th-level artistry (or thereabouts) would never feature a half (of similar musical content) of only 5.5-level artistry because this in itself would be an entirely different music (and thus a different, completely incohesive, music). Much of what the higher ratings could be said to be representative of are higher or more profound, impacting "developments" of all the various art forms, and in many cases, their various genres. So, for instance, A 5.5 level "Tristan and Isolde" would be something not even recognizable to Wagner, comparatively trivial like The Sound of Music soundtrack or something. There's no such thing as a 5.5 level Tristan and Isolde in part because it is perhaps the highest, most emotionally astonishing and creative development of the opera + orchestral score that has ever existed. To lessen this too much (all the way down to 5s and 6s) would be to transform or "devolve" it into a form of opera or theatrical music that is too different and increasingly trivial (as you get closer and closer to the lower scores). It is almost certainly true that, below a certain point, lower-rated halves would have a deteriorating impact relative to a very high half as one gets into the higher ratings. So it should prove true that a 5.7 would not add to but be detrimental to the score of a 9.5, to use your example. That's a MASSIVE drop it quality. Remember too, that this is two equal length halves. So if you can imagine the most incredible music work ever (or close, being a 9.5) -- I don't know what that would be for you -- but let's say something like Beethoven's 9th. So it's 9.5-or-above self for 60 minutes and then suddenly being maybe Wellington's Victory for another hour to complete the work, the overall score would (and should) drop quite a bit with so much discrepancy in quality and so much cumulative qualitative momentum lost.

Current evaluations indicate this may start as high as 6.9 (a very gradual deterioration in accumulative power down to none at probably around 2.5, then "minus accumulation" below that).

Another way to see this is that all the "tenths" of a point are not equal. The tenth of a point that represents the differential in quality between, say, a 5.0 and a 5.1, is not the same as the (much more valuable) tenth of a point between, say, a 9.1 and a 9.2. It only takes some trivial improvement to advance from 5.0 to 5.1. It might take a minor masterpiece added to a work to advance it from 9.1 to 9.2. So these "increments" have different values at certain points of the scale -- not all equal. Which probably goes some way to explaining the "unnatural" upward or downward surges you are seeing at certain junctures of the scale. Again, that doesn't mean there probably isn't a better more accurate representation of them than the current scale shows. I'm open to ideas.
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Rhyner
soft silly music is meaningful magical

Gender: Male
Age: 36
Location: Utah

Good points all. I guess you could sum up the point I was making by noting that the rating-by-halves thing is a simplified, rule-of-thumb method for ease of use rather than mathematical exactitude. I see that you've updated the criteria page since I last read it and you now go over this exact point in detail. Fair enough. I could have perhaps saved us some time by noticing that earlier.

I do want to note that it's precisely because I understand there's a difference in tenths of a point at different values on your scale that the rating-by-halves math is (naively, simplistically, "on the face of it") inconsistent. DelBocaVista pretty much nailed this point, more succinctly than I, in his reply to me.

In any case, I still have lots of thoughts, and lots of questions. Sometime later today I'll get them down in words. I realize you two have probably covered most if not all of the territory that I'm about to ask you to rehash, but maybe not. But even if so, it will help catch me (and anyone else reading this) up on the state of the conversation, and who knows--maybe I can provide a new way of thinking about things that sheds some important light or even breaks a logjam and effects some serious progress. It often seriously helps to have a new set of eyes on a problem. On your critera page you say:

AfterHours wrote:

This Ratings Scale has been fine tuned over years of experience to be very aligned and logical, without being too complicated. It is likely that a more detailed or advanced math would produce an even more exacting and intricate version, with more complex formulas than what I've provided, but in the interest of simplicity of understanding and ease of application, I've maintained it as is. Also, I am not sure I could muster the time or the advanced math that might produce such a version, but if I did (or someone else did) it would likely smooth out some very minor uneven gradations and slight inconsistencies between some of the formulas in relation to others.

I'd like to think I could be that "someone else", or at least a major contributor in this endeavor.

So yeah, later today I'll be asking you a bunch of questions. I think I'll probably have to break them up into multiple posts, because I have a lot of them. Brace yourselves.

AfterHours

Gender: Male
Location: originally from scaruffi.com ;-)

Thanks Rhyner, looking forward to what you come up with and will do my best to answer your questions. DelBocaVista, i imagine too, and will probably be better with more detailed math stuff.

Please note too, that I am using the following post (below in quotes) to provide (and keep updating) certain album ratings by tracks that DelBoca and I have been discussing and testing to see if we can solve those that seem to have anomalies (don't add up) and those we can use as comparison. Etc.

It also lists a version (an abbreviated one) of the ratings scale (ratings by halves) that is closer to accurate per current evaluations. If you're going to use numbers from that scale, it would probably be better to start with this newer one than what's currently listed on the criteria page.

(And I will bump the post every now and then should it get too far behind the thread)

AfterHours wrote:

Albums - with track ratings (plus some notes) - currently under discussion:

NONE are "final" or "official". Still under consideration, being worked on...

Ys - Joanna Newsom
1: 7.3
2: 6.0
3: 7.1
4: 7.4
5: 5.0

Misc notes...

Ys is among the "anomalies" that don't seem to follow my ratings scale despite having excellent "continuity" and not having "disparate halves" or really any disparate tracks (like, for instance Ummagumma) that would upset the accumulation and cause its parts to be more of an average of their ratings instead of an accumulation of them.

Tracks 1-3, collectively "feels like" (palpable impact) approx 8.0 (even though it "should" accumulate higher per the numbers?)
Tracks 4-5 collectively "feels like" 7.4-7.5 (even though it "should" accumulate higher?)

By "feel" or "palpable impact" = at least 15.5. Per (probably incorrect) "criteria page" ratings scale, this would mean a 9.0. This is probably no longer accurate. (See scale being considered below). 15.5 would now mean 8.5. Still doesn't explain...

-Why doesn't Ys seem to accumulate (qualitatively) above 8.5? Or, even lower, Scaruffi's 8 (8.2?)? Per "ratings by halves" that are under consideration, it should at least be 8.8 (mathematically, if not palpably). (Sometimes it seems like 8.8-8.9 palpably too, but more often, around 8.5)
-Is it because the tracks, even though individually rating high enough, don't "accumulate" from each other to higher qualitative degrees because they are each developing too similarly and not quite varied enough?
-Are the lower rated tracks (2, 5) enough to bring it down whereas "criteria page" ratings scale and prior incarnations don't indicate this? How much value does a 6 and 5 add (or detract) from the higher rated tracks? Has this been underestimated?

Lorca - Tim Buckley
1: 7.7-7.8
2: 7.0-7.1
3: 5.8-6.0????
4: 7.0-7.1
5: 7.1-7.2

-This provides a good point of comparison with Ys because they're both 5, generally lengthy tracks. And Lorca is for sure (both palpably, and by rating the tracks) 9.0 at least and probably 9.1, maybe even 9.2/10.
-It may be important to note that Lorca achieves its "9.1" in about 39.5 minutes. Ys achieves its rating (whatever it is) in about 55.5 minutes. Does time added to an achievement (thus less consistency per unit of time) affect the overall rating more than previously thought or accounted for by the ratings scale?

Spiderland - Slint (1991)
1: TBD ... 6.8+?
2: TBD ... 6.8+?
3: TBD ... 6.5+?
4: TBD ... 6.8+?
5: TBD
6: 7.1

-Potentially another good point of comparison... Just need to work out the track ratings to compare. Also 39.5 minutes. "Palpably" feels higher than Ys (most listens) despite possibly having lower track ratings. Is the 16 minute faster running time the main explanation for the discrepancy? Or, again, is Ys having 2 tracks below 6.5 enough to justify?

Astral Weeks - Van Morrison (1968)
1: 6.9-7.0
2: 7.0-7.1
3: 5.3???
4: 7.0-7.1
5: 5.6???
6: 6.9-7.0
7: 6.6-6.8?
8: 6.3???

Astral Weeks is one of the more similar 8.8+ albums to Ys ("narrative style", compositionally, type of emotional expressivity). It is certainly superior to Ys overall (not necessarily by a huge margin) but this gives a good point of comparison because I/we know Ys must be lower than it yet is also comparable so as to figure out why there is a discrepancy between it's "math" rating and "palpable" rating (as in, Ys can't be higher than 9.0 yet seems to be per the "math" so obviously something is incorrect about this).

(Note that probably the most musically similar album to Ys of all the 7.3+ albums would be Joni Mitchell's Hejira, so this can be used as well to give a lower 8 context)

Blonde on Blonde - Bob Dylan (1966)

1:
2:
3: 7.0-7.1
4: 6.7-6.9?
5:
6: 6.4-6.5?
7:
8:
9:
10:
11: 6.5-6.9?
12:
13:
14: 7.6-7.7

Happy Sad - Tim Buckley (1968)

1: 6.6-6.8?
2: 6.4?
3: 6.4-6.9???
4: 6.3?
5: 7.3
6: 5.8-6???

Note: Lots of question marks for these especially while I am still working out "smaller scale" ratings 6.9 and below...

"NEW" RATINGS SCALE "Combo Ratings" (aka "Ratings by Halves" (UNDER CONSIDERATION / MID TESTING / UNOFFICIAL)

13.6-13.7 = 7.8
13.8-13.9 = 7.9
14.0-14.1 = 8.0
14.2-14.3 = 8.1
14.4-14.5 = 8.2
14.6-14.7 = 8.3
14.8-14.9 = 8.4
15.0-15.1 = 8.5
15.2-15.3 = 8.6
15.4-15.5 = 8.7
15.6-15.7 = 8.8
15.8-15.9 = 8.9
16.0-16.1 = 9.0
16.2-16.3 = 9.1
16.4-16.5 = 9.2
16.6-16.7 = 9.3
16.8-16.9 = 9.4
9.5+ ???? TBD

_________________
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Best Films
Best Paintings

AfterHours

Gender: Male
Location: originally from scaruffi.com ;-)

Albums - with track ratings (plus some notes) - currently under discussion:

NONE are "final" or "official". Still under consideration, being worked on...

Ys - Joanna Newsom
1: 7.3
2: 6.0
3: 7.1
4: 7.4
5: 5.0

Misc notes...

Ys is among the "anomalies" that don't seem to follow my ratings scale despite having excellent "continuity" and not having "disparate halves" or really any disparate tracks (like, for instance Ummagumma) that would upset the accumulation and cause its parts to be more of an average of their ratings instead of an accumulation of them.

Tracks 1-3, collectively "feels like" (palpable impact) approx 8.0 (even though it "should" accumulate higher per the numbers?)
Tracks 4-5 collectively "feels like" 7.4-7.5 (even though it "should" accumulate higher?)

By "feel" or "palpable impact" = at least 15.5. Per (probably incorrect) "criteria page" ratings scale, this would mean a 9.0. This is probably no longer accurate. (See scale being considered below). 15.5 would now mean 8.5. Still doesn't explain...

-Why doesn't Ys seem to accumulate (qualitatively) above 8.5? Or, even lower, Scaruffi's 8 (8.2?)? Per "ratings by halves" that are under consideration, it should at least be 8.8 (mathematically, if not palpably). (Sometimes it seems like 8.8-8.9 palpably too, but more often, around 8.5)
-Is it because the tracks, even though individually rating high enough, don't "accumulate" from each other to higher qualitative degrees because they are each developing too similarly and not quite varied enough?
-Are the lower rated tracks (2, 5) enough to bring it down whereas "criteria page" ratings scale and prior incarnations don't indicate this? How much value does a 6 and 5 add (or detract) from the higher rated tracks? Has this been underestimated?

Lorca - Tim Buckley
1: 7.7-7.8
2: 7.0-7.1
3: 5.8-6.0????
4: 7.0-7.1
5: 7.1-7.2

-This provides a good point of comparison with Ys because they're both 5, generally lengthy tracks. And Lorca is for sure (both palpably, and by rating the tracks) 9.0 at least and probably 9.1, maybe even 9.2/10.
-It may be important to note that Lorca achieves its "9.1" in about 39.5 minutes. Ys achieves its rating (whatever it is) in about 55.5 minutes. Does time added to an achievement (thus less consistency per unit of time) affect the overall rating more than previously thought or accounted for by the ratings scale?

Spiderland - Slint (1991)
1: 7.0?
2: 6.6?
3: 6.2?
=7.9?

4: 6.7?
5: 5.3?
6: 7.1
=7.7-7.8?

=8.8-8.9/10

-Potentially another good point of comparison... Just need to work out the track ratings to compare. Also 39.5 minutes. "Palpably" feels higher than Ys (most listens) despite possibly having lower track ratings. Is the 16 minute faster running time the main explanation for the discrepancy? Or, again, is Ys having 2 tracks below 6.5 enough to justify?

Astral Weeks - Van Morrison (1968)
1: 6.9-7.0
2: 7.0-7.1
3: 5.3???
4: 7.0-7.1
5: 5.6???
6: 6.9-7.0
7: 6.6-6.8?
8: 6.3???

Astral Weeks is one of the more similar 8.8+ albums to Ys ("narrative style", compositionally, type of emotional expressivity). It is certainly superior to Ys overall (not necessarily by a huge margin) but this gives a good point of comparison because I/we know Ys must be lower than it yet is also comparable so as to figure out why there is a discrepancy between it's "math" rating and "palpable" rating (as in, Ys can't be higher than 9.0 yet seems to be per the "math" so obviously something is incorrect about this).

(Note that probably the most musically similar album to Ys of all the 7.3+ albums would be Joni Mitchell's Hejira, so this can be used as well to give a lower 8 context)

Blonde on Blonde - Bob Dylan (1966)

1:
2:
3: 7.0-7.1
4: 6.7-6.9?
5:
6: 6.4-6.5?
7:
8:
9:
10:
11: 6.5-6.9?
12:
13:
14: 7.6-7.7

Happy Sad - Tim Buckley (1968)

1: 6.6-6.8?
2: 6.4?
3: 6.4-6.9???
4: 6.3?
5: 7.3
6: 5.8-6???

Note: Lots of question marks for these especially while I am still working out "smaller scale" ratings 6.9 and below...

The Black Saint & The Sinner Lady - Charles Mingus (1963)

1: 6.8+?
2: 6.8+?
3: 6.8+?
4: 7.9-8.0?

Sgt Pepper's Lonely Hearts Club Band - The Beatles (1967)

Overall: 7.0-7.1

1: 4.3?
2: 4.0?
3: 5.1?
4: 5.0?
5: 3.8?
6: 4.3?
7: 5.3?
8: 5.8-6.0
9: 3.5?
10: 3.8?
11: 5.3?
12: 3.5?
13: 6.5-6.9

A Hard Day's Night - The Beatles (1964)

Overall: 5.0-5.1

1: 5.0?
2: 3.8?
3: 3.5?
4: 3.0?
5: 4.0?
6: 4.0?
7: 4.0?
8: 4.0?
9: 3.0?
10: 3.5?
11: 3.9?
12: 3.6?
13: 4.0?

Films:

Rosemary's Baby - Roman Polanski (1968)

1st half: 7.1-7.3???
2nd half: 7.6-7.9???

Overall rating seems like: 8.4-8.6
Rating, per Scaruffi, is: 9.0

If "new" ratings scale (below) is correct or close, it seems like an anomaly that RB would be 9.0 (per Scaruffi; 8.4 - 8.6 per me, which would also be more in tune with the scale numbers I have). On the other hand, there is a possibility that film, dealing more with "total continuity" than most albums, as it tends (most cases) to follow a complete, very cohesive narrative from start to finish (especially directors like Polanski that take great care that practically every scene is both narrative and emotional/thematic development towards a whole) may be able to attain "more than the sum of its halves" than the ratings scale indicates. Film in particular offers potential evidence that an extraordinary degree of continuity can potentially bring smaller sums to higher ratings than the scale otherwise indicates and there may need to be additional "equations" to reflect this (as DelBoca and I have discussed on many occasions). Albums like Mingus' Black Saint, Slint's Spiderland, and others may be very good rock/jazz comparisons for this phenomena.

Note that Films seem to follow more closely to the "old" ratings scale (the one still displayed on my criteria page), so perhaps those are still correct or close under the circumstance of "ideal continuity".

Brazil - Terry Gilliam (1985)

1st half: 7.2-7.4?
2nd half: 8.0-8.1+?

"Palpably" it definitely seems to accumulate, impact, have the depth of, on the order of a high-8.9, or 9.0. So, the "math" needs to be made sense of as it doesn't seem to add up to the new scale (but, as it is 15.2 or possibly above, it works out or surpasses the "old" one still listed on my criteria page). So, again, may be a case of "total continuity" making the overall score greater than the apparent sum of its parts...

North by Northwest - Alfred Hitchcock (1959)

1st half: 7.3-7.5?
2nd half: 7.6-7.9?

Touch of Evil - Orson Welles (1958)

1st half: 7.5-7.6?
2nd half: 7.9?

"NEW" RATINGS SCALE "Combo Ratings" (aka "Ratings by Halves" (UNDER CONSIDERATION / MID TESTING / UNOFFICIAL)

13.6-13.7 = 7.8
13.8-13.9 = 7.9
14.0-14.1 = 8.0
14.2-14.3 = 8.1
14.4-14.5 = 8.2
14.6-14.7 = 8.3
14.8-14.9 = 8.4
15.0-15.1 = 8.5
15.2-15.3 = 8.6
15.4-15.5 = 8.7
15.6-15.7 = 8.8
15.8-15.9 = 8.9
16.0-16.1 = 9.0
16.2-16.3 = 9.1
16.4-16.5 = 9.2
16.6-16.7 = 9.3
16.8-16.9 = 9.4
9.5+ ???? TBD
_________________
Best Classical
Best Films
Best Paintings

Last edited by AfterHours on 03/01/2022 03:53; edited 3 times in total

Rhyner
soft silly music is meaningful magical

Gender: Male
Age: 36
Location: Utah

Okay, here we go. As I already said, there's too much that I want to ask about for me to fit it all reasonably into a single post, so I'm breaking it up into sections. This first section is just three questions I have about the scale itself. These questions might concern things that you've obliquely addressed in previous things you've posted, but as far as I can tell they haven't been answered head on. And fyi I did read the newly updated (to me, at least) criteria page, so I think I'm fairly up to date on what you've posted in the forums on the topic. I'm trying to build a mental picture of every aspect of this scale and how you envision it being used, because all of that is very helpful in developing a precise mathematical formula/function/algorithm that accurately models what you're going for. I'm trying to build from first principles.

These four questions don't (yet) have anything to do with the whole rating-by-halves math, or how a rating is determined. They're only about the ten point scale itself--its structure, how it relates to itself, what its mathematical "essence" is, etc...

--------------------------------------------

First, I'm curious about how you fundamentally and conceptually divide it up, structurally ("at its joints", so to speak). Let me give you an example to help explain what I mean. The Celsius temperature scale is defined by setting 0 as the freezing point of water and 100 as its boiling point. Other temperatures also have significant importance, such as -273.15 being the lowest possible temperature, but the two fixed points of 0 and 100 by themselves define the scale perfectly well, and everything else follows from there.

What I'm wondering is if there are perhaps a couple of similar fixed points that define your scale, from which everything else follows. The obvious, go-to answer would be the extremes, 0 and 10. Zero sets a floor of lowest quality beyond which nothing can be worse, just as 10 similarly sets a ceiling of highest quality. But in what you've written about your scale, I see some other potential "joints". The number 2.5 has especially jumped out at me in what you've said recently, as a turning point of sorts such that above that point quality generally accumulates in a positive way, whereas below it there is a "negative" accumulation. I like analogies, so I'm going to relate this to the temperature scale I've been discussing. This particular "turning point" property of the 2.5 point makes me think of the freezing point (0 degrees Celsius, above which things pleasantly thaw and warm and below which things grow ever colder and less hospitable). And naturally the correlate of absolute zero (-273.15 C) is your scale's lowest value, 0. Other numbers that strike me as having significance are 5 and 7.5. Five could correspond with something like room temperature, or perhaps human body temperature (average, nothing particularly special, etc., but right on the cusp of beginning to distinguish itself/starting to be noteworthy at all). Then 7.5 (or 7.3?) naturally takes the boiling point role ("perhaps the lowest point that will remain truly extraordinary"), another transition point. And 10 is naturally the highest possible temperature, beyond which physics breaks down. This particular division is nicely symmetrical, with the evenly spaced points of 0, 2.5, 5, 7.5, and 10 defining four important segments, each with a different character in some sense.

I'm not saying I think this lines up perfectly, one-to-one, or even that this necessarily even a good ballpark analogy to how you structurally conceive of your scale, but it should give a pretty good idea of what I mean by the following, my first official question of this post:

1. What are the significant turning points, or "joints", of your scale (if it has any), and do you consider any of these to be fixed points that define the rest of the scale?

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Second, and relatedly, I'd like to understand the origins/rationale behind how you have chosen to structurally conceive of your scale, in order to better point the way to an ultimate rating formula/function/algorithm for it. Any way you choose to quantify things on a scale is in some sense arbitrary, and could have been done differently. With temperature this is obviously so, as there are three different scales in widespread use (Celsius, Fahrenheit, and Kelvin). Any one of the three is a perfectly intelligible temperature scale, but the three have clear differences (e.g. 0 C = 32 F = 273.15 K; does doubling this temperature make more sense in one of the three scales than it does the other two?).

Let's assume for the moment that I'm correct in 2.5 being a crucial fixed point of your scale that helps define it. What I'm wondering in this hypothetical case is why you chose to fix this 2.5 positive-vs.-negative-accumulation turning-point concept at 2.5 rather than at, say, 5. Five seems a perfectly natural point for that, assuming we're starting from scratch in assembling a rating scale. Is there any particular guiding principle you have that dictates having 2.5 be the correct number of that specific fixed point? I presume, based on what you've previously written, that trying to get your scale calibrated/aligned with that of Scaruffi plays a big role here, but is there some other fundamental aspect of how you choose to rate art that has naturally led to these decisions?

Tl;dr, here's the second question:

2. What is the origin/rationale behind how and where you have decided to structurally fix the "joints" (as discussed in question one) of your scale?

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Third, a bit on the logarithmic nature of your scale. Logarithmic scales can be counterintuitive (for evidence just look back at your discussion with Seth about how the rating-by-halves math "doesn't make any sense"), but they're really just a more manageable way of looking at data with high variability that might be unwieldy when dealt with in its otherwise more intuitive "raw" form. To quote Wikipedia on one of the most famous logarithmic scales, the Richter scale: "it's essential to understand the Richter scale uses logarithms simply to make the measurements manageable (i.e., a magnitude 3 quake factors 10³ while a magnitude 5 quake is 100 times stronger than that)." It's much easier to talk about threes and fives and eights rather than 1000s and 100000s and 100000000s.

But behind the threes and fives and eights are these more unwieldy numbers. I'd like to know if the same is true in principle with your logarithmic-type rating scale. For instance, on your scale two 7.0s might be equivalent to an 8.0, but in the same way as with the Richter scale, are there "raw" versions of these scores that can be added in the traditional arithmetic way? To pick numbers arbitrarily, let's say the "raw" quality score, not yet converted to your logarithmic-type ten point scale, of a 7.0 is 85. Then two of these would add to 170. Which means 170 is the "raw quality" score of the more tidy and manageable 8.0. And since two 8.0s make a 9.0, the "raw" quality, logarithmically "de-converted" score of 9.0 is 340. And so on. (Don't worry about the numbers being at all correct; I just want to know if the principle applies.)

Thus:

3. Would it be fair to say that whatever the function/process is that determines the numerical "level of quality" of a work, the last step in giving it a rating is in some sense logarithmically converting the "raw" quality score to a more tidy numerical value on your ten point scale, such that you could take these ten point scale scores and run the process backwards in order to deal with these scores in their more "raw" form? Or is there something fundamentally keeping us from doing that?

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That's it for now. I'll have some more questions formulated for you tomorrow, most likely.

AfterHours

Gender: Male
Location: originally from scaruffi.com ;-)

Rhyner wrote:

Okay, here we go. As I already said, there's too much that I want to ask about for me to fit it all reasonably into a single post, so I'm breaking it up into sections. This first section is just three questions I have about the scale itself. These questions might concern things that you've obliquely addressed in previous things you've posted, but as far as I can tell they haven't been answered head on. And fyi I did read the newly updated (to me, at least) criteria page, so I think I'm fairly up to date on what you've posted in the forums on the topic. I'm trying to build a mental picture of every aspect of this scale and how you envision it being used, because all of that is very helpful in developing a precise mathematical formula/function/algorithm that accurately models what you're going for. I'm trying to build from first principles.

These four questions don't (yet) have anything to do with the whole rating-by-halves math, or how a rating is determined. They're only about the ten point scale itself--its structure, how it relates to itself, what its mathematical "essence" is, etc...

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First, I'm curious about how you fundamentally and conceptually divide it up, structurally ("at its joints", so to speak). Let me give you an example to help explain what I mean. The Celsius temperature scale is defined by setting 0 as the freezing point of water and 100 as its boiling point. Other temperatures also have significant importance, such as -273.15 being the lowest possible temperature, but the two fixed points of 0 and 100 by themselves define the scale perfectly well, and everything else follows from there.

What I'm wondering is if there are perhaps a couple of similar fixed points that define your scale, from which everything else follows. The obvious, go-to answer would be the extremes, 0 and 10. Zero sets a floor of lowest quality beyond which nothing can be worse, just as 10 similarly sets a ceiling of highest quality. But in what you've written about your scale, I see some other potential "joints". The number 2.5 has especially jumped out at me in what you've said recently, as a turning point of sorts such that above that point quality generally accumulates in a positive way, whereas below it there is a "negative" accumulation. I like analogies, so I'm going to relate this to the temperature scale I've been discussing. This particular "turning point" property of the 2.5 point makes me think of the freezing point (0 degrees Celsius, above which things pleasantly thaw and warm and below which things grow ever colder and less hospitable). And naturally the correlate of absolute zero (-273.15 C) is your scale's lowest value, 0. Other numbers that strike me as having significance are 5 and 7.5. Five could correspond with something like room temperature, or perhaps human body temperature (average, nothing particularly special, etc., but right on the cusp of beginning to distinguish itself/starting to be noteworthy at all). Then 7.5 (or 7.3?) naturally takes the boiling point role ("perhaps the lowest point that will remain truly extraordinary"), another transition point. And 10 is naturally the highest possible temperature, beyond which physics breaks down. This particular division is nicely symmetrical, with the evenly spaced points of 0, 2.5, 5, 7.5, and 10 defining four important segments, each with a different character in some sense.

I'm not saying I think this lines up perfectly, one-to-one, or even that this necessarily even a good ballpark analogy to how you structurally conceive of your scale, but it should give a pretty good idea of what I mean by the following, my first official question of this post:

1. What are the significant turning points, or "joints", of your scale (if it has any), and do you consider any of these to be fixed points that define the rest of the scale?

Thanks Rhyner, good questions. I don't recall how much these have been discussed here or maybe by PM but it's no matter. They're pretty essential to know and to build from.

Yes, you're right, I have defined it primarily by those points. It remains possible they are subject to change as the lowest and highest are the most difficult to test consistently (few examples), and I sometimes think 2.5 is maybe "really 2.0" but let's stick with this (and if it needs adjustment, we can do that).

But yes, 0 ... 2.5 ... 5 ... 7.5 (with 7.3 being the same with "some" minor reservations, just like 8.8 could be called a "9" with some mild inconsistencies or reservations but still the main qualities) ... And then of course 10 at the top as the ultimate ideal above all.

Your idea of each seems fine. Seems like you get the idea of these "joints".

Another important point that is gaining steam recently is the idea that the accumulative power of a part may start gradually declining below 7.0 (so 6.9). It still accumulates but the "added value" when "combined" with an equal part, may get less and less on down from there.

Rhyner wrote:

Second, and relatedly, I'd like to understand the origins/rationale behind how you have chosen to structurally conceive of your scale, in order to better point the way to an ultimate rating formula/function/algorithm for it. Any way you choose to quantify things on a scale is in some sense arbitrary, and could have been done differently. With temperature this is obviously so, as there are three different scales in widespread use (Celsius, Fahrenheit, and Kelvin). Any one of the three is a perfectly intelligible temperature scale, but the three have clear differences (e.g. 0 C = 32 F = 273.15 K; does doubling this temperature make more sense in one of the three scales than it does the other two?).

Let's assume for the moment that I'm correct in 2.5 being a crucial fixed point of your scale that helps define it. What I'm wondering in this hypothetical case is why you chose to fix this 2.5 positive-vs.-negative-accumulation turning-point concept at 2.5 rather than at, say, 5. Five seems a perfectly natural point for that, assuming we're starting from scratch in assembling a rating scale. Is there any particular guiding principle you have that dictates having 2.5 be the correct number of that specific fixed point? I presume, based on what you've previously written, that trying to get your scale calibrated/aligned with that of Scaruffi plays a big role here, but is there some other fundamental aspect of how you choose to rate art that has naturally led to these decisions?

Tl;dr, here's the second question:

2. What is the origin/rationale behind how and where you have decided to structurally fix the "joints" (as discussed in question one) of your scale?

First and foremost, based on "testing", comparing many works (thousands of rock, jazz albums, classical, paintings, films) and the accompanying "qualitative phenomena" that one experiences across the scale, relative to the different levels. Ex: Actually experiencing over and over again, that at "X level" it is twice the impact of this "Z lower level", and so on. And then seeing more and more how aligned this tended to be by a peculiar consistent rise and fall across the scale. And this got increasingly fine tuned and adjusted as I experienced more and more works across the scale.

TO BE CONTINUED (including probably more to this answer) ... (Sorry short on time, have to answer in parts)
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AfterHours

Gender: Male
Location: originally from scaruffi.com ;-)

CONTINUED FROM ABOVE...

Rhyner wrote:

2. What is the origin/rationale behind how and where you have decided to structurally fix the "joints" (as discussed in question one) of your scale?

Scaruffi did help a lot with the "goal posts". And obviously his reviews/insights have influenced my own evaluations in many cases (particularly Rock). Not that he came up with a 10 point scale for me (or anyone) obviously. Tons of people use that, and I was using a 10-point scale long before I came across him.

But certainly, the more I recognized the (much more often than not) consistent accuracy in his ratings and (especially) how they seemed to be placed on an aligned scale that was made up of a very logical "mathematical" progression as the one I've gradually arrived at over time, this of course was (and remains) as "goal posts" that greatly assisted in organizing my own.

But this still had to be observed and "discovered" as he provides little to no clarification of this (I've even asked him directly and his response was basically "I'll leave that for you to figure out Smile

" ). And the only way to plausibly "discover" this is to go through enough of it oneself and draw the conclusions oneself as per the first part of this answer. So, yes, he was and continues to be very influential, but it is an over simplification if we declare only that my scale is based on his (I know you're not saying this). My earliest Scaruffi-esque lists and criteria page (which can probably still he found on listology via way back machine) would demonstrate a pretty long term gradual progression towards what I've arrived at. Early on I was rating many of the 8.8-9.2 works (plus a number of others no longer rated so high) as 9.6s, 9.7s, 9.8s and what-not because I was less familiar with the very highest works and parts of the scale that I am now. Gradually those came down closer to his ratings. And as the highest parts of the scale were more closely evaluated and in some cases newly "discovered" and "tested" (the return to Classical after years with just Rock and Jazz, evaluation of paintings and Sistine Chapel...), a new height to the scale came to view. For a long time there was "no" 10. I think I had Beethoven and Mahler's 9th at the very top around 9.6 or 9.7 or 9.8 and just didn't have a 10, but assumed if it existed that it would be just a bit above those and went from there to compare against on down to the lower ratings.

This may seem like a tangent, but I am mainly illustrating the idea that the scale had to be "discovered" through testing, comparing many works, across multiple art forms...

It is first and foremost based on comparable qualitative phenomena; the "math" is second to that, an attempt to clarify the values (which are only meaningful in comparison to each other) across the scale.

SORRY I HAVE TO GO AGAIN. WILL TRY AND FINISH UP RESPONDING TO YOUR WHOLE POST LATER TODAY/TONIGHT

TO BE CONTINUED...
_________________
Best Classical
Best Films
Best Paintings

AfterHours

Gender: Male
Location: originally from scaruffi.com ;-)

@ Rhyner

Just wanted to drop in and let you know that about a week ago I suddenly got a major family and work related situation (simultaneously) on my plate and have just been too exhausted by the end of each day to delve into this and put together a decent response. BUT I do want to reassure you that I am not ignoring you and I certainly haven't forgot. I am pretty sure I'll have a day off this upcoming Tuesday, so if I haven't replied any further before then, I should be able to no later than on Tuesday.
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Rhyner
soft silly music is meaningful magical

Gender: Male
Age: 36
Location: Utah

No worries at all. I totally understand that real life gets in the way of this silly internet stuff. I was planning on putting up another batch of questions last weekend but similarly got distracted by things I consider more pressing. So I get it. Take all the time you need. To be honest, I was worried you might be getting annoyed with me for not responding yet to what you said. I'll get around to that (and lots more questions)...eventually.