Wikipedia:Reference desk/Archives/Entertainment/2018 March 24

= March 24 =

The Last Naruto the Movie
I have been working on the article The Last: Naruto the Movie and I've been wondering if there were more skilled writers who commented about it besides the typical reviews it got. Nothing in particular. Cheers.Tintor2 (talk) 01:38, 24 March 2018 (UTC)

Systems of tuning not closed under inversion
The system of tuning (elementary intervals) supposedly underlying Indian traditional music (see first table at Shruti (music)) is not closed under inversion. Are all European/Western systems of tuning closed under inversion? Is that a requirement for the coherence of such a system? What problems occur if a system of tuning is not closed under inversion? Thanks. Basemetal 12:33, 24 March 2018 (UTC)

Footnote: The Indian system is built up of 22 elementary steps, called shrutis. No system based on an even number of elementary steps can ever be closed under inversion, unless it includes the interval √2 which is its own inversion, but will never be present in systems based on rational intervals such as the Indian shruti system, our Pythagorean scale, etc. Besides one can check that directly in the table mentioned in the question: there are two kinds of perfect 4ths: 4/3 and 27/20 but only one kind of perfect 5th: 2/3; there is no perfect 5th of 40/27 and so the perfect 4th of 27/20 is not invertible, it is left dangling. There are two other examples, the two kinds of augmented 4th/diminished 5th: 45/32 and 729/512, which are not inversions of one another, but it is not clear to me at this point whether that's a problem with the system or with the data used and its source. Basemetal 12:53, 24 March 2018 (UTC)


 * Unless I am mistaken, the fact that musical systems are closed under inversion (by which is meant, apparently, that any inversion of an interval in the system also is an interval in the system) is not a property of their tuning, but of their definition. The conditions are (1) a limited number of fixed degrees in the octave, and (2) fixed names given to these degrees and to the intervals between them. The tuning system is not concerned.
 * Consider the interval between one key of a keyboard and the 8th key above it; these keys may be named, for instance, C and G♯, and the interval between them is an augmented fifth. The inversion of this interval, the interval between the 8th key and the 12th, is a diminished fourth, in any tuning. This results from the fact that there are only 12 keys in the octave and that the names of the intervals are determined by the names given to the keys. One could have named the same keys C and A♭, and the intervals would have been a minor sixth and a major third respectively – which shows that the intervals depend on the name given to the keys, not on the tuning. One cannot say that the inversion of an agmented fifth is a major third, nor that the inversion of a minor sixth is an augmented fourth, because that would involve two different names at one single moment for the same key (even although it would involve the same pitches).
 * To verify that the tuning is not involved, one may ask the same question to a singer or to the performer on an instrument of movable intonations, say a violin. The fact is that the intervals there have no fixed inversion. Because the intonations are movable, any played interval may take on different values and nothing can guarantee that the particular interval played actually has the particular inversion that would complete the octave – in addition, nothing indicates when that particular inversion might or should be played.
 * The first table at Shruti (music) is based on the assumption that all shrutis are exactly of the same size. But India knows few instruments of fixed sounds – fretted instruments are quite mobile because the frets are high above the fretboard. That shruti are all the same may be wishful thinking, and so is the idea that there are 22 identical shrutis (each equal to 22√2) in the octave (see Shruti_(music)).
 * To sum up, the "invertibility" of a musical system is a matter of theory, not one of tuning. Western theory is so conceived that its musical system(s) is (are) invertible. About Indian theory, I don't know. — Hucbald.SaintAmand (talk) 07:35, 28 March 2018 (UTC)
 * You are mistaken. Inversion is a relationship between frequency ratios (rational or not). E.g. 3/2 is the inversion of 4/3 and vice versa. (In this example the frequency ratios are rational). Generally speaking if x is a frequency ratio (rational or not) then 2/x is its inversion and vice versa. It is true that in the case of 12TET as used in the context of European tonal music (or other systems where each frequency ratio can be given several distinct names in a specific theoretical framework) there's also a layer of theory. Two identical frequency ratios can have multiple names (possibly an infinite number of names in fact). In that case inversion is also a symmetrical relationship in that space that refines but is always compatible with the basic meaning of inversion. But then that's another inversion. For example in 12TET the augmented 4th is the inversion of the diminished 5th and you distinguish augmented 4th and diminished 5th even though as frequency ratios they're both equal to √2. As to your claim that the table assumes all shrutis are of the same size I just don't know what to say. Have you even taken a look at that table? Basemetal  15:18, 28 March 2018 (UTC)
 * Indeed, I didn't look at the table. Having looked, however, I am all the more puzzled. This table certainly does not show what I thought to know about shrutis. I utterly wonder where it comes from (there is no reference given). What it shows, however, appears to be some sort of just intonation. That is to say that this table as a whole can be tuned with pure fifths (3:2) and pure major thirds (5:4).
 * For the sake of concision, I'll describe the degrees with their values in cent, but your could check my description by computing ratios between ratios. The central series of fiths starts from 90 cents and follows for eleven fifths up to 612 (that is 90 792 294 998 498 0 702 203 906 407 1110 612; the italicized values in cents are slightly inexact in the table, but the ratios are correct). Then, on both sides, the next value is not a pure fifth lower or higher than the last ones in the central series, but a pure major third from another note in the series: on the flat side, 590 (the pure 5th would be 588) is a pure major third above 203; on the sharp side, 112 (the pure 5th would be 114) is a pure major third below 498. On either side, the series continues with pure 5ths (i.e. 182 884 386 1088 590 on the flat side, 112 814 316 1017 519 on the sharp side), which are all a pure third below or above notes of the central series. This enharmonic spelling reminds me of the enharmonisches Verwechslung mentioned (by Liberty Manik) for the 13th-century tuning of the Arabic theorist Safi al-Din al-Urmawi, but discussing this will have to be left for another occasion.
 * In other words, this "Indian" tuning of the table at Shruti (music) consists in a full chromatic octave in Pythagorean tuning, say Db Ab Eb Bb F C G D A E B F#, five pure major third above Bb F C G D, and five pure major thirds below F C G D A – needless to say, the notes in these two series of five are pure fifths between each other. Many of these notes are labelled enharmonically in the table, but that changes little to their tuning. Check the ratios, they all fit.
 * I cannot figure out how a tuning system made of pure fifths and pure thirds could not be "closed under inversion". If it is so, this can only result from the way the notes are named, not from the tuning itself. But I suspect that there is something essentially wrong with this table and the fact that no reference is given to support it only increases my doubts, to say the least. — Hucbald.SaintAmand (talk) 21:21, 28 March 2018 (UTC)
 * The source was there until someone took it out as an "irrelevant reference" and no one said anything. Things like this do tend to happen wherever "anyone can edit". The source was: Donald A. Lentz, Tones and Intervals of Hindu Classical Music, University Of Nebraska Studies, No. 24, January, 1961, which was there when the table was first created: https://en.wikipedia.org/w/index.php?title=Shruti_(music)&oldid=46125896. However there were two errors which were corrected in this edit: https://en.wikipedia.org/w/index.php?title=Shruti_(music)&oldid=60864182. One was a grotesque error in the cent content of an interval. But the other was an interesting error precisely in the context of invertibility. Exercise: Find that error and explain what happened. That error was not random. I'm still trying to find out if the error was in the source or introduced by the contributing editor. That editor can't remember (he actually never noticed there was an error) and can't find his copy of the book to check. I'd tend to believe it was introduced by the editor. As to how such a system can fail to be invertible, it's explained in my question. Did you read my question before you decided to answer it, or do you tend to proceed in the reverse order? Is that system actually Indian? That's a fair question. It's certainly considered by Indians today to be Indian: here's the page on shrutis in the Tamil Wikipedia: ta:சுருதி and here is a page from the site of an Indian guy who markets a "22 shruti harmonium". Are those ratios really implicit in the construction that's supposed to be described in the Natya Shastra, an ancient Sanskrit work on theater? I don't know. It certainly must take some interpretation to go from point A to point B. Sanskrit texts are not exactly transparent and this one seems to be worse than most, as there is no reliable ancient commentary of it (reliable on that point at least). There is a famous commentary of it by Abhinavagupta but Abhinavagupta's commentary is mostly interested in general matters of aesthetics and philosophy, not at all in technical matters. I would certainly like to at least see Lentz's book myself before I can even begin to make up my mind. Basemetal  23:19, 28 March 2018 (UTC)
 * I don't know enough about Indian music to solve these problems, I can only say that there appears to be a real problem. This Shruti (music) article blatantly contradicts the affirmation found in the Music of India article: "Its tonal system divides the octave into 22 segments called Shrutis, not all equal but each roughly equal to a quarter of a whole tone of the Western music." The fact that several web sites reproduce similar tables which may all stem from Lentz' book (or not) does not mean anything to me, and I see no reason to trust them more than other WP articles that they contradict (without being better sourced, though).
 * I read and reread your question and the more I read it, the less I understand it. Inversion as you describe it is with respect to the octave (2:1); it is obtained by dividing by 2 the ratio considered. The inversion of the 5th, 3:2, for instance, is 3:4, the 4th (with an inversion of the direction: if a degree is a 5th above another, it is a 4th under the octave of this other). I cannot imagine a ratio that could not be divided by 2. When you say that 27:20 "is not invertible", you only mean that its inversion (27:40) is not included in the table, that is that it is not included in the theory that the table is supposed to represent. But that does not make sense: if both the 8ve of 2:1 and the 4th of 27:20 exist in the theory, then any degree that is 27:20 of a given note is also 27:40 of its octave – the interval may have no name in the theory (I doubt that, though), but it does exist. But I'll gladly read your explanation.
 * Hucbald.SaintAmand (talk) 09:19, 30 March 2018 (UTC)
 * Or to state it more directly: inversion (or absence of inversion) loose their meaning once one is speaking in terms of pitch classes, which obviously is the case in our discussion, and also in the table at Shruti (music) where the degrees, although given a frequency, seem implicitly to be found in any octave. — Hucbald.SaintAmand (talk) 15:45, 30 March 2018 (UTC)
 * Yes those are essentially pitch classes but inversion can be defined for pitch classes just as you can define -x in arithmetic mod 12. Watch: take the 12 pitch classes C, C#/Db, E, ..., B. Now "center" that collection in C. Now you can define an inversion (with respect to C). The inversion of C is C, the inversion of C#/Db is B and vice versa, the inversion of D is Bb/A# and vice versa, and so on. Two pitch classes are their own inversion C and F#/Gb. If you center that collection in some other pitch class clearly you get another inversion. Same in arithmetic mod 12: take 0, 1, 2, ..., 11. Now -0 = 0, -1 = 11 and vice versa, -2 = 10 and vice versa and so on. Two numbers are their own "inversions": -0 = 0 and -6 = 6. As to your observation that "the interval may have no name in the theory but it does exists" you're right but that's exactly the problem. For example the note at 27/20 is obviously at 40/27 from the next octave 2/1 but the Indian system has no name for speaking of that 40/27 interval. That's exactly what I mean when I say that system is not invertible. They have 27/20 which they can call "ekshruti madhyam" but if you say start from that note and call it "chandovati" and ask what is the name of 2/1 with respect to that note, you can't answer. There's no name. That interval is not recognized in the system. You can of course say it is at such an such number of nyuna and/or praman and/or puran from 27/20 but that combination has no name in the system. If you're going to define the Indian system as any combination of nyuna, praman and puran then there's no problem any more, except that you'll get lots of notes that simply have no name. Compare with the Pythagorean tuning. Absolutely any note can be named, be it by using multiple sharps or flats (double sharps or flats, triple sharps or flats, quadruple sharps or flats, and so on ad infinitum). To sum up: what I called the Indian system was the intervals and tones that can be named in that system. Apparently that's the source of our misunderstanding. Basemetal  13:31, 31 March 2018 (UTC)
 * @ Basemetal, but it seems to me that if you define "inversion" in this way (wich I'd rather call "symmetry"), only equal temperaments are entirely invertible. Any temperament with two different values of the semitone cannot be symmetric on all its degrees – and more probably is symmetric on only one or two. A Pythagorean tuning with two flats and three sharps (i.e. with pure 5ths from E♭ to G♯), for instance, is symmetric on A and on E♭, but on none other of its degrees, unless I am mistaken. And irregular temperaments (i.e. those with varying values of the 5th) may nowhere be symmetric. (It might be useful to consider here what Barbour describes as symmetric temperaments, in Tuning and Temperament pp. 156-184, but I cannot do that just now.)
 * As to Lentz' table of shrutis, I'd take it with utmost caution, even although I have no idea of the situation in India today. My understanding of the śruti is that they are intervals of roughly 1/22 of an octave and that scales of 7 svara are made of intervals of 2, 3 or 4 śruti – i.e. of roughly 1/2, 3/4 and 1 tone (slightly wide because 1/22 is larger than 1/24, but śruti being irregular anyway). This closely ressembles the situation in "Arabic" music. But the early versions of the Shruti (music) page that you quote state that the table under discussion represents śruti "in terms of just intonation, although many authors assume schismatic temperament implicitly". Now this somewhat cryptic statement furiously reminds of the unfortunate attempt by Safi al-Din al-Urmawi in the 13th century to represent "Arabic" "quarter tones" by syntonic commas, making use in addition of schismatisches Verwechslung to render the whole thing Pythagorean. I suppose that "schismatic temperament" is meant to translate "schismatic exchange" (see Talk:Schismatic_temperament). Anyway, I suspect that Lentz (or anyone else, perhaps one of his Indian informants) tried to explain śruti in terms of just intonation and of schismatic exchange, but I think in the abstract that this is an odd idea. — Hucbald.SaintAmand (talk) 09:35, 1 April 2018 (UTC)

Credits for tracks of an album
What would be the best place(s) to find the production credits for individual tracks of a music album, if I don't have a copy of the album? See this. Jc86035 (talk) 15:16, 24 March 2018 (UTC)
 * Discogs, like here for example. --Viennese Waltz 15:41, 24 March 2018 (UTC)
 * Thanks. Is Discogs usable on Wikipedia as a source, given that it's crowdsourced? Jc86035 (talk) 15:44, 24 March 2018 (UTC)
 * Probably not. See WP:UGC. --Viennese Waltz 15:51, 24 March 2018 (UTC)