Talk:Tritone/Archive 6

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Tritone as irrational ratio

That the equal-tempered tritone stems from an irrational number ratio does not explain it as a dissonance. Except for the octave, all intervals in ET are irrational numbers. The perfect fifth, for instance is 1.4983070768766..., yet it is treated as a consonance. --Myke Cuthbert 01:06, 25 April 2007 (UTC)

We almost need another name for the frequency exactly half way up or down the octave whose frequency is the square root of two times the tonic. "tritone" doesn't quite cover it because it depends which kinds of tone it's three of. ET is an approximation to Pythagorean perfect intervals. The "perfect" fifth sounds consonant in ET and so "is treated as a consonance" because for most ears it is near enough to 1.5. Using the figure above, the ET "perfect" fifth from A440 is 659.2551138257 Hz, the true perfect fifth is 660, so they would beat together at 0.745 Hz, a slow throb that would not be perceived as "out of tune" by most people (two slow even for a vox humana effect). The true root-2 interval is not near to anything. That's the point I've been trying to get across. --Hugh7 08:18, 25 April 2007 (UTC)

It's near to several just intervals, like 7/5. Furthermore irrationality is certainly not the cause of dissonance, and equal temperament is not the cause of the tritone's dissonance. The tritone is still dissonant in just intonation (and it was known to be dissonant long before temperament began). - Rainwarrior 16:05, 25 April 2007 (UTC)

7/5 is pretty remote for a just interval, being the ratio of two non-trivial prime numbers. Two vibrating bodies tuned to 7:5 will pass through their rest-points in the same direction only every 35 cycles, which is rather too many for the ear to "count". Do people hear that as "more harmonious" than an accurate 2^½:1? --Hugh7 07:49, 1 May 2007 (UTC)

And 6/5 only once every 30, but that one's long been catalogued as a consonance, and what about 7/4, shouldn't that be by your logic more consonant than 6/5? The lowest common multiple isn't really a measure of consonance. Dissonance and consonance are largely contrapuntal functions, for instance, 4/3 is "dissonant" in much theory. 7/5 is dissonant in tonal use in general. This has nothing to do with the fact that 7/5 is an audibly pure and stable interval and 2^1/2 is not. If you put it in the context of a justified dominant seventh chord 4:5:6:7, compared to the ET version it is profoundly stable. - Rainwarrior 17:37, 7 July 2007 (UTC)

7/5 and 10/7 are relatively consonant. They just sit there nicely. However, if you stack three large major seconds (9/8), which is what a tritone would literally be (an interval the width of three tones stacked), which is the same as stacking six perfect fifths and subtracting three octaves, or basically stacking prime 3 six times ignoring octaves, you get 729/512 and its inversion 1024/729, both of which are pretty dissonant. That's why the tritone is historically considered dissonant. It has to do with reaching far away using repetitions of the same prime 3, not with reaching nearby for those close friends prime 7 and prime 5. As another illustration, even stacking prime 3 just four times is dissonant. Adjusting for octaves, that gets you the Pythagorean Major Third, 81/64, which is more dissonant than 5/4, even though 5 is a higher prime. 38.86.48.38 (talk) 06:06, 2 May 2015 (UTC)

Copied without credit

A lot of this article is copied verbatim from http://self.gutenberg.org/articles/diminished_fifth, which is "sourced from World Heritage Encyclopedia". That's why there is an odd clause that says "according to a rule explained elsewhere, but there is no explanation. Bolaurent (talk) 22:18, 2 November 2015 (UTC)

Or not. I notice that, at the bottom of the Gutenberg page it says that "World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., ..." (my bolding). This could easily mean that the content there was copied from Wikipedia, not the other way around. The missing "rule explained elsewhere" could just as easily be explained by a deletion of that material at some earlier point in time. Have you checked the edit history?—Jerome Kohl (talk) 00:44, 3 November 2015 (UTC)

Possible problems as of January 2017

I'll try to solve some of them (those I can) if I have time...

1. Inappropriate references Many sections lack any kind of references or have an insufficient number of them, and they often speak of very technical details which should require a proper reference. In the same way, some sections have way too much citations: for example; there's no need to cite 4 different books to say that "an augmented fourth is either 45/32 or 25/18".

2. Probable OR in the "Historical uses" section This sections makes many statements concerning the musical analysis of the pieces contained without referring to any sources (except for the Debussy piece), and links to the related pages (ex. the Siegfried opera don't provide sources for a musical analysis). While the comments may be right (sure, a tritone certainly doesn't mean "all is calm..."), they are not verifiable. Also, I think that the current section should be expended to talk more about the use of tritones in modern music.

3. Excessive use of abbreviations impedes clarity Using "A4" and "d5" repeatedly in the body of the text (the equations are another matter - but whether they should be used or not certainly isn't the problem we should worry about, given the other issues) impedes readability. 69.165.196.103 (talk) 04:35, 28 January 2017 (UTC)