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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)
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)
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)
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