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A tritone is literally half an octave. The very idea of it drove the Pythagoreans crazy. The tritone is the music interval between the first two notes of the song that goes "The-Simps-Ons"♬
Tuning Timbre Spectrum Scale, by William A. Sethares
https://sethares.engr.wisc.edu/ttss.html
Explains dissonance theory, and how any interval can be made either consonant or dissonant by designing a specific non-harmonic spectrum for the sound of its two constituent pitches. [pocmloc, Nov 06 2020, last modified Nov 07 2020]
Design of chimes to produce consonant, non-harmonic scales. Arthur Gretton, Department of Engineering, Australian National University, Canberra. Acoustics Australia, Vol. 27 (1999) No.1 p.11-16
http://www.gatsby.u...apers/Gretton99.pdf
An application of Sethares's principles to manufacture cylindrical chimes to a desired spectral profile. [pocmloc, Nov 07 2020]
[link]
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The chiming element is usually a resonant tube; since that resonance is determined as a function of mass, density, diameter, wall thickness etc., it can be entirely arbitrary. Thus making a set of harmonious or dissonant chimes is just a matter of trimming to size. |
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I think a Trumptone would be a good sound to generate as well. This would take the form of a prolongued cry-baby wailing note similar to that of what an infant would make were its toe to get nipped by the pet crab. (who's Trump? I hear you ask) |
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Tritones are only dissonant if the sounds have harmonic spectra. Chimes are non-harmonic and therefore there is no reason why tritone chimes should not be sweetly consonant. <link> |
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A tritone is literally three tones and is NOT exactly half an octave unless it is arbitrarily defined to be so; three pythagorian whole tones give a frequency ratio of (9/8)^4 = 6561/4096, which is more than half an octave. Half an octave (geometrically) is root two. |
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In practice, there are many intervals which are approximate half an octave. A barbershop seventh chord (or harmonic seventh chord) has the frequency ratios 4:5:6:7 (or an inversion of them); the ratio 5:7 is called a septimal diminished fifth, or a septimal tritone, and is harmonious (even if the sounds have harmonic spectra), in the context of the entire chord. A set of wind chimes in these ratios sounds pleasant and slightly eerie. |
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They are also useful as a mild form of torture. I was once demonstrating the difference between a harmonic seventh chord and a dominant seventh chord and it didn't take her long to say through gritted teeth "Fine, but can you PLEASE resolve it now?" |
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// useful as a mild form of torture. // |
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<Files factoid away for potential future employment, particularly with musicians/> |
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