If you’re wondering how to introduce music theory topics in the classroom, please take note. This article is about how to explain the tritone interval to music students.MENC member Gabriel Villasurda puts the concept in mathematical terms:
The most “harmonious” intervals start with the unison where the frequencies of the two tones are the same – a ratio of 1:1.
The perfect octave is a ratio of 1:2.
The perfect fifth is a ratio of 2:3.
The major third is 3:4, and so on.
The tritone is the most distant and complex relationship of all the ratios of all the tones of the chromatic scale. The exact mathematical number depends on what temperament system being used. Wikipedia gives at least these two ratios:
25:18,
45:32
“Simple” ratios (perfect 5ths, major 3rds) also produce “harmonious” resultant tones (also known as “Tartini tones”). A tritone produces really dissonant resultants – quarter tones or worse.
Intervals are a fascinating subject since beauty seems to have a mathematical basis. This gives credence to the words of the poet:
‘Beauty is truth, truth beauty,—that is all
Ye know on earth, and all ye need to know.’
-Keats
Villasurda continues:
“[The tritone] is the most jarring sound two tones can make. For that reason a lot of train and 18-wheeler horns make use of the tritone. You might also point out that the diminished triad is also a quite unsettling sound, one that soundtrack composers use a lot to portray something sinister or scary.”
MENC member Gabriel A. Villasurda is recently retired from the Greenville, MI Public Schools.
Read tips for ear training and intonation in the orchestra classroom here.
Gregory Lovitt – August 23, 2011. © National Association for Music Education
