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I've always wondered what makes these particular intervals so difficult.

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There was an awesome youtube video about this, but it's been taken down. Here is just the audio, in French with no subtitles. –  rshallit Jun 10 '11 at 2:02
    
Because tritones hurt the ears? :-) (If not yours, more power to you!) –  Monica Cellio Jun 10 '11 at 2:09
    
Funny, that. IMO it's because they stick out so much that they're so easy to remember. Also : blue note, Purple Haze, Sabbath Bloody Sabbath, and the tasty Lydian mode. –  Pif Jun 16 '11 at 8:34
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3 Answers

up vote 6 down vote accepted

The augmented 4th / diminished 5th (aka tritone) is the furthest (enharmonic) note away both in terms of circle of fifths and shared harmonics so it is a very "distant" note.

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+1 - I guess I could have gotten more specific. Good answer, straight to the point. –  balentaw Jun 9 '11 at 22:11
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Ok, I knew they were called tri-tones because of their enharmonic ratios, but I didn't know what made them sound that way. Thanks!! –  user705 Jun 9 '11 at 22:15
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They may not be as hard to sing if you think in your mind of their resolution. Try to think of the augmented fourth going to the 5th and of the diminished 5th resolving in the 4th, depending on the direction of the next notes.

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What makes these intervals so difficult to sing is that they are very dissonant. Dissonance is used all the time in music to set-up tension that will later be "released" by a consonant interval. Augmented fourths and diminished fifths (which are also enharmonic tones) are the two most dissonant intervals.

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