Properties of Perfect Intervals

The intervals of a fourth, a fifth, and an octave/unison. These numbers continually show up again and again in tonal music. They do not imply a major or minor quality, but why call them “perfect”?

  • they contain an open or hollow sound
  • unlike non-perfect intervals, perfect intervals can only be augmented or diminished
  • when inverted, a perfect interval remains perfect. All other types are flipped.
  • they appear at the beginning of the harmonic series, therefore are extremely consonant
  • they are nearly identical in the just intonation and 12TET tuning systems
  • the tritone, an extremely dissonant interval of either an augmented fourth or diminished fifth, lies directly between both P1 and P8, and P4 and P5
  • really… can you deny perfection when you see it?
  • they perform the functions of the tonic, dominant, and subdominant scale degrees and are therefore crucial in establishing tonality
  • most of these do not in fact explain what makes them stand out but are rather direct results of them being chosen in the first place

That’s not nearly as much as I thought. Think of anything else?

The Grace Note

I have been asked to discuss grace notes, so read on if you please. They really are valuable tools to add to the detail of a melody. Whether in jazz or baroque music, the grace note is a fundamental ornament in any type of music.

When a composer decides to notate with these smaller notes, there becomes a bit more ambiguity in the exact performance of the music. This is especially relevant in the Romantic and Contemporary periods, when expression is given much more flexibility and self-interpretation of timing is given more encouragement. There is always more than one way to do something; when composing, there are infinite. However, there are some things a composer ought to know before deciding to notate with these fun additions.

There are two kinds of grace notes, the appogiatura and the acciaccatura. Most elementary musicians connote grace note with the latter term, probably because it looks as if it makes more sense written down. They are both the smaller notes written directly before a regular note, but be aware that the acciaccatura has slash through its stem pointing southwest. It is the acciaccatura (confusingly also called a short appogiatura) that is given less significance than the regular note, and the performer can usually just glide through it. The appogiatura appears with no diagonal stroke, and the exact opposite is done with it. Because it is given more emphasis than the note it precedes, it will often take up more than half the time that the regular is accustomed. The appogiatura is pressed down; it is more important than the notes around it. So why is it not just notated as a regular note? Because 1) the composer chose the ornament 2) the appogiatura was invented long before you thought up anything intelligent, so don’t complain.

Now, remember not to go crazy with them either. Sure, they add interest, but beware of having too much of a good thing. Use them as necessary. I was once asked how to notate an accented grace note. To this I answered, “That would be the appogiatura.” That didn’t seem like a satisfying answer, but it’s true. However, I did realize that the composer simply wanted a short accented note to lead into the next. This is the reason that many contemporary composers avoid the grace note altogether in favor of more explicitly-written regular notes. To have a short, accented note glide into the next, just notate the length of a short, accented note and slur it to the next. If it can be thought, it can be done!

Now remember to be grateful for those grace notes. They could easily not be grace notes, and in that case they would not be giving you as much freedom as you wish.