Large Intervals As Whole Octaves Plus Remainder
The most common way to describe an interval larger than an octave is as a number of whole octaves plus the remaining interval. The degree is that of the remaining interval.
For example, C4-G5 is 1 octave (C4-C5) plus a perfect 5th (C5-G5).
Note: For more on text notation and octave numbering as used in this post, please visit Text Notation, Pitch and Octave Numbering (coming soon).
Large Intervals As A Single Interval Name
Another approach is to describe the interval using a single interval name.
For example, C4-G5 is called a perfect 12th.
Although this method is primarily used for harmonic analysis, the 2nd octave, from 9th to 14th, also forms the basis of how chord extensions (as found in Jazz chords) are named. It’s worth having at least a general understanding of how this works.
Extra octaves don’t affect the interval’s quality, only the degree; the number of letters. For intervals larger than an octave or 8th, just keep counting: an octave plus a 2nd is a 9th, an octave plus a 3rd is a 10th and so on.
You may have noticed that the numbers don’t quite add up: 8 + 2 = 10, yet I’ve said an octave plus a 2nd is a 9th!
Describing an interval as a name for the number of octaves plus a name for the remainder is similar to how we count an interval and it’s inversion. For each complete octave, one note is counted twice.
In our example, C4-G5, we count C4-C5 as 8 letters, then C5-G5 as 5 letters. C5 has been counted twice, both as the upper note of the octave and as the lower note of the remaining 5th.
How To Name A Large Interval
- To count the degree, add up the number of octaves (8ths) and the remaining interval
- Subtract 1 for each whole octave
Note: Technically the first whole octave is 8 letters and we subtract 1 from subsequent octaves and the remaining interval, but it’s easier to count as above.
For example, A2-F5
A2-F5 = 2 octaves + minor 6th = 8+8+6-2 = 20. A2-F5 = minor 20th
OR
- When adding up the degree, count each whole octave as 7 letters instead of 8, then add the remaining interval
For example,
A2-F5 = 2 octaves + minor 6th = 7+7+6 = 20. A2-F5 = minor 20th
Try These…
Name the following large intervals, first as a number of whole octaves plus the remainder, then using a single interval name:
Answers at the end of this post.
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Answers to Try These…
1 octave + major 2nd = major 9th
1 octave + minor 3rd = minor 10th
1 octave + major 7th = major 14th
2 octaves + minor 6th = minor 20th