Overtone scale: Difference between revisions

Line 25:

Another way to write this would be 5:6:7:8:9:10, which shows that the tones form both a scale and a chord; indeed, it is a 9-limit pentad with 5 in the bass. [[Denny Genovese]] would call the above scale "Mode 5 of the Harmonic Series," or "Mode 5" for short. Further examples will be given with a mode number indicated.

A "mode" in other musical contexts is usually a different rotation of the same intervals. In the case of different harmonic modes, that's not exactly the case. However, in some sense it's a reasonable comparison, because as you slide the subset of harmonics around, you're essentially sampling different segments of integers whose prime factorizations follow simple, constant patterns (every 2nd number has a 2, every 3rd number has a 3, every 5th number has a 5) and therefore the full internal interval set (all dyads, triads, tetrads, etc.) from one mode to the next is more alike than it is different.

Any Mode of the Harmonic Series has the characteristic of containing all [[superparticular]] steps ("superparticular" refers to ratios of the form n/(n-1)) that are decreasing in pitch size as one ascends the scale). So for Mode 5 above we have:

@@ Line 25: / Line 25: @@
 Another way to write this would be 5:6:7:8:9:10, which shows that the tones form both a scale and a chord; indeed, it is a 9-limit pentad with 5 in the bass. [[Denny Genovese]] would call the above scale "Mode 5 of the Harmonic Series," or "Mode 5" for short. Further examples will be given with a mode number indicated.
+A "mode" in other musical contexts is usually a different rotation of the same intervals. In the case of different harmonic modes, that's not exactly the case. However, in some sense it's a reasonable comparison, because as you slide the subset of harmonics around, you're essentially sampling different segments of integers whose prime factorizations follow simple, constant patterns (every 2nd number has a 2, every 3rd number has a 3, every 5th number has a 5) and therefore the full internal interval set (all dyads, triads, tetrads, etc.) from one mode to the next is more alike than it is different.
 Any Mode of the Harmonic Series has the characteristic of containing all [[superparticular]] steps ("superparticular" refers to ratios of the form n/(n-1)) that are decreasing in pitch size as one ascends the scale). So for Mode 5 above we have: