Multiplying a note by 2 creates an octave, and multiplying it by 3 creates a perfect fifth.
5/1 is over two octaves above the original note, so you have to reduce it twice (divide by 4) to get it down into the same octave.5-4
This scale is contained in the chord of nature, and it pops up all over the place. A clear example is the bugle.
Bugles have no valves or keys. So how can you play more than one note on one?
A bugle is a long tube full of air, curved so it fits in a small space. The player’s lips get the air column vibrating, and by changing the tightness of her lips, the player can coax the air column into vibrating along its whole length, or get it to break up into sections, just like the jump rope in the Chord of Nature demonstration.
Here are the bugle notes: bugle scale
Two sidebars before I go on.
1) Isn’t it strange that when you multiply by 3 you get a fifth and when you multiply by 5 you get a third? The note names come from their position in a seven-tone scale. Here’s how our new scale fits with the standard do-re-mi. The notes we’ve explored are played louder to set them apart. five notes in do re mi
The 5/4 note pops up third in the scale and the 3/2 note comes up fifth. It’s just a confusing coincidence, based on our fondness for seven-tone scales.
2) Here’s a sneak preview of why I’m going to all this trouble. The equal-tempered major third that we’ve been hearing all these years is not tuned to the 5/4 ratio. It’s tuned sharp, by almost 1%. This isn’t enough to make the note sound obviously sour, but it’s certainly enough to change the feel of it.
Try listening to the following example a few times, and pay attention to how you feel while listening. JI3 vs ET3
The first note you hear is the tonic with a pure major third. The second note is with an equal tempered major third. Then it goes back to the pure 5/4 note. The pitch difference is small, but I perceive an uneasiness, almost a queasiness about the equal-tempered version. Do you hear a difference, and if so, how does it feel to you?
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