When the first sixteen harmonics are octave-displaced and compressed into the span of one octave, the result is an octatonic scale whose pitches have the following frequency ratios:



5:4 (a.k.a. 10:8)


3:2 (a.k.a. 6:4 or 12:8)


7:4 (a.k.a. 14:8)



An example of this scale can be heard here. Press and hold a tile labeled R0 and slide the cursor over to R1. Notice that it sounds similar to the major scale, except the perfect fourth is replaced with a lesser undecimal tritone and the major sixth is replaced with a tridecimal neutral sixth and a septimal minor seventh. These alternative pitches give the scale a steelpan-like, tropical-island-y feel (at least to my ears), with the septimal minor seventh in particular adding a jazzy flair.

Is there a name for this scale? If there isn't one, then the name "harmonic octatonic scale" might be the most logical choice. And is this scale at all useful? Are there any examples of songs which utilize this set of pitches, perhaps from non-Western cultures? Thank you.

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    That web app is very cool ~ – topo Reinstate Monica Mar 9 at 13:21
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    I could play day and night with this fabulous instrument. You can play with the l.h. an accompaniment pattern, Waltz, Alberti basses, odd rhythms .... and with the r.h. melodies (5 voices and also a fugue. I bet Schönberg, Bartok, Stravinsky, Hindemith would have fun with it. Thank you for sharing – Albrecht Hügli Mar 9 at 16:17

I can't think of one, but two modifiers you may consider are acoustic and spectral. And in the absence of better terms, I would argue that something like "acoustic octatonic" or "spectral octatonic" could be meaningful.

"Acoustic" is often used to indicate a connection to the harmonic series, like with the "acoustic scale," which is the scale comprised of the first appearance of each scale degree in the harmonic series. The C acoustic scale, for instance, has both F♯ and B♭ because those are the first appearances of those scale degrees in the harmonic series built on C.

And another term, if a bit less apt, is "spectral." Spectral music emphasizes the natural acoustic properties of sounds, and often that results in composers using the tuning variations inherent in the harmonic series. But spectralism also deals with other acoustic aspects, so perhaps this possibility isn't quite as well-suited as "acoustic."

  • I'm so sorry, I meant to give you the bounty but I accidentally gave it to the person who wrote the answer below. – Mark Morales II Mar 19 at 4:36
  • @MarkMoralesII No worries, I just hope you got some answers you feel are worthwhile! – Richard Mar 19 at 4:38
  • Thank you for understanding. Yeah, it looks like this scale doesn't have an official name, but something like "just acoustic octatonic scale" might make the most sense. :) – Mark Morales II Mar 19 at 4:46

As more of a math person than a music one, I would simply call it a "linearized octave" scale. Not that I have ever met something like it.

It has second and fifth in common with the Pythagorean scale... and nothing else sounding familiar.

Transposition will be ugly even compared with Pythagorean.

On the other hand, a harp-like instrument tuned to it and made of a single type of string may look pretty interesting (octaves being trapezoid).

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