### an approach for non-octave tunings

Posted:

**Thu Feb 25, 2021 10:02 am**Several years ago I had a fling with a nonatonic scale I call 3-TOH (pronounced to rhyme with "Cheetoh", and short for matter-of-factly the "third tritave of odd harmonics")*: a tritave-repeating scale with notes in the frequency ratio 9:11:13:15:17:19:21:23:25 (and then repeat on 27). It popped back in my head this afternoon, and I wondered how I'd notate it in Sagittal. One iteration of the scale would look like this**:

So here's my idea, a bit outside the box: what if you were able to capture the tritave-repeating aspect of this scale by essentially copy+pasting this series of sagittals onto a new nominal 1/1 basis? In other words, continuing up another run of this scale would look like this:

In other words, since the first run of the scale was on E (i.e. 1/1 is E), the next one would switch to being on B. And the tritave below the original tritave would be notated with A as 1/1.

Is that crazy, or heretical? You could perhaps in the legend/instructions for the piece give a visual which shows which nominal is 1/1 in each tritave register.

*It occurred to me when I was learning about modes of the harmonic series, but I wondered why they had to be octave-based. I've always loved Bohlen-Pierce and its idea of eschewing factors of 2. My attempt at notating BP last year when I had way less idea of what I was doing is still sitting there and I haven't taken a second shot at it yet, though. The main idea of this post could potentially be applied to it, too, though.

**Whether you put it in the Prime Factor notation (only Evo flavor) or the JI notation. Technically the Prime Factor notation would use A for 25, but I think that because is not used for any prime up to 61 and is therefore available for use, it should probably be recommended to make that exception generally speaking when using Prime Factor notation. And to be clear, this is using the High precision level of the JI notation, even though it's not recommended; the Medium level won't quite do because it's only 17-limit, but it's not quite the Ultra (Very High) precision level because we drop the accents on the symbol for 13.

So here's my idea, a bit outside the box: what if you were able to capture the tritave-repeating aspect of this scale by essentially copy+pasting this series of sagittals onto a new nominal 1/1 basis? In other words, continuing up another run of this scale would look like this:

In other words, since the first run of the scale was on E (i.e. 1/1 is E), the next one would switch to being on B. And the tritave below the original tritave would be notated with A as 1/1.

Is that crazy, or heretical? You could perhaps in the legend/instructions for the piece give a visual which shows which nominal is 1/1 in each tritave register.

*It occurred to me when I was learning about modes of the harmonic series, but I wondered why they had to be octave-based. I've always loved Bohlen-Pierce and its idea of eschewing factors of 2. My attempt at notating BP last year when I had way less idea of what I was doing is still sitting there and I haven't taken a second shot at it yet, though. The main idea of this post could potentially be applied to it, too, though.

**Whether you put it in the Prime Factor notation (only Evo flavor) or the JI notation. Technically the Prime Factor notation would use A for 25, but I think that because is not used for any prime up to 61 and is therefore available for use, it should probably be recommended to make that exception generally speaking when using Prime Factor notation. And to be clear, this is using the High precision level of the JI notation, even though it's not recommended; the Medium level won't quite do because it's only 17-limit, but it's not quite the Ultra (Very High) precision level because we drop the accents on the symbol for 13.