The Sagittal forum

Maybe a good way for me to approach notating my various bizarre JI scales is to just start with D as my 1/1. Then mark all the places where my pitches are. 1 2 1 1 3 1 2 1 1 1 Fbb Cbb Gbb Dbb Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx Dx Ax Ex Bx Then I would just ...

A chain-of-fifths slide-rule is a solution to many problems. FbbCbbGbbDbbAbbEbbBbbFb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx Dx Ax Ex Bx |--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--|--| offsets from 1/1 -5 -4 -3 -2 -1 0 +1 ...

I guess what would be even better, though, what I really want, rather, is just the feature I have planned for the web app notation calculator, where you can at the click of a button change the 1/1, and see how that affects every pitch in your tuning, so at a glance you can eyeball which 1/1 is best...

I suppose it's the G version which in particular I'd like to see, how the harmonic series happens to fit most closely to the sharp- and flat- less nominals on a chain of Pythagorean fifths when you base it on G. Something like: a ring, corresponding to the octave, with the fifths and the harmonic s...

Correction: "any chord and its inversion" -> "any chord and its inverse". e.g. D:F#:A and G:Bb:D.

Not really sure what you're after. You could directly show on a staff, each of the scales and chords I described.

Ah, okay. So Sagittal is harmonically-based, but still quite suitable in terms of melody in almost all cases. Could anything else cause harmonic and melodic disagreement besides a negative chromatic semitone? Yes. A negative anything. Including F being lower in pitch than E. None of which we do in ...

AFAIK, that choice between harmonic and melodic notations is specific to 23-edo and two other edos on the right of the periodic table, namely 16 and 9, sometimes called the Mavila EDOs. Every sagittal notation is both melodically and harmonically consistent in the sense of that 23-edo article. We ac...

I totally agree. Couldn't have said it better. That's effectively what we say in the XH article when we introduce the Trojan notation: You can just treat them as random symbols (with a rough increase of symbol size with alteration size and some handy flag arithmetic in a few cases). Never mind about...

So I take it there's not a fancy Greek word like "apotome" or "limma" for the whole tone? If there was, we would be using it. I can't find anything like it about town. No. You'd think it might be "tonos" plural "tonoi", but that seems to mean something more l...

In the Periodic table, I'd noticed that vicinities of fifth size are named, e.g. Super-pythagorean, meantone, etc. but I hadn't specifically noticed until just now that the very middle has the words "equal tempered". If that's similarly supposed to be a name for a fifth size, that's confu...