Stein–Zimmermann–Gould notation: Difference between revisions

=== Sharp-1 ===

Sharp-1 edos have a sharp that raises 1 step. Edos of this category include {{EDOs| 5, 12, 19, 26, and 33 }}. Standard chain-of-fifths notation can be used since an up-arrow is exactly equivalent to a sharp.

=== Sharp-2 ===

Sharp-2 edos have a sharp that raises 2 steps. Edos of this category include {{EDOs| 10, 17, 24, 31, 38, and 45 }}. Stein–Zimmermann accidentals, Gould arrows, or a combination of both may be used.  

=== Sharp-3 ===

Sharp-3 edos have a sharp that raises 3 steps. Edos of this category include {{EDOs| 8, 15, 22, 29, 36, 43, and 50 }}. This is first sharpness value where Gould arrows must be used.  

In some cases, some notes or intervals may be best spelled with double arrows:

=== Sharp-4 ===

Sharp-4 edos have a sharp that raises 4 steps. Edos of this category include {{EDOs| 20, 27, 34, 41, 48, 55, and 62 }}. This is first sharpness where the Stein–Zimmermann–Gould notation works in its full form.  

=== Sharp-5 ===

Sharp-5 edos have a sharp that raises 5 steps. Edos of this category include {{EDOs| 32, 39, 46, 53, 60, 67, and 74 }}.

In some cases, some notes or intervals may be best spelled with triple arrows:

=== Sharp-6 ===

Sharp-6 edos have a sharp that raises 6 steps. Edos of this category include {{EDOs| 44, 51, 58, 65, 72, 79, and 86 }}.

Attaching arrows to semi- and sesquisharps and flats is also another option instead of using double arrows:

=== Sharp-7 ===

Sharp-7 edos have a sharp that raises 7 steps. Edos of this category include {{EDOs| 56, 63, 70, 77, 84, 91, and 98 }}.  

=== Sharp-8 ===

Sharp-8 edos have a sharp that raises 8 steps. Edos of this category include {{EDOs| 61, 68, 75, 82, 89, 96, and 103 }}.

=== Higher sharpness values ===

Here is an example of a notation scheme for sharp-10 edos.  

And here is an example for sharp-14.  

=== Flat-1 ===

For edos such as {{EDOs| 9, 16, 23, and 30 }}, if you notate them as if their native antidiatonic scales were diatonic, you would find that the sharp actually ''lowers'' by one step. If one wishes to "translate" diatonic songs into these edos, this is useful.  

However, a much more intuitive solution is to swap the meaning of sharps and flats in regards to fifthspan (so that sharp still raises and flat still lowers), allowing the accidentals to more naturally notate these edos' native antidiatonic (in this case, the normal set of sharp-1 accidentals would be used).   

=== Flat-2 ===

Flat-2 edos (virtually [[11edo]] only), if you pretend their native antidiatonic scales are diatonic, have a sharp that ''lowers'' 2 steps. So besides the special flavor of the sharps and flats, there are also semisharps and semiflats to fill up the spaces between. It makes the most sense to notate them as subsets.  

=== Zero ===

The lower three multiples of 7 ({{EDOs| 7, 14, and 21 }}) are known as "perfect" or sharp-0 edos, since, by tempering out the Pythagorean apotome of [[2187/2048]], the traditional sharps and flats are redundant and cannot raise or lower the pitch. Here, the notes can only be modified by arrows. [[28edo]] and [[35edo]] also fall into this category using their native fifths, but they are better notated as subsets.  

== Limitations ==