Magic Temperament

Magic is a rank 2 temperament class that's exceptionally efficient in the 9-limit. Its complexity is slightly higher than meantone — you need 12 generators for a complete chord — but it gets closer to just intonation.

It's worth considering the 9-limit as distinct from the 7-limit because it means perfect fifths get more weight, which people tend to like, and it allows for more familiar intervals. There are two perfect fifths included in a 4:5:6:7:9 pentad. You also get the subminor triad 6:7:9 and its reflection, the car horn triad.

I wrote an introduction for 19-tone musicians.

I developed Tripod Notation article to work with it. You can get the source code to that article.

A short article about Trippy Trojans (Trojan Sagittal written with tripod names).

A far too long article about tripod notation extended to the 15-limit.

I worked out some keyboard mappings to work with magic temperaments, based on tripod notation. In the first, 18 of the 19 notes of the pengcheng scale are spread across the keyboard. (Not the same 18 in all registers.) This means the tripod scale is on clusters of three keys, alternating black and white. So three black keys, three white keys, three black keys, and so on.

In the other mapping, the 22 notes of the haizhou scale are included in a 24 note keyboard mapping. The 10 black keys to the octave are the tripod scale plus a note that is unreachable by a single accidental, and could be placed on the missing position of tripod notation.

Here are Scala files for the mappings:

Pengcheng 18 from 41-equal 18 from 60-equal 18 from TE-optimal
Haizhou 24 from 41-equal 24 from 60-equal 24 from TE-optimal

The Python file to produce them is in the source code bundle above.

I wrote a CSound instrument some time ago.

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