# Musical cells

**Musical cells** ^{[idiosyncratic term]} are a system of Mario Pizarro for constructing well temperaments. Recently he has connected this to a system of stretched octaves he calls "**toctaves**" ^{[idiosyncratic term]}. This is discussed on *The corrected progression of musical cells*.

## Musical cells

Pizarro's musical cells are based on a set of three commas:

- M: (3
^{8}× 5)/2^{15}(schisma); - J: (2
^{25}× 2^{1/4})/(3^{13}× 5^{2}); - U: (2
^{12}× 5^{2}× 3^{1/2})/3^{11}.

Using combinations of these commas, he defined two "semitone factors" K and P, which he then put together to from the Piagui scale. This well-tempered scale follows an 8L 4s pattern, with large steps K and small steps P. There are three variants (rotations) of this scale: Piagui I (KKP KKP KKP KKP), Piagui II (KPK KPK KPK KPK) and Piagui III (PKK PKK PKK PKK).

## Toctave

The toctave (short for "True Octave") is a frequency ratio of 27 * 2^(1/4) / 16 (ca. 1205.865 cents) which Pizarro came up with in connection with his theory of musical cells.

[math]Toctave=\frac{27}{16}\sqrt[4]{2} \approx 2.0067870065670918\dots[/math]

This is 1/4 of a Pythagorean comma sharp.

Threads/Folders on the tuning list:

- http://launch.groups.yahoo.com/group/tuning/message/100919 - "The True Octave"
- http://launch.groups.yahoo.com/group/tuning/message/101004 - "A new equal tempered scale?"
- MarioPizarro - Google Drive - Collection of materials on the topic