User:Romeolz/Isomorphic layouts: Difference between revisions
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Harmonic mode is the way Lumatone calls the 12edo Harmonic Table layout. It, and others like it, put harmonically related notes very close to each other. Pitch distance is not well represented in these layouts. There may not always be a clear playing direction, or they may be very jagged. The concept of an albitonic scale is often completely disregarded. Harmonic mode maps very nicely to the concept of harmonic bias. | Harmonic mode is the way Lumatone calls the 12edo Harmonic Table layout. It, and others like it, put harmonically related notes very close to each other. Pitch distance is not well represented in these layouts. There may not always be a clear playing direction, or they may be very jagged. The concept of an albitonic scale is often completely disregarded. Harmonic mode maps very nicely to the concept of harmonic bias. | ||
=== Linearity, playing direction | === Linearity, playing direction === | ||
The linearity of a layout refers to how edostepwise motion looks on a layout. This is a notable trait when talking about '''aurally biased''' layouts. | The linearity of a layout refers to how edostepwise motion looks on a layout. This is a notable trait when talking about '''aurally biased''' layouts. | ||
Linearity implies that the layout has a specific direction along which it is most natural to play. On a Lumatone, for example, to an extent you're locked to a horizontal playing style (if you need to access all of the keys that is). This direction is the same as the octave/equave vector on non-jagged layouts (see below). I call this the '''playing direction'''. | Linearity implies that the layout has a specific direction along which it is most natural to play. On a Lumatone, for example, to an extent you're locked to a horizontal playing style (if you need to access all of the keys that is). This direction is the same as the octave/equave vector on non-jagged layouts (see below). I call this the '''playing direction'''. | ||
A rank-1 definition of linearity: | |||
A layout is the most linear when the angle between the unison vector and playing direction is 90°. When this is the case, every ascending edostep is increasingly far away from a line parallel to the unison vector situated at the starting point. | A layout is the most linear when the angle between the unison vector and playing direction is 90°. When this is the case, every ascending edostep is increasingly far away from a line parallel to the unison vector situated at the starting point. | ||
Linearity can be given a numerical value based on the smaller angle (α) between the unison vector and playing direction. α/90° * 100% gives us a value from 0-100% describing the linearity of the layout. | Linearity can be given a numerical value based on the smaller angle (α) between the unison vector and playing direction. α/90° * 100% gives us a value from 0-100% describing the linearity of the layout. | ||
A more general rank-2 definition: (verbose atm) | |||
A layout is 100% perfectly linear when the interval vectors of the period and generator of the albitonic scale, when collapsed/projected onto the playing direction, have their lengths proportional to their pitch heights. | |||
==== Cluster layout ==== | ==== Cluster layout ==== | ||
Cluster layouts are highly linear. This term is based on the term "cluster MOS" which refers to MOSses that have a generator very close to a | Cluster layouts are highly linear. This term is based on the term "cluster MOS" which refers to MOSses that have a generator very close to a\b, where b is a small edo. Due to this fact the chroma is a very small interval. A cluster layout is any layout that has a cluster MOS as its basis (or as its albitonic scale). The chroma is often mapped to the vertical offset, which makes it easily accessible. The horizontal offset is then an approximation of 1\b. They resemble polychromatic layouts (isomorphic or non-isomorphic) like the ones of the Tonal Plexus or the MicroZone. I think they're the most viable way of approaching live playing in free pitch. | ||
=== Jaggedness, (rank-2 not supported, unison vector) === | === Jaggedness, (rank-2 not supported, unison vector) === | ||
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* You physically rotate the keyboard. (This seems obvious but it is an important distinction) | * You physically rotate the keyboard. (This seems obvious but it is an important distinction) | ||
* Often very impractical, especially physical instruments and larger MIDI controllers. The Hexboard is one of the few MIDI controllers where keyboard rotation has been taken into account in the design. It can be rotated 90 degrees, so any layout can be rotated in 30 degree increments | * Often very impractical, especially physical instruments and larger MIDI controllers. The Hexboard is one of the few MIDI controllers where keyboard rotation has been taken into account in the design. It can be rotated 90 degrees, so any layout can be rotated in 30 degree increments in conjunction with offset rotation. | ||
Offset rotation: | Offset rotation: | ||
* This rotates the layout by a multiple of 60 | * This rotates the layout by a multiple of 90 or 60 degrees, and can be achieved by modifying the offsets in a specific way. | ||
* Square grid: (assuming scaleworkshop right → up ↑ convention) | * Square grid: (assuming scaleworkshop right → up ↑ convention) | ||