User:Romeolz/Isomorphic layouts: Difference between revisions
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* Hobbled layouts | * Hobbled layouts | ||
* Coloring (albitonic and kite, edostep or albitonic gradient) | * Coloring (albitonic and kite, edostep or albitonic gradient, RTT kite gradient???) | ||
* <s>scale (1 or 2 axis)</s>, shear, warp(the weird one, apparently just a type of shear) | * <s>scale (1 or 2 axis)</s>, shear, warp(the weird one, apparently just a type of shear) | ||
* Bosanquet modifications | * Bosanquet modifications OR diatonic layouts (would include W-H and other mods) | ||
* pluridiatonic layouts (basically encompasses almost all commonly used temperaments) | |||
* W-H extensions (interlaced) | |||
* HT extensions | * HT extensions | ||
* equivalence continua | * equivalence continua | ||
* images and audio examples for everything | * images and audio examples for everything | ||
= My "inventions" and terminology = | |||
If there are established names for these concepts please let me know!! | If there are established names for these concepts please let me know!! | ||
== Offsets and vectors == | |||
=== Interval vector === | === Interval vector === | ||
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** ⇒ Terpstran: o<sub>v</sub> ⇒ o<sub>h</sub> - o<sub>v</sub> | ** ⇒ Terpstran: o<sub>v</sub> ⇒ o<sub>h</sub> - o<sub>v</sub> | ||
** ⇒ Workshop: o<sub>v</sub> ⇒ -o<sub>v</sub> | ** ⇒ Workshop: o<sub>v</sub> ⇒ -o<sub>v</sub> | ||
[[File:19edo bosanquet interval vector math.png|thumb|600x600px|19edo Bosanquet-Wilson: p<sub>3</sub> - p<sub>2</sub> = p<sub>3/2</sub>, p<sub>5</sub> - | [[File:19edo bosanquet interval vector math.png|thumb|600x600px|19edo Bosanquet-Wilson: p<sub>3</sub> - p<sub>2</sub> = p<sub>3/2</sub>, p<sub>5</sub> - p<sub>3</sub> = p<sub>5/3</sub>.]] | ||
==== Interval math with interval vectors ==== | ==== Interval math with interval vectors ==== | ||
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<small>The really neat thing about this is that the exponents and multiplications in the subscript turn into multiplications and additions respectively. The reason why is because we're going from linear frequency space (Hz) to logarithmic pitch space (cents)! That fact that all isomorphic layouts are logarithmic in nature and the math we do with them reflects that, was groundbreaking to me. Though it's obvious in hindsight...</small> | <small>The really neat thing about this is that the exponents and multiplications in the subscript turn into multiplications and additions respectively. The reason why is because we're going from linear frequency space (Hz) to logarithmic pitch space (cents)! That fact that all isomorphic layouts are logarithmic in nature and the math we do with them reflects that, was groundbreaking to me. Though it's obvious in hindsight...</small> | ||
== Layout behavior == | |||
=== Aural bias vs. harmonic bias === | === Aural bias vs. harmonic bias === | ||
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Though intended for 12edo, these terms can be generalized to other tunings. | Though intended for 12edo, these terms can be generalized to other tunings. | ||
[[File:Lumatone classic mode with playing direction and scale.png|none|thumb|600x600px|Bosanquet-Wilson: the albitonic major scale in blue overlaid with the playing direction/octave vector in purple]] | [[File:Lumatone classic mode with playing direction and scale.png|none|thumb|600x600px|Bosanquet-Wilson: the albitonic major scale in blue overlaid with the playing direction/octave vector in purple]] | ||
Classic mode refers to a 12edo Bosanquet-Wilson layout originally, but I will expand the meaning to include other layouts that have specific properties. Their equave vectors and playing directions are the same, that being horizontal. They're non-[[User:Romeolz/Isomorphic layouts#Jaggedness, (rank-2 not supported, unison vector)|jagged]], and have some easily accessible albitonic scale as their basis. It's a meandering line that closely follows the playing direction. Classic mode is analogous to aural bias. | Classic mode refers to a 12edo Bosanquet-Wilson layout originally, but I will expand the meaning to include other layouts that have specific properties. Their equave vectors and playing directions are the same, that being horizontal (and to the right). They're non-[[User:Romeolz/Isomorphic layouts#Jaggedness, (rank-2 not supported, unison vector)|jagged]], and have some easily accessible albitonic scale as their basis. It's a meandering line that closely follows the playing direction. Classic mode is analogous to aural bias. | ||
[[File:Lumatone melodic mode with playing direction and scale.png|none|thumb|Wicki-Hayden: the albitonic major scale in blue overlaid with the playing direction/octave vector in purple]] | [[File:Lumatone melodic mode with playing direction and scale.png|none|thumb|Wicki-Hayden: the albitonic major scale in blue overlaid with the playing direction/octave vector in purple]] | ||
Melodic mode refers to the Wicki-Hayden layout in 12edo. I will add layouts to the term that adhere to the following. The equave vector is close to vertical, and so is the playing direction. They also have a very clear albitonic scale as their basis, but rather it's laid out in a block-like shape much more densely. It zigzags around the playing direction. Melodic mode can be aurally biased or harmonically biased depending on the harmonic content of the albitonic scale. | Melodic mode refers to the Wicki-Hayden layout in 12edo. I will add layouts to the term that adhere to the following. The equave vector is close to vertical, and so is the playing direction. They also have a very clear albitonic scale as their basis, but rather it's laid out in a block-like shape much more densely. It zigzags around the playing direction. Melodic mode can be aurally biased or harmonically biased depending on the harmonic content of the albitonic scale. | ||
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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 (or close to it). | ||
=== Jaggedness, (rank-2 not supported, unison vector) === | === Jaggedness, (rank-2 not supported, unison vector) === | ||
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A layout is not jagged when you can easily traverse it along the playing direction using your preferred intervals such that you only need to use one shape per interval without veering too far from the playing direction. | A layout is not jagged when you can easily traverse it along the playing direction using your preferred intervals such that you only need to use one shape per interval without veering too far from the playing direction. | ||
A layout is jagged when the aforementioned | A layout is jagged when the aforementioned travel requires regular use of two shapes per interval (or the unison vector) to stay in the playing direction. | ||
==== Jaggedness, legibility and ergonomics ==== | ==== Jaggedness, legibility and ergonomics ==== | ||
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=== Eastern/Western layout === | === Eastern/Western layout === | ||
Kind of a niche term, as I've seen it used in one place. They're part of the layout names for two 53-tone JI presets on terpstrakeyboard. Western refers to how a Bosanquet-Wilson layout is normally presented, with the large step (o<sub>h</sub> axis) pointing slightly upwards. Eastern is the opposite, a vertical flip of the western one, with the large step (o<sub>h</sub> axis) pointing downwards. The terpstrakeyboard webapp also uses the terms male and female, but I prefer using the other terms. | Kind of a niche term, as I've seen it used in one place. They're part of the layout names for two 53-tone JI presets on terpstrakeyboard. Western refers to how a Bosanquet-Wilson layout is normally presented, with the large step (o<sub>h</sub> axis) pointing slightly upwards. Eastern is the opposite, a vertical flip of the western one, with the large step (o<sub>h</sub> axis) pointing downwards. The terpstrakeyboard webapp also uses the terms male and female, but I prefer using the other terms. | ||
== Layout modifying operations == | |||
=== Layout modifying operations (temperament preserving) === | === Layout modifying operations (temperament preserving) === | ||
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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) | ||
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==== Skew ==== | ==== Skew ==== | ||
(i'm struggling with this one) | |||
== Subpages == | |||
[[User:Romeolz/Isomorphic layouts/Harmonic Table extensions]] | readable and possibly useful! todo | |||
[[User:Romeolz/Isomorphic layouts/Diatonic layouts]] (useless atm) | |||