User:Romeolz/Isomorphic layouts: Difference between revisions
warp n stuff |
stretch |
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* Hobbled layouts | * Hobbled layouts | ||
* Coloring (albitonic and kite, edostep or albitonic gradient) | * Coloring (albitonic and kite, edostep or albitonic gradient) | ||
* scale (1 or 2 axis), 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 | ||
* HT extensions | * HT extensions | ||
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(add examples) | (add examples) | ||
==== Lumatone: Classic mode, melodic mode, harmonic mode ==== | |||
Though intended for 12edo, these terms can be generalized to other tunings. | |||
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-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. | |||
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. | |||
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, (rank-2 not supported, unison vector) === | === Linearity, playing direction, (rank-2 not supported, unison vector) === | ||
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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. | 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 (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 when using offset rotation. | |||
Offset rotation: | Offset rotation: | ||
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'''<big>NOT ALL AXES WORK!!!</big>''' (for some reason, I'm still figuring it out) 12edo o<sub>h</sub>=1,o<sub>v</sub>=5, x=-1, y=2 doesn't work (requires 24edo) | '''<big>NOT ALL AXES WORK!!!</big>''' (for some reason, I'm still figuring it out) 12edo o<sub>h</sub>=1,o<sub>v</sub>=5, x=-1, y=2 doesn't work (requires 24edo) | ||
The cardinal directions and diagonals are guaranteed to work because the four keys next to the origin have 1 as the lead digit or gcd(x,y) going off infinitely along the diagonals and rows or columns. (?) | The cardinal directions and diagonals are guaranteed to work because the four keys next to the origin have 1 as the lead digit or gcd(x,y) going off infinitely along the diagonals and rows or columns. (explain why that is?) | ||
* x=-1, 0 or 1 | * x=-1, 0 or 1 | ||
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idk if this matters???: Keyboard rotation can be impractical, so there is also the double warp. It is two repeated single warps, but the same result can be derived with a different single shear operation and a <s>60° offset rotation</s>. | idk if this matters???: Keyboard rotation can be impractical, so there is also the double warp. It is two repeated single warps, but the same result can be derived with a different single shear operation and a <s>60° offset rotation</s>. | ||
=== Layout modifying operations (temperament changing) === | |||
These should only be used with ETs or rank-2s. These are very hard to use with rank-2s if there is a finite scale size constraint, and offsets can't be set to an arbitrary interval. In practice large ETs can be effectively used as an infinite rank-2 lattice, for example setting the tuning as 1200edo and setting the offsets to what are basically rounded cent values of the desired intervals. | |||
==== Stretch (and scaling) ==== | |||
Let s<sub>t</sub> be a stretch multiplier. Along a given axis, when s<sub>t</sub>=2, the distances between the intervals along said axis will become twice (s<sub>t</sub>=2) as long as before. The pitch distance between two neighboring keys on the axis will be halved (1/s<sub>t</sub>=1/2). | |||
When working with ETs, if any offsets are fractional, multiply the ET by s<sub>t</sub>. | |||
Square grid: | |||
* Along o<sub>h</sub>: o<sub>h</sub> ⇒ o<sub>h</sub>/s<sub>t</sub>. | |||
* Along o<sub>v</sub>: o<sub>v</sub> ⇒ o<sub>v</sub>/s<sub>t</sub>. | |||
* Along both (global scaling): o<sub>h</sub> ⇒ o<sub>h</sub>/s<sub>t</sub> and o<sub>v</sub> ⇒ o<sub>v</sub>/s<sub>t</sub>. | |||
Hexagonal layout: | |||
* Along o<sub>h</sub>: o<sub>h</sub> ⇒ o<sub>h</sub>/s<sub>t</sub>. | |||
* Along o<sub>v</sub>: o<sub>v</sub> ⇒ o<sub>v</sub>/s<sub>t</sub>. | |||
* Along o<sub>h</sub> - o<sub>v</sub>: o<sub>v</sub> ⇒ o<sub>h</sub> - (o<sub>h</sub>-o<sub>v</sub>)/s<sub>t</sub>. | |||
* Along all (global scaling): o<sub>h</sub> ⇒ o<sub>h</sub>/s<sub>t</sub> and o<sub>v</sub> ⇒ o<sub>v</sub>/s<sub>t</sub>. | |||
==== Skew ==== | |||
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