Pinetone: Difference between revisions

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Consider instead the just scale: 10/9 6/5 4/3 3/2 5/3 9/5 2/1, a just Dorian scale. This scale has 1 large step of [[9/8]], 4 medium steps of [[10/9]], and 2 small steps of [[27/25]], with step pattern MsMLMsM (mode 0). It can be represented with [[Step pattern|step signature]] and step mapping 1L 4M 2s = (9/8, 10/9, 27/25). This is our just Porcutone diatonic.If we temper out the difference between L and M, we get LsLLLsL, [[Meantone]][7] mode 0: Dorian; if we temper out instead the difference between [[10/9]] and [[27/25]], we get sssLsss, [[Porcupine]][7] mode 0, which is referred to as ''symmetric minor''. In this way, the just Porcutone diatonic represents both [[Porcupine]][7] and [[Meantone]][7].

To name this mode of the Porcutone diatonic, we simply add the mode names together, prefixing the [[Porcupine]][7] functional mode names introduced in Table 1., with the [[Meantone]] diatonic mode names referenced in Table 2., so mode 0 of the Porcutone diatonic is called ''Dorian symmetric minor''. We continue this process with the other 6 modes to arrive at the modes shown in Table 3.

To name this mode of the Porcutone diatonic, we simply add the mode names together, prefixing the [[Porcupine]][7] functional mode names introduced in Table 1., with the [[Meantone]] diatonic mode names referenced in Table 2., so mode 0 of the Porcutone diatonic is called ''Dorian symmetric minor''. Along with the step pattern and mode number, the modes' [[UDP]] are shown in Tables 1. and 2. The UDP show the number of generators in the direction the brighten the intervals of scale, followed the number of generators in the direction that darkens it, (followed by the number of periods per octave, if it is not one. In this case the scale repeats at the octave, so P = 1, and is not shown). We continue this naming process with the other 6 modes to arrive at the modes shown in Table 3.

{| class="wikitable"

|+Table 1. Modes of 5-limit Porcupine[7]

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!Mode as simplest JI pre-image

!Step pattern

!~~[[Modal~~ UDP ~~notation|UDP]]~~

!UDP

!Mode

|-

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 Consider instead the just scale: 10/9 6/5 4/3 3/2 5/3 9/5 2/1, a just Dorian scale. This scale has 1 large step of [[9/8]], 4 medium steps of [[10/9]], and 2 small steps of [[27/25]], with step pattern MsMLMsM (mode 0). It can be represented with [[Step pattern|step signature]] and step mapping 1L 4M 2s = (9/8, 10/9, 27/25). This is our just Porcutone diatonic.If we temper out the difference between L and M, we get LsLLLsL, [[Meantone]][7] mode 0: Dorian; if we temper out instead the difference between [[10/9]] and [[27/25]], we get sssLsss, [[Porcupine]][7] mode 0, which is referred to as ''symmetric minor''. In this way, the just Porcutone diatonic represents both [[Porcupine]][7] and [[Meantone]][7].
-To name this mode of the Porcutone diatonic, we simply add the mode names together, prefixing the [[Porcupine]][7] functional mode names introduced in Table 1., with the [[Meantone]] diatonic mode names referenced in Table 2., so mode 0 of the Porcutone diatonic is called ''Dorian symmetric minor''. We continue this process with the other 6 modes to arrive at the modes shown in Table 3.
+To name this mode of the Porcutone diatonic, we simply add the mode names together, prefixing the [[Porcupine]][7] functional mode names introduced in Table 1., with the [[Meantone]] diatonic mode names referenced in Table 2., so mode 0 of the Porcutone diatonic is called ''Dorian symmetric minor''. Along with the step pattern and mode number, the modes' [[UDP]] are shown in Tables 1. and 2. The UDP show the number of generators in the direction the brighten the intervals of scale, followed the number of generators in the direction that darkens it, (followed by the number of periods per octave, if it is not one. In this case the scale repeats at the octave, so P = 1, and is not shown). We continue this naming process with the other 6 modes to arrive at the modes shown in Table 3.
 {| class="wikitable"
 |+Table 1. Modes of 5-limit Porcupine[7]
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 !Mode as simplest JI pre-image
 !Step pattern
-![[Modal UDP notation|UDP]]
+!UDP
 !Mode
 |-