Pinetone: Difference between revisions

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A 12-note rank-3 [[Meantone]][12] x [[Ripple]][12] [[Fokker block]], a [[step-nested scale]] that also tempers to [[Porcupine]][8], comprising a diatonic [[Meantone]][7]-[[Porcupine]][7]-[[Dicot]][7] [[wakalix]] / 3-[[Step-nested scale|SNS]] on the white keys, and a pentatonic [[Meantone]][5]-[[Father]][5]-[[Bug]][5] [[wakalix]] on the 'black' keys. The G# / Ab key is coloured pink (and the remaining chromatic keys blue), and along with the white keys makes a [[Porcupine]][8] / [[Father]][8] [[Fokker block]].
Built via step nesting from the 5-limit minor seventh tetrad: 6/5 3/2 9/5 2/1, the Porcutone system is a 12-note rank-3 [[Meantone]][12] x [[Ripple]][12] [[Fokker block]], a [[step-nested scale]] that also tempers to [[Porcupine]][8], comprising a diatonic [[Meantone]][7]-[[Porcupine]][7]-[[Dicot]][7] [[wakalix]] / 3-[[Step-nested scale|SNS]] on the white keys, and a pentatonic [[Meantone]][5]-[[Father]][5]-[[Bug]][5] [[wakalix]] on the 'black' keys. The G# / Ab key is coloured pink (and the remaining chromatic keys blue), and along with the white keys makes a [[Porcupine]][8] / [[Father]][8] [[Fokker block]].


== Porcutone diatonic ==
The Porcutone diatonic is a [[wakalix]] (pairwise well-formed scale) and a [[step-nested scale]]: A detempering of [[Meantone]][7] and [[Porcupine]][7], (and also of [[Dicot]][7]), a [[Fokker block]] with [[Unison vector|unison vectors]] of [[81/80]] and [[250/243]] (and [[25/24]]) has 1 large step of 9/8 (L x L), 3 medium steps of 10/9 (L x s), and 3 small steps of 27/25 (s x s)
The Porcutone diatonic is a [[wakalix]] (pairwise well-formed scale) and a [[step-nested scale]]: A detempering of [[Meantone]][7] and [[Porcupine]][7], (and also of [[Dicot]][7]), a [[Fokker block]] with [[Unison vector|unison vectors]] of [[81/80]] and [[250/243]] (and [[25/24]]) has 1 large step of 9/8 (L x L), 3 medium steps of 10/9 (L x s), and 3 small steps of 27/25 (s x s)


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The 11th harmonic as a Porcupine M4 is found at Meantone P4, tempering out 33/32, leading to [[Meanenneadecal]], where 33/32 is tempered out, hence the Ptotemismic Porcupine diatonic is a detempering of [[Meanenneadecal]].
The 11th harmonic as a Porcupine M4 is found at Meantone P4, tempering out 33/32, leading to [[Meanenneadecal]], where 33/32 is tempered out, hence the Ptotemismic Porcupine diatonic is a detempering of [[Meanenneadecal]].


== Porcutone chromatic and Porcutone octatonic ==
If we put the small step into every medium and large step, we get the Porcutone chromatic, which is a detempering of Meantone[12]. (It’s also a detempering of a MODMOS of Diminished[12], and of Ripple[12]).  
If we put the small step into every medium and large step, we get the Porcutone chromatic, which is a detempering of Meantone[12]. (It’s also a detempering of a MODMOS of Diminished[12], and of Ripple[12]).  


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* Mode 4b:  LMLLMLMs -> Porcupine[8]: LLLLLLLs 7|0, Father[8]: LsLLsLsL 4|3 -> Ultharian bright quartal
* Mode 4b:  LMLLMLMs -> Porcupine[8]: LLLLLLLs 7|0, Father[8]: LsLLsLsL 4|3 -> Ultharian bright quartal


== Porcutone harmonic minor and harmonic major ==
Additionally, we have another set of [[Porcupine]][7] modes contained in the Porcutone octatonic: Replacing the G with the G# changes the mode of the Porcupine[7] scale represented, and replaces diatonic with harmonic minor modes for the [[Meantone]][7] scale represented, now a MODMOS.
Additionally, we have another set of [[Porcupine]][7] modes contained in the Porcutone octatonic: Replacing the G with the G# changes the mode of the Porcupine[7] scale represented, and replaces diatonic with harmonic minor modes for the [[Meantone]][7] scale represented, now a MODMOS.


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* Mode 3: Lsmmsms bright major
* Mode 3: Lsmmsms bright major


== Porcutone pentatonic ==
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