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-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.

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]].

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 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)

The six modes of the just porcutone diatonic are:

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* Mode 3: 10/9 5/4 25/18 3/2 5/3 50/27 2/1 = Meantone[7] 6|0 x Porcupine[7] 5|1 = LLLsLLs x sLsssss = MLMsMMs = Lydian x dark major = Lydian dark major

If we temper so that 10/9 ~ 11/10, and 27/25 ~ 12/11 (and 9/8 ~ 25/22) ie., tempering out 100/99, we get the Ptolemismic Porcutone diatonic with modes:

If we temper so that 10/9 ~ 11/10, and 27/25 ~ 12/11 (and 9/8 ~ 25/22) ie., tempering out [[100/99]], we get the Ptolemismic Porcutone diatonic with modes:

* Locrian dark diminished: ~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1

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* Lydian dark major: 174.055 383.834 557.888 704.524 878.579 1052.633 1199.269

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]].

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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27.42 174.055 320.69 348.11 494.745 557.888 704.524 731.943 878.579 1025.214 1052.633 1199.269.

Just porcutone octatonic: 4 large steps of 10/9, 3 medium of 27/25 and 1 small step of 25/24. It also tempers to a MODMOS of Diminished[8], and to Father[8].

Just porcutone octatonic: 4 large steps of 10/9, 3 medium of 27/25 and 1 small step of 25/24. It also tempers to a MODMOS of [[Diminished]][8], and to [[Father]][8].

Let’s introduce functional mode names for Porcupine[8]:

Let’s introduce functional mode names for [[Porcupine]][8]:

* Mode 4: LLLLLLLs – Bright quartal

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

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.

On D we get the scale:

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On F# the major pentatonic is 209.779 383.834 704.524 878.579 1199.269

~ 9/8 5/4 3/2 5/3 2/1 msLsL. Tempers to ssLsL for Meantone[5], LsLsL for Father[5], and sLLLL for Bug[5].

~ 9/8 5/4 3/2 5/3 2/1 msLsL. Tempers to [[2L 3s|ssLsL]] for Meantone[5], [[3L 2s|LsLsL]] for [[Father]][5], and [[4L 1s|sLLLL]] for [[Bug]][5].

The same scale is also available on G.

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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-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.
+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]].
-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 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)
 The six modes of the just porcutone diatonic are:
@@ Line 13: / Line 13: @@
 * Mode 3: 10/9 5/4 25/18 3/2 5/3 50/27 2/1 = Meantone[7] 6|0 x Porcupine[7] 5|1 = LLLsLLs x sLsssss = MLMsMMs = Lydian x dark major = Lydian dark major
-If we temper so that 10/9 ~ 11/10, and 27/25 ~ 12/11 (and 9/8 ~ 25/22) ie., tempering out 100/99, we get the Ptolemismic Porcutone diatonic with modes:
+If we temper so that 10/9 ~ 11/10, and 27/25 ~ 12/11 (and 9/8 ~ 25/22) ie., tempering out [[100/99]], we get the Ptolemismic Porcutone diatonic with modes:
 * Locrian dark diminished: ~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1
@@ Line 33: / Line 33: @@
 * Lydian dark major: 174.055 383.834 557.888 704.524 878.579 1052.633 1199.269
-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]].
 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]).
@@ Line 57: / Line 57: @@
 .42 174.055 320.69 348.11 494.745 557.888 704.524 731.943 878.579 1025.214 1052.633 1199.269.
-Just porcutone octatonic: 4 large steps of 10/9, 3 medium of 27/25 and 1 small step of 25/24. It also tempers to a MODMOS of Diminished[8], and to Father[8].
+Just porcutone octatonic: 4 large steps of 10/9, 3 medium of 27/25 and 1 small step of 25/24. It also tempers to a MODMOS of [[Diminished]][8], and to [[Father]][8].
-Let’s introduce functional mode names for Porcupine[8]:
+Let’s introduce functional mode names for [[Porcupine]][8]:
 * Mode 4: LLLLLLLs – Bright quartal
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 * Mode 4b:  LMLLMLMs -> Porcupine[8]: LLLLLLLs 7|0, Father[8]: LsLLsLsL 4|3 -> Ultharian bright quartal
-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.
 On D we get the scale:
@@ Line 140: / Line 140: @@
 On F# the major pentatonic is 209.779 383.834 704.524 878.579 1199.269
-~ 9/8 5/4 3/2 5/3 2/1 msLsL. Tempers to ssLsL for Meantone[5], LsLsL for Father[5], and sLLLL for Bug[5].
+~ 9/8 5/4 3/2 5/3 2/1 msLsL. Tempers to [[2L 3s|ssLsL]] for Meantone[5], [[3L 2s|LsLsL]] for [[Father]][5], and [[4L 1s|sLLLL]] for [[Bug]][5].
 The same scale is also available on G.