Pinetone: Difference between revisions
mNo edit summary |
m flipped order of modes |
||
| Line 19: | Line 19: | ||
The six modes of the just porcutone diatonic are: | The six modes of the just porcutone diatonic are: | ||
* 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 | |||
* Mode 2: 9/8 5/4 27/20 3/2 5/3 9/5 2/1 = Meantone[7] 4|2 x Porcupine[7] 6|0 = LLsLLsL x Lssssss = LMsMMsM = Mixolydian x bright major = Mixolydian bright major | |||
* Mode 1: 10/9 100/81 4/3 40/27 5/3 50/27 2/1 = Meantone[7] 5|1 x Porcupine[7] 2|4 = LLsLLLs x ssssLss = MMsMLMs = Ionian x bright diminished = Ionian bright diminished | |||
* Mode 0: 10/9 6/5 4/3 3/2 5/3 9/5 2/1 = Meantone[7] 3|3 x Porcupine[7] 3|3 = LsLLLsL x sssLsss = MsMLMsM = Dorian x symmetric minor = Dorian symmetric minor | |||
* Mode -1: 27/25 6/5 27/20 3/2 81/50 9/5 2/1 = Meantone[7] 1|5 x Porcupine[7] 4|2 = sLLLsLL x ssLssss = sMLMsMM = Phrygian x bright minor = Phrygian bright minor | |||
* Mode -2: 10/9 6/5 4/3 40/27 8/5 16/9 2/1 = Meantone[7] 2|4 x Porcupine[7] 0|6 = LsLLsLL x ssssssL = MsMMsML = Aeolian x magical seventh mode = Aeolian magical seventh | |||
* Mode -3: 27/25 6/5 4/3 36/25 8/5 9/5 2/1 = Meantone[7] 0|6 x Porcupine[7] 1|5 = sLLsLLL x sssssLs = sMMsMLs = Locrian x dark diminished = Locrian dark diminished | * Mode -3: 27/25 6/5 4/3 36/25 8/5 9/5 2/1 = Meantone[7] 0|6 x Porcupine[7] 1|5 = sLLsLLL x sssssLs = sMMsMLs = Locrian x dark diminished = Locrian dark diminished | ||
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: | ||
* Lydian dark major: ~ 10/9 5/4 11/8 3/2 5/3 11/6 2/1 | |||
* Mixolydian bright major: ~ 9/8 5/4 15/11 3/2 5/3 9/5 2/1 | |||
* Ionian bright diminished: ~ 10/9 11/9 4/3 22/15 5/3 11/6 2/1 | |||
* Dorian symmetric minor: ~ 10/9 6/5 4/3 3/2 5/3 9/5 2/1 | |||
* Phrygian bright minor: ~ 12/11 6/5 15/11 3/2 18/11 9/5 2/1 | |||
* Aeolian magical seventh: ~ 10/9 6/5 4/3 22/15 8/5 16/9 2/1 | |||
* Locrian dark diminished: ~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1 | * Locrian dark diminished: ~ 12/11 6/5 4/3 16/11 8/5 9/5 2/1 | ||
Tuned to TE (math over, here's tuning of the modes in cents, and their names, which combine the diatonic mode names with the functional Porcupine[7] mode names) | Tuned to TE (math over, here's tuning of the modes in cents, and their names, which combine the diatonic mode names with the functional Porcupine[7] mode names) | ||
* Lydian dark major: 174.055 383.834 557.888 704.524 878.579 1052.633 1199.269 | |||
* Mixolydian bright major: 209.779 383.834 530.469 704.524 878.579 1025.214 1199.269 | |||
* Ionian bright diminished: 174.055 348.11 494.745 668.8 878.579 1052.633 1199.269 | |||
* Dorian symmetric minor: 174.055 320.69 494.745 704.524 878.579 1025.214 1199.269 | |||
* Phrygian bright minor: 146.635 320.69 530.469 704.524 851.159 1025.214 1199.269 | |||
* Aeolian magical seventh: 174.055 320.69 494.745 668.8 815.435 989.49 1199.269 | |||
* Locrian dark diminished: 146.635 320.69 494.745 641.38 815.435 1025.214 1199.269 | * Locrian dark diminished: 146.635 320.69 494.745 641.38 815.435 1025.214 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]]. | ||
| Line 90: | Line 91: | ||
Using a G# instead of an Ab, we get the following modes for porcutone octatonic a: | Using a G# instead of an Ab, we get the following modes for porcutone octatonic a: | ||
* Mode 4a: LMLLMLsM -> Porcupine[8]: LLLLLLsL 6|1, Father[8]: LsLLsLLs 4|3 -> Celephaïsian dark quartal | |||
* Mode 3a: MLMLLMLs -> Porcupine[8]: LLLLLLLs 7|0, Father[8]: sLsLLsLL 0|7 -> Sarnathian bright quartal | |||
* Mode 2a: LLMLsMLM -> Porcupine[8]: LLLLsLLL 4|3, Father[8]: LLsLLsLs 7|0 -> Dylathian middle major | |||
* Mode 1a: MLLMLsML -> Porcupine[8]: LLLLLsLL 5|2, Father[8]: sLLsLLsL 2|5 -> Kadathian bright major | |||
* Mode -1a: LMLsMLML -> Porcupine[8]: LLLsLLLL 3|4, Father[8]: LsLLsLsL 5|2 -> Ultharian dark major | |||
* Mode -2a: LsMLMLLM -> Porcupine[8]: LsLLLLLL 1|6, Father[8]: LLsLsLLs 6|1 -> Illarnekian middle minor | |||
* Mode -3a: MLsMLMLL -> Porcupine[8]: LLsLLLLL 2|5, Father[8]: sLLsLsLL 1|6 -> Hlanithian bright minor | |||
* Mode -4a: sMLMLLML -> Porcupine[8]: sLLLLLLL 0|7, Father[8]: LsLsLLsL 3|4 -> Mnarian dark minor | * Mode -4a: sMLMLLML -> Porcupine[8]: sLLLLLLL 0|7, Father[8]: LsLsLLsL 3|4 -> Mnarian dark minor | ||
We could have chosen to include Ab instead of G# in the porcutone octatonic, which would result in the inverse of everything above, i.e., a chromatic gamut of Gb-B and inverses of the 8 porcutone octatonic modes resulting a different set of modes. | We could have chosen to include Ab instead of G# in the porcutone octatonic, which would result in the inverse of everything above, i.e., a chromatic gamut of Gb-B and inverses of the 8 porcutone octatonic modes resulting a different set of modes. | ||
| Line 111: | Line 112: | ||
Porcutone Chromatic (Gb-B): 146.635 174.055 320.69 467.325 494.745 641.38 704.524 851.159 878.579 1025.214 1171.849 1199.269 | Porcutone Chromatic (Gb-B): 146.635 174.055 320.69 467.325 494.745 641.38 704.524 851.159 878.579 1025.214 1171.849 1199.269 | ||
* 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 | ||
* Mode 3b: LLMLMsLM -> Porcupine[8]: LLLLLsLL 5|2, Father[8]: LLsLsLLs 6|1 -> Illarnekian bright major | |||
* Mode 2b: MLLMLMsL -> Porcupine[8]: LLLLLLsL 6|1, Father[8]: sLLsLsLL 1|6 -> Hlanithian dark quartal | |||
* Mode 1b: LMLMsLML -> Porcupine[8]: LLLLsLLL 4|3, Father[8]: LsLsLLsL 2|5 -> Kadathian middle major | |||
* Mode -1b: LMsLMLLM -> Porcupine[8]: LLsLLLLL 2|5, Father[8]: LsLLsLLs 5|2 -> Celephaïsian bright minor | |||
* Mode -2b: MLMsLMLL -> Porcupine[8]: LLLsLLLL 3|4, Father[8]: sLsLLsLL 0|7 -> Sarnathian dark major | |||
* Mode -3b: LsMLLMLM -> Porcupine[8]: sLLLLLLL 0|7, Father[8]: LLsLLsLs 7|0 -> Dylathian dark minor | |||
* Mode -4b: MsLMLLML -> Porcupine[8]: LsLLLLLL 1|6, Father[8]: sLLsLLsL 3|4 -> Mnarian middle minor | |||
== Porcutone harmonic minor and harmonic major == | == Porcutone harmonic minor and harmonic major == | ||
| Line 129: | Line 130: | ||
We get the following 7 modes of porcutone harmonic minor scale: | We get the following 7 modes of porcutone harmonic minor scale: | ||
* Mode 3: Lsmsmms Lydian ♯2 bright major | |||
* Mode 2: mmsLsms Ionian ♯5 symmetric minor | |||
* Mode 1: msLsmsm Ukranian dorian bright minor | |||
* Mode 0: sLsmsmm Phyrgian dominant dark major | |||
* Mode -1: msmmsLs harmonic minor dark diminished | |||
* Mode -2: smmsLsm Locrian ♮6 bright diminished | |||
* Mode -3: smsmmsL altered diminished magical seventh | * Mode -3: smsmmsL altered diminished magical seventh | ||
Using an Ab instead, we get the scale: | Using an Ab instead, we get the scale: | ||
| Line 143: | Line 144: | ||
Which has porcutone harmonic major modes: | Which has porcutone harmonic major modes: | ||
* Mode | * Mode 3: Lsmmsms Lydian Augmented ♯2 bright major | ||
* Mode | * Mode 2: msLsmms Lydian ♭3 bright minor | ||
* Mode | * Mode 1: sLsmmsm Mixolydian ♭2 dark major | ||
* Mode 0: mmsmsLs harmonic major bright diminished | * Mode 0: mmsmsLs harmonic major bright diminished | ||
* Mode 1: | * Mode -1: msmsLsm Dorian ♭5 dark diminished | ||
* Mode 2: | * Mode -2: smsLsmm Phrygian ♭4 symmetric minor | ||
* Mode 3: | * Mode -3: smmsmsL Locrian magical ♭♭7 | ||
== Porcutone pentatonic == | == Porcutone pentatonic == | ||