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→Other diatonic subsets of the Pinetone chromatic scale: added last table, updated scale names
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The scale D E F G A B C has step pattern MsMLMsM, which tempers to sssLsss under Porcupine (M=s) and LsLLLsL under Meantone (M=L).
The scale D E F G A B C has step pattern MsMLMsM, which tempers to sssLsss under Porcupine (M=s) and LsLLLsL under Meantone (M=L).


Raising an F to an F♯ replaces ~6/5 with ~11/9, i.e., it raises the F by ~55/54, which is tempered out in Porcupine, so the scale D E F♯ G A B C tempers to sssLsss under Porcupine as before, but to LLsLLsL under Meantone (Mixolydian mode rather than Dorian as before), so will call the mode approximating the ratios 10/9 11/9 4/3 3/2 5/3 9/5 2/1 Mixolydian symmetric minor, and use the mode to name the scale as a whole.
Raising an F to an F♯ replaces ~6/5 with ~11/9, i.e., it raises the F by ~55/54, which is tempered out in [[Porcupine]], so the scale D E F♯ G A B C tempers to sssLsss under Porcupine as before, but to LLsLLsL under Meantone (Mixolydian mode rather than Dorian as before), so will call the mode approximating the ratios 10/9 11/9 4/3 3/2 5/3 9/5 2/1 Mixolydian symmetric minor, and use the mode to name the scale as a whole.


To calculate the mode numbers for Tables 4.2-4.5, the mode numbers of their temperings to Porcupine and to Meantone were added, ordered, and renumbered. When two modes are tied, small changes in tuning will affect their order. Given that Ptolemismic Porcupine is more accurate than Ptolemismic Meantone, the Porcupine mode number is weighted more heavily to determine the mode order in the event of any ties.
To calculate the mode numbers for Tables 4.2-4.5, the mode numbers of their temperings to Porcupine and to [[Meantone]] were added, ordered, and renumbered. When two modes are tied, small changes in tuning will affect their order. Given that Ptolemismic Porcupine is more accurate than Ptolemismic Meantone, the Porcupine mode number is weighted more heavily to determine the mode order in the event of any ties. Modes are named via the [[Tetracot]][7] [[MODMOS]] they temper to when [[243/242]] is tempered out (i.e., the difference between [[11/9]] and [[27/22]]), as in [[27edo]], [[34edo]], and [[41edo]].
{| class="wikitable"
{| class="wikitable"
|+Table 4.2. Modes of the Ptolemismic Pinetone Aeolian bright minor
|+Table 4.2. Modes of the Ptolemismic Pinetone Aeolian bright minor
!Mode number
!Mode number
!Pinetone diatonic mode
!Mode name
! colspan="2" |Root note
! colspan="2" |Root note
!Step pattern
!Step pattern
Line 1,489: Line 1,489:
|-
|-
|3
|3
|Ionian bright major*
|Ryonian ♯2♯3*
|G
|G
|A♭
|A♭
Line 1,496: Line 1,496:
|-
|-
|2
|2
|Lydian bright diminished
|Ryonian ♭5
|C
|C
|D♭  
|D♭  
Line 1,503: Line 1,503:
|-
|-
|1
|1
|Mixolydian dark minor
|Karakalian ♭4
|D
|D
|E♭  
|E♭  
Line 1,510: Line 1,510:
|-
|-
|0
|0
|Aeolian bright minor*
|Azurian ♭3*
|E
|E
|F
|F
Line 1,517: Line 1,517:
|-
|-
| -1
| -1
|Locian dark major
|Horthanian ♭2
|F♯  
|F♯  
|G
|G
Line 1,524: Line 1,524:
|-
|-
| -2
| -2
|Phrygian dark diminished
|Phyradian ♭6
|B
|B
|C
|C
Line 1,531: Line 1,531:
|-
|-
| -3
| -3
|Dorian magical seventh
|Duradian♭7
|A
|A
|B♭  
|B♭  
Line 1,541: Line 1,541:
|+Table 4.3. Modes of the Ptolemismic Pinetone Aeolian dark minor
|+Table 4.3. Modes of the Ptolemismic Pinetone Aeolian dark minor
!Mode number
!Mode number
!Pinetone diatonic mode
!Mode name
! colspan="2" |Root note
! colspan="2" |Root note
!Step pattern
!Step pattern
Line 1,547: Line 1,547:
|-
|-
|3
|3
|Ionian dark major*
|Ryonian ♯3*
|F
|F
|E
|E
Line 1,554: Line 1,554:
|-
|-
|2
|2
|Dorian bright major
|Karakalian ♯2
|G
|G
|F♯
|F♯
Line 1,561: Line 1,561:
|-
|-
|1
|1
|Lydian dark diminished
|Horthanian ♯7
|B♭  
|B♭  
|A
|A
Line 1,568: Line 1,568:
|-
|-
| 0
| 0
|Mixolydian bright diminished
|Oukranian ♯6
|C
|C
|B
|B
Line 1,575: Line 1,575:
|-
|-
| -1
| -1
|Aeolian dark minor*
|Duradian ♯5*
|D
|D
|C♯
|C♯
Line 1,582: Line 1,582:
|-
|-
| -2
| -2
|Locrian bright minor
|Phyradian ♯4
|E
|E
|D♯
|D♯
Line 1,589: Line 1,589:
|-
|-
| -3
| -3
|Phrygian magical seventh
|Phyradian ♭6♭7
|A
|A
|G♯
|G♯
Line 1,599: Line 1,599:
|+Table 4.4. Modes of the Ptolemismic Pinetone Dorian bright minor
|+Table 4.4. Modes of the Ptolemismic Pinetone Dorian bright minor
!Mode number
!Mode number
!Pinetone diatonic mode
!Mode name
! colspan="2" |Root note
! colspan="2" |Root note
!Step pattern
!Step pattern
Line 1,605: Line 1,605:
|-
|-
|3
|3
|Lydian bright major*
|Ryonian ♯2♯3♯4*
|G
|G
|A♭
|A♭
Line 1,612: Line 1,612:
|-
|-
|2
|2
|Ionian dark minor
|Ryonian ♭4
|D  
|D  
|E♭
|E♭
Line 1,619: Line 1,619:
|-
|-
| 1
| 1
|Dorian bright minor*
|Karakalian ♭3*
|E
|E
|F
|F
Line 1,626: Line 1,626:
|-
|-
| 0
| 0
|Locrian dark major
|Azurian ♭2
|F♯
|F♯
|G
|G
Line 1,633: Line 1,633:
|-
|-
| -1
| -1
|Mixolydian magical seventh
|Oukranian ♭7
|A
|A
|B♭
|B♭
Line 1,640: Line 1,640:
|-
|-
| -2
| -2
|Phrygian bright diminished
|Phyradian ♭5
|C♯
|C♯
|D
|D
Line 1,647: Line 1,647:
|-
|-
| -3
| -3
|Aeolian dark diminished
|Duradian ♭6
|B
|B
|C
|C
Line 1,656: Line 1,656:
|+Table 4.5. Modes of the Ptolemismic Pinetone Locrian dark minor
|+Table 4.5. Modes of the Ptolemismic Pinetone Locrian dark minor
!Mode number
!Mode number
!Pinetone diatonic mode
!Mode names
! colspan="2" |Root note
! colspan="2" |Root note
!Step pattern
!Step pattern
Line 1,662: Line 1,662:
|-
|-
|3
|3
|Mixolydian dark major*
|Karakalian ♯3*
|F
|F
|E
|E
Line 1,669: Line 1,669:
|-
|-
| 2
| 2
|Lydian bright minor
|Ryonian ♯4
|E♭
|E♭
|D
|D
Line 1,676: Line 1,676:
|-
|-
|1
|1
|Aeolian bright major
|Azurian ♯2
|G
|G
|F♯
|F♯
Line 1,683: Line 1,683:
|-
|-
|0
|0
|Ionian dark diminished
|Oukranian ♯7
|B♭  
|B♭  
|A
|A
Line 1,690: Line 1,690:
|-
|-
| -1
| -1
|Dorian bright diminished
|Duradian ♯6
|C
|C
|B
|B
Line 1,697: Line 1,697:
|-
|-
| -2
| -2
|Locrian dark minor*
|Phyradian ♯5*
|D
|D
|C♯
|C♯
Line 1,704: Line 1,704:
|-
|-
| -3
| -3
|Phrygian magical seventh
|Phyradian ♭5♭6♭7
|A
|A
|G♯
|G♯
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