Comprehensive Scale Catalog: Four-Tone Scales in Alternate Temperaments

This page is part of Flutopedia's Comprehensive Scale Catalog ... a listing of many (many) scales that can be played on Native American flutes.

This page shows only scales with four tones per octave and using alternate temperaments.

The root note of each scale is shown in blue, such as .

Pure Four

Temperament: 12-Tone Overtone Temperament (Over12)
The 12 degrees of this temperament, in cents:
  0–139–267–386–498–603–702–796–884–969–1049–1126–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–603–796–969–1200
  intervals: 1–d5–m6–a6–8
  Root, Diminished 5th, Minor 6th, Quarter 6th-7th, Octave

Pitches starting from C:
  C F♯ G♯ A+ c
  C G♭ A♭ A+ c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Pythagorean Temperament (12Pyth)
The 12 degrees of this temperament, in cents:
  0–90–204–294–408–498–588–702–792–906–996–1110–1200
Notes: From [Rich 2010]: "One of the earliest tuning systems known from history, the Pythagorean scale is constructed from an upward series of pure fifths (3/2) transposed down into a single octave. The tuning works well for monophonic melodies against fifth drones, but has a very narrow palate of good chords to choose from." Uses augmented 4th at 1024/729 (588 cents) rather than diminihsed 5th at 729/512 (611 cents).

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–702–906–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Huang-chung Precise (six-digit) Temperament (12HC6)
The 12 degrees of this temperament, in cents:
  0–114–204–318–408–522–612–702–816–906–1020–1110–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–522–702–906–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Huang-chung Simplified (two-digit) Temperament (12HC2)
The 12 degrees of this temperament, in cents:
  0–110–204–303–408–520–608–702–801–906–1018–1096–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–520–702–906–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Quarter-comma Meantone Temperament (12MeanQC)
The 12 degrees of this temperament, in cents:
  0–76–193–310–386–503–580–697–773–890–1007–1083–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–503–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Werckmeister I Temperament (12Werck1)
The 12 degrees of this temperament, in cents:
  0–90–192–294–390–498–588–696–792–888–996–1092–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–696–888–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Werckmeister II Temperament (12Werck2)
The 12 degrees of this temperament, in cents:
  0–82–196–294–392–498–588–694–784–890–1004–1086–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–694–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Werckmeister III Temperament (12Werck3)
The 12 degrees of this temperament, in cents:
  0–96–204–300–396–504–600–702–792–900–1002–1098–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–504–702–900–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Werckmeister IV Temperament (12Werck4)
The 12 degrees of this temperament, in cents:
  0–91–196–298–395–498–595–698–793–893–1000–1097–1200
Notes: Based on division of a monochord into 196=7x7x4 divisions.

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–698–893–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Just Intoned 5-Limit Symmetric 1 Temperament (12JI5LimS1)
The 12 degrees of this temperament, in cents:
  0–112–204–316–386–498–590–702–814–884–996–1088–1200
Notes: Uses the augmented 4th at 45/32 (590 cents) rather than diminihsed 5th at 64/45 (610 cents).

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–702–884–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Just Intoned 5-Limit Symmetric 2 Temperament (12JI5LimS2)
The 12 degrees of this temperament, in cents:
  0–112–182–316–386–498–590–702–814–884–1018–1088–1200
Notes: Uses the augmented 4th at 45/32 (590 cents) rather than diminihsed 5th at 64/45 (610 cents).

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–702–884–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Just Intoned 5-Limit Asymmetric Standard Temperament (12JI5LimA)
The 12 degrees of this temperament, in cents:
  0–112–204–316–386–498–590–702–814–884–1018–1088–1200
Notes: Uses the augmented 4th at 45/32 (590 cents) rather than diminihsed 5th at 64/45 (610 cents).

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–702–884–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Just Intoned 5-Limit Asymmetric Extended Temperament (12JI5LimAE)
The 12 degrees of this temperament, in cents:
  0–112–204–316–386–498–569–702–814–884–1018–1088–1200
Notes: Uses the augmented 4th at 25/18 (569 cents) rather than diminihsed 5th at 36/25 (631 cents).

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–702–884–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Just Intoned 7-Limit Temperament (12JI7Lim)
The 12 degrees of this temperament, in cents:
  0–112–231–316–386–498–583–702–814–884–969–1088–1200
Notes: Uses the augmented 4th at 7/5 (583 cents) rather than diminihsed 5th at 10/7 (617 cents).

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–702–884–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Temperament: 12-Tone Golden Ratio A Temperament (12Golden-A)
The 12 degrees of this temperament, in cents:
  0–108–175–283–360–458–583–742–836–943–1064–1130–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–458–742–943–1200
  intervals: 1–b4–a5–a6–8
  Root, Quarter 3rd-4th, Quarter-sharp 5th, Quarter 6th-7th, Octave

Pitches starting from C: C E+ G+ A+ c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Temperament: 12-Tone Golden Ratio B Temperament (12Golden-B)
The 12 degrees of this temperament, in cents:
  0–149–236–367–455–560–686–833–916–1004–1099–1149–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–560–833–1004–1200
  intervals: 1–a4–n6–m7–8
  Root, Quarter-sharp 4th, Neutral 6th, Minor 7th, Octave

Pitches starting from C:
  C F+ A– A♯ c
  C F+ A– B♭ c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Temperament: Carlos Harmonic Twelve Tone Temperament (12Carlos)
The 12 degrees of this temperament, in cents:
  0–105–204–298–386–471–551–702–841–906–969–1088–1200
Notes: Wendy Carlos’ twelve-note scale based on octave-repeating harmonics. A = 1/1 (440 Hz). 1/1 17/16 9/8 19/16 5/4 21/16 11/8 3/2 13/8 27/16 7/4 15/8

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–471–702–906–1200
  intervals: 1–b4–5–6–8
  Root, Quarter 3rd-4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C E+ G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone 1/4 Comma A Temperament (12MeanQCA)
The 12 degrees of this temperament, in cents:
  0–76–193–310–386–503–580–697–772–890–1007–1083–1200
Notes: Difference of 773 vs 772 from Wikipedia's version. Probably an error in Sethares.

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–503–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Barca Temperament (12Barca)
The 12 degrees of this temperament, in cents:
  0–92–197–296–393–498–590–698–794–895–996–1092–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–698–895–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Barca A Temperament (12BarcaA)
The 12 degrees of this temperament, in cents:
  0–92–200–296–397–498–594–702–794–899–998–1095–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–702–899–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Bethisy Temperament (12Bethisy)
The 12 degrees of this temperament, in cents:
  0–87–193–289–386–496–587–697–787–890–993–1087–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–496–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Chaumont Temperament (12Chaumont)
The 12 degrees of this temperament, in cents:
  0–76–193–289–386–503–580–697–773–890–996–1083–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–503–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Corrette Temperament (12Corrette)
The 12 degrees of this temperament, in cents:
  0–76–193–289–386–503–580–697–783–890–996–1083–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–503–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone d'Alembert Temperament (12dAlembert)
The 12 degrees of this temperament, in cents:
  0–87–193–290–386–497–587–697–787–890–994–1087–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–497–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Kirnberger 2 Temperament (12Kirn2)
The 12 degrees of this temperament, in cents:
  0–90–204–294–386–498–590–702–792–895–996–1088–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–702–895–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Kirnberger 3 Temperament (12Kirn3)
The 12 degrees of this temperament, in cents:
  0–90–193–294–386–498–590–697–792–890–996–1088–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Marpourg Temperament (12Marpourg)
The 12 degrees of this temperament, in cents:
  0–84–193–294–386–503–580–697–789–890–999–1083–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–503–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Rameau b Temperament (12RameauFlat)
The 12 degrees of this temperament, in cents:
  0–93–193–305–386–503–582–697–800–890–1007–1083–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–503–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Rameau # Temperament (12RameauSharp)
The 12 degrees of this temperament, in cents:
  0–76–193–286–386–498–580–697–775–890–993–1083–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–697–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Vallotti Temperament (12Vallotti)
The 12 degrees of this temperament, in cents:
  0–90–196–294–392–498–588–698–792–894–996–1090–1200
Notes: Note that Sethares mis-spells the name as "Valloti" in Table L.

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–698–894–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Vallotti A Temperament (12ValottiA)
The 12 degrees of this temperament, in cents:
  0–90–200–294–396–498–592–702–792–898–996–1094–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–702–898–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Werkmeister 3 Temperament (S_12Werk3)
The 12 degrees of this temperament, in cents:
  0–90–192–294–390–498–588–696–792–888–996–1092–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–696–888–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Werkmeister 4 Temperament (S_12Werk4)
The 12 degrees of this temperament, in cents:
  0–82–196–294–392–498–588–694–784–890–1004–1086–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–498–694–890–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 12-Tone Werkmeister 5 Temperament (S_12Werk5)
The 12 degrees of this temperament, in cents:
  0–96–204–300–396–504–600–702–792–900–1002–1098–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–504–702–900–1200
  intervals: 1–4–5–6–8
  Root, Perfect 4th, Perfect 5th, Major 6th, Octave

Pitches starting from C: C F G A c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Pure Four

Temperament: 12-Tone Non-Pythagorean Temperament (12NonPyth)
The 12 degrees of this temperament, in cents:
  0–257–441–583–702–792–877–949–1008–1065–1111–1156–1200

Scale steps in semitones: 5–2–2–3

Scale degrees:
  in cents: 0–792–949–1065–1200
  intervals: 1–m6–a6–n7–8
  Root, Minor 6th, Quarter 6th-7th, Neutral 7th, Octave

Pitches starting from C:
  C G♯ A+ B– c
  C A♭ A+ B– c

Pitch Class Set: {0,5,7,9}

Pitch Class Mapping: 673 (Hex 2A1, Binary 001010100001)

The name I use for this scale comes from: Clint's Invented Name

Messiaen truncated mode 6

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

Fingerings on Anasazi-7 tuned Native American flutes:

         or       

Temperament: 6-Tone Equal Temperament (6TET)
The 6 degrees of this temperament, in cents:
  0–200–400–600–800–1000–1200
Notes: This temperament is equivalent to a 12-TET scale with scale steps 2-2-2-2-2-2 (Whole Tone scale).

Scale steps in semitones: 1–2–1–2

Scale degrees:
  in cents: 0–200–600–800–1200
  intervals: 1–2–d5–m6–8
  Root, Major 2nd, Diminished 5th, Minor 6th, Octave

Pitches starting from C:
  C D F♯ G♯ c
  C D G♭ A♭ c

Pitch Class Set: {0,1,3,4}

Pitch Class Mapping: 27 (Hex 1B, Binary 011011)

This scale is a mode (rotation) of these other scales:
  Mode 2 of: Messiaen Truncated Mode 6 Inverse and Messiaen truncated mode 6 inverse
  Mode 3 of: Messiaen Truncated Mode 6 and Messiaen truncated mode 6
  Mode 4 of: Messiaen Truncated Mode 6 Inverse and Messiaen truncated mode 6 inverse

The name I use for this scale comes from: Clint's Invented Name

Scala name: Messiaen truncated mode 6

Messiaen truncated mode 6 inverse

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or       

Fingerings on Anasazi-7 tuned Native American flutes:

         or        

Temperament: 6-Tone Equal Temperament (6TET)
The 6 degrees of this temperament, in cents:
  0–200–400–600–800–1000–1200
Notes: This temperament is equivalent to a 12-TET scale with scale steps 2-2-2-2-2-2 (Whole Tone scale).

Scale steps in semitones: 2–1–2–1

Scale degrees:
  in cents: 0–400–600–1000–1200
  intervals: 1–3–d5–m7–8
  Root, Major 3rd, Diminished 5th, Minor 7th, Octave

Pitches starting from C:
  C E F♯ A♯ c
  C E G♭ B♭ c

Pitch Class Set: {0,2,3,5}

Pitch Class Mapping: 45 (Hex 2D, Binary 101101)

This scale is a mode (rotation) of these other scales:
  Mode 2 of: Messiaen Truncated Mode 6 and Messiaen truncated mode 6
  Mode 3 of: Messiaen Truncated Mode 6 Inverse and Messiaen truncated mode 6 inverse
  Mode 4 of: Messiaen Truncated Mode 6 and Messiaen truncated mode 6

The name I use for this scale comes from: Clint's Invented Name

Scala name: Messiaen truncated mode 6 inverse

Four Out of 19

Temperament: 19-Tone Equal Temperament (19TET)
The 19 degrees of this temperament, in cents:
  0–63–126–189–253–316–379–442–505–568–632–695–758–821–884–947–1011–1074–1137–1200

Scale steps in semitones: 5–4–5–5

Scale degrees:
  in cents: 0–316–568–884–1200
  intervals: 1–m3–a4–6–8
  Root, Minor 3rd, Quarter-sharp 4th, Major 6th, Octave

Pitches starting from C:
  C D♯ F+ A c
  C E♭ F+ A c

Pitch Class Set: {0,5,9,14}

Pitch Class Mapping: 16929 (Hex 04221, Binary 0000100001000100001)

The name I use for this scale comes from: Clint's Invented Name

Scala name: Four out of 19

Genus Primum

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 31-Tone Equal Temperament (31TET)
The 31 degrees of this temperament, in cents:
  0–39–77–116–155–194–232–271–310–348–387–426–465–503–542–581–619–658–697–735–774–813–852–890–929–968–1006–1045–1084–1123–1161–1200

Scale steps in semitones: 5–8–5–13

Scale degrees:
  in cents: 0–194–503–697–1200
  intervals: 1–2–4–5–8
  Root, Major 2nd, Perfect 4th, Perfect 5th, Octave

Pitches starting from C: C D F G c

Pitch Class Set: {0,5,13,18}

Pitch Class Mapping: 270369 (Hex 00042021, Binary 0000000000001000010000000100001)

The name I use for this scale comes from: Clint's Invented Name

Scala name: Genus primum

Genus Quartum

Temperament: 31-Tone Equal Temperament (31TET)
The 31 degrees of this temperament, in cents:
  0–39–77–116–155–194–232–271–310–348–387–426–465–503–542–581–619–658–697–735–774–813–852–890–929–968–1006–1045–1084–1123–1161–1200

Scale steps in semitones: 10–10–10–1

Scale degrees:
  in cents: 0–387–774–1161–1200
  intervals: 1–3–a5–b8–8
  Root, Major 3rd, Quarter-sharp 5th, Quarter-flat Octave, Octave

Pitches starting from C: C E G+ B+ c

Pitch Class Set: {0,10,20,30}

Pitch Class Mapping: 1074791425 (Hex 40100401, Binary 1000000000100000000010000000001)

The name I use for this scale comes from: Clint's Invented Name

Scala name: Genus quartum

Genus Decium

Temperament: 31-Tone Equal Temperament (31TET)
The 31 degrees of this temperament, in cents:
  0–39–77–116–155–194–232–271–310–348–387–426–465–503–542–581–619–658–697–735–774–813–852–890–929–968–1006–1045–1084–1123–1161–1200

Scale steps in semitones: 13–6–6–6

Scale degrees:
  in cents: 0–503–735–968–1200
  intervals: 1–4–a5–a6–8
  Root, Perfect 4th, Quarter-sharp 5th, Quarter 6th-7th, Octave

Pitches starting from C: C F G+ A+ c

Pitch Class Set: {0,13,19,25}

Pitch Class Mapping: 34086913 (Hex 02082001, Binary 0000010000010000010000000000001)

The name I use for this scale comes from: Clint's Invented Name

Scala name: Genus decimum

Chromatic

Temperament: 4-Tone Eland (Bushmen) Temperament (BushEland4)
The 4 degrees of this temperament, in cents:
  0–489–710–954–1200
Notes: From Scala's bushmen.scl: "Observed scale of South-African bushmen, almost (4 notes) equal pentatonic." 5TET is [0, 240, 480, 720, 960, 1200] and this varies by no more than 10 cents. Note also that 954 is somewhat close to 7/4 (969) and 26/15 (952). This scale is exactly as described in Example 8 of [England 1967].

Scale steps in semitones: 1–1–1–1

Scale degrees:
  in cents: 0–489–710–954–1200
  intervals: 1–4–5–a6–8
  Root, Perfect 4th, Perfect 5th, Quarter 6th-7th, Octave

Pitches starting from C: C F G A+ c

Pitch Class Set: {0,1,2,3}

Pitch Class Mapping: 15 (Hex F, Binary 1111)

The name I use for this scale comes from: Aaron Andrew Hunt's bushmen.scl from http://www.h-pi.com/scalavista/scalearchive.php and [England 1967] Example 8

Chromatic

Temperament: 4-Tone Giraffe (Bushmen) Temperament (BushGiraffe4)
The 4 degrees of this temperament, in cents:
  0–249–425–786–1200
Notes: Example 5 of [England 1967].

Scale steps in semitones: 1–1–1–1

Scale degrees:
  in cents: 0–249–425–786–1200
  intervals: 1–a2–b4–m6–8
  Root, Quarter 2nd-3rd, Quarter 3rd-4th, Minor 6th, Octave

Pitches starting from C:
  C D+ E+ G♯ c
  C D+ E+ A♭ c

Pitch Class Set: {0,1,2,3}

Pitch Class Mapping: 15 (Hex F, Binary 1111)

The name I use for this scale comes from: [England 1967] Example 5

Chromatic

Fingerings on most contemporary six-hole pentatonic minor Native American flutes:

         or        

Fingerings on Anasazi-7 tuned Native American flutes:

Temperament: 4-Tone Equal Temperament (4TET)
The 4 degrees of this temperament, in cents:
  0–300–600–900–1200
Notes: This temperament is equivalent to a 12-TET scale with scale steps 3-3-3-3.

Scale steps in semitones: 1–1–1–1

Scale degrees:
  in cents: 0–300–600–900–1200
  intervals: 1–m3–d5–6–8
  Root, Minor 3rd, Diminished 5th, Major 6th, Octave

Pitches starting from C:
  C D♯ F♯ A c
  C E♭ G♭ A c

Pitch Class Set: {0,1,2,3}

Pitch Class Mapping: 15 (Hex F, Binary 1111)

This scale is a mode (rotation) of these other scales:
  Mode 2 of: Diminished Seventh and Chromatic
  Mode 3 of: Diminished Seventh and Chromatic
  Mode 4 of: Diminished Seventh and Chromatic

The name I use for this scale comes from: The general scale name "chromatic" includes all scale steps in this temperament

Notes: This scale is equivalent to a 12-TET scale with scale steps 3-3-3-3.

Harmonic Seventh

Temperament: 4-Tone Overtone Temperament (Over4)
The 4 degrees of this temperament, in cents:
  0–386–702–969–1200
Notes: Overtone series 4:5:6:7:8 = 4/4, 5/4, …, 8/4.

Scale steps in semitones: 1–1–1–1

Scale degrees:
  in cents: 0–386–702–969–1200
  intervals: 1–3–5–a6–8
  Root, Major 3rd, Perfect 5th, Quarter 6th-7th, Octave

Pitches starting from C: C E G A+ c

Pitch Class Set: {0,1,2,3}

Pitch Class Mapping: 15 (Hex F, Binary 1111)

Corresponding Chord: Harmonic Seventh (Barbershop Seventh)

The name I use for this scale comes from: Scale name set by Clint based on the name of the corresponding 4-tone chord

Wikipedia page related to this scale:

• Harmonic Seventh Chord ⇒ Harmonic seventh chord

Notes: An alternate name could be "Chromatic Scale in 4-Tone OverTone Temperment" scale.