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Interlinking the scalescape: Explore hidden inter-scale connections via tags & classifiers (all terms explained below)…

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[under construction]

• Scale Classifiers •

(click red headers for explanations)

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Notes (total: 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10+)
b2 | 2 | b3 | 3 | 4 | #4 | 5 | b6 | 6 | b7 | 7

Absent positions (i.e. not in the scale)
b2 | 2 | b3 | 3 | 4 | #4 | 5 | b6 | 6 | b7 | 7

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Imperfect tones (total: 1 | 2 | 3 | 4+)
1 | b2 | 2 | b3 | 3 | 4 | #4 | 5 | b6 | 6 | b7 | 7

Detached tones (total: 0 | 1 | 2 | 3+)
1 | b2 | 2 | b3 | 3 | 4 | #4 | 5 | b6 | 6 | b7 | 7

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Symmetries: Rotational | Reflectional | Palindromic

Spacings: Anhemitonic | Hemitonic | Cohemitonic | Co-cohemitonic

Quirks: Atritonal | Centred | Fragmented | Maximal | Self-shadowing

—Scale Tones—

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Notes (total: 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10+)

b2 | 2 | b3 | 3 | 4 | #4 | 5 | b6 | 6 | b7 | 7

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How many tones does the scale have? Which notes are present? (n.b. for easier searchability, all enharmonics are grouped under the values above: e.g. the #5 in the Lydian Augmented is counted as a b6, and the bb7 in the Superlocrian Diminished is counted as a ♮6)

(scales containing 5, 6, and 7 tones)

—Absent Tones—

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Absent positions (i.e. not in the scale)

b2 | 2 | b3 | 3 | 4 | #4 | 5 | b6 | 6 | b7 | 7

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Which semitonal positions are absent from the scale? (n.b. as above, all enharmonics are grouped under these listed values)

(scales with 7, 6, and 5 absent tones)

—Imperfect Tones—

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Imperfect tones (total: 1 | 2 | 3 | 4+)

1 | b2 | 2 | b3 | 3 | 4 | #4 | 5 | b6 | 6 | b7 | 7

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Which tones are ‘imperfect’: i.e. the note a Perfect 5th above them is absent? (below: the Lydian‘s #4 lacks the b2 tone +7 semitones above it, and Shivranjani‘s b3 and♮6 possess the same quality)

—Detached Tones—

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Detached tones (total: 0 | 1 | 2 | 3+)

1 | b2 | 2 | b3 | 3 | 4 | #4 | 5 | b6 | 6 | b7 | 7

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Which tones are ‘detached’: i.e. the notes a Perfect 5th above and below them are both absent from the scale? (below: the Phrygian Dominant‘s ♮3 has no tones 7 semitones above or below, in this case the♮6/♮7 – and the Melodic Minor‘s b3 and ♮7 possess the same quality)

—Spacings—

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Spacings: Anhemitonic | Hemitonic | Cohemitonic | Co-cohemitonic

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What is the scale’s largest ‘chromatic cluster’?

–Anhemitonic: Scales with no adjacent semitones (i.e. the smallest interval spans at least 2 semitones)

–Hemitonic: Scales where the longest available ‘chromatic run’ spans exactly 2 semitones (a ‘hemitone’)

–Cohemitonic: Scales where the longest available ‘chromatic run’ spans exactly 3 semitones

–Co-cohemitonic+: Scales where the longest available ‘chromatic run’ spans 4 or more semitones

(Major Pentatonic; Minor Hexatonic; Hungarian Minor; Bebop Dominant)

—Symmetries—

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Symmetries: Rotational | Reflectional

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Does the scale possess ‘rotational‘ symmetry (i.e. their interval sequence produces at least one exact mode of itself)? Does the scale possess ‘reflectional‘ symmetry (i.e. their tone-wheel, if inverted along a theoretical ‘mirror line’, would look the same)?

(Whole-Tone; Superlocrian; Dorian)

—Quirks—

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Features: Atritonal | Centred | Fragm. | Maximal | Palindromic | Self-shadowing

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Which other features and oddities does the scale possess?

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–Atritonal: Scales which permit no tritones (i.e. no note-pairs are separated by exactly 6 semitones)

(Suspended Pentatonic: no tritones are available)

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–Centred: Scales with a ‘constellation’ that ‘balances at the tone-wheel’s centrepoint’ (i.e. its centre of gravity is located at the exact ‘middle of the clock’). All such scales must also be reflectionally symmetric (essentially, ‘balancing along a centre line’)

(‘Centred’ Double Harmonic vs. ‘Tilted’ Insen/Bairagi)

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–Fragmented: Scales where at least half the tones are ‘detached’ (i.e. with no perfect 5ths above or below them)

(Neapolitan Major [4/7 detached] & Whole-Tone [6/6 detached])

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–Maximal: Scales with a ‘constellation’ that fills the largest possible area within the tone-wheel (i.e. its tones are ‘maximally spread out’). For example: the 12-note chromatic scale would fill the entire available space, while a 2-note dyad would merely draw a ‘line’ with zero area – with all other scales falling somewhere between these extremes. ‘Maximal’ scales draw the ‘largest possible shape’ with the number of tones they have available

(‘Maximal’ Scottish Pentatonic vs. ‘Non-Maximal’ In/Miyakobushi)

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–Palindromic: Scales which take the same intervals ‘forwards and backwards’ – i.e. their semitonal ‘jump sequence’ produces the same scale in either direction from the root (essentially just a ‘special case’ of reflectional symmetry, where the mirror line runs from 1 to #4).

(‘Palindromic’ Dorian & Neapolitan Major)

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–Self-shadowing: Scales where the ‘absent tones’ form the shape of the scale itself (i.e. the absent tones are a ‘mode’ of the scale’s interval pattern). Thus, all such scales must have exactly 6 tones (also see rotational symmetry).

(The Minor Hexatonic‘s absent tones form a mode of the scale itself: if the missing #4 is taken as a ‘new root’, the same interval pattern emerges…)

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