Jatzek MusicMaster Periodic 3
Complete Scale Catalogue and Verified ShadowScale Chains
This catalogue contains all 462 seven-note collections that include D: 161 accept an exact five-note complement overlay and 301 require a derived companion chain. The pairing tables follow the recalculated Appendix C, retaining D and applying a semitone-adjacent removal at every step. The active Jatzek listening parents are referenced separately below; the complete D-root catalogue remains mathematically unchanged.
Listening edition 11 October 2026. Active parents: ACG C D D# F# A A# B (FOUND +2); CDG A A# B D D# E F (FOUND -10, pitch-class equivalent +2); AFG C D E F# G# A A# (FOUND +2). D is the performance root confirmed by listening. D minor is the accompaniment reference. Comparison roots are B, B and C respectively. Historical FOUND notes are retained only as provenance.
(c) 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT) All Rights Reserved!
How to read the catalogue
The missing-note column is the five-note chromatic complement, not an already shifted overlay. An exact overlay moves all five complement pitches by one uniform semitone distance and places every shifted pitch inside the parent. Catalogue names below are retained from the supplied reference edition; this revision checks the note sets and transformations.
For each unresolved chain stage, choose a complement shift with four shared pitches and one outside pitch. Add that outside pitch and remove a parent pitch one semitone away while retaining D. Recalculate the new complement and repeat until it has an exact overlay. Breadth-first search chooses a shortest resolving route. Equal-length routes prefer the smaller absolute shift, then a positive shift, then the lower removed pitch. Alternative valid routes may exist.
Under this rule, 230 catalogue chains resolve at Tier 1, 63 at Tier 2 and 8 at Tier 3. Chain numbers and transitions agree with the recalculated Appendix C. The earlier distribution and one-step pairings are superseded.
Matching ShadowScales
|
Seven parent notes |
Five missing notes |
Supplied catalogue name |
Exact shifts |
|---|---|---|---|
|
D D# E F F# G G# |
A A# B C C# |
Heptatonic Chromatic |
+5, +6, +7 |
|
D D# E F F# G A |
G# A# B C C# |
Ultra-Alt 67 |
+6 |
|
D D# E F F# G A# |
G# A B C C# |
Incoherent |
+6 |
|
D D# E F F# G B |
G# A A# C C# |
Infra-Alt 5 double-flat double-flat 6 |
+6 |
|
D D# E F F# G C |
G# A A# B C# |
Infra-Alt 5 flat 7 double-flat double-flat 6 |
+6 |
|
D D# E F F# G C# |
G# A A# B C |
Alt natural 7 double-flat 34 flat double-flat 5 double-flat double-flat 6 |
+5, +6, +7 |
|
D D# E F F# G# C |
G A A# B C# |
Infra-Alt 56 flat 7 |
+5, +7 |
|
D D# E F F# G# C# |
G A A# B C |
Alt natural 7 double-flat 34 flat double-flat 56 |
+6 |
|
D D# E F F# A C# |
G G# A# B C |
Byzantine Minor |
+6 |
|
D D# E F F# A# C# |
G G# A B C |
Byzantine |
+6 |
|
D D# E F F# B C# |
G G# A A# C |
Quixotic |
+6 |
|
D D# E F F# C C# |
G G# A A# B |
Heptatonic Chromatic III |
+5, +6, +7 |
|
D D# E F G G# C |
F# A A# B C# |
Eurean Mode III |
+6 |
|
D D# E F G A C |
F# G# A# B C# |
Alt double-flat 3 double-flat 4 double-flat 5 double-flat 6 |
+6 |
|
D D# E F G A# C |
F# G# A B C# |
Lipsean Mode IV |
+6 |
|
D D# E F G B C |
F# G# A A# C# |
Alt natural 6 double-flat 345 |
+6 |
|
D D# E F G B C# |
F# G# A A# C |
Alt natural 67 double-flat 345 |
+5, +7 |
|
D D# E F G C C# |
F# G# A A# B |
Alt natural 7 sharp 6 double-flat 345 |
+6 |
|
D D# E F G# A A# |
F# G B C C# |
Infra-Alt 7 flat 5 |
+3, +9 |
|
D D# E F G# C C# |
F# G A A# B |
Alt natural 7 sharp 6 double-flat 34 |
+6 |
|
D D# E F A A# B |
F# G G# C C# |
Phrygian double-flat 3 double-flat 4 double-flat 7 |
+3, +9 |
|
D D# E F A C C# |
F# G G# A# B |
Neapolitan Major double-flat 3 double-flat 4 sharp 6 |
+6 |
|
D D# E F A# C C# |
F# G G# A B |
Phrygian + double-flat 34 |
+6 |
|
D D# E F B C C# |
F# G G# A A# |
Heptatonic Chromatic IV |
+5, +6, +7 |
|
D D# E F# G G# B |
F A A# C C# |
Infra-Alt 6 flat 4 |
+6 |
|
D D# E F# G A B |
F G# A# C C# |
Phrygian Double-Flat |
+6 |
|
D D# E F# G A# B |
F G# A C C# |
Alt double-flat 3 double-flat 5 double-flat 7 |
+2, +6, +10 |
|
D D# E F# G B C |
F G# A A# C# |
Alt natural 6 double-flat 35 |
+6 |
|
D D# E F# G B C# |
F G# A A# C |
Alt natural 67 double-flat 35 |
+6 |
|
D D# E F# G# A A# |
F G B C C# |
Alt double-flat 3 double-flat 6 flat double-flat 7 |
+3, +9 |
|
D D# E F# G# A# C |
F G A B C# |
Leading Whole-Tone Inverse |
+1, +3, +5, +7, +9, +11 |
|
D D# E F# G# B C# |
F G A A# C |
Bohemian |
+6 |
|
D D# E F# A B C# |
F G G# A# C |
Erratic |
+6 |
|
D D# E F# A# B C# |
F G G# A C |
Kaikian Mode V |
+6 |
|
D D# E F# A# C C# |
F G G# A B |
Crater Scale |
+5, +7 |
|
D D# E F# B C C# |
F G G# A A# |
Alt natural 7 sharp 6 double-sharp 5 double-flat 3 |
+6 |
|
D D# E G G# A A# |
F F# B C C# |
Locrian double-flat 3 double-flat 6 flat double-flat 7 |
+3, +9 |
|
D D# E G G# A C# |
F F# A# B C |
Apathetic Minor |
+3, +9 |
|
D D# E G G# A# B |
F F# A C C# |
Locrian double-flat 3 double-flat 7 |
+2, +10 |
|
D D# E G G# B C |
F F# A A# C# |
Locrian natural 6 double-flat 3 |
+2, +6, +10 |
|
D D# E G A B C |
F F# G# A# C# |
Rāga Bhanumati |
+6 |
|
D D# E G A# B C |
F F# G# A C# |
Dominant + flat 2 double-flat 3 |
+6 |
|
D D# E G B C C# |
F F# G# A A# |
Ionian flat 2 double-flat 3 double-sharp 5 sharp 6 |
+6 |
|
D D# E G# A A# B |
F F# G C C# |
Alt natural 5 sharp 437 |
+3, +9 |
|
D D# E G# A A# C |
F F# G B C# |
Mela Jalarnava |
+3, +9 |
|
D D# E G# A A# C# |
F F# G B C |
Rāga Varali |
+3, +9 |
|
D D# E G# B C C# |
F F# G A A# |
Phrygian + double-sharp 5 double-flat 3 |
+6 |
|
D D# E A B C C# |
F F# G G# A# |
Phrygian + double-flat 3 double-sharp 45 |
+6 |
|
D D# E A# B C C# |
F F# G G# A |
Heptatonic Chromatic V |
+5, +6, +7 |
|
D D# F F# G G# A# |
E A B C C# |
Kaikian Mode II |
+6 |
|
D D# F F# G A A# |
E G# B C C# |
Alt double-flat 5 double-flat 6 flat double-flat 7 |
+6 |
|
D D# F F# G A# B |
E G# A C C# |
Mixolocrian |
+2, +6, +10 |
|
D D# F F# G A# C |
E G# A B C# |
Alt double-flat 5 |
+6 |
|
D D# F F# G A# C# |
E G# A B C |
Unorthodox |
+6 |
|
D D# F F# G# A# C |
E G A B C# |
Superlocrian |
+1, +11 |
|
D D# F F# G# A# C# |
E G A B C |
Alt natural 7 |
+6 |
|
D D# F F# A A# B |
E G G# C C# |
Alt natural 5 double-flat 7 |
+2, +10 |
|
D D# F F# A A# C# |
E G G# B C |
Neapolitan Minor flat 4 |
+2, +6, +10 |
|
D D# F F# A# B C# |
E G G# A C |
Neapolitan Major flat 4 sharp 5 |
+6 |
|
D D# F F# A# C C# |
E G G# A B |
Phrygian + flat 4 |
+6 |
|
D D# F G G# A C# |
E F# A# B C |
Pacific Minor |
+3, +9 |
|
D D# F G G# A# C |
E F# A B C# |
Locrian |
+1, +6, +11 |
|
D D# F G A A# C |
E F# G# B C# |
Phrygian |
+1, +6, +11 |
|
D D# F G A B C |
E F# G# A# C# |
Dorian flat 2 |
+1, +11 |
|
D D# F G A B C# |
E F# G# A# C |
Neapolitan Major |
+1, +3, +5, +7, +9, +11 |
|
D D# F G A# B C |
E F# G# A C# |
Dorian + flat 2 |
+6 |
|
D D# F G A# C C# |
E F# G# A B |
Neapolitan Maj sharp 5 sharp 6 |
+6 |
|
D D# F G# A# C C# |
E F# G A B |
Enigmatic Minor |
+6 |
|
D D# F A A# C C# |
E F# G G# B |
Phrygian + double-sharp 4 |
+6 |
|
D D# F A B C C# |
E F# G G# A# |
Phrygian + double-sharp 45 |
+5, +7 |
|
D D# F A# B C C# |
E F# G G# A |
Phrygian + double-sharp 5 sharp double-sharp 4 |
+6 |
|
D D# F# G G# A C# |
E F A# B C |
Rāga Pushp Ranjani |
+3, +9 |
|
D D# F# G G# A# B |
E F A C C# |
Locrian natural 3 double-flat 7 |
+2, +6, +10 |
|
D D# F# G G# B C |
E F A A# C# |
Tsinganikos |
+2, +10 |
|
D D# F# G G# C C# |
E F A A# B |
Ionian flat 2 flat 5 sharp 6 |
+3, +9 |
|
D D# F# G A A# B |
E F G# C C# |
Rāga Kalakanthi |
+2, +6, +10 |
|
D D# F# G A A# C# |
E F G# B C |
Double Harmonic |
+2, +10 |
|
D D# F# G A# B C |
E F G# A C# |
Dominant + flat 2 |
+2, +6, +10 |
|
D D# F# G A# B C# |
E F G# A C |
Ionian + flat 2 |
+2, +6, +10 |
|
D D# F# G# A# B C# |
E F G A C |
Lydian Augmented flat 2 |
+6 |
|
D D# F# A A# B C# |
E F G G# C |
Ionian + flat 2 double-sharp 4 |
+6 |
|
D D# F# A# B C C# |
E F G G# A |
Ionian flat 2 sharp double-sharp 4 double-sharp 5 sharp 6 |
+6 |
|
D D# G G# A A# C# |
E F F# B C |
Lydian flat 2 sharp 3 flat 6 |
+3, +9 |
|
D D# G G# A B C# |
E F F# A# C |
Lydian flat 2 sharp 3 |
+3, +9 |
|
D D# G G# A C C# |
E F F# A# B |
Lydian flat 2 sharp 3 sharp 6 |
+3, +9 |
|
D D# G G# A# B C |
E F F# A C# |
Hijaz Major |
+6 |
|
D D# G A A# B C |
E F F# G# C# |
Dominant + flat 2 sharp 3 double-sharp 4 |
+6 |
|
D D# G A# B C C# |
E F F# G# A |
Superlydian Augmented flat 2 sharp double-sharp 4 double-sharp 5 |
+6 |
|
D D# G# A# B C C# |
E F F# G A |
Superlydian Augmented flat 2 double-sharp 3 sharp double-sharp 4 double-sharp 5 |
+6 |
|
D D# A A# B C C# |
E F F# G G# |
Heptatonic Chromatic VI |
+5, +6, +7 |
|
D E F F# G G# A |
D# A# B C C# |
Alt natural 2 double-flat 5 flat double-flat 6 double-flat double-flat 7 |
+6 |
|
D E F F# G G# A# |
D# A B C C# |
Alt natural 2 double-flat 5 flat double-flat 67 |
+5, +7 |
|
D E F F# G A A# |
D# G# B C C# |
Alt natural 2 double-flat 56 flat double-flat 7 |
+6 |
|
D E F F# G A B |
D# G# A# C C# |
Alt natural 2 double-flat 567 |
+6 |
|
D E F F# G A C |
D# G# A# B C# |
Alt natural 2 double-flat 56 |
+6 |
|
D E F F# G A C# |
D# G# A# B C |
Alt natural 27 double-flat 56 |
+6 |
|
D E F F# G# A C# |
D# G A# B C |
Nomadic Minor |
+6 |
|
D E F F# G# A# C |
D# G A B C# |
Semilocrian flat 4 |
+1, +3, +5, +7, +9, +11 |
|
D E F F# A A# C# |
D# G G# B C |
Harmonic Minor flat 4 |
+2, +6, +10 |
|
D E F F# A B C# |
D# G G# A# C |
Melodic flat 4 |
+6 |
|
D E F F# A C C# |
D# G G# A# B |
Varunapriya flat 4 |
+6 |
|
D E F F# A# B C |
D# G G# A C# |
Dorian + flat 4 |
+3, +9 |
|
D E F G G# A C |
D# F# A# B C# |
Modified Blues |
+6 |
|
D E F G G# A# C |
D# F# A B C# |
Half-Diminished |
+1, +11 |
|
D E F G A A# C |
D# F# G# B C# |
Aeolian |
+1, +6, +11 |
|
D E F G A B C |
D# F# G# A# C# |
Dorian |
+1, +6, +11 |
|
D E F G A B C# |
D# F# G# A# C |
Melodic Minor |
+1, +11 |
|
D E F G A C C# |
D# F# G# A# B |
Rāga Daulati |
+6 |
|
D E F G# A A# C# |
D# F# G B C |
Double Harmonic Minor |
+2, +10 |
|
D E F G# A C C# |
D# F# G A# B |
Mela Nitimati |
+2, +6, +10 |
|
D E F A A# C C# |
D# F# G G# B |
Melodic + sharp 6 double-sharp 4 |
+6 |
|
D E F A B C C# |
D# F# G G# A# |
Eurean Mode VI |
+6 |
|
D E F# G G# A B |
D# F A# C C# |
Lipsean Mode II |
+6 |
|
D E F# G G# A# C |
D# F A B C# |
Major Locrian |
+1, +3, +5, +7, +9, +11 |
|
D E F# G G# C C# |
D# F A A# B |
Ionian flat 5 sharp 6 |
+3, +9 |
|
D E F# G A A# B |
D# F G# C C# |
Mararanjani |
+6 |
|
D E F# G A A# C |
D# F G# B C# |
Mixolydian flat 6 |
+1, +11 |
|
D E F# G A B C |
D# F G# A# C# |
Mixolydian |
+1, +6, +11 |
|
D E F# G A B C# |
D# F G# A# C |
Major |
+1, +6, +11 |
|
D E F# G# A A# C |
D# F G B C# |
Lydian Minor |
+1, +3, +5, +7, +9, +11 |
|
D E F# G# A B C |
D# F G A# C# |
Acoustic |
+1, +11 |
|
D E F# G# A B C# |
D# F G A# C |
Lydian |
+1, +6, +11 |
|
D E F# G# A# B C |
D# F G A C# |
Synthetic Mixture sharp 5 |
+1, +3, +5, +7, +9, +11 |
|
D E F# G# A# B C# |
D# F G A C |
Lydian Augmented |
+1, +11 |
|
D E F# G# A# C C# |
D# F G A B |
Leading Whole-Tone |
+1, +3, +5, +7, +9, +11 |
|
D E F# A A# B C# |
D# F G G# C |
Ionian + double-sharp 4 |
+6 |
|
D E F# A B C C# |
D# F G G# A# |
Ionian double-sharp 4 double-sharp 5 sharp 6 |
+6 |
|
D E G G# A B C |
D# F F# A# C# |
Lydian 7 sharp 3 |
+6 |
|
D E G A A# B C |
D# F F# G# C# |
Dominant + sharp 3 double-sharp 4 |
+6 |
|
D E G A B C C# |
D# F F# G# A# |
Rāga Sorati |
+6 |
|
D E G# A B C C# |
D# F F# G A# |
Kaikian Mode VII |
+6 |
|
D E G# A# B C C# |
D# F F# G A |
Superlydian Augmented natural 2 double-sharp 35 sharp double-sharp 4 |
+5, +7 |
|
D E A A# B C C# |
D# F F# G G# |
Superlydian Augmented natural 2 double-sharp 5 sharp double-sharp 34 |
+6 |
|
D F F# G G# A A# |
D# E B C C# |
Major Locrian sharp 2 double-flat 6 flat double-flat 7 |
+6 |
|
D F F# G G# C C# |
D# E A A# B |
Ionian sharp 2 flat 5 sharp 6 |
+3, +9 |
|
D F F# G A A# B |
D# E G# C C# |
Rāga Kalahamsa |
+6 |
|
D F F# G A A# C |
D# E G# B C# |
Rāga Cudamani |
+6 |
|
D F F# G A A# C# |
D# E G# B C |
Rāga Gangatarangini |
+2, +6, +10 |
|
D F F# G A# B C# |
D# E G# A C |
Ionian Augmented sharp 2 |
+2, +10 |
|
D F F# G B C C# |
D# E G# A A# |
Ionian sharp 2 double-sharp 5 sharp 6 |
+3, +9 |
|
D F F# G# A A# C# |
D# E G B C |
Mela Dhatuvardhani |
+2, +6, +10 |
|
D F F# G# A C C# |
D# E G A# B |
Rasikapriya |
+2, +10 |
|
D F F# A A# B C# |
D# E G G# C |
Ionian + sharp 2 double-sharp 4 |
+2, +6, +10 |
|
D F F# A A# C C# |
D# E G G# B |
Ionian + sharp 26 double-sharp 4 |
+2, +6, +10 |
|
D F G G# A A# C |
D# E F# B C# |
Lydian 7 flat 6 sharp 23 |
+6 |
|
D F G A A# B C |
D# E F# G# C# |
Dominant + sharp 23 double-sharp 4 |
+6 |
|
D F G A A# C C# |
D# E F# G# B |
Superlydian Augmented double-sharp 4 |
+6 |
|
D F G# A A# C C# |
D# E F# G B |
Superlydian Augmented double-sharp 3 double-sharp 4 |
+6 |
|
D F A A# B C C# |
D# E F# G G# |
Superlydian Augmented sharp double-sharp 3 sharp double-sharp 4 double-sharp 5 |
+6 |
|
D F# G G# A A# B |
D# E F C C# |
Lydian double-sharp 2 sharp 3 flat 6 double-flat 7 |
+6 |
|
D F# G G# A C C# |
D# E F A# B |
Lydian double-sharp 2 sharp 3 sharp 6 |
+3, +9 |
|
D F# G G# A# C C# |
D# E F A B |
Superlydian Augmented double-sharp 2 |
+3, +9 |
|
D F# G G# B C C# |
D# E F A A# |
Superlydian Augmented double-sharp 2 double-sharp 5 |
+3, +9 |
|
D F# G A A# B C |
D# E F G# C# |
Dominant + sharp 3 double-sharp 24 |
+6 |
|
D F# G A A# B C# |
D# E F G# C |
Ionian + sharp 3 double-sharp 24 |
+6 |
|
D F# G# A A# B C |
D# E F G C# |
Dominant + double-sharp 234 |
+5, +7 |
|
D F# G# A A# B C# |
D# E F G C |
Ionian + double-sharp 234 |
+6 |
|
D F# A A# B C C# |
D# E F G G# |
Superlydian Augmented double-sharp 2 sharp double-sharp 3 sharp double-sharp 4 double-sharp 5 |
+6 |
|
D G G# A A# B C |
D# E F F# C# |
Dominant + double-sharp 34 sharp double-sharp 2 |
+6 |
|
D G A A# B C C# |
D# E F F# G# |
Superlydian Augmented sharp double-sharp 2 sharp double-sharp 3 sharp double-sharp 4 double-sharp 5 |
+6 |
|
D G# A A# B C C# |
D# E F F# G |
Alt-Maximus |
+5, +6, +7 |
Mismatched ShadowScales
|
Seven parent notes |
Five missing notes |
Supplied catalogue name |
Exact shifts |
|---|---|---|---|
|
D D# E F F# G# A |
G A# B C C# |
Ultra-Alt 7 |
No exact shift |
|
D D# E F F# G# A# |
G A B C C# |
Infra-Alt 567 |
No exact shift |
|
D D# E F F# G# B |
G A A# C C# |
Infra-Alt 56 |
No exact shift |
|
D D# E F F# A A# |
G G# B C C# |
Infra-Alt 57 |
No exact shift |
|
D D# E F F# A B |
G G# A# C C# |
Infra-Alt 5 |
No exact shift |
|
D D# E F F# A C |
G G# A# B C# |
Infra-Alt 5 flat 7 |
No exact shift |
|
D D# E F F# A# B |
G G# A C C# |
Infra-Alt 5 flat 6 |
No exact shift |
|
D D# E F F# A# C |
G G# A B C# |
Alt double-flat 3 double-flat 4 flat double-flat 5 |
No exact shift |
|
D D# E F F# B C |
G G# A A# C# |
Alt natural 6 double-flat 34 flat double-flat 5 |
No exact shift |
|
D D# E F G G# A |
F# A# B C C# |
Infra-Alt 6 double-flat double-flat 7 |
No exact shift |
|
D D# E F G G# A# |
F# A B C C# |
Infra-Alt 67 |
No exact shift |
|
D D# E F G G# B |
F# A A# C C# |
Infra-Alt 6 |
No exact shift |
|
D D# E F G G# C# |
F# A A# B C |
Quixotic Minor |
No exact shift |
|
D D# E F G A A# |
F# G# B C C# |
Infra-Alt 7 |
No exact shift |
|
D D# E F G A B |
F# G# A# C C# |
Alt double-flat 3 double-flat 4 double-flat 5 double-flat 6 double-flat 7 |
No exact shift |
|
D D# E F G A C# |
F# G# A# B C |
Arcadian Minor |
No exact shift |
|
D D# E F G A# B |
F# G# A C C# |
Alt double-flat 3 double-flat 4 double-flat 5 double-flat 7 |
No exact shift |
|
D D# E F G A# C# |
F# G# A B C |
Alt natural 7 double-flat 345 |
No exact shift |
|
D D# E F G# A B |
F# G A# C C# |
1MI & 2∆7 |
No exact shift |
|
D D# E F G# A C |
F# G A# B C# |
Alt double-flat 3 double-flat 4 double-flat 6 |
No exact shift |
|
D D# E F G# A C# |
F# G A# B C |
Alt natural 7 double-flat 346 |
No exact shift |
|
D D# E F G# A# B |
F# G A C C# |
Superlocrian double-flat 3 double-flat 7 |
No exact shift |
|
D D# E F G# A# C |
F# G A B C# |
Alt double-flat 3 double-flat 4 |
No exact shift |
|
D D# E F G# A# C# |
F# G A B C |
Alt natural 7 double-flat 34 |
No exact shift |
|
D D# E F G# B C |
F# G A A# C# |
Alt natural 6 double-flat 34 |
No exact shift |
|
D D# E F G# B C# |
F# G A A# C |
Alt natural 67 double-flat 34 |
No exact shift |
|
D D# E F A A# C |
F# G G# B C# |
Alt natural 5 double-flat 34 |
No exact shift |
|
D D# E F A A# C# |
F# G G# B C |
Alt natural 57 double-flat 34 |
No exact shift |
|
D D# E F A B C |
F# G G# A# C# |
Zephyrean Mode V |
No exact shift |
|
D D# E F A B C# |
F# G G# A# C |
Erratic Minor |
No exact shift |
|
D D# E F A# B C |
F# G G# A C# |
Alt natural 6 sharp 5 double-flat 34 |
No exact shift |
|
D D# E F A# B C# |
F# G G# A C |
Alt natural 67 sharp 5 double-flat 34 |
No exact shift |
|
D D# E F# G G# A |
F A# B C C# |
Borean Mode II |
No exact shift |
|
D D# E F# G G# A# |
F A B C C# |
Infra-Alt 67 flat 4 |
No exact shift |
|
D D# E F# G G# C |
F A A# B C# |
Alt double-flat 3 double-flat 5 flat double-flat 6 |
No exact shift |
|
D D# E F# G G# C# |
F A A# B C |
Alt natural 7 double-flat 35 flat double-flat 6 |
No exact shift |
|
D D# E F# G A A# |
F G# B C C# |
Infra-Alt 7 flat 4 |
No exact shift |
|
D D# E F# G A C |
F G# A# B C# |
Alt double-flat 3 double-flat 5 double-flat 6 |
No exact shift |
|
D D# E F# G A C# |
F G# A# B C |
Arcadian |
No exact shift |
|
D D# E F# G A# C |
F G# A B C# |
Elephant Scale |
No exact shift |
|
D D# E F# G A# C# |
F G# A B C |
Unorthodox Minor |
No exact shift |
|
D D# E F# G C C# |
F G# A A# B |
Alt natural 7 sharp 6 double-flat 35 |
No exact shift |
|
D D# E F# G# A B |
F G A# C C# |
Triadic Heptatonic 29 |
No exact shift |
|
D D# E F# G# A C |
F G A# B C# |
Alt double-flat 3 double-flat 6 |
No exact shift |
|
D D# E F# G# A C# |
F G A# B C |
Phlegmatic Minor |
No exact shift |
|
D D# E F# G# A# B |
F G A C C# |
Ultralocrian double-flat 3 |
No exact shift |
|
D D# E F# G# A# C# |
F G A B C |
Phlegmatic |
No exact shift |
|
D D# E F# G# B C |
F G A A# C# |
Alt natural 6 double-flat 3 |
No exact shift |
|
D D# E F# G# C C# |
F G A A# B |
Alt natural 7 sharp 6 double-flat 3 |
No exact shift |
|
D D# E F# A A# B |
F G G# C C# |
Chromatic Phrygian Inverse |
No exact shift |
|
D D# E F# A A# C |
F G G# B C# |
Astrocyte |
No exact shift |
|
D D# E F# A A# C# |
F G G# B C |
Bohemian Minor |
No exact shift |
|
D D# E F# A B C |
F G G# A# C# |
Midlocrian |
No exact shift |
|
D D# E F# A C C# |
F G G# A# B |
Alt natural 57 sharp 6 double-flat 3 |
No exact shift |
|
D D# E F# A# B C |
F G G# A C# |
Alt natural 6 sharp 5 double-flat 3 |
No exact shift |
|
D D# E G G# A B |
F F# A# C C# |
Phrygian Hungarian Minor |
No exact shift |
|
D D# E G G# A C |
F F# A# B C# |
Chromatic Mixolydian |
No exact shift |
|
D D# E G G# A# C |
F F# A B C# |
Locrian double-flat 3 |
No exact shift |
|
D D# E G G# A# C# |
F F# A B C |
Apathetic |
No exact shift |
|
D D# E G G# B C# |
F F# A A# C |
Supine Minor |
No exact shift |
|
D D# E G G# C C# |
F F# A A# B |
Locrian double-flat 3 sharp 6 natural 7 |
No exact shift |
|
D D# E G A A# B |
F F# G# C C# |
Kanakangi |
No exact shift |
|
D D# E G A A# C |
F F# G# B C# |
Rāga Phenadyuti |
No exact shift |
|
D D# E G A A# C# |
F F# G# B C |
Mela Ganamurti |
No exact shift |
|
D D# E G A B C# |
F F# G# A# C |
Rāga Manoranjani |
No exact shift |
|
D D# E G A C C# |
F F# G# A# B |
Rāga Tanukirti |
No exact shift |
|
D D# E G A# B C# |
F F# G# A C |
Ionian + flat 2 double-flat 3 |
No exact shift |
|
D D# E G A# C C# |
F F# G# A B |
Neapolitan Major double-flat 3 sharp 5 sharp 6 |
No exact shift |
|
D D# E G# A B C |
F F# G A# C# |
Navaneetam |
No exact shift |
|
D D# E G# A B C# |
F F# G A# C |
Lydian flat 2 double-flat 3 |
No exact shift |
|
D D# E G# A C C# |
F F# G A# B |
Mela Raghupriya |
No exact shift |
|
D D# E G# A# B C |
F F# G A C# |
Lydian 7+ flat 23 |
No exact shift |
|
D D# E G# A# B C# |
F F# G A C |
Zephyrean Mode VI |
No exact shift |
|
D D# E G# A# C C# |
F F# G A B |
Phrygian + double-flat 3 |
No exact shift |
|
D D# E A A# B C |
F F# G G# C# |
Alt natural 6 sharp 5 double-flat 3 double-sharp 4 |
No exact shift |
|
D D# E A A# B C# |
F F# G G# C |
Borean Mode VI |
No exact shift |
|
D D# E A A# C C# |
F F# G G# B |
Phrygian + double-flat 3 double-sharp 4 |
No exact shift |
|
D D# F F# G G# A |
E A# B C C# |
Alt double-flat 5 flat double-flat 6 double-flat double-flat 7 |
No exact shift |
|
D D# F F# G G# B |
E A A# C C# |
Superlocrian double-flat 5 flat double-flat 6 double-flat 7 |
No exact shift |
|
D D# F F# G G# C |
E A A# B C# |
Alt double-flat 5 flat double-flat 6 |
No exact shift |
|
D D# F F# G G# C# |
E A A# B C |
Alt natural 7 double-flat 5 flat double-flat 6 |
No exact shift |
|
D D# F F# G A B |
E G# A# C C# |
Ultralocrian double-flat 5 |
No exact shift |
|
D D# F F# G A C |
E G# A# B C# |
Ceiling Scale |
No exact shift |
|
D D# F F# G A C# |
E G# A# B C |
Exotic Minor |
No exact shift |
|
D D# F F# G B C |
E G# A A# C# |
Alt natural 6 double-flat 5 |
No exact shift |
|
D D# F F# G B C# |
E G# A A# C |
Alt natural 67 double-flat 5 |
No exact shift |
|
D D# F F# G C C# |
E G# A A# B |
Alt natural 7 sharp 6 double-flat 5 |
No exact shift |
|
D D# F F# G# A A# |
E G B C C# |
Alt double-flat 6 flat double-flat 7 |
No exact shift |
|
D D# F F# G# A B |
E G A# C C# |
Alternating Heptamode |
No exact shift |
|
D D# F F# G# A C |
E G A# B C# |
Alt double-flat 6 |
No exact shift |
|
D D# F F# G# A C# |
E G A# B C |
Exotic |
No exact shift |
|
D D# F F# G# A# B |
E G A C C# |
Ultralocrian |
No exact shift |
|
D D# F F# G# B C |
E G A A# C# |
Superlocrian sharp 6 |
No exact shift |
|
D D# F F# G# B C# |
E G A A# C |
Dysphoric |
No exact shift |
|
D D# F F# G# C C# |
E G A A# B |
Alt natural 7 sharp 6 |
No exact shift |
|
D D# F F# A A# C |
E G G# B C# |
Maqam Saba Zamzam |
No exact shift |
|
D D# F F# A B C |
E G G# A# C# |
Dorian flat 2 flat 4 |
No exact shift |
|
D D# F F# A B C# |
E G G# A# C |
Neapolitan Major flat 4 |
No exact shift |
|
D D# F F# A C C# |
E G G# A# B |
Neapolitan Major flat 4 sharp 6 |
No exact shift |
|
D D# F F# A# B C |
E G G# A C# |
Alt natural 6 sharp 5 |
No exact shift |
|
D D# F F# B C C# |
E G G# A A# |
Alt natural 7 sharp 6 double-sharp 5 |
No exact shift |
|
D D# F G G# A A# |
E F# B C C# |
Locrian double-flat 6 flat double-flat 7 |
No exact shift |
|
D D# F G G# A B |
E F# A# C C# |
1SUS4 & flat 3∅7 |
No exact shift |
|
D D# F G G# A C |
E F# A# B C# |
Blues Phrygian |
No exact shift |
|
D D# F G G# A# B |
E F# A C C# |
Locrian double-flat 7 |
No exact shift |
|
D D# F G G# A# C# |
E F# A B C |
Locrian natural 7 |
No exact shift |
|
D D# F G G# B C |
E F# A A# C# |
Locrian natural 6 |
No exact shift |
|
D D# F G G# B C# |
E F# A A# C |
Neapolitan Major flat 5 |
No exact shift |
|
D D# F G G# C C# |
E F# A A# B |
Locrian natural 7 sharp 6 |
No exact shift |
|
D D# F G A A# B |
E F# G# C C# |
Rāga Malini |
No exact shift |
|
D D# F G A A# C# |
E F# G# B C |
Neapolitan Minor |
No exact shift |
|
D D# F G A C C# |
E F# G# A# B |
Mela Rupavati |
No exact shift |
|
D D# F G A# B C# |
E F# G# A C |
Neapolitan Major sharp 5 |
No exact shift |
|
D D# F G B C C# |
E F# G# A A# |
Neapolitan Maj double-sharp 5 sharp 6 |
No exact shift |
|
D D# F G# A A# B |
E F# G C C# |
Mela Gavambodhi |
No exact shift |
|
D D# F G# A A# C |
E F# G B C# |
Mela Bhavapriya |
No exact shift |
|
D D# F G# A A# C# |
E F# G B C |
Chromatic Lydian Inverse |
No exact shift |
|
D D# F G# A B C |
E F# G A# C# |
Rāga Sthavarajam |
No exact shift |
|
D D# F G# A B C# |
E F# G A# C |
Rāga Sauviram |
No exact shift |
|
D D# F G# A C C# |
E F# G A# B |
Mela Divyamani |
No exact shift |
|
D D# F G# A# B C |
E F# G A C# |
Lydian 7+ flat 23 |
No exact shift |
|
D D# F G# A# B C# |
E F# G A C |
Lydian + flat 23 |
No exact shift |
|
D D# F G# B C C# |
E F# G A A# |
Phrygian +5 |
No exact shift |
|
D D# F A A# B C |
E F# G G# C# |
Dorian + flat 2 double-sharp 4 |
No exact shift |
|
D D# F A A# B C# |
E F# G G# C |
Neapolitan Maj double-sharp 4 sharp 5 |
No exact shift |
|
D D# F# G G# A A# |
E F B C C# |
Major Locrian flat 2 double-flat 6 flat double-flat 7 |
No exact shift |
|
D D# F# G G# A B |
E F A# C C# |
Ionian flat 2 flat 5 double-flat 6 double-flat 7 |
No exact shift |
|
D D# F# G G# A C |
E F A# B C# |
Locrian natural 3 double-flat 6 |
No exact shift |
|
D D# F# G G# A# C |
E F A B C# |
Locrian Dominant |
No exact shift |
|
D D# F# G G# A# C# |
E F A B C |
Rāga Suddha Pancama |
No exact shift |
|
D D# F# G G# B C# |
E F A A# C |
Chromatic Lydian |
No exact shift |
|
D D# F# G A A# C |
E F G# B C# |
Phrygian Dominant |
No exact shift |
|
D D# F# G A B C |
E F G# A# C# |
Dominant flat 2 |
No exact shift |
|
D D# F# G A B C# |
E F G# A# C |
Rāga Supradhipam |
No exact shift |
|
D D# F# G A C C# |
E F G# A# B |
Mela Hatakambari |
No exact shift |
|
D D# F# G A# C C# |
E F G# A B |
Enigmatic Descending |
No exact shift |
|
D D# F# G B C C# |
E F G# A A# |
Ionian flat 2 double-sharp 5 sharp 6 |
No exact shift |
|
D D# F# G# A A# B |
E F G C C# |
Mela Dhavalambari |
No exact shift |
|
D D# F# G# A A# C |
E F G B C# |
Namanarayani |
No exact shift |
|
D D# F# G# A A# C# |
E F G B C |
Chromatic Hypolydian |
No exact shift |
|
D D# F# G# A B C |
E F G A# C# |
Lydian 7 flat 2 |
No exact shift |
|
D D# F# G# A B C# |
E F G A# C |
Mela Gamanasrama |
No exact shift |
|
D D# F# G# A C C# |
E F G A# B |
Lydian flat 2 sharp 6 |
No exact shift |
|
D D# F# G# A# B C |
E F G A C# |
Persichetti |
No exact shift |
|
D D# F# G# A# C C# |
E F G A B |
Enigmatic |
No exact shift |
|
D D# F# G# B C C# |
E F G A A# |
Lydian flat 2 double-sharp 5 sharp 6 |
No exact shift |
|
D D# F# A A# B C |
E F G G# C# |
Dominant + flat 2 double-sharp 4 |
No exact shift |
|
D D# F# A A# C C# |
E F G G# B |
Enigmatic double-sharp 4 |
No exact shift |
|
D D# F# A B C C# |
E F G G# A# |
Aeryrian |
No exact shift |
|
D D# G G# A A# B |
E F F# C C# |
Lydian flat 2 sharp 3 flat 6 double-flat 7 |
No exact shift |
|
D D# G G# A A# C |
E F F# B C# |
Lydian 7 flat 26 sharp 3 |
No exact shift |
|
D D# G G# A B C |
E F F# A# C# |
Lydian 7 flat 2 sharp 3 |
No exact shift |
|
D D# G G# A# B C# |
E F F# A C |
Lydian + flat 2 sharp 3 |
No exact shift |
|
D D# G G# A# C C# |
E F F# A B |
Phrygian + sharp 3 |
No exact shift |
|
D D# G G# B C C# |
E F F# A A# |
Phrygian + sharp 3 double-sharp 5 |
No exact shift |
|
D D# G A A# B C# |
E F F# G# C |
Ionian + flat 2 sharp 3 double-sharp 4 |
No exact shift |
|
D D# G A A# C C# |
E F F# G# B |
Superlydian Augmented flat 2 double-sharp 4 |
No exact shift |
|
D D# G A B C C# |
E F F# G# A# |
Superlydian Augmented flat 2 double-sharp 4 double-sharp 5 |
No exact shift |
|
D D# G# A A# B C |
E F F# G C# |
Dominant + flat 2 double-sharp 34 |
No exact shift |
|
D D# G# A A# B C# |
E F F# G C |
Ionian + flat 2 double-sharp 34 |
No exact shift |
|
D D# G# A A# C C# |
E F F# G B |
Borean Mode VII |
No exact shift |
|
D D# G# A B C C# |
E F F# G A# |
Superlydian Augmented flat 2 double-sharp 3 double-sharp 4 double-sharp 5 |
No exact shift |
|
D E F F# G G# B |
D# A A# C C# |
Debussy's Heptatonic |
No exact shift |
|
D E F F# G G# C |
D# A A# B C# |
Alt natural 2 double-flat 5 flat double-flat 6 |
No exact shift |
|
D E F F# G G# C# |
D# A A# B C |
Alt natural 27 double-flat 5 flat double-flat 6 |
No exact shift |
|
D E F F# G A# B |
D# G# A C C# |
Aeolian flat 4 double-flat 5 double-flat 7 |
No exact shift |
|
D E F F# G A# C |
D# G# A B C# |
Alt natural 2 double-flat 5 |
No exact shift |
|
D E F F# G A# C# |
D# G# A B C |
Alt natural 27 double-flat 5 |
No exact shift |
|
D E F F# G B C |
D# G# A A# C# |
Rāga Ravikosh |
No exact shift |
|
D E F F# G B C# |
D# G# A A# C |
Euphoric |
No exact shift |
|
D E F F# G C C# |
D# G# A A# B |
Borean Mode IV |
No exact shift |
|
D E F F# G# A A# |
D# G B C C# |
Alt natural 2 double-flat 6 flat double-flat 7 |
No exact shift |
|
D E F F# G# A B |
D# G A# C C# |
Superlocrian natural 2 double-flat 6 double-flat 7 |
No exact shift |
|
D E F F# G# A C |
D# G A# B C# |
Alt natural 2 double-flat 6 |
No exact shift |
|
D E F F# G# A# B |
D# G A C C# |
Superlocrian natural 2 double-flat 7 |
No exact shift |
|
D E F F# G# A# C# |
D# G A B C |
Eccentric |
No exact shift |
|
D E F F# G# B C |
D# G A A# C# |
Dorian Blues |
No exact shift |
|
D E F F# G# B C# |
D# G A A# C |
Nomadic |
No exact shift |
|
D E F F# G# C C# |
D# G A A# B |
Alt natural 27 sharp 6 |
No exact shift |
|
D E F F# A A# B |
D# G G# C C# |
Chromatic Hypodorian |
No exact shift |
|
D E F F# A A# C |
D# G G# B C# |
Sabach |
No exact shift |
|
D E F F# A B C |
D# G G# A# C# |
Dorian flat 4 |
No exact shift |
|
D E F F# A# B C# |
D# G G# A C |
Melodic + flat 4 |
No exact shift |
|
D E F F# A# C C# |
D# G G# A B |
Melodic + sharp 6 flat 4 |
No exact shift |
|
D E F F# B C C# |
D# G G# A A# |
Notoean Mode V |
No exact shift |
|
D E F G G# A A# |
D# F# B C C# |
Locrian natural 2 double-flat 6 flat double-flat 7 |
No exact shift |
|
D E F G G# A B |
D# F# A# C C# |
Locrian natural 2 double-flat 67 |
No exact shift |
|
D E F G G# A C# |
D# F# A# B C |
Supine |
No exact shift |
|
D E F G G# A# B |
D# F# A C C# |
Hungarian Major Inverse |
No exact shift |
|
D E F G G# A# C# |
D# F# A B C |
Harmonic Minor flat 5 |
No exact shift |
|
D E F G G# B C |
D# F# A A# C# |
Dorian flat 5 |
No exact shift |
|
D E F G G# B C# |
D# F# A A# C |
Jeths' Mode |
No exact shift |
|
D E F G G# C C# |
D# F# A A# B |
Melodic flat 5 sharp 6 |
No exact shift |
|
D E F G A A# B |
D# F# G# C C# |
Rāga Jhankara Bhramavi |
No exact shift |
|
D E F G A A# C# |
D# F# G# B C |
Harmonic Minor |
No exact shift |
|
D E F G A# B C |
D# F# G# A C# |
Dorian Augmented |
No exact shift |
|
D E F G A# B C# |
D# F# G# A C |
Melodic + |
No exact shift |
|
D E F G A# C C# |
D# F# G# A B |
Melodic + sharp 6 |
No exact shift |
|
D E F G B C C# |
D# F# G# A A# |
Melodic double-sharp 5 sharp 6 |
No exact shift |
|
D E F G# A A# B |
D# F# G C C# |
Mela Syamalangi |
No exact shift |
|
D E F G# A A# C |
D# F# G B C# |
Mela Sanmukhapriya |
No exact shift |
|
D E F G# A B C |
D# F# G A# C# |
Dorian sharp 4 |
No exact shift |
|
D E F G# A B C# |
D# F# G A# C |
Lydian Diminished |
No exact shift |
|
D E F G# A# B C |
D# F# G A C# |
Lydian 7+ flat 3 |
No exact shift |
|
D E F G# A# B C# |
D# F# G A C |
Lydian Augmented flat 3 |
No exact shift |
|
D E F G# A# C C# |
D# F# G A B |
Phrygian + natural 2 |
No exact shift |
|
D E F G# B C C# |
D# F# G A A# |
Melodic sharp 4 double-sharp 5 sharp 6 |
No exact shift |
|
D E F A A# B C |
D# F# G G# C# |
Dorian + double-sharp 4 |
No exact shift |
|
D E F A A# B C# |
D# F# G G# C |
Melodic + double-sharp 4 |
No exact shift |
|
D E F A# B C C# |
D# F# G G# A |
Melodic sharp double-sharp 4 double-sharp 5 sharp 6 |
No exact shift |
|
D E F# G G# A A# |
D# F B C C# |
Major Locrian double-flat 6 flat double-flat 7 |
No exact shift |
|
D E F# G G# A C |
D# F A# B C# |
Major Locrian double-flat 6 |
No exact shift |
|
D E F# G G# A C# |
D# F A# B C |
Bucolic |
No exact shift |
|
D E F# G G# A# B |
D# F A C C# |
Major Locrian double-flat 7 |
No exact shift |
|
D E F# G G# A# C# |
D# F A B C |
Harmonic Major flat 5 |
No exact shift |
|
D E F# G G# B C |
D# F A A# C# |
Mixolydian flat 5 |
No exact shift |
|
D E F# G G# B C# |
D# F A A# C |
Ionian flat 5 |
No exact shift |
|
D E F# G A A# C# |
D# F G# B C |
Harmonic Major |
No exact shift |
|
D E F# G A C C# |
D# F G# A# B |
Mela Naganandini |
No exact shift |
|
D E F# G A# B C |
D# F G# A C# |
Mixolydian Augmented |
No exact shift |
|
D E F# G A# B C# |
D# F G# A C |
Major Augmented |
No exact shift |
|
D E F# G A# C C# |
D# F G# A B |
Ionian + sharp 6 |
No exact shift |
|
D E F# G B C C# |
D# F G# A A# |
Rāga Rageshri |
No exact shift |
|
D E F# G# A A# B |
D# F G C C# |
Mela Kantamani |
No exact shift |
|
D E F# G# A A# C# |
D# F G B C |
Lydian Harmonic Major |
No exact shift |
|
D E F# G# A C C# |
D# F G A# B |
Mela Citrambari |
No exact shift |
|
D E F# G# B C C# |
D# F G A A# |
Ionian sharp 4 double-sharp 5 sharp 6 |
No exact shift |
|
D E F# A A# B C |
D# F G G# C# |
Dominant + double-sharp 4 |
No exact shift |
|
D E F# A A# C C# |
D# F G G# B |
Ionian + sharp 6 double-sharp 4 |
No exact shift |
|
D E F# A# B C C# |
D# F G G# A |
Ionian sharp double-sharp 4 double-sharp 5 sharp 6 |
No exact shift |
|
D E G G# A A# B |
D# F F# C C# |
Tanarupi IV |
No exact shift |
|
D E G G# A A# C |
D# F F# B C# |
Lydian Minor sharp 3 |
No exact shift |
|
D E G G# A A# C# |
D# F F# B C |
Lydian sharp 3 flat 6 |
No exact shift |
|
D E G G# A B C# |
D# F F# A# C |
Lydian sharp 3 |
No exact shift |
|
D E G G# A C C# |
D# F F# A# B |
Rāga Loom Sarang |
No exact shift |
|
D E G G# A# B C |
D# F F# A C# |
Lydian 7+ sharp 3 |
No exact shift |
|
D E G G# A# B C# |
D# F F# A C |
Lydian Augmented sharp 3 |
No exact shift |
|
D E G G# A# C C# |
D# F F# A B |
Lydian + sharp 36 |
No exact shift |
|
D E G G# B C C# |
D# F F# A A# |
Lydian sharp 3 double-sharp 5 sharp 6 |
No exact shift |
|
D E G A A# B C# |
D# F F# G# C |
Noh |
No exact shift |
|
D E G A A# C C# |
D# F F# G# B |
Ionian + sharp 36 double-sharp 4 |
No exact shift |
|
D E G A# B C C# |
D# F F# G# A |
Ionian sharp 3 sharp double-sharp 4 double-sharp 5 sharp 6 |
No exact shift |
|
D E G# A A# B C |
D# F F# G C# |
Dominant + double-sharp 34 |
No exact shift |
|
D E G# A A# B C# |
D# F F# G C |
Ionian + double-sharp 34 |
No exact shift |
|
D E G# A A# C C# |
D# F F# G B |
Ionian + sharp 6 double-sharp 34 |
No exact shift |
|
D F F# G G# A B |
D# E A# C C# |
Major Locrian sharp 2 double-flat 6 double-flat 7 |
No exact shift |
|
D F F# G G# A C |
D# E A# B C# |
Tanarupi V |
No exact shift |
|
D F F# G G# A C# |
D# E A# B C |
Raghupriya V |
No exact shift |
|
D F F# G G# A# B |
D# E A C C# |
Major Locrian sharp 2 double-flat 7 |
No exact shift |
|
D F F# G G# A# C |
D# E A B C# |
Major Locrian sharp 2 |
No exact shift |
|
D F F# G G# A# C# |
D# E A B C |
Harmonic Maj sharp 2 flat 5 |
No exact shift |
|
D F F# G G# B C |
D# E A A# C# |
Dominant sharp 2 flat 5 |
No exact shift |
|
D F F# G G# B C# |
D# E A A# C |
4∆7 & 7MA |
No exact shift |
|
D F F# G A B C |
D# E G# A# C# |
Rāga Ganavaridhi |
No exact shift |
|
D F F# G A B C# |
D# E G# A# C |
Rāga Sailadesakshi |
No exact shift |
|
D F F# G A C C# |
D# E G# A# B |
Rāga Madhuranjani |
No exact shift |
|
D F F# G A# B C |
D# E G# A C# |
Rāga Dvigandharabushini |
No exact shift |
|
D F F# G A# C C# |
D# E G# A B |
Chromatic Phrygian |
No exact shift |
|
D F F# G# A A# B |
D# E G C C# |
Mela Sucaritra |
No exact shift |
|
D F F# G# A A# C |
D# E G B C# |
Jyoti Swarupini |
No exact shift |
|
D F F# G# A B C |
D# E G A# C# |
Hungarian Major |
No exact shift |
|
D F F# G# A B C# |
D# E G A# C |
Aeolian Harmonic |
No exact shift |
|
D F F# G# A# B C |
D# E G A C# |
Lydian 7+ sharp 2 |
No exact shift |
|
D F F# G# A# B C# |
D# E G A C |
Aeolian Flat |
No exact shift |
|
D F F# G# A# C C# |
D# E G A B |
Lydian + sharp 26 |
No exact shift |
|
D F F# G# B C C# |
D# E G A A# |
1∅7 & 3SUS4 |
No exact shift |
|
D F F# A A# B C |
D# E G G# C# |
Dominant + sharp 24 |
No exact shift |
|
D F F# A B C C# |
D# E G G# A# |
Rāga Homshikha |
No exact shift |
|
D F F# A# B C C# |
D# E G G# A |
Ionian sharp 2 sharp double-sharp 4 double-sharp 5 sharp 6 |
No exact shift |
|
D F G G# A A# B |
D# E F# C C# |
Lydian sharp 2 sharp 3 flat 6 double-flat 7 |
No exact shift |
|
D F G G# A A# C# |
D# E F# B C |
Lydian sharp 2 sharp 3 flat 6 |
No exact shift |
|
D F G G# A B C |
D# E F# A# C# |
Lydian 7 sharp 23 |
No exact shift |
|
D F G G# A B C# |
D# E F# A# C |
1SUS4 & 77 |
No exact shift |
|
D F G G# A C C# |
D# E F# A# B |
Chromatic Hypophrygian |
No exact shift |
|
D F G G# A# B C |
D# E F# A C# |
Lydian 7+ sharp 23 |
No exact shift |
|
D F G G# A# B C# |
D# E F# A C |
Lydian Augmented sharp 2 sharp 3 |
No exact shift |
|
D F G G# A# C C# |
D# E F# A B |
Superlydian Augmented |
No exact shift |
|
D F G G# B C C# |
D# E F# A A# |
Superlydian Augmented double-sharp 5 |
No exact shift |
|
D F G A A# B C# |
D# E F# G# C |
Ionian + sharp 23 double-sharp 4 |
No exact shift |
|
D F G A B C C# |
D# E F# G# A# |
Superaugmented sharp 3 double-sharp 4 double-sharp 5 |
No exact shift |
|
D F G A# B C C# |
D# E F# G# A |
Tanarupi III |
No exact shift |
|
D F G# A A# B C |
D# E F# G C# |
Dominant + sharp 2 double-sharp 34 |
No exact shift |
|
D F G# A A# B C# |
D# E F# G C |
Ionian + sharp 2 double-sharp 34 |
No exact shift |
|
D F G# A B C C# |
D# E F# G A# |
Superlydian Augmented 345 |
No exact shift |
|
D F G# A# B C C# |
D# E F# G A |
Bonian |
No exact shift |
|
D F# G G# A A# C |
D# E F B C# |
Lydian 7 flat 6 sharp 3 double-sharp 2 |
No exact shift |
|
D F# G G# A A# C# |
D# E F B C |
Lydian double-sharp 2 sharp 3 flat 6 |
No exact shift |
|
D F# G G# A B C |
D# E F A# C# |
Lydian 7 sharp 3 double-sharp 2 |
No exact shift |
|
D F# G G# A B C# |
D# E F A# C |
Rāga Hindolita |
No exact shift |
|
D F# G G# A# B C |
D# E F A C# |
Lydian 7+32 |
No exact shift |
|
D F# G G# A# B C# |
D# E F A C |
Lydian + sharp 3 double-sharp 2 |
No exact shift |
|
D F# G A A# C C# |
D# E F G# B |
Superlydian Augmented double-sharp 2 double-sharp 4 |
No exact shift |
|
D F# G A B C C# |
D# E F G# A# |
Rāga Madhuri |
No exact shift |
|
D F# G A# B C C# |
D# E F G# A |
Raghupriya III |
No exact shift |
|
D F# G# A A# C C# |
D# E F G B |
Superlydian Augmented 234 |
No exact shift |
|
D F# G# A B C C# |
D# E F G A# |
Superlydian Augmented double-sharp 2 double-sharp 3 double-sharp 4 double-sharp 5 |
No exact shift |
|
D F# G# A# B C C# |
D# E F G A |
Superlydian Augmented double-sharp 2 double-sharp 3 sharp double-sharp 4 double-sharp 5 |
No exact shift |
|
D G G# A A# B C# |
D# E F F# C |
Superlydian Augmented natural 6 double-sharp 34 sharp double-sharp 2 |
No exact shift |
|
D G G# A A# C C# |
D# E F F# B |
Superlydian Augmented sharp double-sharp 2 double-sharp 3 double-sharp 4 |
No exact shift |
|
D G G# A B C C# |
D# E F F# A# |
Borean Mode I |
No exact shift |
|
D G G# A# B C C# |
D# E F F# A |
Superlydian Augmented sharp double-sharp 2 double-sharp 3 sharp double-sharp 4 double-sharp 5 |
No exact shift |
Reconciled ascending and descending chains
Each row contains the full selected chain. Tier names are looked up by the exact seven-note set in the supplied catalogue. Every final shadow is checked against the final tier own complement. Shift values are upward semitones modulo twelve.
|
Chain and source name |
Seven notes at each stage |
Uniform shift and adjacent replacement |
Resolved tier and five-note overlay |
|---|---|---|---|
|
1 |
Asc: D D# E F F# G# A |
T1: +8; add G, remove G# |
Ultra-Alt 67 |
|
2 |
Asc: D D# E F F# G# A# |
T1: +7; add G, remove G# |
Incoherent |
|
3 |
Asc: D D# E F F# G# B |
T1: +5; add C, remove B |
Infra-Alt 56 flat 7 |
|
4 |
Asc: D D# E F F# A A# |
T1: +9; add G#, remove A |
Incoherent |
|
5 |
Asc: D D# E F F# A B |
T1: +4; add C, remove B |
Alt double-flat 3 double-flat 4 double-flat 5 double-flat 6 |
|
6 |
Asc: D D# E F F# A C |
T1: +8; add G, remove F# |
Alt double-flat 3 double-flat 4 double-flat 5 double-flat 6 |
|
7 |
Asc: D D# E F F# A# B |
T1: +10; add G, remove F# |
Alt double-flat 3 double-flat 5 double-flat 7 |
|
8 |
Asc: D D# E F F# A# C |
T1: +5; add C#, remove C |
Byzantine |
|
9 |
Asc: D D# E F F# B C |
T1: +4; add C#, remove C |
Quixotic |
|
10 |
Asc: D D# E F G G# A |
T1: +8; add F#, remove G |
Ultra-Alt 67 |
|
11 |
Asc: D D# E F G G# A# |
T1: +8; add A, remove G# |
Infra-Alt 7 flat 5 |
|
12 |
Asc: D D# E F G G# B |
T1: +2; add C, remove B |
Eurean Mode III |
|
13 |
Asc: D D# E F G G# C# |
T1: +8; add F#, remove G |
Alt natural 7 double-flat 34 flat double-flat 56 |
|
14 |
Asc: D D# E F G A A# |
T1: +9; add G#, remove G |
Infra-Alt 7 flat 5 |
|
15 |
Asc: D D# E F G A B |
T1: +11; add C, remove B |
Alt double-flat 3 double-flat 4 double-flat 5 double-flat 6 |
|
16 |
Asc: D D# E F G A C# |
T1: +7; add F#, remove G |
Byzantine Minor |
|
17 |
Asc: D D# E F G A# B |
T1: +10; add F#, remove F |
Alt double-flat 3 double-flat 5 double-flat 7 |
|
18 |
Asc: D D# E F G A# C# |
T1: +4; add C, remove C# |
Lipsean Mode IV |
|
19 |
Asc: D D# E F G# A B |
T1: +10; add A#, remove B |
Infra-Alt 7 flat 5 |
|
20 |
Asc: D D# E F G# A C |
T1: +10; add B, remove C |
Infra-Alt 7 flat 5 |
|
21 |
Asc: D D# E F G# A C# |
T1: +9; add G, remove G# |
Byzantine Minor |
|
22 |
Asc: D D# E F G# A# B |
T1: +2; add A, remove G# |
Phrygian double-flat 3 double-flat 4 double-flat 7 |
|
23 |
Asc: D D# E F G# A# C |
T1: +1; add G, remove G# |
Lipsean Mode IV |
|
24 |
Asc: D D# E F G# A# C# |
T1: +4; add B, remove A# |
Bohemian |
|
25 |
Asc: D D# E F G# B C |
T1: +10; add G, remove G# |
Alt natural 6 double-flat 345 |
|
26 |
Asc: D D# E F G# B C# |
T1: +8; add F#, remove F |
Bohemian |
|
27 |
Asc: D D# E F A A# C |
T1: +3; add B, remove C |
Phrygian double-flat 3 double-flat 4 double-flat 7 |
|
28 |
Asc: D D# E F A A# C# |
T1: +10; add F#, remove F |
Neapolitan Minor flat 4 |
|
29 |
Asc: D D# E F A B C |
T1: +4; add A#, remove B |
Phrygian double-flat 3 double-flat 4 double-flat 7 |
|
30 |
Asc: D D# E F A B C# |
T1: +5; add C, remove B |
Neapolitan Major double-flat 3 double-flat 4 sharp 6 |
|
31 |
Asc: D D# E F A# B C |
T1: +9; add F#, remove F |
Kaikian Mode V |
|
32 |
Asc: D D# E F A# B C# |
T1: +4; add C, remove B |
Phrygian + double-flat 34 |
|
33 |
Asc: D D# E F# G G# A |
T1: +9; add A#, remove A |
Kaikian Mode II |
|
34 |
Asc: D D# E F# G G# A# |
T1: +5; add F, remove E |
Kaikian Mode II |
|
35 |
Asc: D D# E F# G G# C |
T1: +7; add F, remove F# |
Eurean Mode III |
|
36 |
Asc: D D# E F# G G# C# |
T1: +3; add C, remove C# |
Eurean Mode III |
|
37 |
Asc: D D# E F# G A A# |
T1: +10; add B, remove A# |
Phrygian Double-Flat |
|
38 |
Asc: D D# E F# G A C |
T1: +1; add B, remove C |
Phrygian Double-Flat |
|
39 |
Asc: D D# E F# G A C# |
T1: +4; add C, remove C# |
Phrygian Double-Flat |
|
40 |
Asc: D D# E F# G A# C |
T1: +11; add G#, remove G |
Leading Whole-Tone Inverse |
|
41 |
Asc: D D# E F# G A# C# |
T1: +2; add B, remove A# |
Alt natural 67 double-flat 35 |
|
42 |
Asc: D D# E F# G C C# |
T1: +8; add F, remove F# |
Alt natural 7 sharp 6 double-flat 345 |
|
43 |
Asc: D D# E F# G# A B |
T1: +11; add C, remove B |
Leading Whole-Tone Inverse |
|
44 |
Asc: D D# E F# G# A C |
T1: +11; add A#, remove A |
Leading Whole-Tone Inverse |
|
45 |
Asc: D D# E F# G# A C# |
T1: +9; add G, remove F# |
Apathetic Minor |
|
46 |
Asc: D D# E F# G# A# B |
T1: +11; add C, remove B |
Leading Whole-Tone Inverse |
|
47 |
Asc: D D# E F# G# A# C# |
T1: +1; add C, remove C# |
Leading Whole-Tone Inverse |
|
48 |
Asc: D D# E F# G# B C |
T1: +1; add A#, remove B |
Leading Whole-Tone Inverse |
|
49 |
Asc: D D# E F# G# C C# |
T1: +7; add F, remove F# |
Alt natural 7 sharp 6 double-flat 34 |
|
50 |
Asc: D D# E F# A A# B |
T1: +10; add F, remove E |
Alt natural 5 double-flat 7 |
|
51 |
Asc: D D# E F# A A# C |
T1: +1; add G#, remove A |
Leading Whole-Tone Inverse |
|
52 |
Asc: D D# E F# A A# C# |
T1: +10; add F, remove E |
Neapolitan Minor flat 4 |
|
53 |
Asc: D D# E F# A B C |
T1: +11; add G, remove F# |
Rāga Bhanumati |
|
54 |
Asc: D D# E F# A C C# |
T1: +4; add B, remove C |
Erratic |
|
55 |
Asc: D D# E F# A# B C |
T1: +5; add C#, remove C |
Kaikian Mode V |
|
56 |
Asc: D D# E G G# A B |
T1: +10; add A#, remove A |
Locrian double-flat 3 double-flat 7 |
|
57 |
Asc: D D# E G G# A C |
T1: +2; add C#, remove C |
Apathetic Minor |
|
58 |
Asc: D D# E G G# A# C |
T1: +1; add F#, remove G |
Leading Whole-Tone Inverse |
|
59 |
Asc: D D# E G G# A# C# |
T1: +10; add A, remove A# |
Apathetic Minor |
|
60 |
Asc: D D# E G G# B C# |
T1: +2; add C, remove C# |
Locrian natural 6 double-flat 3 |
|
61 |
Asc: D D# E G G# C C# |
T1: +2; add B, remove C |
Locrian natural 6 double-flat 3 |
|
62 |
Asc: D D# E G A A# B |
T1: +2; add G#, remove G |
Alt natural 5 sharp 437 |
|
63 |
Asc: D D# E G A A# C |
T1: +11; add F, remove E |
Phrygian |
|
64 |
Asc: D D# E G A A# C# |
T1: +2; add G#, remove G |
Rāga Varali |
|
65 |
Asc: D D# E G A B C# |
T1: +1; add F#, remove G |
Erratic |
|
66 |
Asc: D D# E G A C C# |
T1: +4; add A#, remove A |
Neapolitan Maj sharp 5 sharp 6 |
|
67 |
Asc: D D# E G A# B C# |
T1: +10; add F#, remove G |
Kaikian Mode V |
|
68 |
Asc: D D# E G A# C C# |
T1: +8; add F, remove E |
Neapolitan Maj sharp 5 sharp 6 |
|
69 |
Asc: D D# E G# A B C |
T1: +2; add G, remove G# |
Rāga Bhanumati |
|
70 |
Asc: D D# E G# A B C# |
T1: +3; add A#, remove B |
Rāga Varali |
|
71 |
Asc: D D# E G# A C C# |
T1: +10; add F, remove E |
Mela Nitimati |
|
72 |
Asc: D D# E G# A# B C |
T1: +3; add A, remove A# |
Rāga Bhanumati |
|
73 |
Asc: D D# E G# A# B C# |
T1: +4; add A, remove A# |
Rāga Varali |
|
74 |
Asc: D D# E G# A# C C# |
T1: +5; add B, remove A# |
Phrygian + double-sharp 5 double-flat 3 |
|
75 |
Asc: D D# E A A# B C |
T1: +3; add G#, remove A |
Rāga Bhanumati |
|
76 |
Asc: D D# E A A# B C# |
T1: +9; add F, remove E |
Phrygian + double-sharp 4 |
|
77 |
Asc: D D# E A A# C C# |
T1: +4; add B, remove A# |
Phrygian + double-flat 3 double-sharp 45 |
|
78 |
Asc: D D# F F# G G# A |
T1: +4; add E, remove D# |
Alt natural 2 double-flat 5 flat double-flat 6 double-flat double-flat 7 |
|
79 |
Asc: D D# F F# G G# B |
T1: +10; add A#, remove B |
Kaikian Mode II |
|
80 |
Asc: D D# F F# G G# C |
T1: +8; add A, remove G# |
Alt double-flat 5 |
|
81 |
Asc: D D# F F# G G# C# |
T1: +9; add A, remove G# |
Alt natural 27 double-flat 56 |
|
82 |
Asc: D D# F F# G A B |
T1: +11; add C, remove B |
Alt double-flat 5 |
|
83 |
Asc: D D# F F# G A C |
T1: +11; add A#, remove A |
Alt double-flat 5 |
|
84 |
Asc: D D# F F# G A C# |
T1: +5; add E, remove D# |
Alt natural 27 double-flat 56 |
|
85 |
Asc: D D# F F# G B C |
T1: +2; add A#, remove B |
Alt double-flat 5 |
|
86 |
Asc: D D# F F# G B C# |
T1: +7; add E, remove F |
Alt natural 67 double-flat 35 |
|
87 |
Asc: D D# F F# G C C# |
T1: +3; add B, remove C |
Alt natural 67 double-flat 35 |
|
88 |
Asc: D D# F F# G# A A# |
T1: +10; add B, remove A# |
Superlocrian |
|
89 |
Asc: D D# F F# G# A B |
T1: +11; add C, remove B |
Superlocrian |
|
90 |
Asc: D D# F F# G# A C |
T1: +11; add A#, remove A |
Superlocrian |
|
91 |
Asc: D D# F F# G# A C# |
T1: +10; add A#, remove A |
Alt natural 7 |
|
92 |
Asc: D D# F F# G# A# B |
T1: +11; add C, remove B |
Superlocrian |
|
93 |
Asc: D D# F F# G# B C |
T1: +1; add A#, remove B |
Superlocrian |
|
94 |
Asc: D D# F F# G# B C# |
T1: +1; add A#, remove B |
Alt natural 7 |
|
95 |
Asc: D D# F F# G# C C# |
T1: +4; add B, remove C |
Alt natural 7 |
|
96 |
Asc: D D# F F# A A# C |
T1: +1; add G#, remove A |
Superlocrian |
|
97 |
Asc: D D# F F# A B C |
T1: +11; add G, remove F# |
Dorian flat 2 |
|
98 |
Asc: D D# F F# A B C# |
T1: +11; add G, remove F# |
Neapolitan Major |
|
99 |
Asc: D D# F F# A C C# |
T1: +2; add A#, remove A |
Phrygian + flat 4 |
|
100 |
Asc: D D# F F# A# B C |
T1: +10; add G, remove F# |
Dorian + flat 2 |
|
101 |
Asc: D D# F F# B C C# |
T1: +8; add E, remove F |
Alt natural 7 sharp 6 double-sharp 5 double-flat 3 |
|
102 |
Asc: D D# F G G# A A# |
T1: +3; add E, remove F |
Locrian double-flat 3 double-flat 6 flat double-flat 7 |
|
103 |
Asc: D D# F G G# A B |
T1: +11; add C, remove B |
Locrian |
|
104 |
Asc: D D# F G G# A C |
T1: +11; add A#, remove A |
Locrian |
|
105 |
Asc: D D# F G G# A# B |
T1: +11; add C, remove B |
Locrian |
|
106 |
Asc: D D# F G G# A# C# |
T1: +1; add C, remove C# |
Locrian |
|
107 |
Asc: D D# F G G# B C |
T1: +1; add A#, remove B |
Locrian |
|
108 |
Asc: D D# F G G# B C# |
T1: +11; add A, remove G# |
Neapolitan Major |
|
109 |
Asc: D D# F G G# C C# |
T1: +9; add F#, remove F |
Ionian flat 2 flat 5 sharp 6 |
|
110 |
Asc: D D# F G A A# B |
T1: +11; add C, remove B |
Phrygian |
|
111 |
Asc: D D# F G A A# C# |
T1: +1; add C, remove C# |
Phrygian |
|
112 |
Asc: D D# F G A C C# |
T1: +1; add B, remove C |
Neapolitan Major |
|
113 |
Asc: D D# F G A# B C# |
T1: +1; add A, remove A# |
Neapolitan Major |
|
114 |
Asc: D D# F G B C C# |
T1: +7; add E, remove F |
Ionian flat 2 double-flat 3 double-sharp 5 sharp 6 |
|
115 |
Asc: D D# F G# A A# B |
T1: +10; add E, remove F |
Alt natural 5 sharp 437 |
|
116 |
Asc: D D# F G# A A# C |
T1: +1; add G, remove G# |
Phrygian |
|
117 |
Asc: D D# F G# A A# C# |
T1: +10; add E, remove D# |
Double Harmonic Minor |
|
118 |
Asc: D D# F G# A B C |
T1: +1; add G, remove G# |
Dorian flat 2 |
|
119 |
Asc: D D# F G# A B C# |
T1: +1; add G, remove G# |
Neapolitan Major |
|
120 |
Asc: D D# F G# A C C# |
T1: +10; add E, remove D# |
Mela Nitimati |
|
121 |
Asc: D D# F G# A# B C |
T1: +1; add G, remove G# |
Dorian + flat 2 |
|
122 |
Asc: D D# F G# A# B C# |
T1: +11; add F#, remove F |
Lydian Augmented flat 2 |
|
123 |
Asc: D D# F G# B C C# |
T1: +4; add A#, remove B |
Enigmatic Minor |
|
124 |
Asc: D D# F A A# B C |
T1: +4; add G#, remove A |
Dorian + flat 2 |
|
125 |
Asc: D D# F A A# B C# |
T1: +5; add C, remove B |
Phrygian + double-sharp 4 |
|
126 |
Asc: D D# F# G G# A A# |
T1: +10; add B, remove A# |
Locrian natural 3 double-flat 7 |
|
127 |
Asc: D D# F# G G# A B |
T1: +10; add A#, remove A |
Locrian natural 3 double-flat 7 |
|
128 |
Asc: D D# F# G G# A C |
T1: +2; add C#, remove C |
Rāga Pushp Ranjani |
|
129 |
Asc: D D# F# G G# A# C |
T1: +1; add F, remove F# |
Locrian |
|
130 |
Asc: D D# F# G G# A# C# |
T1: +10; add A, remove G# |
Double Harmonic |
|
131 |
Asc: D D# F# G G# B C# |
T1: +2; add C, remove C# |
Tsinganikos |
|
132 |
Asc: D D# F# G A A# C |
T1: +1; add F, remove F# |
Phrygian |
|
133 |
Asc: D D# F# G A B C |
T1: +1; add F, remove F# |
Dorian flat 2 |
|
134 |
Asc: D D# F# G A B C# |
T1: +1; add F, remove F# |
Neapolitan Major |
|
135 |
Asc: D D# F# G A C C# |
T1: +10; add G#, remove A |
Ionian flat 2 flat 5 sharp 6 |
|
136 |
Asc: D D# F# G A# C C# |
T1: +2; add B, remove C |
Ionian + flat 2 |
|
137 |
Asc: D D# F# G B C C# |
T1: +2; add A#, remove B |
Ionian + flat 2 |
|
138 |
Asc: D D# F# G# A A# B |
T1: +2; add G, remove G# |
Rāga Kalakanthi |
|
139 |
Asc: D D# F# G# A A# C |
T1: +11; add E, remove D# |
Lydian Minor |
|
140 |
Asc: D D# F# G# A A# C# |
T1: +2; add G, remove F# |
Lydian flat 2 sharp 3 flat 6 |
|
141 |
Asc: D D# F# G# A B C |
T1: +11; add E, remove D# |
Acoustic |
|
142 |
Asc: D D# F# G# A B C# |
T1: +11; add E, remove D# |
Lydian |
|
143 |
Asc: D D# F# G# A C C# |
T1: +2; add G, remove F# |
Lydian flat 2 sharp 3 sharp 6 |
|
144 |
Asc: D D# F# G# A# B C |
T1: +11; add E, remove D# |
Synthetic Mixture sharp 5 |
|
145 |
Asc: D D# F# G# A# C C# |
T1: +1; add F, remove F# |
Enigmatic Minor |
|
146 |
Asc: D D# F# G# B C C# |
T1: +4; add A, remove G# |
Ionian double-sharp 4 double-sharp 5 sharp 6 |
|
147 |
Asc: D D# F# A A# B C |
T1: +2; add G, remove F# |
Dominant + flat 2 sharp 3 double-sharp 4 |
|
148 |
Asc: D D# F# A A# C C# |
T1: +10; add F, remove F# |
Phrygian + double-sharp 4 |
|
149 |
Asc: D D# F# A B C C# |
T1: +8; add E, remove D# |
Ionian double-sharp 4 double-sharp 5 sharp 6 |
|
150 |
Asc: D D# G G# A A# B |
T1: +2; add F#, remove G |
Rāga Kalakanthi |
|
151 |
Asc: D D# G G# A A# C |
T1: +9; add C#, remove C |
Lydian flat 2 sharp 3 flat 6 |
|
152 |
Asc: D D# G G# A B C |
T1: +10; add E, remove D# |
Lydian 7 sharp 3 |
|
153 |
Asc: D D# G G# A# B C# |
T1: +2; add F#, remove G |
Lydian Augmented flat 2 |
|
154 |
Asc: D D# G G# A# C C# |
T1: +3; add A, remove A# |
Lydian flat 2 sharp 3 sharp 6 |
|
155 |
Asc: D D# G G# B C C# |
T1: +3; add A, remove G# |
Superlydian Augmented flat 2 sharp double-sharp 4 double-sharp 5 |
|
156 |
Asc: D D# G A A# B C# |
T1: +7; add C, remove C# |
Dominant + flat 2 sharp 3 double-sharp 4 |
|
157 |
Asc: D D# G A A# C C# |
T1: +4; add G#, remove A |
Lydian flat 2 sharp 3 sharp 6 |
|
158 |
Asc: D D# G A B C C# |
T1: +5; add A#, remove A |
Superlydian Augmented flat 2 sharp double-sharp 4 double-sharp 5 |
|
159 |
Asc: D D# G# A A# B C |
T1: +8; add C#, remove C |
Dominant + flat 2 sharp 3 double-sharp 4 |
|
160 |
Asc: D D# G# A A# B C# |
T1: +3; add G, remove G# |
Dominant + flat 2 sharp 3 double-sharp 4 |
|
161 |
Asc: D D# G# A A# C C# |
T1: +9; add E, remove D# |
Kaikian Mode VII |
|
162 |
Asc: D D# G# A B C C# |
T1: +4; add A#, remove A |
Superlydian Augmented flat 2 double-sharp 3 sharp double-sharp 4 double-sharp 5 |
|
163 |
Asc: D E F F# G G# B |
T1: +8; add A, remove G# |
Alt natural 2 double-flat 567 |
|
164 |
Asc: D E F F# G G# C |
T1: +5; add D#, remove E |
Alt double-flat 5 |
|
165 |
Asc: D E F F# G G# C# |
T1: +4; add D#, remove E |
Alt natural 27 double-flat 56 |
|
166 |
Asc: D E F F# G A# B |
T1: +2; add D#, remove E |
Mixolocrian |
|
167 |
Asc: D E F F# G A# C |
T1: +1; add A, remove A# |
Alt natural 2 double-flat 56 |
|
168 |
Asc: D E F F# G A# C# |
T1: +10; add A, remove A# |
Alt natural 27 double-flat 56 |
|
169 |
Asc: D E F F# G B C |
T1: +9; add A#, remove B |
Alt natural 2 double-flat 56 |
|
170 |
Asc: D E F F# G B C# |
T1: +8; add G#, remove G |
Melodic flat 4 |
|
171 |
Asc: D E F F# G C C# |
T1: +3; add B, remove C |
Melodic flat 4 |
|
172 |
Asc: D E F F# G# A A# |
T1: +7; add G, remove G# |
Alt natural 2 double-flat 56 flat double-flat 7 |
|
173 |
Asc: D E F F# G# A B |
T1: +4; add G, remove G# |
Alt natural 2 double-flat 567 |
|
174 |
Asc: D E F F# G# A C |
T1: +11; add A#, remove A |
Semilocrian flat 4 |
|
175 |
Asc: D E F F# G# A# B |
T1: +11; add C, remove B |
Semilocrian flat 4 |
|
176 |
Asc: D E F F# G# A# C# |
T1: +1; add C, remove C# |
Semilocrian flat 4 |
|
177 |
Asc: D E F F# G# B C |
T1: +1; add A#, remove B |
Semilocrian flat 4 |
|
178 |
Asc: D E F F# G# B C# |
T1: +11; add A, remove G# |
Melodic flat 4 |
|
179 |
Asc: D E F F# G# C C# |
T1: +9; add G, remove F# |
Rāga Daulati |
|
180 |
Asc: D E F F# A A# B |
T1: +2; add D#, remove E |
Alt natural 5 double-flat 7 |
|
181 |
Asc: D E F F# A A# C |
T1: +1; add G#, remove A |
Semilocrian flat 4 |
|
182 |
Asc: D E F F# A B C |
T1: +11; add G, remove F# |
Dorian |
|
183 |
Asc: D E F F# A# B C# |
T1: +2; add A, remove A# |
Melodic flat 4 |
|
184 |
Asc: D E F F# A# C C# |
T1: +7; add D#, remove E |
Phrygian + flat 4 |
|
185 |
Asc: D E F F# B C C# |
T1: +3; add A#, remove B |
Phrygian + flat 4 |
|
186 |
Asc: D E F G G# A A# |
T1: +4; add D#, remove E |
Locrian double-flat 3 double-flat 6 flat double-flat 7 |
|
187 |
Asc: D E F G G# A B |
T1: +11; add C, remove B |
Modified Blues |
|
188 |
Asc: D E F G G# A C# |
T1: +2; add C, remove C# |
Modified Blues |
|
189 |
Asc: D E F G G# A# B |
T1: +11; add C, remove B |
Half-Diminished |
|
190 |
Asc: D E F G G# A# C# |
T1: +1; add C, remove C# |
Half-Diminished |
|
191 |
Asc: D E F G G# B C |
T1: +1; add A#, remove B |
Half-Diminished |
|
192 |
Asc: D E F G G# B C# |
T1: +11; add A, remove G# |
Melodic Minor |
|
193 |
Asc: D E F G G# C C# |
T1: +10; add A, remove G# |
Rāga Daulati |
|
194 |
Asc: D E F G A A# B |
T1: +11; add C, remove B |
Aeolian |
|
195 |
Asc: D E F G A A# C# |
T1: +1; add C, remove C# |
Aeolian |
|
196 |
Asc: D E F G A# B C |
T1: +1; add A, remove A# |
Dorian |
|
197 |
Asc: D E F G A# B C# |
T1: +1; add A, remove A# |
Melodic Minor |
|
198 |
Asc: D E F G A# C C# |
T1: +1; add A, remove A# |
Rāga Daulati |
|
199 |
Asc: D E F G B C C# |
T1: +4; add A#, remove B |
Rāga Daulati |
|
200 |
Asc: D E F G# A A# B |
T1: +2; add D#, remove E |
Alt natural 5 sharp 437 |
|
201 |
Asc: D E F G# A A# C |
T1: +1; add G, remove G# |
Aeolian |
|
202 |
Asc: D E F G# A B C |
T1: +1; add G, remove G# |
Dorian |
|
203 |
Asc: D E F G# A B C# |
T1: +1; add G, remove G# |
Melodic Minor |
|
204 |
Asc: D E F G# A# B C |
T1: +11; add F#, remove F |
Synthetic Mixture sharp 5 |
|
205 |
Asc: D E F G# A# B C# |
T1: +11; add F#, remove F |
Lydian Augmented |
|
206 |
Asc: D E F G# A# C C# |
T1: +11; add F#, remove F |
Leading Whole-Tone |
|
207 |
Asc: D E F G# B C C# |
T1: +2; add A, remove G# |
Eurean Mode VI |
|
208 |
Asc: D E F A A# B C |
T1: +3; add F#, remove F |
Synthetic Mixture sharp 5 |
|
209 |
Asc: D E F A A# B C# |
T1: +10; add F#, remove F |
Ionian + double-sharp 4 |
|
210 |
Asc: D E F A# B C C# |
T1: +8; add D#, remove E |
Phrygian + double-sharp 5 sharp double-sharp 4 |
|
211 |
Asc: D E F# G G# A A# |
T1: +5; add F, remove E |
Major Locrian sharp 2 double-flat 6 flat double-flat 7 |
|
212 |
Asc: D E F# G G# A C |
T1: +1; add B, remove C |
Lipsean Mode II |
|
213 |
Asc: D E F# G G# A C# |
T1: +3; add D#, remove E |
Rāga Pushp Ranjani |
|
214 |
Asc: D E F# G G# A# B |
T1: +11; add C, remove B |
Major Locrian |
|
215 |
Asc: D E F# G G# A# C# |
T1: +1; add C, remove C# |
Major Locrian |
|
216 |
Asc: D E F# G G# B C |
T1: +1; add A#, remove B |
Major Locrian |
|
217 |
Asc: D E F# G G# B C# |
T1: +11; add A, remove G# |
Major |
|
218 |
Asc: D E F# G A A# C# |
T1: +1; add C, remove C# |
Mixolydian flat 6 |
|
219 |
Asc: D E F# G A C C# |
T1: +1; add B, remove C |
Major |
|
220 |
Asc: D E F# G A# B C |
T1: +1; add A, remove A# |
Mixolydian |
|
221 |
Asc: D E F# G A# B C# |
T1: +1; add A, remove A# |
Major |
|
222 |
Asc: D E F# G A# C C# |
T1: +11; add G#, remove G |
Leading Whole-Tone |
|
223 |
Asc: D E F# G B C C# |
T1: +9; add F, remove E |
Ionian sharp 2 double-sharp 5 sharp 6 |
|
224 |
Asc: D E F# G# A A# B |
T1: +11; add C, remove B |
Lydian Minor |
|
225 |
Asc: D E F# G# A A# C# |
T1: +1; add C, remove C# |
Lydian Minor |
|
226 |
Asc: D E F# G# A C C# |
T1: +1; add B, remove C |
Lydian |
|
227 |
Asc: D E F# G# B C C# |
T1: +1; add A#, remove B |
Leading Whole-Tone |
|
228 |
Asc: D E F# A A# B C |
T1: +1; add G#, remove A |
Synthetic Mixture sharp 5 |
|
229 |
Asc: D E F# A A# C C# |
T1: +1; add G#, remove A |
Leading Whole-Tone |
|
230 |
Asc: D E F# A# B C C# |
T1: +7; add D#, remove E |
Ionian flat 2 sharp double-sharp 4 double-sharp 5 sharp 6 |
|
231 |
Asc: D E G G# A A# B |
T1: +4; add F, remove E |
Lydian 7 flat 6 sharp 23 |
|
232 |
Asc: D E G G# A A# C |
T1: +1; add F#, remove G |
Lydian Minor |
|
233 |
Asc: D E G G# A A# C# |
T1: +10; add D#, remove E |
Lydian flat 2 sharp 3 flat 6 |
|
234 |
Asc: D E G G# A B C# |
T1: +1; add F#, remove G |
Lydian |
|
235 |
Asc: D E G G# A C C# |
T1: +10; add D#, remove E |
Lydian flat 2 sharp 3 sharp 6 |
|
236 |
Asc: D E G G# A# B C |
T1: +1; add F#, remove G |
Synthetic Mixture sharp 5 |
|
237 |
Asc: D E G G# A# B C# |
T1: +1; add F#, remove G |
Lydian Augmented |
|
238 |
Asc: D E G G# A# C C# |
T1: +1; add F#, remove G |
Leading Whole-Tone |
|
239 |
Asc: D E G G# B C C# |
T1: +2; add F, remove E |
Superlydian Augmented double-sharp 2 double-sharp 5 |
|
240 |
Asc: D E G A A# B C# |
T1: +1; add F#, remove G |
Ionian + double-sharp 4 |
|
241 |
Asc: D E G A A# C C# |
T1: +11; add F, remove E |
Superlydian Augmented double-sharp 4 |
|
242 |
Asc: D E G A# B C C# |
T1: +4; add A, remove A# |
Rāga Sorati |
|
243 |
Asc: D E G# A A# B C |
T1: +7; add C#, remove C |
Ionian + double-sharp 4 |
|
244 |
Asc: D E G# A A# B C# |
T1: +4; add G, remove G# |
Ionian + double-sharp 4 |
|
245 |
Asc: D E G# A A# C C# |
T1: +5; add B, remove A# |
Kaikian Mode VII |
|
246 |
Asc: D F F# G G# A B |
T1: +4; add E, remove F |
Lipsean Mode II |
|
247 |
Asc: D F F# G G# A C |
T1: +8; add B, remove C |
Lipsean Mode II |
|
248 |
Asc: D F F# G G# A C# |
T1: +10; add A#, remove A |
Rāga Gangatarangini |
|
249 |
Asc: D F F# G G# A# B |
T1: +5; add A, remove G# |
Rāga Kalahamsa |
|
250 |
Asc: D F F# G G# A# C |
T1: +1; add E, remove F |
Major Locrian |
|
251 |
Asc: D F F# G G# A# C# |
T1: +10; add A, remove G# |
Rāga Gangatarangini |
|
252 |
Asc: D F F# G G# B C |
T1: +10; add C#, remove C |
Ionian sharp 2 flat 5 sharp 6 |
|
253 |
Asc: D F F# G G# B C# |
T1: +2; add C, remove B |
Ionian sharp 2 flat 5 sharp 6 |
|
254 |
Asc: D F F# G A B C |
T1: +1; add E, remove F |
Mixolydian |
|
255 |
Asc: D F F# G A B C# |
T1: +1; add E, remove F |
Major |
|
256 |
Asc: D F F# G A C C# |
T1: +10; add G#, remove G |
Rasikapriya |
|
257 |
Asc: D F F# G A# B C |
T1: +10; add C#, remove C |
Ionian Augmented sharp 2 |
|
258 |
Asc: D F F# G A# C C# |
T1: +2; add B, remove C |
Ionian Augmented sharp 2 |
|
259 |
Asc: D F F# G# A A# B |
T1: +7; add G, remove G# |
Rāga Kalahamsa |
|
260 |
Asc: D F F# G# A A# C |
T1: +1; add E, remove F |
Lydian Minor |
|
261 |
Asc: D F F# G# A B C |
T1: +1; add E, remove F |
Acoustic |
|
262 |
Asc: D F F# G# A B C# |
T1: +1; add E, remove F |
Lydian |
|
263 |
Asc: D F F# G# A# B C |
T1: +1; add E, remove F |
Synthetic Mixture sharp 5 |
|
264 |
Asc: D F F# G# A# B C# |
T1: +1; add E, remove F |
Lydian Augmented |
|
265 |
Asc: D F F# G# A# C C# |
T1: +1; add E, remove F |
Leading Whole-Tone |
|
266 |
Asc: D F F# G# B C C# |
T1: +10; add G, remove G# |
Ionian sharp 2 double-sharp 5 sharp 6 |
|
267 |
Asc: D F F# A A# B C |
T1: +10; add C#, remove C |
Ionian + sharp 2 double-sharp 4 |
|
268 |
Asc: D F F# A B C C# |
T1: +2; add A#, remove B |
Ionian + sharp 26 double-sharp 4 |
|
269 |
Asc: D F F# A# B C C# |
T1: +2; add A, remove A# |
Ionian + sharp 26 double-sharp 4 |
|
270 |
Asc: D F G G# A A# B |
T1: +8; add C, remove B |
Lydian 7 flat 6 sharp 23 |
|
271 |
Asc: D F G G# A A# C# |
T1: +2; add F#, remove G |
Mela Dhatuvardhani |
|
272 |
Asc: D F G G# A B C |
T1: +1; add E, remove F |
Lydian 7 sharp 3 |
|
273 |
Asc: D F G G# A B C# |
T1: +1; add E, remove F |
Lydian |
|
274 |
Asc: D F G G# A C C# |
T1: +2; add F#, remove F |
Lydian double-sharp 2 sharp 3 sharp 6 |
|
275 |
Asc: D F G G# A# B C |
T1: +8; add A, remove G# |
Dominant + sharp 23 double-sharp 4 |
|
276 |
Asc: D F G G# A# B C# |
T1: +1; add E, remove F |
Lydian Augmented |
|
277 |
Asc: D F G G# A# C C# |
T1: +1; add E, remove F |
Leading Whole-Tone |
|
278 |
Asc: D F G G# B C C# |
T1: +2; add F#, remove F |
Superlydian Augmented double-sharp 2 double-sharp 5 |
|
279 |
Asc: D F G A A# B C# |
T1: +1; add E, remove F |
Ionian + double-sharp 4 |
|
280 |
Asc: D F G A B C C# |
T1: +1; add E, remove F |
Rāga Sorati |
|
281 |
Asc: D F G A# B C C# |
T1: +4; add G#, remove G |
Superlydian Augmented sharp double-sharp 3 sharp double-sharp 4 double-sharp 5 |
|
282 |
Asc: D F G# A A# B C |
T1: +4; add G, remove G# |
Dominant + sharp 23 double-sharp 4 |
|
283 |
Asc: D F G# A A# B C# |
T1: +2; add F#, remove F |
Ionian + double-sharp 234 |
|
284 |
Asc: D F G# A B C C# |
T1: +10; add E, remove F |
Kaikian Mode VII |
|
285 |
Asc: D F G# A# B C C# |
T1: +5; add A, remove G# |
Superlydian Augmented sharp double-sharp 3 sharp double-sharp 4 double-sharp 5 |
|
286 |
Asc: D F# G G# A A# C |
T1: +7; add B, remove C |
Lydian double-sharp 2 sharp 3 flat 6 double-flat 7 |
|
287 |
Asc: D F# G G# A A# C# |
T1: +2; add F, remove F# |
Mela Dhatuvardhani |
|
288 |
Asc: D F# G G# A B C |
T1: +4; add F, remove F# |
Lydian 7 sharp 3 |
|
289 |
Asc: D F# G G# A B C# |
T1: +9; add C, remove B |
Lydian double-sharp 2 sharp 3 sharp 6 |
|
290 |
Asc: D F# G G# A# B C |
T1: +5; add A, remove G# |
Dominant + sharp 3 double-sharp 24 |
|
291 |
Asc: D F# G G# A# B C# |
T1: +2; add F, remove F# |
Lydian Augmented |
|
292 |
Asc: D F# G A A# C C# |
T1: +2; add F, remove F# |
Superlydian Augmented double-sharp 4 |
|
293 |
Asc: D F# G A B C C# |
T1: +3; add G#, remove A |
Superlydian Augmented double-sharp 2 double-sharp 5 |
|
294 |
Asc: D F# G A# B C C# |
T1: +3; add G#, remove G |
Superlydian Augmented double-sharp 2 sharp double-sharp 3 sharp double-sharp 4 double-sharp 5 |
|
295 |
Asc: D F# G# A A# C C# |
T1: +7; add B, remove C |
Ionian + double-sharp 234 |
|
296 |
Asc: D F# G# A B C C# |
T1: +4; add G, remove G# |
Superlydian Augmented double-sharp 2 double-sharp 5 |
|
297 |
Asc: D F# G# A# B C C# |
T1: +5; add A, remove G# |
Superlydian Augmented double-sharp 2 sharp double-sharp 3 sharp double-sharp 4 double-sharp 5 |
|
298 |
Asc: D G G# A A# B C# |
T1: +8; add C, remove C# |
Dominant + double-sharp 34 sharp double-sharp 2 |
|
299 |
Asc: D G G# A A# C C# |
T1: +3; add F#, remove G |
Ionian + double-sharp 234 |
|
300 |
Asc: D G G# A B C C# |
T1: +4; add A#, remove A |
Superlydian Augmented sharp double-sharp 2 sharp double-sharp 3 sharp double-sharp 4 double-sharp 5 |
|
301 |
Asc: D G G# A# B C C# |
T1: +4; add A, remove G# |
Superlydian Augmented sharp double-sharp 2 sharp double-sharp 3 sharp double-sharp 4 double-sharp 5 |
Active Jatzek family reference
|
Family |
Active listening parent |
Exact complement shifts |
|---|---|---|
|
AFG |
C D E F# G# A A# |
+1, +3, +5, +7, +9, +11 |
|
CDG |
B D D# E F A A# |
+3, +9 |
|
ACG |
B C D D# F# A A# |
No exact parent overlay |
The active ACG companion route in Periodic 1 replaces A with G# at Tier 1 and D# with E at Tier 2, using +7 at both transitions. Appendix C also illustrates the transposed shortest alternative: +2, add G, remove F#, resolving at Tier 1. These are separate valid companion routes. Both use the active ACG parent C D D# F# A A# B.
Diagrams retain tuning D G C F A D with string 6 at the top and frets 20 to 0 from left to right. A comparison root does not establish a conventional major or minor key.
Independent checks
FURTHER DOCUMENTATION | Independent checks for a catalogue row
Research addition • 26 September 2026 • Philip John Jatzek & STORM (ChatGPT)
For any listed seven-note scale, count seven unique pitch classes and calculate the five unused chromatic pitch classes. Convert the seven-note collection to semitone offsets from the stated D root. Compare that interval identity with the cited catalogue, allowing enharmonic spellings while keeping the source label visible.
A derived descending entry needs a second, separate check: compute its own five-note complement after its pitches have been fixed. Never reuse the ascending complement for the descending entry. An external catalogue name is a naming cross-check, not proof of a particular ascending-to-descending derivation.
Reference websites consulted
https://ianring.com/musictheory/scales/
https://ianring.com/musictheory/scales/finder/
The external references explain standard music concepts; MusicMaster-specific scale and ShadowScale results retain the definitions and evidence levels given in this periodical.
NEED TO KNOW | PERIODICAL 3
Catalogue comparison and quality control
Keep an auditable scale identifier
Record the tonic, ordered interval cycle, absolute pitch classes, and chosen spelling with each catalogue entry. This makes the 462 entries easier to check independently.
Define what a match means
An exact match uses the same pitch classes; a transpositional match allows a uniform shift; an inversional match also allows reflection. Label each kind in the pairing chart.
Count shared notes before judging fit
For a proposed pair, show intersection and unique tones. A high shared tone count is useful for smooth transitions, but does not prove that the pair works over a particular chord.
Check duplicates mechanically
Sort each pitch class set after reduction modulo 12, then compare canonical signatures. Preserve the original spelling and interval order alongside that computed check.
Further reading
https://ianring.com/musictheory/book/
https://www.musictheory.net/lessons
Music glossary
This chapter is a catalogue. Read each name alongside its note set, interval signature, source, and match status. One interval structure may appear in multiple transposed rows without becoming a new scale.
|
Term |
Definition |
|---|---|
|
227-entry review |
The document’s historical recheck of 227 rows formerly called uncatalogued; repeated rows reduced to fewer distinct structures. |
|
85 unique structures |
The distinct five-note interval sets found after normalizing and deduplicating those 227 reviewed rows. |
|
Ascending-descending pair |
One mismatched ascending parent followed by its selected sequence of derived descending tiers, ending in an exact complement overlay. |
|
Auditable identifier |
A stable row or structure label that lets a reader trace a listed set back to its notes and reference. |
|
Catalogue correspondence |
An exact interval-content match between a listed set and a documented scale catalogue entry. |
|
Catalogue identity |
The known concert or formal catalogue name for a pitch structure, retained across transpositions. |
|
Catalogue row |
A table record containing the notes, scale or shadow category, interval information and source. |
|
Chromatic complement |
The five pitch classes missing from a seven-note scale when compared against all twelve. |
|
Closest placement |
The incomplete transposition with the most tones shared with a parent when no exact five-note overlay exists. |
|
Concert scale name |
An established name or formal catalogue description of the pitch structure when one has been verified. |
|
D-root convention |
The choice to show D as the master performance and naming reference in this edition. |
|
Derived note replacement |
The documented swap of a conflicting parent pitch when constructing a playable descending scale. |
|
Descending construction |
A seven-note companion tier created by adding a shifted complement outside note and removing a semitone-adjacent parent pitch. |
|
Descending overlay |
A five-note candidate evaluated against a derived descending parent. |
|
Duplicate pitch set |
A repeated occurrence of the same normalized pitch-class collection in multiple rows or keys. |
|
Enharmonic normalization |
Comparing equal-tempered pitch classes despite alternate spellings such as D♯ and E♭, while retaining the useful written names. |
|
Exact five-note overlay |
A whole five-note template that maps to a parent scale without a pitch substitution. |
|
Five-note interval template |
The intervals of five distinct notes measured from the candidate root and compared under transposition. |
|
Forte number |
An identifier for a pitch-class set class; it is not necessarily a rooted concert scale name. |
|
Four-of-five match |
An incomplete overlay with exactly four shared pitch classes and one conflict. |
|
Indented descendant |
A derived tier belonging to its identified ascending family; the reconciled table lists every selected stage explicitly. |
|
Interval signature |
The ordered interval distances used to recognize a pitch collection across transpositions. |
|
Key field |
The table location stating the named or reference key for a listed candidate. |
|
Matching table |
Rows whose five absent chromatic notes can be transposed intact into at least one complete overlay. |
|
Mismatch table |
Rows with no complete unchanged five-note overlay under the stated matching rule. |
|
Missing-note inventory |
A row’s explicit list of the five chromatic pitch classes absent from its seven-note scale. |
|
Named reference |
A documented source showing an established name or formal catalogue identity for the exact interval structure. |
|
Naming claim |
An assertion that a listed structure is new or already named; verify it against the notes and catalogues before publishing. |
|
Octave repeat removal |
Dropping the final repeated root of a played scale before counting distinct pitch classes. |
|
One-to-one pairing |
Each ascending mismatch parent has one selected route in this edition; that route may contain several derived tiers. |
|
Overlay completeness |
The number of candidate tones that land within the parent, up to the required five out of five. |
|
Overlay status |
A label separating exact matches, partial mismatches, and adjusted directional results. |
|
Pairing row |
The grouped ascending parent, derived tiers, transition operations and resolved shadow for one catalogue chain. |
|
Parent note list |
The seven distinct notes of the scale whose shadow pitches are being calculated. |
|
Pitch-class reduction |
Replacing a note’s octave-specific pitch with its class modulo twelve for comparison. |
|
Pitch-class sorting |
Putting a set’s distinct classes in a consistent order before mechanical duplicate checks. |
|
Prime-form comparison |
A set-theory check of equivalence classes after transposition and inversion normalization. |
|
Reference source |
The named publication or catalogue used to confirm a row’s established identity. |
|
Root normalization |
Measuring each candidate’s pitches from its stated root so interval formulas can be compared fairly. |
|
Row provenance |
The source and transformation path explaining how a table row was obtained. |
|
Scale interval template |
The semitone relationships that remain the same when a scale is transposed. |
|
Scale note field |
The table column listing the seven scale notes rather than its five absent shadow notes. |
|
Semitone conflict |
A nearby incompatible pitch that prevents a raw five-note template from fitting intact. |
|
Shadow-note field |
The table column listing pitch classes excluded by the seven-note parent. |
|
Shared-tone count |
How many notes a candidate placement has in common with the stated parent scale. |
|
Source family |
The parent or derived descent from which a shadow candidate was calculated. |
|
Structural equivalence |
Identity of interval structure under the comparison operation specified by the catalogue. |
|
Structure identifier |
A label assigned to one unique interval structure, shared by its transpositions. |
|
Table cross-check |
Verifying a row by independently recomputing the note set, absent notes, overlay and name. |
|
Transposed row |
A representation of the same interval template in another key, not a new unique structure. |
|
Uncatalogued label |
A provisional status used until a thorough interval-based catalogue search establishes whether a formal match exists. |
|
Unique structure |
A distinct normalized pitch-class configuration counted once despite duplicate or transposed rows. |
|
Verification lookup |
Searching a reference by exact intervals and root after removing octave repetitions and normalizing spelling. |
|
Whole-set match |
A comparison in which every distinct pitch class agrees with the reference after the allowed normalization. |
(c) 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT) All Rights Reserved!
__JATZEK: Given the fact that all scales have been cataloged for over 2000 years. what do i name the uncataloged scales as??? find their catlog or simply JATZEK scales
02.09.2026 0 points
