Hi Julia,
Thanks very much for sharing the links and information about this new record release, as well as your fascinating scale, which was interesting in that, upon analysis, was revealed to be a three-distributional-even (D3), Messiaen-like, mode-of-limited-transposition from 18 tone equal temperament, with three repeating blocks of intervals: L2 s1 s1 L2; a modal form which I'm quite passionate about.
I took the liberty of creating a SCL file of your mode, which I'm pasting here along with a basic analysis, and I'm assuming that since the tuning was intended for piano timbre and gesture, your reference pitch was likely A.69 at 440 Hz, so I'm also pasting the linear KBM data to map it to a Halberstadt style MIDI controller (and Pianoteq) this way.
I've enjoyed listening to the album preview on Bandcamp and playing your scale using the Bösendorfer 280VC model, as well as the Felt variants.
Hoping all is well,
Jacky
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Werntz Nocturne Scale
|
0: 1/1 C unison, perfect prime
1: 133.333 cents C#| D;;
2: 200.000 cents D
3: 266.667 cents D|| Eb;
4: 400.000 cents E
5: 533.333 cents F| Gb;;
6: 600.000 cents F# Gb
7: 666.667 cents F#|| G;
8: 800.000 cents G# Ab
9: 933.333 cents A| Bb;;
10: 1000.000 cents A# Bb
11: 1066.667 cents A#|| B;
12: 2/1 C octave
|
0: 133.3333 cents C#| D;;
1: 133.3333 cents C#| D;;
2: 66.6667 cents C|| Db;
3: 66.6667 cents C|| Db;
4: 133.3333 cents C#| D;;
5: 133.3333 cents C#| D;;
6: 66.6667 cents C|| Db;
7: 66.6667 cents C|| Db;
8: 133.3333 cents C#| D;;
9: 133.3333 cents C#| D;;
10: 66.6667 cents C|| Db;
11: 66.6667 cents C|| Db;
12: 133.3333 cents C#| D;;
|
1 2 3 4 5 6 7 8 9 10 11 12
0.0 : 133.3 200.0 266.7 400.0 533.3 600.0 666.7 800.0 933.3 1000.0 1066.7 1200.0
133.3 : 66.7 133.3 266.7 400.0 466.7 533.3 666.7 800.0 866.7 933.3 1066.7 1200.0
200.0 : 66.7 200.0 333.3 400.0 466.7 600.0 733.3 800.0 866.7 1000.0 1133.3 1200.0
266.7 : 133.3 266.7 333.3 400.0 533.3 666.7 733.3 800.0 933.3 1066.7 1133.3 1200.0
400.0 : 133.3 200.0 266.7 400.0 533.3 600.0 666.7 800.0 933.3 1000.0 1066.7 1200.0
533.3 : 66.7 133.3 266.7 400.0 466.7 533.3 666.7 800.0 866.7 933.3 1066.7 1200.0
600.0 : 66.7 200.0 333.3 400.0 466.7 600.0 733.3 800.0 866.7 1000.0 1133.3 1200.0
666.7 : 133.3 266.7 333.3 400.0 533.3 666.7 733.3 800.0 933.3 1066.7 1133.3 1200.0
800.0 : 133.3 200.0 266.7 400.0 533.3 600.0 666.7 800.0 933.3 1000.0 1066.7 1200.0
933.3 : 66.7 133.3 266.7 400.0 466.7 533.3 666.7 800.0 866.7 933.3 1066.7 1200.0
1000.0: 66.7 200.0 333.3 400.0 466.7 600.0 733.3 800.0 866.7 1000.0 1133.3 1200.0
1066.7: 133.3 266.7 333.3 400.0 533.3 666.7 733.3 800.0 933.3 1066.7 1133.3 1200.0
1200.0
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Parent Gamut: ED2-18
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ED2-18 - Equal division of harmonic 2 into 18 parts
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0: 1/1 C unison, perfect prime
1: 66.667 cents C|| Db;
2: 133.333 cents C#| D;;
3: 200.000 cents D
4: 266.667 cents D|| Eb;
5: 333.333 cents D#| E;;
6: 400.000 cents E
7: 466.667 cents E|| F;
8: 533.333 cents F| Gb;;
9: 600.000 cents F# Gb
10: 666.667 cents F#|| G;
11: 733.333 cents G| Ab;;
12: 800.000 cents G# Ab
13: 866.667 cents G#|| A;
14: 933.333 cents A| Bb;;
15: 1000.000 cents A# Bb
16: 1066.667 cents A#|| B;
17: 1133.333 cents B| C;;
18: 2/1 C octave
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Werntz Nocturne Scale
ED2-18 - MLT-12 - L2 s1 s1 L2 - P2
Number of notes : 12
-- Interval properties --
Smallest interval : 66.66667 cents, class 1
Largest one step interval : 133.33333 cents
Scale is proper
Scale has 3 repeating blocks of 4 notes
Scale is 3-distributional even (D3)
Scale is a mode of a 18-tone equal temperament with octave 2/1
degrees: 2 3 4 6 8 9 10 12 14 15 16 18
Step pattern alph. order: ABBAABBAABBA
Step pattern size order : LssLLssLLssL
Interval vector is [ 6 9 6 9 6 12 6 9 3 ]
Number of different interval sizes : 17 = 1.54545 / class
Number of one step interval sizes : 2 (binary scale)
Highest interval variety : 3
Smallest interval difference : 66.66666 cents
Most common intervals : 400.00000 cents & inv., amount: 12
Most common triad is 0.0 400.000 800.000 cents, amount: 12
Number of recognisable fifths : 0
Limited transpositions :
4 8
Limited inverse transpositions :
4 8
Inversional symmetry on degrees :
0 2 4 6 8 10
...
! 69-440-69 Concert A.kbm
!
! Size of map:
0
! First MIDI note number to retune:
0
! Last MIDI note number to retune:
127
! Middle note where the first entry in the mapping is mapped to:
69
! Reference note for which frequency is given:
69
! Frequency to tune the above note to (floating point e.g. 440.0):
440.000000
! Scale degree to consider as formal octave:
0
! Mapping.
