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scales.ml
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scales.ml
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(**********************************************************************************)
(* Fingerboard - a microtonal geography of the cello fingerboard *)
(* Copyright (C) 2022-2024 Mathieu Barbin <[email protected]> *)
(* *)
(* This file is part of Fingerboard. *)
(* *)
(* Fingerboard is free software: you can redistribute it and/or modify it under *)
(* the terms of the GNU Affero General Public License as published by the Free *)
(* Software Foundation, either version 3 of the License, or any later version. *)
(* *)
(* Fingerboard is distributed in the hope that it will be useful, but WITHOUT *)
(* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or *)
(* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License *)
(* for more details. *)
(* *)
(* You should have received a copy of the GNU Affero General Public License *)
(* along with Fingerboard. If not, see <https://www.gnu.org/licenses/>. *)
(**********************************************************************************)
let make_scale t ~characterized_scale ~from =
System.make_scale t ~characterized_scale ~from ~to_:Cello.fingerboard_highest_note
;;
let make_major_pythagorean_scale ~from =
let t = force Just.t in
make_scale t ~characterized_scale:Characterized_scale.major_pythagorean ~from
;;
let make_major_just_scale ~from =
let t = force Just.t in
make_scale t ~characterized_scale:Characterized_scale.major_just ~from
;;
let lower_c =
let t = force Just.t in
System.open_string t IV |> Option.value_exn ~here:[%here]
;;
let%expect_test "c_major_just" =
let scale = make_major_just_scale ~from:lower_c in
print_s [%sexp (scale : Located_note.t list)];
[%expect
{|
(((note (
(letter_name C)
(symbol Natural)
(octave_designation 2)))
(fingerboard_location (
(fingerboard_position (
(name 0)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string Zero)))
(string_number IV))))
((note (
(letter_name D)
(symbol Natural)
(octave_designation 2)))
(fingerboard_location (
(fingerboard_position (
(name M2p)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent -3))
((prime 3) (exponent 2)))))))
(string_number IV))))
((note (
(letter_name E)
(symbol Natural)
(octave_designation 2)))
(fingerboard_location (
(fingerboard_position (
(name M3z)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent -2))
((prime 5) (exponent 1)))))))
(string_number IV))))
((note (
(letter_name F)
(symbol Natural)
(octave_designation 2)))
(fingerboard_location (
(fingerboard_position (
(name 4p)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 2))
((prime 3) (exponent -1)))))))
(string_number IV))))
((note (
(letter_name G)
(symbol Natural)
(octave_designation 2)))
(fingerboard_location (
(fingerboard_position (
(name 0)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string Zero)))
(string_number III))))
((note (
(letter_name A)
(symbol Natural)
(octave_designation 2)))
(fingerboard_location (
(fingerboard_position (
(name M2z)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 1))
((prime 3) (exponent -2))
((prime 5) (exponent 1)))))))
(string_number III))))
((note (
(letter_name B)
(symbol Natural)
(octave_designation 2)))
(fingerboard_location (
(fingerboard_position (
(name M3z)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent -2))
((prime 5) (exponent 1)))))))
(string_number III))))
((note (
(letter_name C)
(symbol Natural)
(octave_designation 3)))
(fingerboard_location (
(fingerboard_position (
(name 4p)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 2))
((prime 3) (exponent -1)))))))
(string_number III))))
((note (
(letter_name D)
(symbol Natural)
(octave_designation 3)))
(fingerboard_location (
(fingerboard_position (
(name 0)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string Zero)))
(string_number II))))
((note (
(letter_name E)
(symbol Natural)
(octave_designation 3)))
(fingerboard_location (
(fingerboard_position (
(name M2z)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 1))
((prime 3) (exponent -2))
((prime 5) (exponent 1)))))))
(string_number II))))
((note (
(letter_name F)
(symbol Natural)
(octave_designation 3)))
(fingerboard_location (
(fingerboard_position (
(name m3p)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 5))
((prime 3) (exponent -3)))))))
(string_number II))))
((note (
(letter_name G)
(symbol Natural)
(octave_designation 3)))
(fingerboard_location (
(fingerboard_position (
(name 4p)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 2))
((prime 3) (exponent -1)))))))
(string_number II))))
((note (
(letter_name A)
(symbol Natural)
(octave_designation 3)))
(fingerboard_location (
(fingerboard_position (
(name 5z)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 3))
((prime 3) (exponent -3))
((prime 5) (exponent 1)))))))
(string_number II))))
((note (
(letter_name B)
(symbol Natural)
(octave_designation 3)))
(fingerboard_location (
(fingerboard_position (
(name M2z)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 1))
((prime 3) (exponent -2))
((prime 5) (exponent 1)))))))
(string_number I))))
((note (
(letter_name C)
(symbol Natural)
(octave_designation 4)))
(fingerboard_location (
(fingerboard_position (
(name m3p)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 5))
((prime 3) (exponent -3)))))))
(string_number I))))
((note (
(letter_name D)
(symbol Natural)
(octave_designation 4)))
(fingerboard_location (
(fingerboard_position (
(name 4p)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 2))
((prime 3) (exponent -1)))))))
(string_number I))))
((note (
(letter_name E)
(symbol Natural)
(octave_designation 4)))
(fingerboard_location (
(fingerboard_position (
(name 5z)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 3))
((prime 3) (exponent -3))
((prime 5) (exponent 1)))))))
(string_number I))))
((note (
(letter_name F)
(symbol Natural)
(octave_designation 4)))
(fingerboard_location (
(fingerboard_position (
(name m6p)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 7))
((prime 3) (exponent -4)))))))
(string_number I))))
((note (
(letter_name G)
(symbol Natural)
(octave_designation 4)))
(fingerboard_location (
(fingerboard_position (
(name m7p)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 4))
((prime 3) (exponent -2)))))))
(string_number I))))
((note (
(letter_name A)
(symbol Natural)
(octave_designation 4)))
(fingerboard_location (
(fingerboard_position (
(name 8z)
(at_octave 0)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 5))
((prime 3) (exponent -4))
((prime 5) (exponent 1)))))))
(string_number I))))
((note (
(letter_name B)
(symbol Natural)
(octave_designation 4)))
(fingerboard_location (
(fingerboard_position (
(name M2z)
(at_octave 1)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 1))
((prime 3) (exponent -2))
((prime 5) (exponent 1)))))))
(string_number I))))
((note (
(letter_name C)
(symbol Natural)
(octave_designation 5)))
(fingerboard_location (
(fingerboard_position (
(name m3p)
(at_octave 1)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 5))
((prime 3) (exponent -3)))))))
(string_number I))))
((note (
(letter_name D)
(symbol Natural)
(octave_designation 5)))
(fingerboard_location (
(fingerboard_position (
(name 4p)
(at_octave 1)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 2))
((prime 3) (exponent -1)))))))
(string_number I))))
((note (
(letter_name E)
(symbol Natural)
(octave_designation 5)))
(fingerboard_location (
(fingerboard_position (
(name 5z)
(at_octave 1)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 3))
((prime 3) (exponent -3))
((prime 5) (exponent 1)))))))
(string_number I))))
((note (
(letter_name F)
(symbol Natural)
(octave_designation 5)))
(fingerboard_location (
(fingerboard_position (
(name m6p)
(at_octave 1)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 7))
((prime 3) (exponent -4)))))))
(string_number I))))
((note (
(letter_name G)
(symbol Natural)
(octave_designation 5)))
(fingerboard_location (
(fingerboard_position (
(name m7p)
(at_octave 1)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 4))
((prime 3) (exponent -2)))))))
(string_number I))))
((note (
(letter_name A)
(symbol Natural)
(octave_designation 5)))
(fingerboard_location (
(fingerboard_position (
(name 8z)
(at_octave 1)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 5))
((prime 3) (exponent -4))
((prime 5) (exponent 1)))))))
(string_number I))))
((note (
(letter_name B)
(symbol Natural)
(octave_designation 5)))
(fingerboard_location (
(fingerboard_position (
(name M2z)
(at_octave 2)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 1))
((prime 3) (exponent -2))
((prime 5) (exponent 1)))))))
(string_number I))))
((note (
(letter_name C)
(symbol Natural)
(octave_designation 6)))
(fingerboard_location (
(fingerboard_position (
(name m3p)
(at_octave 2)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 5))
((prime 3) (exponent -3)))))))
(string_number I))))
((note (
(letter_name D)
(symbol Natural)
(octave_designation 6)))
(fingerboard_location (
(fingerboard_position (
(name 4p)
(at_octave 2)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 2))
((prime 3) (exponent -1)))))))
(string_number I))))
((note (
(letter_name E)
(symbol Natural)
(octave_designation 6)))
(fingerboard_location (
(fingerboard_position (
(name 5z)
(at_octave 2)
(basis_acoustic_interval_to_the_open_string
(Reduced_natural_ratio (
((prime 2) (exponent 3))
((prime 3) (exponent -3))
((prime 5) (exponent 1)))))))
(string_number I))))) |}];
print_s [%sexp (List.length scale : int)];
[%expect {| 31 |}];
print_s
[%sexp (scale |> List.map ~f:Located_note.to_abbrev : Located_note.Abbrev.t list)];
[%expect
{|
((C2 0 IV)
(D2 M2p IV)
(E2 M3z IV)
(F2 4p IV)
(G2 0 III)
(A2 M2z III)
(B2 M3z III)
(C3 4p III)
(D3 0 II)
(E3 M2z II)
(F3 m3p II)
(G3 4p II)
(A3 5z II)
(B3 M2z I)
(C4 m3p I)
(D4 4p I)
(E4 5z I)
(F4 m6p I)
(G4 m7p I)
(A4 8z I)
(B4 M2z-1 I)
(C5 m3p-1 I)
(D5 4p-1 I)
(E5 5z-1 I)
(F5 m6p-1 I)
(G5 m7p-1 I)
(A5 8z-1 I)
(B5 M2z-2 I)
(C6 m3p-2 I)
(D6 4p-2 I)
(E6 5z-2 I)) |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV (
(C2 0)
(D2 M2p)
(E2 M3z)
(F2 4p)))
(III (
(G2 0)
(A2 M2z)
(B2 M3z)
(C3 4p)))
(II (
(D3 0)
(E3 M2z)
(F3 m3p)
(G3 4p)
(A3 5z)))
(I (
(B3 M2z)
(C4 m3p)
(D4 4p)
(E4 5z)
(F4 m6p)
(G4 m7p)
(A4 8z)
(B4 M2z-1)
(C5 m3p-1)
(D5 4p-1)
(E5 5z-1)
(F5 m6p-1)
(G5 m7p-1)
(A5 8z-1)
(B5 M2z-2)
(C6 m3p-2)
(D6 4p-2)
(E6 5z-2)))) |}];
()
;;
(* Since [Just] is a superset of [Pythagorean], it supports all of the
same pythagorean scales. We only test one here, since they all
already appear in [pythagorean/scales.ml]. *)
let%expect_test "c_major_pythagorean" =
let scale = make_major_pythagorean_scale ~from:lower_c in
print_s [%sexp (List.length scale : int)];
[%expect {| 31 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV (
(C2 0)
(D2 M2p)
(E2 M3p)
(F2 4p)))
(III (
(G2 0)
(A2 M2p)
(B2 M3p)
(C3 4p)))
(II (
(D3 0)
(E3 M2p)
(F3 m3p)
(G3 4p)))
(I (
(A3 0)
(B3 M2p)
(C4 m3p)
(D4 4p)
(E4 5p)
(F4 m6p)
(G4 m7p)
(A4 0-1)
(B4 M2p-1)
(C5 m3p-1)
(D5 4p-1)
(E5 5p-1)
(F5 m6p-1)
(G5 m7p-1)
(A5 0-2)
(B5 M2p-2)
(C6 m3p-2)
(D6 4p-2)
(E6 5p-2)))) |}];
()
;;
let lower_dz_flat =
let t = force Just.t in
{ Located_note.note = { letter_name = D; symbol = Flat; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `m2z
; string_number = IV
}
}
;;
let%expect_test "d_flat_major_just" =
let scale = make_major_just_scale ~from:lower_dz_flat in
print_s [%sexp (List.length scale : int)];
[%expect {| 31 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV (
(Db2 m2z)
(Eb2 m3z)
(F2 4p)
(Gb2 d5z)))
(III (
(Ab2 m2z)
(Bb2 m3p)
(C3 4p)
(Db3 d5z)))
(II (
(Eb3 m2z)
(F3 m3p)
(Gb3 d4z)
(Ab3 d5z)))
(I (
(Bb3 m2p)
(C4 m3p)
(Db4 d4z)
(Eb4 d5z)
(F4 m6p)
(Gb4 d7z)
(Ab4 d8z)
(Bb4 m2p-1)
(C5 m3p-1)
(Db5 d4z-1)
(Eb5 d5z-1)
(F5 m6p-1)
(Gb5 d7z-1)
(Ab5 d8z-1)
(Bb5 m2p-2)
(C6 m3p-2)
(Db6 d4z-2)
(Eb6 d5z-2)
(F6 m6p-2)))) |}];
()
;;
let lower_d =
let t = force Just.t in
{ Located_note.note = { letter_name = D; symbol = Natural; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `M2p
; string_number = IV
}
}
;;
let%expect_test "d_major_just" =
let scale = make_major_just_scale ~from:lower_d in
print_s [%sexp (List.length scale : int)];
[%expect {| 30 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV (
(D2 M2p)
(E2 M3p)
(F#2 A4z)))
(III (
(G2 0)
(A2 M2p)
(B2 M3z)
(C#3 A4z)))
(II (
(D3 0)
(E3 M2p)
(F#3 M3z)
(G3 4p)))
(I (
(A3 0)
(B3 M2z)
(C#4 M3z)
(D4 4p)
(E4 5p)
(F#4 M6z)
(G4 m7p)
(A4 0-1)
(B4 M2z-1)
(C#5 M3z-1)
(D5 4p-1)
(E5 5p-1)
(F#5 M6z-1)
(G5 m7p-1)
(A5 0-2)
(B5 M2z-2)
(C#6 M3z-2)
(D6 4p-2)
(E6 5p-2)))) |}];
()
;;
let lower_ez_flat =
let t = force Just.t in
{ Located_note.note = { letter_name = E; symbol = Flat; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `m3z
; string_number = IV
}
}
;;
let%expect_test "e_flat_major_just" =
let scale = make_major_just_scale ~from:lower_ez_flat in
print_s [%sexp (List.length scale : int)];
[%expect {| 30 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV (
(Eb2 m3z)
(F2 4z)))
(III (
(G2 0)
(Ab2 m2z)
(Bb2 m3z)
(C3 4p)))
(II (
(D3 0)
(Eb3 m2z)
(F3 m3z)
(G3 4p)
(Ab3 d5z)))
(I (
(Bb3 m2z)
(C4 m3p)
(D4 4p)
(Eb4 d5z)
(F4 m6z)
(G4 m7p)
(Ab4 d8z)
(Bb4 m2z-1)
(C5 m3p-1)
(D5 4p-1)
(Eb5 d5z-1)
(F5 m6z-1)
(G5 m7p-1)
(Ab5 d8z-1)
(Bb5 m2z-2)
(C6 m3p-2)
(D6 4p-2)
(Eb6 d5z-2)
(F6 m6z-2)))) |}];
()
;;
let lower_e =
let t = force Just.t in
{ Located_note.note = { letter_name = E; symbol = Natural; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `M3p
; string_number = IV
}
}
;;
let%expect_test "e_major_just" =
let scale = make_major_just_scale ~from:lower_e in
print_s [%sexp (List.length scale : int)];
[%expect {| 29 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV (
(E2 M3p)
(F#2 A4p)))
(III (
(G#2 A1z)
(A2 M2p)
(B2 M3p)
(C#3 A4z)))
(II (
(D#3 A1z)
(E3 M2p)
(F#3 M3p)
(G#3 A4z)))
(I (
(A3 0)
(B3 M2p)
(C#4 M3z)
(D#4 A4z)
(E4 5p)
(F#4 M6p)
(G#4 M7z)
(A4 0-1)
(B4 M2p-1)
(C#5 M3z-1)
(D#5 A4z-1)
(E5 5p-1)
(F#5 M6p-1)
(G#5 M7z-1)
(A5 0-2)
(B5 M2p-2)
(C#6 M3z-2)
(D#6 A4z-2)
(E6 5p-2)))) |}];
()
;;
let lower_fp =
let t = force Just.t in
{ Located_note.note = { letter_name = F; symbol = Natural; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `P4p
; string_number = IV
}
}
;;
let%expect_test "fp_major_just" =
let scale = make_major_just_scale ~from:lower_fp in
print_s [%sexp (List.length scale : int)];
[%expect {| 12 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV ((F2 4p)))
(III (
(G2 0)
(A2 M2z)
(Bb2 m3p)
(C3 4p)
(D3 5z)))
(II (
(E3 M2z)
(F3 m3p)
(G3 4p)
(A3 5z)))
(I (
(Bb3 m2p)
(C4 m3p)))) |}];
()
;;
let lower_fz =
let t = force Just.t in
{ Located_note.note = { letter_name = F; symbol = Natural; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `P4z
; string_number = IV
}
}
;;
let%expect_test "fz_major_just" =
let scale = make_major_just_scale ~from:lower_fz in
print_s [%sexp (List.length scale : int)];
[%expect {| 1 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV ((F2 4z)))) |}];
()
;;
let lower_fp_sharp =
let t = force Just.t in
{ Located_note.note = { letter_name = F; symbol = Sharp; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `A4p
; string_number = IV
}
}
;;
let%expect_test "f_sharp_major_just" =
let scale = make_major_just_scale ~from:lower_fp_sharp in
print_s [%sexp (List.length scale : int)];
[%expect {| 2 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV ((F#2 A4p)))
(III ((G#2 A1p)))) |}];
()
;;
let lower_gz_flat =
let t = force Just.t in
{ Located_note.note = { letter_name = G; symbol = Flat; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `d5z
; string_number = IV
}
}
;;
let%expect_test "g_flat_major_just" =
let scale = make_major_just_scale ~from:lower_gz_flat in
print_s [%sexp (List.length scale : int)];
[%expect {| 28 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((IV ((Gb2 d5z)))
(III (
(Ab2 m2z)
(Bb2 m3p)
(Cb3 d4z)
(Db3 d5z)))
(II (
(Eb3 m2p)
(F3 m3p)
(Gb3 d4z)
(Ab3 d5z)))
(I (
(Bb3 m2p)
(Cb4 d3z)
(Db4 d4z)
(Eb4 d5p)
(F4 m6p)
(Gb4 d7z)
(Ab4 d8z)
(Bb4 m2p-1)
(Cb5 d3z-1)
(Db5 d4z-1)
(Eb5 d5p-1)
(F5 m6p-1)
(Gb5 d7z-1)
(Ab5 d8z-1)
(Bb5 m2p-2)
(Cb6 d3z-2)
(Db6 d4z-2)
(Eb6 d5p-2)
(F6 m6p-2)))) |}];
()
;;
let lower_g =
let t = force Just.t in
{ Located_note.note = { letter_name = G; symbol = Natural; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `open_string
; string_number = III
}
}
;;
let%expect_test "g_major_just" =
let scale = make_major_just_scale ~from:lower_g in
print_s [%sexp (List.length scale : int)];
[%expect {| 27 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((III (
(G2 0)
(A2 M2p)
(B2 M3z)
(C3 4p)))
(II (
(D3 0)
(E3 M2z)
(F#3 M3z)
(G3 4p)))
(I (
(A3 0)
(B3 M2z)
(C4 m3p)
(D4 4p)
(E4 5z)
(F#4 M6z)
(G4 m7p)
(A4 0-1)
(B4 M2z-1)
(C5 m3p-1)
(D5 4p-1)
(E5 5z-1)
(F#5 M6z-1)
(G5 m7p-1)
(A5 0-2)
(B5 M2z-2)
(C6 m3p-2)
(D6 4p-2)
(E6 5z-2)))) |}];
()
;;
let lower_az_flat =
let t = force Just.t in
{ Located_note.note = { letter_name = A; symbol = Flat; octave_designation = 2 }
; fingerboard_location =
{ fingerboard_position = Cello.find_fingerboard_position_exn t `m2z
; string_number = III
}
}
;;
let%expect_test "a_flat_major_just" =
let scale = make_major_just_scale ~from:lower_az_flat in
print_s [%sexp (List.length scale : int)];
[%expect {| 27 |}];
print_s [%sexp (scale |> Located_note.to_scale_abbrev : Located_note.Scale_abbrev.t)];
[%expect
{|
((III (
(Ab2 m2z)
(Bb2 m3z)
(C3 4p)
(Db3 d5z)))
(II (
(Eb3 m2z)
(F3 m3p)
(G3 4p)
(Ab3 d5z)))
(I (
(Bb3 m2z)
(C4 m3p)
(Db4 d4z)