[fb] Determine harmonic intervals with interval quality

[WolfgangDrescher]

This PR implements the a new --hint option to display harmonic intervals with interval quality in a **hint spine instead of a **fb and figured bass intervals (without interval quality but accidentals).

The original hint humdrum tool is not able to handle intervals when a null token is involved, which is not ideal for analytical purposes.

Note that this new option can be combined with -c to always display non-compound intervals (compare with the original humdrum tool hint -c flag).

Also note that the difference between two pitches is calculated as an absolute number so always the lowest pitch will be the base note. Otherwise augmented and diminished interval qualities will be wrong.

Click to show examples

Example 1

Input:

**kern	**kern
4c	4A--
4c	4A-
4c	4A
4c	4A#
4c	4A##
=	=
4c	4B--
4c	4B-
4c	4B
4c	4B#
4c	4B##
=	=
4c	4c--
4c	4c-
4c	4c
4c	4c#
4c	4c##
=	=
4c	4d--
4c	4d-
4c	4d
4c	4d#
4c	4d##
=	=
4c	4e--
4c	4e-
4c	4e
4c	4e#
4c	4e##
=	=
4c	4f--
4c	4f-
4c	4f
4c	4f#
4c	4f##
=	=
4c	4g--
4c	4g-
4c	4g
4c	4g#
4c	4g##
=	=
4c	4a--
4c	4a-
4c	4a
4c	4a#
4c	4a##
=	=
4c	4b--
4c	4b-
4c	4b
4c	4b#
4c	4b##
=	=
4c	4cc--
4c	4cc-
4c	4cc
4c	4cc#
4c	4cc##
=	=
4c	4dd--
4c	4dd-
4c	4dd
4c	4dd#
4c	4dd##
=	=
4c	4ee--
4c	4ee-
4c	4ee
4c	4ee#
4c	4ee##
=	=
*-	*-

open in VHV

Output:

**kern	**hint	**kern
4c	A3	4A--
4c	M3	4A-
4c	m3	4A
4c	d3	4A#
4c	dd3	4A##
=	=	=
4c	A2	4B--
4c	M2	4B-
4c	m2	4B
4c	d2	4B#
4c	dd2	4B##
=	=	=
4c	dd1	4c--
4c	d1	4c-
4c	P1	4c
4c	A1	4c#
4c	AA1	4c##
=	=	=
4c	d2	4d--
4c	m2	4d-
4c	M2	4d
4c	A2	4d#
4c	AA2	4d##
=	=	=
4c	d3	4e--
4c	m3	4e-
4c	M3	4e
4c	A3	4e#
4c	AA3	4e##
=	=	=
4c	dd4	4f--
4c	d4	4f-
4c	P4	4f
4c	A4	4f#
4c	AA4	4f##
=	=	=
4c	dd5	4g--
4c	d5	4g-
4c	P5	4g
4c	A5	4g#
4c	AA5	4g##
=	=	=
4c	d6	4a--
4c	m6	4a-
4c	M6	4a
4c	A6	4a#
4c	AA6	4a##
=	=	=
4c	d7	4b--
4c	m7	4b-
4c	M7	4b
4c	A7	4b#
4c	AA7	4b##
=	=	=
4c	dd8	4cc--
4c	d8	4cc-
4c	P8	4cc
4c	A8	4cc#
4c	AA8	4cc##
=	=	=
4c	d9	4dd--
4c	m9	4dd-
4c	M9	4dd
4c	A9	4dd#
4c	AA9	4dd##
=	=	=
4c	d10	4ee--
4c	m10	4ee-
4c	M10	4ee
4c	A10	4ee#
4c	AA10	4ee##
=	=	=
*-	*-	*-

Example 2

Chord are also supported.

Input:

**kern	**kern	**kern
4c	4A--	4%5e
4c	4A-	.
4c	4A	.
4c	4A#	.
4c	4A##	.
=	=	=
4c	4B--	4%5f
4c	4B-	.
4c	4B	.
4c	4B#	.
4c	4B##	.
=	=	=
4c	4c--	4%5g
4c	4c-	.
4c	4c	.
4c	4c#	.
4c	4c##	.
=	=	=
4c	4d--	4%5a
4c	4d-	.
4c	4d	.
4c	4d#	.
4c	4d##	.
=	=	=
4c	4e--	4%5b
4c	4e-	.
4c	4e	.
4c	4e#	.
4c	4e##	.
=	=	=
4c	4f--	4%5cc
4c	4f-	.
4c	4f	.
4c	4f#	.
4c	4f##	.
=	=	=
4c	4g--	4%5dd
4c	4g-	.
4c	4g	.
4c	4g#	.
4c	4g##	.
=	=	=
4c	4a--	4%5ee
4c	4a-	.
4c	4a	.
4c	4a#	.
4c	4a##	.
=	=	=
4c	4b--	4%5ff
4c	4b-	.
4c	4b	.
4c	4b#	.
4c	4b##	.
=	=	=
4c	4cc--	4%5gg
4c	4cc-	.
4c	4cc	.
4c	4cc#	.
4c	4cc##	.
=	=	=
4c	4dd--	4%5gg
4c	4dd-	.
4c	4dd	.
4c	4dd#	.
4c	4dd##	.
=	=	=
4c	4ee--	4%5gg
4c	4ee-	.
4c	4ee	.
4c	4ee#	.
4c	4ee##	.
=	=	=
*-	*-	*-

open in VHV

Output:

**kern	**hint	**kern	**kern
4c	M3 A3	4A--	4%5e
4c	M3 M3	4A-	.
4c	M3 m3	4A	.
4c	M3 d3	4A#	.
4c	M3 dd3	4A##	.
=	=	=	=
4c	P4 A2	4B--	4%5f
4c	P4 M2	4B-	.
4c	P4 m2	4B	.
4c	P4 d2	4B#	.
4c	P4 dd2	4B##	.
=	=	=	=
4c	P5 dd1	4c--	4%5g
4c	P5 d1	4c-	.
4c	P5 P1	4c	.
4c	P5 A1	4c#	.
4c	P5 AA1	4c##	.
=	=	=	=
4c	M6 d2	4d--	4%5a
4c	M6 m2	4d-	.
4c	M6 M2	4d	.
4c	M6 A2	4d#	.
4c	M6 AA2	4d##	.
=	=	=	=
4c	M7 d3	4e--	4%5b
4c	M7 m3	4e-	.
4c	M7 M3	4e	.
4c	M7 A3	4e#	.
4c	M7 AA3	4e##	.
=	=	=	=
4c	P8 dd4	4f--	4%5cc
4c	P8 d4	4f-	.
4c	P8 P4	4f	.
4c	P8 A4	4f#	.
4c	P8 AA4	4f##	.
=	=	=	=
4c	M9 dd5	4g--	4%5dd
4c	M9 d5	4g-	.
4c	M9 P5	4g	.
4c	M9 A5	4g#	.
4c	M9 AA5	4g##	.
=	=	=	=
4c	M10 d6	4a--	4%5ee
4c	M10 m6	4a-	.
4c	M10 M6	4a	.
4c	M10 A6	4a#	.
4c	M10 AA6	4a##	.
=	=	=	=
4c	P11 d7	4b--	4%5ff
4c	P11 m7	4b-	.
4c	P11 M7	4b	.
4c	P11 A7	4b#	.
4c	P11 AA7	4b##	.
=	=	=	=
4c	P12 dd8	4cc--	4%5gg
4c	P12 d8	4cc-	.
4c	P12 P8	4cc	.
4c	P12 A8	4cc#	.
4c	P12 AA8	4cc##	.
=	=	=	=
4c	P12 d9	4dd--	4%5gg
4c	P12 m9	4dd-	.
4c	P12 M9	4dd	.
4c	P12 A9	4dd#	.
4c	P12 AA9	4dd##	.
=	=	=	=
4c	P12 d10	4ee--	4%5gg
4c	P12 m10	4ee-	.
4c	P12 M10	4ee	.
4c	P12 A10	4ee#	.
4c	P12 AA10	4ee##	.
=	=	=	=
*-	*-	*-	*-

[craigsapp]

One long-term thought would be to use base-600 rather than base-40. This would allow triple-flats/sharp, and all of the way up to 42 sharps/flats on a note (I choose 600 arbitrarily as a round number).

There is already a class implemented in verovio that can/will be copied over (after removing verovio-specific code):

https://github.com/rism-digital/verovio/blob/develop/include/vrv/transposition.h
https://github.com/rism-digital/verovio/blob/develop/src/transposition.cpp

This would allow using either base-40 (with a limit of double/sharps flats) or base-600 for more theoretical interval alterations (when needed).