! ji_hca02.scl by Orjan Hansson, 2004-07-17
!
JI for hca (2nd pos)
!
! For major diatonic (Richter) harmonica played in 2nd position.
!
! Tuning a hca in JI (just intonation) in 1st pos (ji_hca01.scl) is
! not good for playing chords in 2nd pos. There are problems with the
! major whole tone (in 6D and 10D) and the flattened seventh (in 5D
! and 9D). However, all other intervals are in perfect JI in 2nd pos.
!
! The note in 6D (and 10D) should be a major whole tone (9/8) above
! the root in 2nd pos. Thus, it should be tuned at 27/16 = (3/2)x(9/8)
! above the 1st pos root. This is 6 cents above 12TET (12-tone equal
! temperament). In 1st pos this note is a major sixth (5/3) which is
! -16 cents from 12TET. Thus, if the hca is tuned to JI in 1st pos,
! this note will sound 22 cent flat in 2nd pos. The workaround is to
! increase the major sixth from 5/3 to 27/16. This will make it sound
! good in 2nd pos but 22 cent sharp in 1st pos.
!
! The note in 5D (and 9D) should be a flattened seventh in 2nd pos. In
! order to get a chord (2-3-4-5 draw) without beating (dissonance),
! this note should be an augmented sixth (6#, also called a dominant
! seventh) at 7/4 above the 2nd pos root. Thus, it should be tuned at
! 21/16 = (3/2)x(7/4)x(1/2) above the 1st pos root. This is -29 cents
! from 12TET. In 1st pos this note is a perfect fourth (4/3) which is
! -2 cents from 12TET. Thus, if the hca is tuned to JI in 1st pos,
! this note will correspond to a diminished seventh (bb7, 16/9) in 2nd
! pos and will sound 27 cent sharper than the beatless augmented sixth.
! The workaround is to decrease the perfect fourth from 4/3 to 21/16.
! This will make it sound good in 2nd pos but 27 cent flat in 1st pos.
!
 7
!
 9/8 Major whole tone
 5/4 Major third
 21/16 Perfect fourth decreased with 27 cent
 3/2 Perfect fifth
 27/16 Major sixth increased with 22 cent
 15/8 Major seventh
 2/1 Octave
!
! Deviations in cent from 12-tone equal temperament
! (no octave stretching)											
! Hole  1   2   3   4   5   6   7   8   9  10
! Blow  0 -14   2   0 -14   2   0 -14   2   0
! Draw  4   2 -12   4 -29   6 -12   4 -29   6
!
! Recommendations for use with Chromatia Tuner 3.0 ("Options/Tuning"):
!
! Scale root key:
! Set this to the key of the hca.
!
! Octave stretch:
! 2 cent/octave is usually recommended.
!
! Master tuning:
! Usually, hca:s are tuned a little sharp, for example to A4 = 443 Hz
! (12 cent above 440 Hz). With "Chromatia", it is important to set
! the master tuning to the desired frequency of the scale root key.
! For a C hca, one should set C4 to 263 Hz (9 semitones of equal
! temperament below A4 = 443 Hz).
!
! References:
!
! The temperaments in this set of files (ji_hca*.scl) are based on
! recommendations by Pat Missin. See his text "Altered tunings".
! (www.patmissin.com)
!
! The Chromatia instrument tuner is made by FMJ-Software.
! (www.fmjsoft.com)
!
! The Scala scale file format used here is becoming a standard for
! exchange of scales and can be read by "Chromatia".
! (www.xs4all.nl/~huygensf/scala/)