! ji_hca03.scl by Orjan Hansson, 2004-07-17
!
JI for hca (3rd pos)
!
! For major diatonic (Richter) harmonica played in 3rd position.
!
! Tuning a hca in JI (just intonation) in 1st pos (ji_hca01.scl) is
! not good for playing chords in 3rd pos. There are problems with the
! perfect fifth (in 6D and 10D) and the minor third (in 5D and 9D) as
! well as with the major whole tone (in 2B, 5B and 8B) and the
! flattened seventh (in 1B, 4B, 7B and 10B) The rest of the intervals
! are in perfect JI in 3rd pos.
!
! The note in 6D (and 10D) should be a perfect fifth (3/2) above the
! root in 3rd 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 3rd pos. The workaround is to
! increase the major sixth from 5/3 to 27/16. This will make it sound
! good in 3rd pos but 22 cent sharp in 1st pos.
!
! The note in 5D (and 9D) should be a minor third in 3rd pos. In order
! to get a chord (4-5-6 draw) without beating (dissonance), it should
! be tuned at 6/5 above the 3rd pos root. Thus, it should be tuned at
! 27/20 = (6/5)x(9/8) above the 1st pos root. This is 20 cent above
! 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 sound 22 cent flat in 3rd pos. The workaround is to
! increase the perfect fourth from 4/3 to 27/20. This will make it
! sound good in 3rd pos but 22 cent sharp in 1st pos.
!
! The major whole tone and the flattened seventh should also be 
! adjusted. Since these are blow notes they are not used in the tonic
! chord in 3rd pos. However, they are part of a dominant minor seventh
! chord (eg 4-5-6 blow). But if all blow notes are tuned in JI in 1st
! pos, this chord will be beatless and sound good in 3rd pos playing.
!
 7
!
 9/8 Major whole tone
 5/4 Major third
 27/20 Perfect fourth increased with 22 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  20   6 -12   4  20   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/)