Now you've decided that Miracle temperament will change your musical life, here's how to fit it to your keyboard.
I use a mapping with 24 notes to the acoustic octave, so that the pattern repeats by octaves. The black notes are tuned to decimal nominals, starting with 0 as C#.
Where there are two white notes between a pair of black keys, the one one the left is tuned a quomma sharp of the one to its right. And the one on the right is tuned a quomma flat of the one on its right. Where there's only one white note between a pair of black notes, it can either be tuned a quomma sharp of the black note to its left, or a quomma flat of the black note to its right.
Whichever rule is applied for those ambiguous notes, so long as it's consistent you get a complete Blackjack scale. The first, where ambiguous notes are a quomma flat of the black note to their right, I call the low mapping. Here's what it looks like:
First keyboard octave
0v 0 1v 1 1^ 2v 2 3v 3 4v 4 4^ C D E F G A B
Second keyboard octave
5v 5 6v 6 6^ 7v 7 8v 8 9v 9 9^ C D E F G A B
This gives you a Blackjack with 1^, 4^ and 6^ as bonus notes. The high mapping makes the other choice for the ambiguous notes.
First keyboard octave
0v 0 0^ 1 1^ 2v 2 2^ 3 2^ 4 4^ C D E F G A B
Second keyboard octave
5v 5 5^ 6 6^ 7v 7 7^ 8 8^ 9 9^ C D E F G A B
With this 2v, 5v and 7v are outside the Blackjack.
The agreed Blackjack standard is centered on B[ (the quartertone below B), or midway between G and D. The suggested tonic is G. On the low keyboard mapping 0 is C, G is 6 and D is 2v. On the high keyboard mapping 0 is B[, D is 3 and G is 7^. I'm going for the low alternative, because C is nicer than B[ and it means the Blackjack nominal is at least on a black key. The only thing going for the low mapping is that it does happen to map G to a G key.
This also indulges me in having the decimal note indicated by the first decimal place of the base 2 logarithm of the frequency in Hz. I'm standardising on C as 2^8.04 Hz or 263.2 Hz.
You can cut and paste these or, if I remember, I'll upload them.
low mapping reference C
--------------------snip------------------- !low version of 24 note Miracle tuning !tuning to 72-equal tonic 64 8.04 coords 2 s 0.09722222 q 0.02777778 notes 24 0 0 -1 1 0 0 2 1 -1 3 1 0 4 1 1 5 2 -1 6 2 0 7 3 -1 8 3 0 9 4 -1 10 4 0 11 4 1 12 5 -1 13 5 0 14 6 -1 15 6 0 16 6 1 17 7 -1 18 7 0 19 8 -1 20 8 0 21 9 -1 22 9 0 23 9 1 24 10 1 --------------------snip-------------------
high mapping reference C
--------------------snip------------------- !high version of 24 note Miracle tuning !tuning to 72-equal tonic 64 8.04 coords 2 s 0.09722222 q 0.02777778 notes 24 0 0 -1 1 0 0 2 0 1 3 1 0 4 1 1 5 2 -1 6 2 0 7 2 1 8 3 0 9 3 1 10 4 0 11 4 1 12 5 -1 13 5 0 14 5 1 15 6 0 16 6 1 17 7 -1 18 7 0 19 7 1 20 8 0 21 8 1 22 9 0 23 9 1 24 10 1 --------------------snip-------------------
I might add other absolute pitches one day, and tuning files for a straight 21 note Blackjack, but that'll do for now.
--------------------snip------------------- ! miracle_24lo.scl ! 24 note mapping for Miracle scale ! ! low version, tuned to 72-equal ! 24 ! 33.3333333333333333 116.666666666666667 150.0 183.333333333333333 233.333333333333333 266.666666666666667 350.0 383.333333333333333 466.666666666666667 500.0 533.333333333333333 583.333333333333333 616.666666666666667 700.0 733.333333333333333 766.666666666666667 816.666666666666667 850.0 933.333333333333333 966.666666666666667 1050.0 1083.33333333333333 1116.66666666666667 1200.0 --------------------snip-------------------
--------------------snip------------------- ! miracle_24hi.scl ! 24 note mapping for Erlich/Keenan Miracle scale ! ! high version, tuned to 72-equal ! 24 ! 33.3333333333333333 66.6666666666666667 150.0 183.333333333333333 233.333333333333333 266.666666666666667 300.0 383.333333333333333 416.666666666666667 500.0 533.333333333333333 583.333333333333333 616.666666666666667 650.0 733.333333333333333 766.666666666666667 816.666666666666667 850.0 883.333333333333333 966.666666666666667 1000.0 1083.33333333333333 1116.66666666666667 1200.0 --------------------snip-------------------
keyboard mapping for reference C
--------------------snip------------------- ! Size of map (greater than or equal to the number of notes in the scale ! to be mapped). Zero means linear mapping. 0 ! First MIDI note number to retune: 0 ! Last MIDI note number to retune: 127 ! Middle note where scale degree 0 is mapped to: 60 ! Reference note for which frequency is given: 61 ! Frequency to tune the above note to (floating point e.g. 440.0): 263.2 ! Scale degree to consider as formal octave (determines difference in pitch ! between adjacent mapping patterns): 24 --------------------snip-------------------
keyboard mapping for reference A
! Size of map (greater than or equal to the number of notes in the scale ! to be mapped). Zero means linear mapping. 0 ! First MIDI note number to retune: 0 ! Last MIDI note number to retune: 127 ! Middle note where scale degree 0 is mapped to: 60 ! Reference note for which frequency is given: 79 ! Frequency to tune the above note to (floating point e.g. 440.0): 440.0 ! Scale degree to consider as formal octave (determines difference in pitch ! between adjacent mapping patterns): 24 --------------------snip-------------------
I might add other absolute pitches one day, but that'll do for now.
Not many people have Kyma. But if you do, you can get a bit clever. Stick this into the Map box of a MIDIMapper
"Two different tunings: you can use either or crossfade between them"
"24 note Miracle tuning on the sharp side"
!High31 is: (
`MIDIKeyNumber -60 //12 * 15
+ (
(`MIDIKeyNumber - 60 mod: 12)
of: { #(-1 0 1 3 4 5 6 7 9 10 12 13)}
)
"corrected to give pure 24-note octaves"
+ (`MIDIKeyNumber -60 //24)
* 12/31) nn + 4c nn + (!PitchBend*2) nn.
"24 note Miracle tuning on the flat side"
!Low31 is: (
`MIDIKeyNumber -60 //12 * 15
+
(
(`MIDIKeyNumber - 60 mod: 12)
of: { #(-1 0 2 3 4 5 6 8 9 11 12 13)}
)
"correct to give pure 24-note octaves"
+ (`MIDIKeyNumber -60 //24)
* 12/31) nn + 4c nn + (!PitchBend*2) nn.
"24 note Miracle tuning on the sharp side"
!High41 is: (
`MIDIKeyNumber -60 //12 * 20
+ (
(`MIDIKeyNumber - 60 mod: 12)
of: { #(-1 0 1 4 5 7 8 9 12 13 16 17)}
)
"corrected to give pure 24-note octaves"
+ (`MIDIKeyNumber -60 //24)
* 12/41) nn + 4c nn + (!PitchBend*2) nn.
"24 note Miracle tuning on the flat side"
!Low41 is: (
`MIDIKeyNumber -60 //12 * 20
+
(
(`MIDIKeyNumber - 60 mod: 12)
of: { #(-1 0 3 4 5 7 8 11 12 15 16 17)}
)
"correct to give pure 24-note octaves"
+ (`MIDIKeyNumber -60 //24)
* 12/41) nn + 4c nn + (!PitchBend*2) nn.
Then make any Frequency fields
( (!High41-!Low41 * !Swapper + !Low41) - (!High31-!Low31 * !Swapper + !Low31) *!Chorus + (!High31-!Low31 * !Swapper + !Low31) ) nn
You can set !Chorus to be a continous controller, and !Swapper to be a switch (default off). Move !Chorus between 0 and 1, and the tuning varies between 31- and 41-equal. 72-equal is around 0.5. Put your foot on the switch, and you get the high mapping instead of the low one.