Using Scala to retune common practice music in meantone
Composing in meantone
The good news about composing in meantone is that you may already know how to do it. The bad news is that this does not matter unless you can actually tune the music you make in meantone. To sequence the music you compose in a meantone tuning, I suggest you get the program Scala. This needs to be version 2.21j or later, so if you have an earlier version and want to try these suggestions out, you need to upgrade. The Scala program is completely free, amazingly powerful, and available for most operating systems.
Retuning a midi file
Suppose we take a midi file, such as this one for Frere Jacques. If we take Scala and invoke the menu item, under Tools, of "Transform MIDI to sequence file" we can convert it into a Scala sequence file, which is a kind of ascii score file which allows us to use Scala to sequence midi files. When we open a midi file with Scala, we get a dialog box, which has the options "write scale degree numbers" (the default) and "write note names". Check the box for "write note names", choose a name for the output file, and click OK. When we do that, we get a Scala sequence file, which begins as follows:
! Transformed by Scala from frere.mid with 2 tracks
! Octave degree number in mapping: 12
!
0 exclude 10
0 division 256
0 notation E12
0 frequency 261.6255653
!
0 text "Scala midi-file frere.mid" ! track 1
0 text "text" ! track 2
0 text "Voice" ! track 2
0 text "Alto" ! track 2
0 text "Violoncello" ! track 2
0 timesig 4/4 24 8
0 tempo 550000
!
0 track 1
0 program 79 ! Whistle
0 note F.0 256 75
256 note G.0 256 87
512 note A.0 256 87
and etc. This seq file tells us, on the line which says "0 notation E12", that the notation is the standard notation for the (now) standard tuning of equal temperament. In order to convert it to a seq file which can be used to produce a midi file using Scala, we need to make only one change--a line telling Scala what tuning to use. If we add a line saying "0 equal 12", so that the file now starts
! Transformed by Scala from frere.mid with 2 tracks
! Octave degree number in mapping: 12
!
0 exclude 10
0 division 256
0 notation E12
0 equal 12
0 frequency 261.6255653
we have a file which can be used to make a midi file. Note that it is important that the file have the extension "seq", and not "txt", and that it be a text file. If we go to the Tools menu again, and go down to "Transform sequence to MIDI-file", we open up a dialog box which, using the default settings given (including "Use pitch bend tuning") will create a midi file and save it to disk. You can listen to it and hear that it sounds just the same as the file you started from.
However, we don't need to use the same notation and tuning. To create a midi file tuned in meantone instead, edit the top of the seq file so that now it says
! Transformed by Scala from frere.mid with 2 tracks
! Octave degree number in mapping: 12
!
0 exclude 10
0 division 256
0 notation P31
0 equal 31
0 frequency 261.6255653
!
This tells Scala to use a system of notation which allows notes not only to have sharps and flats (such as Bb or A#), but also double flats (such as Gbb) or double sharps, notated by an "x", so that Ex means E##. It is important to use the "x" notation (standard on musical scores) and not "##" so that Scala can recognize it. However, in this case there is no problem since there are no double flats or double sharps. We simply take the score as it is, and tell Scala (using the line "0 equal 31") to interpret it in a system of 31 notes to the octave rather than 12. The fact that there are now 31 notes to the octave need not worry us, because we can just ignore that!
If you've done this correctly, and now tell Scala to turn the result into a midi file, you should get this. Congratulations, you've just retuned a midi file!
Correct spelling
Can it possibly be as simple as all that? Well, of course not--if it was, anyone could do it. To see what can go wrong, consider what happens if Frere Jacques is in F# rather than F, as in this midi file. If as before we add a line saying "0 equal 12" and tell Scala to convert the seq file to a midi file, we get the same piece back again. However, if instead we replace "0 notation E12" with "0 notation P31", and then add the line "0 equal 31", it doesn't sound the same. What has happened?
If we look at the seq file, we find out. The piece is in F# (in fact it is more or less stuck on the F# major chord.) But in the seq file, we see Bb and Eb. Scala is using enharmonicaly equivalent names for the A# and D# which actually belong to the key of F#. The trouble is, these are only enharmonically equivalent in equal temperament, and are by no means the same in meantone. The F# major chord which should be spelled F#-A#-C# instead is spelled F#-Bb-C#. The interval F#-Bb is not a major third, but a diminished fourth. You may recall from theory classes discussions of intervals such as the diminished fourth, and wondered what the big deal was. The big deal is that in the meantone era , which involves a huge hunk of the common practice period, these two intervals are not the same. In fact, the diminished fourth, though called a "fourth", actually has the effect of a sharp third. Though not a harshly grating dissonance it also wasn't the effect we were looking for. To fix the problem, simply open the seq file in a text editor such as WordPad, and do a global replace of all "Bb" with "A#", and all "Eb" with "D#". The file is now correctly spelled for the key of F# major, and will give the correct result of a piece retuned in meantone.
Spelling correctly is the key to composing in meantone. In meantone we have not just one size of semitone, but two--the chromatic semitone, as for instance between C and C#, and the diatonic semitone, as for instance between B and C. Students (and teachers!) are often confused by these two types of semitone, because "they are the same size". Well, only in equal temperament; in meantone the diatonic semitone is larger, so that Eb ends up sharper than D#.
Chords of meantone
A chord everyone knows is the dominant seventh, which in C major is G-B-D-F. It combines dominant harmony in the form of a dominant major triad with the root of the subdominant chord, and has a dynamic quality. In comparison to the triad, it is relatively dissonant. It is, of course, available in meantone also. You may also know about the German sixth. In Eb major, the dominant seventh would be Bb-D-F-Ab, whereas a typical German sixth would be Bb-D-F-G#. In other words, they are enharmonically equivalent, once again leading to the question "what's the big deal?" Of course, in meantone tuning they are not equivalent. In the meantone era, a keyboard instrument might be tuned from Eb to G#, which would mean that in Eb major, if you tried to play a dominant seventh, you'd get a German sixth instead. On the other hand, in C minor it and the same chord rooted on Eb would form a natural addition to the harmonic palette for someone using meantone tuning, and this seems to be how it entered common practice harmony, a fact completely obscured when equal temperament is used instead, which replaces the sweet sound of the German sixth with the harsher dominant seventh sound. Similar remarks apply to the other chords using an augmented sixth interval, the Italian sixth and the French sixth.
Using Scala to tune meantone you are free to put this classic chord of the meantone era in any key you like, so long as you spell it correctly. It can really be considered as something analogous to the triad, the basic tetrad. Outside of barbershop quartet harmony, where it is in constant use, it is no longer heard very much, but it could be.
Aside from the major and minor triads, we have the diminished fourth or supermajor triad, C-Fb-G, which we've already experienced, and the augmented second or subminor triad, C-D#-G, which is really quite a nice, harmonious alternative to the ordinary minor triad. In the meantone era these triads would show up in remote keys in the place of ordinary major or minor triads; they are not the same as chords with a wolf interval, which is a very different matter. In meantone as we can use it, they can show up anywhere, or never be heard at all, as the composer chooses.
Other chords to consider are the diminished triad, the augmented triad, and the diminished seventh chord. Here instead of just one form of the chord, we have several. C-Eb-F#, C-D#-F#, and C-Eb-Gb are all are worthy versions of the diminished triad, and C-D#-Ex has something of the same sound, while exploring the exotic C-Ex (or C-Gbb) interval, about which more below. A diminished seventh chord consists of three minor thirds and an augmented second, and therefore has various inversions rather than sounding the same in all positions. A typical example would be B-D-F-G#, where B-D-F-Ab would also be a diminished seventh, only in another inversion. By swapping minor thirds with augmented seconds, we can get sequences of diminished seventh chords to ooze about in strange ways impossible in equal temperament, and not much explored in any era. The same remark applies to the augmented triad, which can be C-E-G#, C-E-Ab, or C-Fb-Ab.
Exotic eleven
In meantone, we can represent an approximate 8:11 frequency ratio by means of C-Ex, C-Gbb, or both, depending on the exact tuning. In the tuning system under discussion here, which divides the octave into 31 equal parts, the two are enharmonically equivalent. Possible chords are C-Ex-A#, the 7-11 chord, and C-Ex-G#, the train-whistle augmented triad. Use them at your own risk.
Symphonic music
A problem sometimes arises when using this system with symphonic music. Symphonic music can have so many channels the system of pitch bending no longer works correctly, or at all, and Scala can be forced into unfortunate compromises or fail to produce a midi file at all. The cure for this is the official midi tuning standard, or MTS. When Scala opens a dialog box after you ask it to "Transform sequence to midi-file", it opens a dialog box. Instead of leaving "Use pitch bend tuning" checked, you can check "Use MIDI standard tuning". Your problems producing a midi file will now go away. Unfortunately, the midi tuning standard is not well supported. However, if you go here and download Timidity, you have a first-rate, totally free program which can render a midi file using MTS to a wav file, saving it to disk.
The howl of the wolf
If you are restricted to just twelve notes and have tuned to meantone, you eventually reach a point on the circle of fifths where you find it isn't actually a circle and what you've got is not really a fifth. If you tune a keyboard instrument from Eb to G#, then the interval G#-Eb is called the wolf, because musicians of that era felt it howled like one. In the meantone tuning we are using, it is certainly too sharp to make a very good fifth. On the other hand it is very close to an interval of 17:26. Unless you like the effect of this exotic interval and want to use it, you should be careful to spell your notes so as to avoid the howl of the wolf
List of notes
Here is a list of all 31 notes in the octave in the P31 notation system. Note that it is not necessary to pay any attention to this if you want to compose music in a common-practice style. On the other hand, if you want exotic stepwise progressions it could be just what you are looking for.
0: C
1: Dbb Bx
2: C#
3: Db
4: Cx
5: D
6: Ebb
7: D#
8: Eb
9: Dx Fbb
10: E
11: Fb
12: E#
13: F
14: Gbb Ex
15: F#
16: Gb
17: Fx
18: G
19: Abb
20: G#
21: Ab
22: Gx
23: A
24: Bbb
25: A#
26: Bb
27: Ax Cbb
28: B
29: Cb
30: B#
31: C