Midi Tempering Walk-Through
by Fred Nachbaur ©2002
(This walkthrough also included in the distribution package as "walkthru.txt")

V2.3b, Feb. 10, 2002

To get a feel for the usage of this program suite, here is a walk-through for those who want to jump right in. Following through this is especially appropriate if you don't have much experience running DOS programs.

I'll assume that you've got the program installed in the default C:\HARMONIC directory, and are running from Windows. Keep the window containing this walk-through file open, so that you can refer to it as you go through the process. Alternately, or if you're running from DOS, print it out for easy reference.

  1. Launch Harmonic Analyser:
    From Windows Explorer (or File Manager), navigate to the C:\Harmonic directory (folder). Double-click on the file Harmonic.exe. If the program comes up in full-screen mode, press ALT-Enter to run it in a window. At the upper-left corner there is a little pull- down menu from which you can select your font size (and therefore window size). I find the 10x18 option to be the most pleasing. Whichever you choose, Windows should remember your setting for next time.

  2. Get started:
    For now, just press [Enter] when you've looked over the pretty (?) cover screen. Through the entire program suite, defaults are accepted by simply pressing the [Enter] key. In this case, we're just skipping the "set custom colours" option.

  3. How many harmonics?:
    Again, just press [Enter] to accept the default of 39 harmonics to compare against. You are now presented with a column of numbers showing the "note values" (ratios) of the harmonics up to number 39. OK fine, press [Enter] again to see the second page of numbers.

  4. Choose a temperament:
    Press [Enter] again. You now should see a menu of available temperament options. The first time through, for the purpose of this demo, select "Harmonic1 (27 limit)" by typing 13, then [Enter]. You now get a report of the tone values (ratios) of the selected temperament. Press [Enter] (or any other key) to move on.

  5. Choose a tonic:
    Since the midi files we're using for the demo are in the key of A minor (shares the same key signature with C major), select "C", either by entering "4" (no quotes), or by accepting the default and pressing [Enter] by itself.

  6. Choose a tone-centre:
    Read the following screen. If it doesn't make much sense first time through, don't worry about it. Go ahead and accept the default of A=440 by pressing [Enter].

  7. Shift tone-center?
    Since we chose a tonic other than A (i.e. C), you are now presented with the option to shift your scale such that the note "A" lands on the selected tone-centre. Press the "Y" key to answer "yes." The program then reports that it found an "A" tone at note number 10. Perfect, that's where A indeed is. (The reason for this is that extreme tone-centre shifts can give wrong results, and you're forewarned so you can correct for it in a subsequent run.) Press [Enter].

  8. Calculate/edit:
    You're now shown an info screen that explains (sort of) what is happening now. Press [Enter]. This takes you to the final results and editor screen. Move the flashing cursor up and down using the up/down cursor keys. Note that you can edit any tone from 2 through 12 (last tone in the scale). This is because 1, being the tonic, is always fixed at 1.00000. Position the cursor to the ratio corresponding to Note# 5 and and press [Enter]. The cursor changes to a large block, indicating input mode. Enter a number, for instance "1.30". The table is recalculated. Again press [Enter] and enter a ratio; for example "6/5". Note that this is also taken as valid input. Finally, enter an "absolute cents" value, for example "525.0 c" (the "c" indicating "cents"). This too is a valid input format, and is recalculated to the equivalent ratio.

    If you enter "nonsense" (as far as the program is concerned) you get a brief error message, and the old value is retained.

    When you're done experimenting, restore the original value for Note# 5 by entering "1.25". Then press the [ESC] key to go to the "End Menu."

  9. Tempering a midi file using MidiTemper:
    From the end menu, select "Run MidiTemper with current data" by pressing the [4] key. This launches MidiTemper, while keeping Harmonic Analyser in memory. You're asked for an input midi filename: type "caverns.mid" (no quotes) then [Enter]. (This is one of my compositions, "Caverns of the Heart", slightly modified from the original to make it temperable using MidiTemp; i.e. multiple monotonic tracks).

  10. Enter output filename:
    You're prompted for a filename for the output midi. Type "caverns1.mid" [Enter]. You are now shown the tempering data once again, for verification. (This data has been "shuttled" directly from the Harmonic Analyser module.) Press [Enter].

  11. Verbose output?
    If you want to see what additions are being made to your midi file in real-time, press [Space Bar] (not recommended for slower computers). Otherwise, press [Enter] or some other key.

  12. Pitch-bend reset option:
    Select 4, or press [Enter].

  13. Process midi file:
    Wait until the processing is complete. The program reports successful tempering, repeats the output filename, and reports on the number of note "collisions" that have been logged to COLLISN.LOG. Note that there are some 17 such collisions reported; however, since they all happen on fast harp arpeggios, it's unlikely that these would ever be noticed. Finally, press [Enter]. You're returned to the Harmonic Analyser end menu.

  14. Tempering a midi file using PianoTuner:
    From the end menu, select "Run PianoTuner with current data" by pressing the [5] key.

    This launches PianoTuner, while keeping Harmonic Analyser in memory. You're asked for an input midi filename: type "cavpian.mid" (no quotes) then [Enter]. (This is a nifty piano reduction of "Caverns of the Heart" by Anthony Wilson, in a single, polyphonic, Type 0 track).

  15. Enter output filename:
    You're prompted for a filename for the output midi. Type "cavpian1.mid" [Enter]. You are now shown the tempering data once again, for verification. (This data has been "shuttled" directly from the Harmonic Analyser module.) Press [Enter].

  16. Tempering options:
    Accept the default for all the subsequent tempering options:
    Volume changes: [0] (or [Enter])
    Pan changes: [0] (or [Enter])
    Pitch bends: [0] (or [Enter])
    Other contr: [0] (or [Enter])
    Sysex: [0], [1], or [Enter] (doesn't matter, no sysex in this file)

    If you made a mistake, press [Space bar] to redo, otherwise press [Enter].

  17. Select an instrument patch:
    Type [1] (acoustic piano) then [Enter]

  18. Processing data:
    Watch the pretty dots while the program creates your new file, a tempered multi-channel monotonic version of the original polyphonic single-channel file.

  19. Restart Harmonic Analyser:
    Press [3] to return to the "Number of Harmonics" screen. Go back to step 3 above, and repeat the entire process using the "Pythagorean" temperament (option 1), naming your MidiTemp file "caverns2.mid" and the PianoTuner file "cavpian2.mid". Then do it all again, using the "Werckmeister" temperament (option 6), naming your output files "caverns3.mid" and "cavpian3.mid" respectively.

  20. End off:
    When all done, select option [6] (or press the [ESC] key) from the Harmonic Analyser end menu. This closes the program.


Finally, navigate to the C:\HARMONIC\MIDI subdirectory (folder). You'll see your new, tempered midis there. Have a listen to the originals first, then listen to each of the tempered files.

  1. (caverns1.mid and cavpian1.mid) "Harmonic1" temperament. These will most likely sound decidedly "out of tune." This just goes to show that just because notes are harmonically related to the tonic, this DOES NOT guarantee that it will sound good!

  2. (caverns2.mid and cavpian2.mid) "Pythagorean" temperament. Pythagoras and his crew obviously realised the limitations of the single-tonic harmonic series approach, and came up with a harmonically related "Circle of Fifths." In other words, with the tonic on C, the fifth (at G) will be exactly 3/2 the frequency, or 1.5000. The note D will be 3/2 of G, A will be 3/2 of D, and so on. One slight problem: By the time it rolls through all twelve notes of the chromatic scale, the result (another C) is NOT an exact octave multiple of the original one! This deviation is called the "Pythagorean Comma", and is the bane of temperament authors since way back BC. Have a listen to the Pythagorean tempered files; while they have moments that are brilliant, there are other moments (such as the section in C minor) that.. er.. still crunch a little. The effect is not so bad in the timbres selected for the "orchestral" version of Caverns, but is quite apparent in the piano version.

  3. (caverns3.mid and cavpian3.mid) "Werckmeister" temperament. There ensued after Pythagoras a vast number of schemes to "divvy up" the Pythagorean Comma amongst the various intervals constituting the scale, in an effort to achieve a melodious compromise. Most of these sounded quite good in a given range of keys, but fell apart when going off into others. The "well" tempers (of which Werckmeister is but one example) attempted to achieve a compromise that worked well in ALL keys. (Note that this is NOT the same as equal temperament, which is the de-facto standard nowadays. It bears pointing out that in equal temperament, NONE of the tones are exactly harmonically related!) You'll find by listening to these files why the well tempers achieved such popularity. It's my considered opinion that these are still the best way to tune a piano, as you can verify (or not..) especially by listening to the cavpian3.mid version.


Comments? Suggestions? E-mail me at fnachbaur@netscape.net

Website: http://www3.telus.net/dogstarmusic

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Copyright ©2002 by Fred Nachbaur

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---This page last updated Feb. 10, 2002.---