Introducing the Harmonic 7th Chord

If you want to experience Just Intonation first hand then please visit the Online Terpstra Keyboard and experiment for yourself.  This was originally created by James Fenn.  I have added a few additions and will continue to build upon his wonderful work.  You can even use this on an iPad or tablet of your choice in order to use multiple fingers for chords and scales.

Online Terpstra Keyboard

Make sure “Enumerate Scale” is not checked, scroll to the bottom and click on  “MAKE ME A MICROTONAL KEYBOARD!”.

Click around to hear how this Just Intonation scale sounds.  If you’re on a laptop or desktop then hold down the space-bar for sustain, or if using a tablet then shake it until you see a message that says “Sustain On” You can turn sustain off by shaking it again (working out the details on that).

To play a Harmonic 7th chord play the following notes:  R, 5/4, 3/2, 7/4.  What you have here is a very stable and consonant chord that is unavailable to you if playing on a piano in 12ET.  This is only a very small beginning of what awaits you in new musical sounds and textures.

13 thoughts on “Introducing the Harmonic 7th Chord”

  1. Nice to see the keyboard again!

    If you’re adding features, you might want to fix the existing bugs first – send me an email, I know a couple of the simple fixes.


  2. Thank you so much! I was devastated to see that the original had disappeared and am really glad to see it back again. Now I can experiment with microtones and different tunings and keyboard layouts again! (as the Axis-49 is no longer made and I’m too poor to afford anything else, and don’t know enough to make my own…)

    I wish it was available as a stand-alone program, so there wouldn’t be a risk of it disappearing again (or did I miss something and that’s possible already?)…

  3. You’re most welcome! I agree with the standalone idea. The way I was able to reupload it was by storing a local copy just in case it went offline… I would have also been devastated if I hadn’t!

    For iPad and Android tablets it would be great to have this as an app… perhaps that’s something to consider for the future.

  4. Thanks for the tip, I’ve saved a local copy now, just in case. 🙂

    Also, I hope you don’t mind, I added a link here from the Jammer Wikipedia article:

    An app would indeed be nice, some day. I currently have the open-source Hexiano app installed on my Android tablet, which is pretty good, but you can’t change the scale and layout on it like you can on this one.

  5. Don’t mind at all, thanks. 🙂 I will be uploading a small update with a select box that has a list of common tunings and layouts. So that initially it will be easier to switch between them easily. Currently it is possible to bookmark any settings and come right back to them, but a select box might make things even more convenient for first time users.

    1. Would it be possible, I wonder, to have a copy of the 4500 scale files from here: (it’s only just over a megabyte) and to have a box where simply typing in the filename of the scale would automatically paste the data for the scale in question into the “Scale (scala format)” box? I do that right now by open the .scl file in a text reader and copy+pasting the contents. But it’s awkward and time-consuming to do on a tablet.

      If that were done, I could just have this page open in a browser:
      and copy+paste whichever file names I want to try.

      It would also be nice if there was an option to have the note names be automatically generated from the .scl file, rather than having to put them in manually (the option is nice, but most of the time I prefer to have the same names as in the scala file).

  6. Yes that is possible. And is a great idea! I actually just made a small update early this morning. But your suggesstions will be part of the next update. Thanks! I’ll add another page for updates related to the Online Terpstra Keyboard.

  7. Hey, I noticed that you made some changes a few days ago, though there hasn’t been any news…

    I thought I’d share something I’ve been doing with this lately.

    Scale Link

    Ancient Greek Aulos modes! Based on the descriptions in Maria Renold’s book (“Intervals, Scales, Tones and the Concert Pitch c=128Hz”), based on 1939 book about the Greek Aulos modes by Kathleen Schlesinger, curator of old musical instruments at British museum.

    Apparently, there were two competing tuning systems in Ancient Greece. The one most familiar to us is the “Pythagorean”, used by lyre players, and the basis of medieval European music theory. It was based on perfect fifths. A rather different one was used by aulos players, which was forgotten in Western Europe but apparently survived in many other cultures. It was based on undertones (the Greek aulos had equidistant fingering holes).

    There were 7 possible modes, depending on which low note you start with, moving up. Modes can contain either the 8/14 or 8/15 degree, but not both. If your mode starts on:
    -8/8 or 8/9, you must skip 8/14 as you move up
    -8/14, you must skip 8/15 as you move up
    -any other note, you can choose EITHER 8/14 or 8/15 to skip as you move up
    -(a scale cannot begin on 8/15)

    The modes are associated with celestial objects, from bottom to top:
    8/8 = Saturn (Hypodorian)
    8/9 = Jupiter (Hypophrygian)
    8/10 = Mars (Hypolydian)
    8/11 = Sun (Dorian)
    8/12 = Venus (Phrygian)
    8/13 = Mercury (Lydian)
    8/14 = Moon (Mixolydian)
    (this is the also the order of how fast these celestial objects appear to move in the night sky. See p. 304 in “Quadrivium” by Wooden Books)

    The Sun mode was most common. The link above has the fundamental 8/8 tuned at 176*4=704, which allows the 1st note of the Sun mode (8/11) to be tuned at 128Hz (a common tuning back then).

    Note that the Sun mode (particularly if you use 8/14 instead of 8/15) sounds like the whole tone scale of Debussy, etc. The Saturn mode sounds like the scales used in a lot of Middle Eastern music. The Jupiter mode sounds like the Misheberakh/Hungarian/Ukrainian Dorian scales.

    Anyway, having this online keyboard was very helpful in letting me hear what the book was talking about! Maria Renold actually recommends not using speakers but building your own monochord instead, but… well, I don’t have the skills to do that. :\

  8. Thanks Esn, the scale sounds amazing. I will check that book out it sounds very useful as well. For some reason I had to modify the link because it was weirdly formated:

    Scale Link

    I got a bit too excited with the new updates so I went ahead and released it. I’m still working on a few more features for the next update. Mainly the ones that you mentioned earlier. 🙂

  9. This keyboard is awesome! But there’s some issue though.
    Timbre is irregular over keys. This is very distracting, because change of timbre makes listening to intervals and their combinations harder.

  10. Hi zukaboo,

    Thanks, yeah that is a good point. It mostly has to do with the samples. At least the ones that I made (the Organ and Organ Leslie) they are just samples that I recorded from GarageBand. I’m sure there’s a better way of doing that, but haven’t been able to get around to looking into that yet!

  11. Well, you can synth some timbres in realtime. There’s a lot of libraries for JS. Tone.js looks fine, for example.
    Better to use a simple synth that doesn’t require too much CPU.

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