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It stands for the Interactive Scale Tutorial for Honing Musical Understanding Skills. That'll teach you to ask idle questions.
Yeah, shaddup. When I first started working on Isthmus I envisioned a tutorial that would describe the uses of different scales and the theory behind them. Isthmus is the first stage of that project, a tool for exploring the relationships between scales and chords. This first stage has taken up enough time that I do not plan on creating the full-blown tutorial. Consider Isthmus a self-directed study.
Yes. Visit the MIDI Isthmus page. To use it, you will need to have the Java 1.3 plugin installed for your browser. Downloading the plugin can be a bit of a hassle, but it makes learning the scales a lot more fun.
When Isthmus displays related scales (in particular, inversions,) it builds the scales on the notes of the original scale, even if those notes have double sharps or flats. However, scales built on root notes with double sharps or double flats are cumbersome to use. Cbb major would have 14 flats in the key signature, and Cbb Locrian would have 19! As a result, when you double-click on a scale to view it, Isthmus converts the root note of the scale to a note that has at most one sharp or flat. If you really want to know what Dbb major is like, view Db major and mentally add a flat to every note and chord name you see.
The algorithm I'm using for figuring out what the fingerings should be isn't very smart yet. For now, consider them reasonable hints and feel free to come up with more sensible fingerings on your own.
When you type in notes or chords to build a scale on, Isthmus tries to find a unique pre-defined scale that matches those notes or chords. If there is no exact match, Isthmus creates a temporary scale so you can still look for inversions, one-off scales, etc. Isthmus gives the name "(user-defined)" to the temporary scale. Isthmus only allows one user-defined scale at the same time, so if you enter another series of notes or chords that doesn't have an exact match, the new temporary scale will overwrite the old one.
Inversions are scales containing the same sequence of notes but starting in a different place. C major (C D E F G A B C) and A minor (A B C D E F G A) are inversions of each other.
'One-off scale' is my term to describe scales that differ in only one place, i.e. you can convert one to the other by inserting one note, deleting one note, or changing one note. C major (C D E F G A B C) and C Lydian (C D E F# G A B C) are one-off scales from each other.
'Enclosing scale' is my term for a scale that contains another scale. C major (C D E F G A B C) is an enclosing scale for C pentatonic major (C D E G A C) because all of the notes in C pentatonic major are also in C major.
'Embedded scale' is my term for a scale that is contained in another scale. C pentatonic major (C D E G A C) is an embedded scale of C major (C D E F G A B C) because all of the notes in C pentatonic major are also in C major. If scale #1 encloses scale #2, then scale #2 is embedded in scale #1.
Triads are built on the unison; major or minor third; and perfect, augmented, or diminished fifth intervals of a scale from a given root note. The three intervals together must form a major, minor, diminished, or augmented chord. For example, in C major (C D E F G A B C), the triad built on C would be C major (C E G), the triad built on D would be D minor (D F A), etc. If more than one such triad exists, Isthmus makes no attempt to resolve the ambiguity. For example, in a C extended pentatonic minor scale (C D Eb F Gb G Bb B C), both C minor (C Eb G) and C diminished (C Eb Gb) can be formed, so Isthmus does not list any chord built on C in the Related Chords list.
If a triad cannot be formed this way, Isthmus will try to find a triad built on the given root note that contains pitches that are present in the scale. For example, in a C pentatonic Lydian (C D E Gb Ab C) scale, the unison, third, and fifth intervals from C would form (C E Gb), which is not a valid triad. However, one can form a C augmented triad (C E G#) from the pitches in the scale, rewriting the Ab as a G#. Music purists might have a fit about this, but if you're just looking for a chord to play that will sound right in the scale, this works out fine.
Sevenths are formed analogously from unison, third, fifth, and seventh intervals. The valid seventh chords are (dominant) seventh, minor seventh, major seventh, minor/major seventh, diminished seventh, seventh flat five, seventh sharp five, half-diminished seventh, major seventh flat five, and major seventh sharp five. Note that some spellings of diminished seventh chords might not be technically accurate. For example, Cbdim7 should be spelled (Cb Eb Gbb Bbbb Cb). Since Isthmus does not allow triple flats, Cbdim7 is instead spelled (Cb Eb Gbb Ab Cb).
Technically the melodic minor is played one way when ascending (1 2 b3 4 5 6 7 8) and reverts to the natural minor/Aeolian mode when descending (1 2 b3 4 5 b6 b7 8). It's inconvenient to compare the relationships between scale patterns when a scale can take on two different forms, and the natural minor is already its own scale, so I only included the ascending version of the melodic minor. To get even more technical, the jazz melodic minor scale, which is listed below as being the same as the melodic minor, is the same both ascending and descneding. Aren't you glad you asked?
The chromatic scale wouldn't be very interesting. Its inversions are 11 other versions of itself, it is an enclosing scale for all other scales, all other scales are embedded in it, and trying to figure out triads and sevenths built on it is meaningless. If you feel like your music theory education will not be complete until you see it, here it is: (1 b2 2 b3 3 4 b5 5 b6 6 b7 7 8).
Each scale is listed under a single name, even if it commonly goes by several. I have tried to pick the most common name for a given scale, or, in cases where there was no clear favorite, the name that was the least ambiguous. In some cases I invented names, usually to distinguish between variants of a scale that had the same name.
Here are the redundant scales and the names used for them in the tutorial:
| Canonical name | Definition | Also known as |
|---|---|---|
| Acoustic | 1 2 3 4 5 b6 b7 8 | Bartok, Hindustan (M3 variant) |
| Ascending melodic minor | 1 2 b3 4 5 6 7 8 | Jazz melodic minor |
| Chinese b4 | 1 3 4 5 7 8 | Semitonal pentatonic |
| Dorian | 1 2 b3 4 5 6 b7 8 | Jazz minor |
| Dorian #4 | 1 2 b3 #4 5 6 b7 8 | Romanian minor |
| Double harmonic major | 1 b2 3 4 5 b6 7 8 | Bhairava, Gypsy major |
| Double harmonic minor | 1 2 b3 #4 5 b6 7 8 | Algerian, Gypsy minor (M7 variant), Hungarian minor |
| Hirajoshi | 1 2 b3 5 b6 8 | Japanese Traditional |
| Hungarian Gyspy | 1 2 b3 #4 5 b6 b7 8 | Gypsy minor (m7 variant) |
| Inverted diminished | 1 #1 #2 3 #4 5 6 b7 8 | Octotonic (variant), Symmetrical |
| Japanese | 1 b2 4 5 b6 8 | In |
| Locrian major | 1 2 3 4 b5 b6 b7 8 | Arabian |
| Lydian b7 | 1 2 3 #4 5 6 b7 8 | Overtone |
| Minor | 1 2 b3 4 5 b6 b7 8 | Ethiopian, Hindustan (m3 variant), natural minor |
| Pentatonic Dorian | 1 2 4 5 b7 8 | Egyptian |
| Pentatonic major | 1 2 3 5 6 8 | Mongolian |
| Pentatonic Mixolydian | 1 2 4 5 6 8 | Ritusen |
| Pentatonic Phyrgian | 1 b3 4 b6 b7 8 | Egyptian (minor variant) |
| Phygrian major | 1 b2 3 4 5 b6 b7 8 | Arabic, Jewish, Spanish |
The virtual piano used in Isthmus was originally based on Brian Lichtenwalter's MidiSynth class in the Java Sound Demo.
The following were used as references for scale information:
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Last edited 7/11/02