Using chords in any transposition

Continuing the discussion from Chord feature suggestions:

[quote=“oscarwildone, post:5, topic:95, full:true”][…] I understand that F Lydian has the same chords as C Major but how did you work out that you borrow from Locrian?
It appears that a lot of Hookpad users have difficulty using supermodal chords where necessary. Some would resort to using secondary chords where possible (clearly they do not encompass all 12 root pitches, and they also have lost the meaning of secondary chords), but in order to create something like this, here are two methods to access these supermodal chords:

The first method: It is important to realize that borrowing a chord from another mode is effectively the same as transposing the diatonic scale, which in turn is equivalent to temporarily changing the key signature by adding or removing a number of sharps or flats. We arrange all the 7 diatonic modes in order of the number of accidentals applied, relative to the Locrian mode, although this will work using any other diatonic mode as a reference point:

Lydian Major Mixolydian Dorian Minor Phrygian Locrian
  6      5       4        3      2      1        0

Also one should remember that, for diatonic key signatures, a sharp is equivalent to raising the tonic by a fifth, and a flat by a fourth. Using the key of C as an example, all 12 keys can be reached by adding the following numbers of sharps (+ve) or flats (-ve): (both F♯ and G♭ can be reached but they are enharmonic)

C   Db  D   Eb  E   F  [F# Gb] G   Ab  A   Bb  B
0   -5  2   -3  4   -1 [6  -6] 1   -4  3   -2  5

In borrowing a chord from another mode, the change in the key signature due to the modes simply needs to match that due to transposition. The tonic of the current key does not matter. Here are some examples:

  • To get A7 in the key of D Minor, which has C7, we have to transpose this dominant seventh chord by three semitones downwards. From the circle of fifths we know that A is reached from C by raising 3 fifths. Now the Minor mode has 2 sharps (relative to Locrian), and we want a mode containing 2 + 3 = 5 sharps (relative to Locrian). We find V7 (A7) by borrowing from the Major mode.

  • To get D7 in the key of F Major, which has C7, we need to borrow from a mode that has 5 + 2 = 7 sharps - but that is impossible since the most sharpened mode, Lydian, has 6 sharps. Instead, we temporarily switch to a more flattened relative mode in the key menu, and from there we can access D7. For example, if we change to G Dorian, we only need a mode with 3 + 2 = 5 sharps, therefore we could find V7 (D7) by borrowing from the Major mode, which becomes IV7</sup< once we return our Theorytab to the key of F Major.

  • To get B7 in the key of F Minor, which has E♭7, we need to borrow from a mode that has 2 - 4 = -2 sharps (2 flats); so we switch to the relative A♭ Major, and then borrow from Phrygian that has 5 - 4 = 1 sharp, and ♭III♭7 (B7) will be there.

  • Tritone substitution for any chord can be achieved by transposing the current chord by 6 fifths or 6 fourths. In C Major, to get the tritone substitution of G7, we can reach ♯I7 (C♯7) by borrowing the Lydian ♯II7 from B Locrian, or reach ♭II♭7 (D♭7) by borrowing the Locrian ♭VI♭7 from F Lydian.

The second method: For more experienced users it might be even easier to remember only the transposition between modes, as in this table of semitones of the relative tonics transposed upwards from the tonic in the Major:

Major Dorian Phrygian Lydian Mixolydian Minor Locrian Major
  0     2       4       5        7        9     11     12

Now the inverse transposition due to the mode will have to match the transposition of the chord’s root pitch. For instance, to get B7 in C Major, we transpose G7 upwards by 4 semitones, or downwards by 8 semitones. We notice that borrowing from the Major mode in the relative Phrygian mode does give us V7 (B7) since Major = 12, Phrygian = 4, and 12 - 4 = 8. Here is the full transposition table, using the abbreviations from the Trends API: (“I” represents Major; once again, borrowing from Lydian in Locrian is enharmonic to borrowing from Locrian to Lydian)

        I  D  Y  L  M  b  C
From I  0  2  4  5 -5 -3 -1
     D -2  0  2  3  5 -5 -3
     Y -4 -2  0  1  3  5 -5
     L -5 -3 -1  0  2  4  6
     M  5 -5 -3 -2  0  2  4
     b  3  5 -5 -4 -2  0  2
     C  1  3  5 -6 -4 -2  0

Hopefully this will assist many Hookpad users in fully utilizing Hookpad’s capabilities. Last words:

  1. If a supermodal chord of the Major mode has the same constituent notes as a secondary chord (e,g, III7 and V7/vi in Major), it will be recognized as such in the Trends API. Other supermodal chords are currently unsupported in the Trends API.
  2. Borrowed chords of the Major mode that are identical to the non-borrowed chords are counted as separate entries in the Trends API, for example Lydian I7 (“L17”), Mixolydian vi (“M6”) etc.
  3. Similarly, two borrowed chords in the Major mode that are identical will be regarded as separate chords nonetheless, for example the Dorian, Minor, and Phrygian i (“D1”, “b1”, “Y1”).
  4. Switching modes “around” may raise or lower all melody notes by an octave due to a Hookpad bug.
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Thank you @HertzDevil for an excellent description of modes in Hookpad.

Supermodes were originally implemented to handle the transposition of borrowed chords between modes when the final mode was not one of standard supported modes. At the time, we didn’t really view these higher modes as a feature as much as a device for ensuring consistency when transposing between modes.

We are working to address the bugs mentioned in this post as well as consolidating enharmonically equivalent chords to make them more useful in the Trends API.

More on the Trends API: It seems that only III (supermodal) is treated as identical to V/vi so that Theorytabs in Minor mode can use V, but not other secondary dominants; and I believe that for the same reason only #v° is realized as vii°/vi but not other secondary leading-tones none of the borrowed diminished chords are realized as equivalent secondary leading-tones even when they exist. Supermodal chords not recognized by the Trends API will cause no difficulty to be assigned to the Theorytabs, so I hope this observation could help rectify certain enharmonic chords before implementing the popular music style Roman numerals in the API.

@Ryan, I read @HertzDevil 's post many, many times (@HertzDevil thank you for the information).

I think I finally understand how Supermodes are intended to work. But to make sure let me restate in my own words using a bit of a metaphor. If I’m missing relevant documentation let me know, all I’ve found on the topic is here:

Let’s say for the purpose of discussion that the progression of a song is: C D7 F C E7 F

First, when you fire up Theorytab, you find yourself in the key of C Major. Two of the chords C & F are in that key, so no worries.

To find the D7, I could use the Applied Chord: D7, V of V; however, though this is the correct chord, it is not behaving as the V of V. Because this is the incorrect choice in this context (correct when D7 leads to G) I should look to borrow the chord from another mode.

To assist in this process I created the following visualization, consider a Mode Hotel, 7 floors, Lydian is staying in the Penthouse, Locrian, the Ground Floor. Keys are ordered in the cycle of fifths. Since I’m in Ionian/Major, I’m on the sixth floor.

7 - Lydian ------------- (G) - #
6 - Ionian/Major ------ ©
5 - Mixolydian --------- (F) - b
4 - Dorian ------------- (Bb) - bb
3 - Aeolian/Minor ---- (Eb) - bbb
2 - Phrygian ---------- (Ab) - bbbb
1 - Locrian ------------ (Db) - bbbbb

The chord I need is a D7: (D,F#,A,C). Since there are no #'s in the key of C, I know from the diagram that I need to call up to a floor with more sharps. I know F# is available in the key of G, so I call the Lydian Penthouse, 1 floor above, and sure enough I find a D7.

Similarly with E7 (E,G#,B,D) I could incorrectly use a V/vi (correct when E7 leads to A-) but to correctly analyze the song, I should look to borrow.

In this case, I need a G# for my chord, which (for one) is in the key of A. That’s 3 floors above C and there aren’t that many more floors in the hotel!

The solution is to go down several floors by changing the mode of the song. In this case I visit the Dorian floor, again I call the Lydian Penthouse, now 3 floors above and sure enough there is my E7. When I switch back to Major, the chord is an E7 labeled as a Major III, which is exactly what I wanted.

If the above is an accurate description, then a quick rule of thumb is: in Major, you are likely to find flatted borrowed chords by calling floors below, but, if you need sharp borrowed chords, you should visit a lower floor and call above.

As to why it’s called a Supermode, I imagine it’s because the next ‘imaginary’ floor in the Hotel would be the key of D, which contains a C#, rather than the tonic C.

Please let me know if I have missed anything regarding TheoryTab usage. If the above is correct, I may have some follow up questions which I’ll locate in separate topics. Thanks.

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Correct, and it’s a very vivid description. Penthouse of C With supermodes:

 6 - S(6) Supermode     (F#) - ######
 5 - S(5) Supermode      (B) - #####
 4 - S(4) Supermode      (E) - ####
 3 - S(3) Supermode      (A) - ###
 2 - S(2) Supermode      (D) - ##
 1 - Lydian              (G) - # 
 G - Ionian/Major        (C)
B1 - Mixolydian          (F) - b
B2 - Dorian             (Bb) - bb
B3 - Aeolian/Minor      (Eb) - bbb
B4 - Phrygian           (Ab) - bbbb
B5 - Locrian            (Db) - bbbbb
B6 - ???? Supermode     (Gb) - bbbbbb

Bear in mind once again that in Minor mode, chords borrowed from a mode above Dorian will become supermodal in the relative Major key, and Major V in Minor is the only exception of a supermodal chord to contain data in Magic Chord (as “S(3)3”).

@smitchmor and @HertzDevil,

Yes, this is exactly right. Thank you for the great analogy!