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I'm trying to learn more about Music Theory, and I'm currently looking into modulation, more specifically CTM (Common Tone Modulation).

As far as I understand it, the concept is pretty straight forward that (at least) one tone has to be common or sustained between 2 chords.

What I have a problem with understanding is a CTM example that was made on a Lynda.com tutorial (Music Theory for Songwriters: Harmony) and is also stated on Wikipedia in the Modulation: CTM section, that for a given chord one could possibly modulate via CTM to 12 different, other chords.

Wikipedia states this example here:

"Starting from a major chord, for example G (G-B-D), there are twelve potential goals using a common-tone modulation: G minor, G♯ minor, B♭ major, B major, B minor, C major, C minor, D minor, D major, E♭ major, E major, E minor".

but clearly - this is the part that confuses me - when just looking to keep one tone in common, there are more than 12 potential keys one can modulate to from a G major triad (G,B,D)... so I'm missing something.

***** added information *****

via the Wikipedia example from above using CTM to modulate to other keys from a G maj triad G,B,D in key of G major (targeting major/nat minor scales only):

(1) the note of G is found in 17 keys in the following position:

Ab Major 7th
A Natural Minor 7th
A# Major 6th (as F##) (duplicate to Bb Major)
Bb Major 6th
B Natural Minor 6th
C Major 5th
C Natural Minor 5th
D Major 4th
D Natural Minor 4th
D# Major 3rd (as F##) (duplicate to Eb Major)
Eb Major 3rd
E Natural Minor 3rd
F Major 2nd
F Natural Minor 2nd
G Major 1st (duplicate, original key)
G Natural Minor 1st
G# Major 7th (as F##) (duplicate to Ab Major)

--> leaving a total of 13 unique keys as a CTM target for the note of G

(2) the note of B is found in 19 keys in the following position:

Ab Natural Minor 3rd (as Cb) (duplicate to G# Minor)
A Major 2nd
A Natural Minor 2nd (duplicate, already listed)
B Major 1st
B Natural Minor 1st (duplicate, already listed)
C Major 7th (duplicate, already listed)
C# Natural Minor 7th
Db Natural Minor 7th (as Cb) (duplicate to C# Minor)
D Major 6th (duplicate, already listed)
D# Natural Minor 6th
Eb Natural Minor 6th (as Cb) (duplicate to D# Minor)
E Major 5th
E Natural Minor 5th (duplicate, already listed)
F# Major 4th
F# Natural Minor 4th
Gb Major 4th (as Cb) (duplicate to F# Major)
Gb Natural Minor 4th (as Cb) (duplicate to F# Minor)
G Major 3rd (duplicate, original key)
G# Natural Minor 3rd

--> leaving a total of 8 additional unique keys as a CTM target for the note of B

(3) the note of D is found in 17 keys in the following position:

A Major 4th (duplicate, already listed)
A Natural Minor 4th (duplicate, already listed)
A# Major 3rd (as C##) (duplicate to Bb Major)
Bb Major 3rd (duplicate, already listed)
B Natural Minor 3rd (duplicate, already listed)
C Major 2nd (duplicate, already listed)
C Natural Minor 2nd (duplicate, already listed)
D Major 1st (duplicate, already listed)
D Natural Minor 1st (duplicate, already listed)
D# Major 7th (as C##) (duplicate to Eb Major)
Eb Major 7th (duplicate, already listed)
E Natural Minor 7th (duplicate, already listed)
F Major 6th (duplicate, already listed)
F# Natural Minor 6th (duplicate, already listed)
Gb Natural Minor 6th (as Ebb) (duplicate to F# Minor)
G Major 5th (duplicate, original key)
G Natural Minor 5th (duplicate, already listed)

--> leaving a total of 0 additional unique keys as a CTM target for the note of D

The resulting 21 unique keys are (incl. resulting triads w/ note positions):

Ab Major 7th (G,Bb,Db)
A Major 2nd (B,D,F#), 4th (D,F#,A)
A Natural Minor 2nd (B,D,F), 4th (D,F,A), 7th (G,B,D)
Bb Major 3rd (D,F,A), 6th (G,Bb,D)
B Major 1st (B,D#,F#)
B Natural Minor 1st (B,D,F#), 3rd (D,F#,A), 6th (G,B,D)
C Major 2nd (D,F,A), 5th (F,A,C), 7th (B,D,F)
C Natural Minor 2nd (D,F,Ab), 5th (G,Bb,D)
C# Natural Minor 7th (B,D#,F#)
D Major 1st (D,F#,A), 4th (G,B,D), 6th (B,D,F#)
D Natural Minor 1st (D,F,A), 4th (G,Bb,D)
D# Natural Minor 6th (B,D#,F#)
Eb Major 3rd (G,Bb,D), 7th (D,F,Ab)
E Major 5th (B,D#,F#)
E Natural Minor 3rd (G,B,D), 5th (B,D,F#), 7th (D,F#,A)
F Major 2nd (G,Bb,D), 6th (D,F,A)
F Natural Minor 2nd (G,Bb,Db)
F# Major 4th (B,D#,F#)
F# Natural Minor 4th (B,D,F#), 6th (D,F#,A)
G Natural Minor 1st (G,Bb,D), 5th (D,F,A)
G# Natural Minor 3rd (B,D#,F#)

--> the only way to cut this to 12 results is by only considering keys that have the notes G, B or D in either position 1, 3 or 5...

WHY is the note position a requirement for CTM ? The note of G (when sustained between 2 chords) is the note of G, independent of it's position within a scale...

Please enlighten me !

In addition - example 2:

if we want to use CTM from a G major triad in key of B Nat Minor, which has G in 6th position ergo the triad contains notes in positions 6,1,3 would we then only target keys that contain G,B,D at position 6,1 or 3 ?

Thanks !

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  • 1
    Great question. Welcome to Music.SE! – Richard Nov 4 '16 at 3:54
  • Not seen this concept, but it appears that any chord (triads for now) share one common note. With Gmaj that's down to 3 choices:G-B-D Using G note, that gives Gmaj, Gmin, Cmaj, Cmin, Eb(D#),Em.. Using B, it's B, Bm, E,Em,G, Abm(G#m). Using D, it's D,Dm, Bb,Bm,G,Gm. Yes, more than 12 - 13! There's probably a maths formula which could explain that.. Can't be avoided, it seems! – Tim Nov 4 '16 at 8:28
  • I'm not sure this is the correct terminology. Does the OP mean Pivot chord when he says Common Tone Modulation? – Neil Meyer Nov 4 '16 at 11:45
  • @NeilMeyer - common tone mod is about modulating from one key to another, using consecutive chords that both contain a common note/tone. Common chord mod is using pivot chords, which are chords common to both keys - as in going from key C to key F, the common chords to both are Dm and Am (as well as the obvious C and F). Incidentally, OP is using only maj and min triads. – Tim Nov 4 '16 at 12:44
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If you write out all the possibilities and count them, you do get 12.

Starting from G major, the common tone can be G, B, or D

There are 3 major and 3 minor keys containing the tone G:

(G maj) Eb maj C maj

G min E min C min

so there are 5 keys you can modulate to with common tone G, starting from G maj.

For common tone B, the keys are

B maj (G maj) E maj

B min G# min E min

which gives 4 new keys, since E min has been counted already.

For common tone D,

D maj Bb maj (G maj)

D min B min G min

which gives 3 more keys, since G min and B min have already been counted.

So in total there are 5 + 4 + 3 = 12 keys you can modulate to.

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  • Hi Alephzero, I get 14 possible chords I can modulate to for G alone (I've included note position for each match): G Major (Ionian) 1st, G Natural Minor (Aeolian) 1st, Eb Major (Ionian) 3rd, E Natural Minor (Aeolian) 3rd, C Natural Minor (Aeolian) 5th, C Major (Ionian) 5th, A Natural Minor (Aeolian) 7th, Bb Major (Ionian) 6th, B Natural Minor (Aeolian) 6th, D Major (Ionian) 4th, D Natural Minor (Aeolian) 4th, F Major (Ionian) 2nd, F Natural Minor (Aeolian) 2nd, Ab Major (Ionian) 7th. Your answer seems to be implying an additional logic of matching the positions of 1,3 or 5. Why is that ? – m_j Nov 4 '16 at 7:18
  • @mike - the 1,3 and 5 are the notes making up a basic maj/min triad. The concept is to move to another triad, retaining just one existing note, which then has two others making a new triad. Your Fm 2nd note, F maj 2nd note, and Ab 7th note therefore won't qualify. Abm does as it contains a B (aka Cb). – Tim Nov 4 '16 at 12:04
  • @Tim, I only know triad qualities like major/minor/diminished/augmented/perfect/etc - not "basic". but the additional logic that results in 12 results is actually requiring a target triad that contains degrees of either 1,3 or 5... it's EITHER position 1, 3 or 5 for ANY of the notes from the original triad chord... which, makes no sense to me. so u could take B (original position was 3) at position 5 in a new chord in key of E major (B,D#,F#) with position 5, 7, 2... requiring ANY (not necessarily the same) degree from the old chord makes very little harmonic sense to me... What am I missing ? – m_j Nov 4 '16 at 12:30
  • @mike - this seems to only include maj and min triads, used to modulate from one key to another, using a note in a chord from the old key which is cotained also in the chord from the new key. All I'm saying is that using Gmaj (GBD) as the old triad, Fm and F maj wont wior in this way, as neither has a G,B or D. All the others you quote do, thus they're part of the scheme.Incidentally, Ionian and Aeolian are modes rather than maj or min chords, and 'perfect' triads don't exist. – Tim Nov 4 '16 at 12:39
  • sorry, typo mistake, in my first reply above I meant 14 possible KEYS I can modulate to that contain the note G. The position I posted for each key is the position of G within that key. Key of F major and F minor both contain the note of G. I don't think that the 2nd conditional logic is that target chord has to be a major/minor triad as G is 7th degree in key of A nat minor and the root of a major triad but not listed amongst the "12 correct results" - but that triad contains positions 7,2,4 which does not match any position of 1,3 or 5 from the old triad - which seems to be the requirement. – m_j Nov 4 '16 at 13:23
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Look at what chords share a tone with the G chord. Duplicates are flagged with a * (including the stay in the same key duplicate).

G as root: G*, g G as third: Eb, e G as fifth: C, c Five chords here. B as root: B, b B as third: G*, G# B as fifth: E, e* Four new chords. D as root: D, d D as third: Bb, b* D as fifth: G*, g* Three new chords. By enumeration, there are distinct chords sharing the notes G,B,D. A movement from a G chord to any of these retains one or more of the notes of the G chord.

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  • Hi ttm, could u please explain WHY u are only considering note positions 1,3 or 5 for finding target keys that contain the notes G, B or D ? – m_j Nov 5 '16 at 4:06
  • The definition of common tone modulation is to move from one chord to another while holding at least one note constant. So from G, we only look at chords containing G, B, or D. – ttw Nov 5 '16 at 4:22
  • ttw..... the part with the sustained note is clear. but - in addition to that - your results ONLY consider other keys where G,B,D are in scale degree / position 1, 3 or 5. WHY IS THAT ? (see OP) – m_j Nov 5 '16 at 8:04
  • Because 1,3,5 make a chord. The listed chords are the only triads with a common tone with the first chord. It's just counting how many ways one can link up a triad using one of the notes of the starting chord. – ttw Nov 5 '16 at 12:55
  • if u look at my updated OP, u'll see there are 21 unique keys that contain the note of G, B or D - all possible targets. U say 1,3,5 make a chord. Yeah sure, but 2,4,6 also makes "a chord". U have not yet explained why I can only modulate to another chord that has the same note positions/degrees within the new scale ? (that is the missing part !) For example, look at my revised OP: key of A Major contains B in 2nd degree and D in 4th degree - we can sustain either B or D... so why is key of A major not listed in ur results ? – m_j Nov 5 '16 at 13:24
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The Lynda.com tutorial seems to be restricting itself to diatonic pivot notes. However, much music makes much use of notes outside the home scale. A classic (but not "classical") example are most of the songs in "West Side Story". A hallmark of the show is frequent use of the #4 in a major key. That note could be used as a pivot. What's happening here, for instance... ?enter image description here

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CTM is a music theory concept most likely derived from the analysis of more traditional western classical music where chords are mainly triads made from 1 3 and 5, except for the dominant 7. Modulation from one key to another using CTM usually involves going from one tonic key to another tonic chord in a new key, so you would only consider the tonic triad in the first key compared to the tonic triad in the new key. This concept has probably held over to using 1 3 and 5 in order to clearly establish the new key. Adding extended chord tones may weaken the establishment of the new key. However there is no reason not to experiment with some of the options you mention above.

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