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In major and minor keys, the perfect cadence is V to I
Will this structure remain the same in a different mode?
I.e. E Phrygian Mode in the key of C (E F G A B C D), the tonic chord is the iii of the key of C major. So, the scale would be iii IV V vi viio I ii iii (expressed relative to C major). So would viio to iii be a perfect cadence?
A couple comments may help.
A perfect cadence is distinguished from an imperfect cadence by its dominant->tonic motion in the melody, not necessarily in the harmony.
When describing the harmonic properties of the mode, it's simpler to consider the example to be in the key of the mode itself, not the relative ionian scale. So E-phrygian is harmonized i ♭II ♭III iv vø ♭VI ♭vii. So, you really can't form a perfect cadence in E-phrygian because there's no D♯ to put in the melody. vø->i might be the closest you can get without altering the scale to create a secondary dominant. Diminished->tonic, even a minor tonic, gives a strong resolution. Or ♭II->i is quite dramatic, too.
Please also see Maika-san's answer which is much more comprehensive.
Keys use tonal approaches by using functional harmony. The two main types of final cadences in tonal music are known as authentic and plagal.
Authentic cadence in major key: V-I (Ex. G-C)
Authentic cadence in minor key: V-i (Ex. E-Am) (or sometimes v-i (Ex. Em-Am) but very rare.)
Plagal cadence in major key: IV-I (Ex. F-C)
Plagal cadence in minor key: iv-i (Ex. Dm-Am)
Modes use modal approaches by character emphasis. In fact, if you want to give a more modal approach, no V-I, IV-I, V-i, iv-i, or v-i is appropriate here.
So the answer is: a big NO.
If you want to write a modal cadence, follow the requirements below:
No tritone in any chord. (It sounds more tonal.)
No leading tone should be used. (It also sounds more tonal.)
Keep the character of the mode. (Use the characteristic tone in the first chord of the cadence.)
No V-I, IV-I, V-i, iv-i, or v-i. (Mentioned above.)
The notes (scale degrees) of each of the seven modes are: (Bold: characteristic tone)
Ionian: P1-M2-M3-P4-P5-M6-M7-P8
Dorian: P1-M2-m3-P4-P5-M6-m7-P8
Phrygian: P1-m2-m3-P4-P5-m6-m7-P8
Lydian: P1-M2-M3-A4-P5-M6-M7-P8
Mixolydian: P1-M2-M3-P4-P5-M6-m7-P8
Aeolian: P1-M2-m3-P4-P5-m6-m7-P8
Locrian: P1-m2-m3-P4-d5-m6-m7-P8
The diatonic chords are: (Bold: characteristic chords, containing the characteristic tone)
Ionian: I ii iii IV V vi viio I
Dorian: i ii III IV v vio VII i
Phrygian: i II III iv vo VI vii i
Lydian: I II iii ivo V vi vii I
Mixolydian: I ii iiio IV v vi VII I
Aeolian: i iio III iv v VI VII i
Locrian: io II iii iv V VI vii io
Notice how all seven modes contain three characteristic chords - one major, one minor, and one diminished. However, that doesn't mean every chord is useful; we should avoid using the following:
Ionian: IV, viio
Dorian: IV, vio
Phrygian: vo
Lydian: ivo, vii
Mixolydian: iiio, v
Aeolian: iio, iv
Locrian: io (Truncate this chord to just root and third.), V
Imagine one writes V-I or IV-I in Ionian. Is this viewed as modal? No. Modal cadences would meet the requirements that I've listed above. They are not to set up a strong resolution to the tonic chord like how tonal cadences would, but to show the character of the mode.
So ii6(5)-I in Ionian (Ex. Dm(7)/F-C) would be viewed as a more modal cadence.
In Dorian, you would use ii6(5)-i. (Ex. Em(7)/G-Dm)
In Phrygian, you would use II (or vii6) -i. (Ex. F (or Dm/F) -Em)
In Lydian, you would use II6-I. (Ex. G/B-F)
In Mixolydian, you would use VII-I. (Ex. F-G)
In Aeolian, you would use VI-i. (Ex. F-Am)
In Locrian, you would use iii6-i(no5). (Ex. Dm/F-Bm(no5))
Notice how all modes use their characteristic chords as the first chord of their cadences and the tonic triads as the second. Also, realize how they have their characteristic tones as the bass of the first chords, except for Dorian, which rather has it on either the soprano or the inner voice.
If you want to read further, see Cadences for Modes.
Do different modes have the same cadence structure?
No
In major and minor keys, the perfect cadence is V to I
Correct. For minor keys some write the Roman numerals V i with lower case for the minor tonic. Keep in mind that the dominant triad must be major for a major/minor key perfect cadence.
Will this structure remain the same in a different mode?
Yes and no. It depends on the harmonic style and whether the cadence is kept purely diatonic or is chromatically altered.
As you rotate the diatonic triads through the various modes the triad build on the dominant will change through the three different chord qualities: major, minor, diminished. Only those modes with a major dominant will have the perfect cadence available as a diatonic option: Ionian and Lydian.
However, in Medieval modal style musica ficta is used to add accidentals to the ^7 scale degree in the other modes to create a proper cadence, a clausula vera. A clausula vera is not exactly the same as a perfect cadence, because it doesn't have the descending fifth in the bass, but it is essentially the same major dominant to tonic harmony.
In modal folk music the bVII chord is often used as a kind of substitute dominant in cadences like bVII i. Obviously that isn't a perfect cadence, there isn't a V chord. I think the common use of the bVII i cadence is harmonizing a phrase ending ^2 ^1, from that melodic perspective it is serving a similar purpose as the V i perfect cadence, but with a substitute chord.
E Phrygian Mode in the key of C (E F G A B C D) ...the scale would be iii IV V vi viio I ii iii (expressed relative to C major).
You should use the Roman numerals to start on the tonic so the E minor chord is i and the full list of chords is i bII III iv vo VI vii, the dominant triad is diminished and the seventh degree triad is minor.
So would viio to iii be a perfect cadence?
No. Let's re-label that to vo i. It's not a perfect cadence, because the dominant isn't major.
The clausula vera for Phrygian would be vii6 i.
The folk cadence (for lack of a better term) would be II i or to make the Phrygian quality clear use a flat sign bII i.
Some answered questions posted after this one cover many of these point separately:
Perfect cadences are all about functional harmony. Harmony with dominant seventh chords that include nice sharp leading notes itching to resolve to the tonic.
Modes need a different language and a different approach.
With respect to your second question, I would say in this case yes, it would be a perfect cadence. B --> E is V --> I (key of Emin in this example). This is the same as representing B as the viii(dim) and E as the iii in the key of Cmaj.
