musical modes.docx

8/13/2019 Musical Modes.docx

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Musical Modes

By Crispin Sexi, January 2003

As musicians we learn about today's major and minor keys that are fundamental tothe structure of modern western music. These two keys and the tuning system for

the notes they use were settled on during the 17th century, but there was a longhistory behind them. Knowing more about this history helps us better understand

medieval and renaissance music, and some of the curious sounds that come of it.

Greek Origins of Tones

Legend has it that Pythagoras, whilst out walking one day, heard the sounds of

blacksmiths at work and noted the harmonious sounds of the hammers ringing out.So in the interests of science he returned later at night and pinched the hammers.

He took them home and weighed them and found them to be 12, 9, 8 and 6 cubitsrespectively. He noted that when the 12 and 6 cubit hammers were struck, the

sound blended nicely, and the same for the 12 and 9 and the 12 and 8 hammers. Butthe sounds of the 9 and 8 hammers together clashed.

Liking numbers, and especially fractions, Pythagoras spent a noisy eveningworking out these ratios, and saw that by applying the 12:8 ratio and then doubling

the size of the result and repeating this process (now known as a "cycle of 5ths"),

you could get a set of tones that could be used to make pretty good music, and atthe same time drive all the neighbours crazy. He noted that the simpler the ratio

between two tones, the more consonant they sounded.

Interval Ratio Derivation Cents Upper Note

Unison 1:1 Unison 1:1 0.00 C

Minor Second 256:243 Octave - M7 90.22 Db

Major Second 9:8 (3:2)^2 203.91 D

Minor Third 32:27 Octave - M6 294.13 Eb

Major Third 81:64 (3:2)^4 407.82 E

Fourth 4:3 Octave - 5 498.04 F

Tritone 729:512 (3:2)^6 611.73 Gb

Fifth 3:2 (3:2)^1 701.96 G

Minor Sixth 128:81 Octave - M3 792.18 Ab

Major Sixth 27:16 (3:2)^3 905.87 A

Minor Seventh 16:9 Octave - M2 996.09 Bb

Major Seventh 243:128 (3:2)^5 1109.78 B

Octave 2:1 Octave 2:1 1200.00 C

Table 1: Cents are a modern measurement; there are 1200 cents per octave. Uppernotes are based on a lower note of C.


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Using these ratios as justification, Pythagoras proved that the unison, the octave,

the 5th and the 4th were pretty good and the tritone was ghastly.

A short cycle of 5ths (eg: F-C-D-G-A) can be used to produce the pentatonic scale(C-D-F-G-A), and this is the basis of folk music in many cultures. Continuing the

series will derive the 12 tone octave that our modern music is based on. The onlyreal problem with using these ratios is that as you continue the cycle of 5ths, thetones derived slowly move further away from being in tune with the original

starting note, and the interval between any two tones near either end of the cycle

sounds really bad. Thus the scale developed by the Greeks was good, but had itslimits. For one thing, you would need to re-cast your hammers if you wished to

transpose to a different key.

The Greeks went on to describe a set of scales; Dorian (starting on E), Phrygian

(D), Lydian (C) and Mixolydian (B), that could be used as the basis for music.They also transposed all of these scales into the octave E to e, just to create

headaches for instrument makers.

Early Gregorian Chant

Named after someone called Greg, Gregorian chants were simple melodies that thecongregation would sing liturgies to in church. Following Pythagorean tuning,

chant melodies generally had a pattern of an initial rise to a "tenor" note that wasmuch repeated, and ending off with falling to a "finale" note. After a few hundred

years of this, people such as Guido of Arezzo wrote up rules for the "modes" ofGregorian chant:

1. The vocal range of the chants tended to be up to an 8ve.2. The finale note was usually D, E, F or G.3. The melodies tended to rise to a tenor (or dominant) pitch above the finale

note.4.Notes were either all above the finale (authentic) or a mixture of above and

below (plagal).

Eight modes were specified to classify this behaviour. These were called 1, 2, 3, 4,5, 6, 7 & 8. See the main table for details.

Later Gregorian Chant

By about the year 1000 composers began to agree with Pythagoras that the tritone

sucked, so a few of the modes were modified so that B was never used as adominant. Taking further heed of the wisdom of the ancient Greeks, they renamedthe nodes with their Greek names, but of course got them mixed up.


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Fig 1: Example Dorian chant, showing tenor A and finale D (Jeppesen, p64).

Chants got longer and more complicated as the art form developed, and the modes

even had an impact on pop music of the time. This applies more to the trouveres,who were educated, than the troubadours, who weren't.

Early Polyphony

Polyphony started out in Europe with people humming along a 5th above the chant,

and soon developed into a bona-fide compositional technique, featuring unisons,

4ths, 5ths and 8ves, and maybe 2nds and 3rds for a bit of dissonance. The finalenote gained in importance, featuring more prominently throughout the piece, re-

enforcing the mode's foundation to make it satisfying to the listener's ear.

The problem is that, with all the 5ths and 4ths being sung at the same time, you'll

get tritones happening when ever B and F are sung together. People worked out thatif they calculated B by going down by a 5th from F, they wouldn't have a tritone.

So composers started marking B's as "b" for this new flatter B and "#" for the oldB. Since this new B was used so much, in or about the 12thC they invented the key

signature, such that the B-flat could be default throughout the piece of music. Ofcourse then you start getting a tritone between B-flat and E, but you can't win themall.

The Renaissance

By the 16thC flats and sharps were being used willy-nilly throughout music, as

were 3rds and 6ths, and suspended dissonances (the bare perfect 4th was nowrelegated to a dissonance).

The subtonic, when used as a leading tone to get to the tonic, was set to be a halfstep. In some modes this meant the leading tone was sharpened with an accidental.


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This gave a major 3rd to the dominant chord. People also decided that it sounded

much cooler to end on a major chord, so the third of the final chord was allowed tobe sharpened (if necessary) to do this. This gave three commonly altered notes; B

which was raised or lowered no matter what the mode, the leading tone, and the 3rdin the final chord.

Composers had also worked out that if the pitch of the piece was in a bad range,you could transpose up a 4th and add a B-flat key signature to make it easier to

sing. To some extent you could also up it again and add an E-flat (also marked by a

"b", to save confusion) to the key signature.

The change to polyphony had made it very difficult in to tell the difference between

plagal and authentic modes, so the plagal ones were, in general, given the flick.

And, noticing that you could continue the series, modes on A (Aeolian) and C

(Ionian) were added, though still no-one wanted to have a mode based on B,because of the tritone between the tonic and dominant.

Fig 1: The basic scales for each mode. The "finale" and "tenor" are marked.

Lastly, composers realised that if you transposed Ionian up a 4th it sounded just thesame as Lydian, except better because you avoided the B natural, so they also gaveLydian the flick too.

Solving Transposition


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5 Lydian F-f F c E

6 Hypolydian C-c F a E

7 Myxolydian G-g G d F

8 Hypomixolydian D-d G c FDominant changed

to avoid tritone.

16th C

1 Dorian D-d D a C#Up a 4th

to G

Plagal and

authentic merged

due to polyphony.

If there's a B-flat

key sig, it is

transposed.

Didn't want a mode

starting on b

because of tritone.

Lydian dropped in

favour of Ionian.

3 Phrygian E-e E a FUp a 4th

to a

7 Myxolydian G-g G d F#Up a 4th

to c

9 Aeolian a-aa a e G#Up a 4th

to d

11 Ionian c-cc c g bUp a 4th

to f

17th C

9 Minor a-aa a e G#To any

keyWell tempered

tuning allows full

transposability.11 Major c-cc c g bTo any

key

Some Examples

Some of these are fromThe Lochac Song Book,published by Dafydd of the Glens.You can also try theChoral Public Domain Library.

Doriano Alle Psalliteo 3 Country Dances(originally set in G)

Phrygiano Mille Regretzby Josquin Des Prezo Example 9from Agricola's Rudimenta Musices (1539):Noteworthyo Example 13from Agricola's Rudimenta Musices (1539):Noteworthyo I Allwaies Begby John Wilbye:Noteworthy

Lydian

o Fi Marisby Adam de la Halle Mixolydian

o Petit Vriens, a 15thC Itallian dance. Aeolian

o April Is In My Mistress Faceby Thomas Morley Ionian

o Change Then For Lo!by William Holborne

Bibliography
http://www.goldgryph.com/songbook/index.htmhttp://www.goldgryph.com/songbook/index.htmhttp://www.goldgryph.com/songbook/index.htmhttp://www.cpdl.org/http://www.cpdl.org/http://www.cpdl.org/http://aelflaed.homemail.com.au/doco/imgmod/phrygian9.nwchttp://aelflaed.homemail.com.au/doco/imgmod/phrygian9.nwchttp://aelflaed.homemail.com.au/doco/imgmod/phrygian9.nwchttp://aelflaed.homemail.com.au/doco/imgmod/phrygian13.nwchttp://aelflaed.homemail.com.au/doco/imgmod/phrygian13.nwchttp://aelflaed.homemail.com.au/doco/imgmod/phrygian13.nwchttp://aelflaed.homemail.com.au/doco/imgmod/16iallwaiesbeg.nwchttp://aelflaed.homemail.com.au/doco/imgmod/16iallwaiesbeg.nwchttp://aelflaed.homemail.com.au/doco/imgmod/16iallwaiesbeg.nwchttp://aelflaed.homemail.com.au/doco/imgmod/16iallwaiesbeg.nwchttp://aelflaed.homemail.com.au/doco/imgmod/phrygian13.nwchttp://aelflaed.homemail.com.au/doco/imgmod/phrygian9.nwchttp://www.cpdl.org/http://www.goldgryph.com/songbook/index.htm


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Hindemith, Paul, The Craft of Musical Composition, Book 1, Schott, Mainz, 1970.

Jeppesen, Knud, Counterpoint, The Polyphonic Vocal Style of the Sixteenth

Century, Dover Publications, New York, 1992.

Morley, Thomas,A Plaine and Easie Introduction to Practicall Music, Peter Short,London, 1597.

Seay, Albert,Music In The Medieval World, Prentice-Hall, Englewood Cliffs, New

Jersey, 1975.

Agricola, Martin (Tr. John Trowell) The Rudiments of Music (Rudimenta Musices),B. Rainbow (Ed), Boethius Press, Aberystwyth, Wales, 1991 (1539).

Copyright Jaysen Ollerenshaw, 2001. Free use for non-profit.

This article first appeared in issue 18 ofCockatrice.

Joan & Crispin's Homepage:http://aelflaed.homemail.com.au/
http://www.sca.org.au/cockatrice/http://www.sca.org.au/cockatrice/http://www.sca.org.au/cockatrice/http://aelflaed.homemail.com.au/index.htmlhttp://aelflaed.homemail.com.au/index.htmlhttp://aelflaed.homemail.com.au/index.htmlhttp://aelflaed.homemail.com.au/index.htmlhttp://www.sca.org.au/cockatrice/

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