Musical Architectures

• Makams and Cents
• Middle Eastern and Mediterranean Music Rhythms
• Nine-Eight Rhythms

INTERVALS are the FOUNDATION

Interval sizes in Western music increment by half-steps (or SEMI-TONES) and are frequently demonstrated on a piano keyboard.

Looking at the diagram at the right: every movement from one key to the very next key is a half step (1/2). If you start on a black key, any movement, left (down) or right (up) to the next key is to a white key. If you start on a white key, you will usually end up on a black key.

Much of our emotional response to music is tied to the intervals between notes. Play both ends of an interval at once and you hear a chord. Play the ends in sequence and you have part of a tune. Both invoke feeling in many people. This association of feelings with intervals is built over a lifetime, which is why Western people listening to Middle Eastern or Eastern music, which includes intervals that we are not familiar with, frequently describe what they hear as wailing cats.

"Two notes are described as being enharmonic when they refer to the same pitch: C# and Db are enharmonic, as are F# and Gb. At least they are these days. They weren't before the time of Bach." —Simon Bennett.

"Well, for instance, a perfect third is about 15 cents flat of equal temperament. If you were to play a third on a piano, it sounds aweful. A third is about 15 cents flat, a fourth is close enough, a fifth is close enough, a sixth is about 11 cents flat again – but you can do all that [play perfect intervals, rather than equal temperament] on a fiddle, and you can't do it on a fixed pitch instrument." —Caoimhin O Raghaillagh

Scales are built from Intervals

DIATONIC SCALEs are seven-note scales (not counting the repeating note at the top). Major scales, Minor scales, and Modes are diatonic. The seven pitches of any diatonic scale can be obtained using a chain of six perfect fifths. diatonic scale can be also described as two tetrachords (two perfect fiourths containing 5 semitones each) separated by a whole tone.

MAJOR SCALES

Or, in shorthand; W - W - H - W - W - W - H. If you start on any piano key, white OR black, and use these intervals you will be playing a major scale.

MINOR SCALES

Natural minor keys are constructed with the same intervals as a series of eight white keys on a piano, starting at A. Or, in shorthand; W - H - W - W - H - W - W. If you start on any piano key, white OR black, and use these intervals you will be playing a natural minor scale.

*The Harmonic minor is also frequently used. This is constructed by enlarging the interval between the 6th and seventh note by half a step and diminishing the interval between the seventh and eighth tone by a half step.

In short: Natural minor intervals are W - H - W - W - H - W - W.
Harmonic minor intervals: W - H - W - W - H - WH- H.

MUSICAL MODES

Any starting note can be chosen. Every key signature can generate seven possible modes. Using the model of the white keys of a piano assists with visualization of the intervals, but some of the notes within many modes are going to be sharps or flats.

*Ionian = major scale, **Aeolian = minor scale. These modes survived the historical transition from modes to scales in art music.

The charts illustrate why it can be difficult for musicians who are used to thinking in terms of major keys to jam with a folk musician whose repertoire centers around modal music. A key signature of F# and C# means D major to a Western musician, with D the tone that serves as the tonic the tune will resolve to. But in the Irish and Appalachian music world, a key signature of F# and C# often means a mode of A Mixolydian, with the tune resolving to A.

GAPPED SCALES

Western art music is based on a 7-note octave with the notes spaced at whole and half steps in specfic patterns. Pentatonic scales (5-note octaves) include two one-and-a-half-step intervals and hexatonic (6-note octaves) scales have one such interval. Pentatonic scales form the backbone for traditional music all over the world.

The most common pentatonic construction in Western music is built on a circle of fifths. The 4th and the 7th scale degrees are skipped. This would correspond to Mode 3 in Cecil Sharp's Pentatonic Modes chart. Mr Sharp identified FIVE pentatonic scale patterns in use in Appalachian songs at the turn of the 20th century.

Using the piano keyboard as a visual reference: Major pentatonic scales have the same intervals as the five black keys in an octave on the piano, starting on the F#. If you can transpose the tune so that it can be played on the black keys, then the scale is Pentatonic.

Another Pentatonic construction: Use the same intervals as those that result when omitting the third and seventh degrees of the C major scale. This construction is the one documented in Sharpe's book on Appalachian music.

Minor pentatonic, skipping the 2nd and 6th scale tone of the natural minor.

REFERENCES

Simon Bennett, Ravenspiral Gide to Music Theory.

David Brody, Fiddler Fakebook, Oak Publications, 1992.

Campbell and Sharp, English Folks Songs from the Southern Appalachians, Archive.org.

Scales, Harmonies and Modes, EducationScotland.gov.uk

Beth Isbell, A Simple Way to Understand Modes for Guitar, web, GuitarNoise.com

A Beginner Guide to Modal Harmony, web, StandingStones.com

Brendan Taaffe, Caomimhin O Raghallaigh: Irish Music at a Local Level, Web, Fiddle.com.

Diatonic scale, Wikipedia.

Pentatonic scale, Wikipedia.

Pitch Constellations are an efficient way to diagram scale, chord and mode degrees using a diagram similiar to a 12-hour clock face. Wikipedia.