To our modern minds, a scale is a succession of notes ascending in degree-wise progression.  The very word 'scale', taken from the Latin "scala", meaning, 'ladder', gives the impression of an ascending group of notes.  In all modern music we keep this impression of rising notes, we figure an interval from the lowest to the highest note; the formation of our chords is a succession of notes built one on top of the other.

However, the ancient Greeks, from whom we evolved our music, always considered their modes as descending.

When St. Ambrose borrowed some Greek airs in 384 A.D. and introduced them in his church in Milan, it is logical to assume that he little understood the music, and certainly nothing of their theory or formation.

THE MINORS

After their introduction into the Christian church, the scales and modes were considered as ascending and called Church Modes.  This adoption somewhat explains the peculiarities of some of our modern scales; the Harmonic Minor; the change of the Melodic Minor in ascending and descending.

There were nine Greek Modes, each contained within an octave (commencing, on A above Middle C -- called the Nete- to A in first bass space - called the Proslambanomenos).

Amongst the principle Greek modes and scales were the Aeolian, Mixo-Lydian, Lydian, Hypo-Lydian , Hyper-Phrygian and Hyper-Lydian (these were all figured downwards).

After the adoption of these modes into the Christian Church, the names were retained but the mode was considered as ascending, hence all scales were now figured upwards.

AUTHENTIC & PLAGAL

They were divided into two modes, the "Authentic" and the "Plagal".  The Authentic was the modern dominant harmonization and the Plagal was the sub-dominant.  In harmony, the Authentic cadence is the progression from the dominant to the Tonic, the Plagal is the Sub-Dominant to the Tonic.

The ancient Persian scale and other Eastern scale systems divided the scale into seventeen equal parts.  It was equivalent to the modern quarter-tone scale which divides each whole tone into four equal parts.

The ancient Greeks also had this quarter-tone scale, but like their other modes it was always considered as descending.

Although the modern tempered scale gives notes like C# and Db the same pitch, the ancient Greek system like the modern quarter-tone scale (called also the enharmonic scale) gives these notes their individual pitch.  They are as distinct from each other as C# is from D#

PENTATONIC SCALE

The pentatonic was a five-tone scale, so named from the Greek word "Pentatone" meaning five-tone.  It is like the modern Major Scale, omitting the fourth and seventh steps.  The mode is widely used in music for modern bagpipes and the scale is sometimes called the "Scotch" scale.

The Arabic scale multiplies its oriental flavor by two Harmonic intervals, one from the 2nd to the 3rd degree, one from the 6th to the 7th.

The Chinese scale was composed of five whole tones, written on a vertical staff.  The Chinese were probably the earliest inventors of the scale and notation.  Their system goes back to the time of Yao 2200 BC!