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Encyclopedia of Microtonal Music Theory

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Lesser Perfect System (LPS)

[John Chalmers, Divisions of the Tetrachord]

The three tetrachords Hypaton, Meson, and Synemmenon, plus Proslambanomenos, formed the Conjunct or Lesser Perfect (or Complete) System. See "Systema".

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[Joe Monzo]

The LPS, together with the Greater Perfect System (GPS), made up the "complete" Perfect Immutable System (PIS).

Shown below is my very general schematic illustrating the Greek names for the LPS in the diatonic genus, in descending order, along with approximate letter-names to help the Western reader to comprehend.

              -  D  nete synemmenon
 tetrachord  |   C  paranete synemmenon
 synemmenon  |
             |   Bb  trite synemmenon
              -  A  mese
  tetrachord |   G  lichanos meson
    meson    |
             |   F  parhypate meson
              -  E  hypate meson
  tetrachord |   D  lichanos hypaton
   hypaton   |
             |   C  parhypate hypaton
             |   B  hypate hypaton
                 A  Proslambanomenos

Note that the intervallic structure of all tetrachords is identical. Also note that the synemmenon tetrachord contains a note which we call "Bb", but that the hypaton tetrachord contains a regular "B".

The tuning of the diatonic genus was almost always given by theorists as Pythagorean, i.e., 3-limit, as shown in the following lattice-diagram:

Bb -- F --- C --- G --- D --- A --- E

-5   -4    -3    -2    -1     0     1

            exponent of 3

Note that the two inner notes in each tetrachord could be retuned to other pitches in the chromatic and enharmonic genera, and even in different shades of the diatonic genus.

After the use of the other genera ceased, sometime during the "dark ages" -- i.e., between the German invasions of the Roman Empire (400s AD) and the emergence of the oldest surviving Frankish music-theory treatises (c. 750 AD) -- this conception of the Pythagorean diatonic scale as the only "proper" tuning lasted at least until the writings of Marchetto of Padua (1318).

The synemmenon tetrachord was always assumed to be a normal part of the gamut of musical pitch resources during this time, and when theorists began adapting the alphabet to the nomenclature of pitches, notating the two different forms of "B" (what we would call "B" and "Bb") became an important desiderata, and the different shapes used for the letter "b" eventually led to the formation of our three standard accidental symbols: the flat (b), sharp (#), and natural. (see "mutation" for more on this.)

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