Reference work
Soon the English version:
Nabih GEDEON
How to find the right pitch straight away
G System:
Positions and expressivity
Singers, choristers, violinists, cellists and players of other instruments
Music teachers and professors, choir masters, orchestra conductors,…
You are bound to be concerned by this book.
You cannot imagine how much better the music you make will be.
A theory must always be applicable, if not, it can only be a bad theory that cannot help good practice. As far as natural intervals are concerned, all the theories previous to the G System fell short of the mark.
Contrary to all the systems of scales that have ever been suggested from ancient times up to now (by scholars such as Pythagoras, Al-Farabi, Zarlino, Werkmeister and his well-tempered scale, Holder, Daniélou…) and which are all totally inapplicable*, at least in classical Western music, at last we have the RIGHT THEORY of intervals, which is applied and is clearly applicable, and which follows good practice perfectly, that of good musicians of all time.
* The Pythagorean scale haphazardly mixed in with the natural scale (as described by the G System), can be used in Oriental music, in spite of the Pythagorean rigid semitone, when one is talking about major or minor modes. Orientals are used to large minor seconds (“three quarters” of a tone), which makes us think that the Pythagorean scale may have been used by the ancient Greeks and in Western Europe before the classical period, as well as the natural scale, of course.
Besides, the Pythagorean scale can be taken as a separate mode, “the Pythagorean mode”, in which all notes are in a middle position, and sought after for its own sake, in spite of the fact that the Pythagorean scale is not as easy to produce as the natural one. An example of the use of the rigid semitone which is perfectly acceptable is Carmina Burana, by Carl Orff, among other applications: in this case, one may consider that the notes of this scale sound “in tune”. On the other hand, certain notes of Zarlino’s scale sound quite out of tune, although all musicologists consider this scale to be the most consonant!
(Page 10) Yet, tell me, Maria Callas, what system of intervals were you using when you sang your sublime arias? Was it the Pythagorean system? Of course not! Your warm, melodious minor second is much more compact than the “limma” (the remainder = 256/243) produced by the sort of wild chase between fifths and octaves (3 octaves and 5 fifths ascending; 5 fifths and 3 octaves descending). Was it the Zarlinian system, so dear to the hearts of musicologists specialized in the primary harmonics? Not the least in the world! The minor second (16/15) is too big, even bigger than the Pythagoras “limma”! Was it the equal temperament of Werckmeister? How could anyone maintain that when everyone knows that a C# sung so marvelously by you is not identical to a Db? Well, dear Maria Callas, let me tell you: apart from a few “gaps” or differences which, it is said, are all part of the charm of any performer’s artistry, you were singing intervals according to the system presented in this study (G System), without realizing it, since your practice is without doubt, good practice, that of fine performers of all time, and that this system is above all, a logical description, with corroborating proof, of good practice.
* * * * *
Two major DISCOVERIES, with enormous consequences:
1) the exact representation of the NATURAL SEMITONE (with a frequency ratio of 22/21) from which all the others follow;
2) The POSITIONS (low 1, medium 2, high 3) by which any note can be situated, according to the key,
and The EXPRESSIVITY linked to each position.
Ses below: “Rules concerning positions“
THE POSITIONS and their EXPRESSIVITY – let us not be afraid of saying
how FANTASTIC a discovery no-one had ever thought of before!
* * * * *
The structure of the work
• It is presented as methodical, reasoned, progressive research into just intonation. The guiding principle of this quest for the ‘Holy Grail’ is pure logic. After a brief over-view of several systems of intervals representing past errors, including my own, logic brings us from basic notions of frequency ratios to the changes in position and coding, via the discovery of the natural semitone, and the building blocks of scales and score marking.
• Annex II presents the G System Player, a user-friendly tool enabling anyone to have a sound illustration and a computer model of the solid foundations of System G and just intonation.
• Annex III describes the logical foundations for the building of the “Gédéon” synthesizer of just intonation, in order to play music based on the G System in real time.
• Annexes IV and V are dedicated to the Arabic and Byzantine tones : the logical structure of scales, specific intervals, coding and score marking.
* * * * *
The natural intervals of the G System
with the approximative commas of each interval, for an OCTAVE OF 600 COMMAS exactly,
in order to compare more easily the width of the intervals among themselves:
CANONICAL C MAJOR:
C | D | E | F(1) | G | A | B(3) | C | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
9/8 | 9/8 | 22/21 | 112/99 | 9/8 | 112/99 | 22/21 | = 2 | |||||||
G commas (approx.) | 102 | 102 | 40 | 107 | 102 | 107 | 40 | = 600 |
CANONICAL D MINOR:
D | E | F(1) | G | A | Bb(1) | C | D | |||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
9/8 | 22/21 | 112/99 | 9/8 | 22/21 | 112/99 | 9/8 | = 2 | |||||||
(G commas approx.) | 102 | 40 | 107 | 102 | 40 | 107 | 102 | = 600 |
In the section “Western music playlist”:
Comparison between 4 major and minor scales.
The emphasis is on the semitones. It will be easy to see that the semitone of the G System
is pleasant to our ear and corresponds to natural practice,
unlike that of the other three scales: Pythagorean, Zarlino’s and tempered.
Difference between two close positions: 896/891 (5 commas)
This is the difference between:
– the Pythagorean semitone (256/243) and the G system’s minimal semitone (22/21)
– the Pythagorean tone (9/8) and the maximal tone of the G system (112/99)
– the Pythagorean minor third (32/27) and the minimal third of the G system (33/28)
– the Pythagorean major third (81/64) and the maximal third of the G system (14/11)
– the Pythagorean perfect fourth (4/3) and the weak fourth that makes up the first tetrachord of the major mode in the G system (297/224)
– and so on.
Examples :
The difference between the subdominant F1 of C major (lower position) and
the subdominant F of C minor (middle position): 896/891 (5 commas)
The difference between the mediant B of G major (middle position) and
the leading note B3 of C major or minor (upper position): 896/891 (5 commas)
The difference between the subtonic Bb1 of D minor (lower position) and
the tonic Bb of B major or minor (middle position): 896/891 (5 commas)
Rules concerning positions in the major and minor
CANONICAL scales
••• Major tonality : the notes of the scale are in a MEDIUM position (2)* also called Pythagorian (neutral expressivity, serenity), except the sub-dominant, which is in a LOW position (1 – sadness, languor, moderately), and the leading note, which is in a HIGH position (3 – intensity, ardor, moderately).
••• Minor tonality : the notes of the scale are in a MEDIUM position (2)* also called Pythagorian (neutral expressivity, serenity), except the mediant and the submediant, which are in a LOW position (1 – sadness, languor, moderately), and the leading note (as the case may be), which is in a HIGH position (3 – intensity, ardor, moderately).
* The absence of the number next to the note is indicative of the middle position (2).
For example, for canonical C major, the notes are written as follows:
… Gg – Ag – Bg3 – C – D – E – F1 -G – A – B3 – Ch – Dh – Eh – Fh1 – Gh…
>>> g = note belonging to the lower octave than the C note of the octave containing A 440 Hz.
>>> h = note belonging to the octave higher than the B note of the octave containing A 440 Hz.
>>> gg = 2 times lower; hh = 2 times higher; hhh = 3 times higher..
For example, for canonical G minor, the notes are written as follows:
… D – Eb1 – F – Fd3 – G – A – Bb1 – Ch – Dh – Ehb1 – Fh – Fhd3 – Gh – Ah – Bhb1 – Chh – Dhh…
>>> Fd3 = F sharp in high position.
>>> Bhb1 = B flat (high octave) in low position.
Exceptions
In major tonalities:
• In the same chord with the mediant (middle position), the seventh (leading note) abandons its position of leading note (high position) and takes the middle position (at a Pythagorean semitone 256/243 from the tonic) to be at a perfect fifth / perfect fourth from the mediant.
• In the same chord with the tonic (middle position), the subdominant abandons its low position and takes the middle position to be at a perfect fifth / perfect fourth from the tonic.
In minor tonalities:
• In the same chord with the mediant (low position), the subtonic abandons its middle position and takes the low position (at a maximal tone 112/99 from the tonic) to be at a perfect fifth / perfect fourth from the mediant.
• In the same chord with this same subtonic in low position, the subdominant abandons its middle position and takes itself a low position (at a maximal tone 112/99 from the dominant) to be at a perfect fifth / perfect fourth from the subtonic.
Major and Minor VARIANT scales
(for certain modulations)
••• Major tonality: all notes of the scale are in MIDDLE position (2)*, known as Pythagorean position (neutral expression, serenity), except for the mediant and the leading note, which are in HIGH position (3 – intensity, ardor, moderately).
••• Minor tonality: all notes of the scale are in MIDDLE position (2)*, known as Pythagorean position (neutral expression, serenity), except for the supertonic, which is in HIGH position (3 – intensity, ardor, moderately), the submediant, which is in LOW position (1 – sadness, languor, moderately), and the leading note (if applicable), which is in HIGH position (3 – intensity, ardor, moderately).
* The absence of the number next to the note is indicative of the middle position (2).
MARKING OF SCORES
With appropriate markings on the sheet music and a little practice, finding the RIGHT PITCH immediately becomes child’s play.
The simplest marking method involves surrounding notes in the LOW position (1 – sadness, languor, moderately) with a small CIRCLE and notes in the HIGH position (3 – intensity, ardor, moderately) with a small DIAMOND, with no marking for notes in the MIDDLE position (2 – neutral expressivity, serenity).
- – For Western scores, please refer to the section titled:
- “Marking of Western scores“.
- – For Oriental scores, please refer to the section titled:
- “Marking of Oriental scores“.
Two other (less convenient) ways to mark Western scores are:
- – By color: red note = low position; green note = high position.
- – By shape: square note = low position; diamond note = high position.
* * * * *
No longer settling for the “quasi-just”! Finally mastering ACCURACY!
Moreover, knowing with certainty that you have mastered accuracy
provides an additional satisfaction.
Without a doubt, the G System is bound to revolutionize musical INTERPRETATION
– both vocal and instrumental. From beginners to seasoned professionals and even “celebrities”
(the best sometimes miss accuracy!), everyone
will find something to improve upon.