Conjunct & Disjunct Tetrachord Combinations in Makam

In Uzeir Hajibeyov's (1885 - 1948) book, Principles of Azerbaijan Folk Music, Hajibeyov's sketches out the system of Azeri mugam, or Makam, drawing mostly from traditional sources. While he is debt to Pythagoras, Farabi, Al Kindi and others, the system he lays out is basically the one the 12th Century musican Safiaddin Urmevi derived from Greek ratios, and Urmavi ended up separated the octave into 17 parts. Later on in the Turkish system of makam there were added a few more divisions to make it a 24 note octave, but I think the additions weren't that overly notable, but I'll investigate that further down the line...

The following quote notates how the pentachord and the tetrachord is combined to create a full scale, the page online has midi examples, so go to that if you are really interested.

II. WAYS OF TETRACHORDS COMBINING

Scales of Azerbaijani modes are structured by combination of tetrachords represented in succession of 4 diatonic degrees.

Tetrachords within perfect quartes (Perfect 4ths) are called perfect ones.

Tetrachords within increased quartes (Augmented 4ths) are called increased.

Tetrachords within diminished quartes (Diminished 4ths) are called diminished.

Tetrachords can be combined in 4 ways:

1st way - chain combination, i.e. a combination where the last tone of the lower tetrachord coincides with the first tone of the upper tetrachord. An interval formed is a perfect prima. In the manuals on music theory such combinations are called conjoint ones.

2-nd way - mixed combination, i. e. a combination where the last tone of the lower and the first tone of the upper tetrachords form the interval of the major second which is called separate combination.

3-rd way - combination by intermediate semitone, i.e. a combination where an interval of the minor third is formed between the last tone of the lower and the first tone of the upper tetrachords.

4-th way - combination by intermediate tone, i. e. a combination where an interval of the major third is formed between the last tone of the lower and the first tone of the upper tetrachords.

Combined or joined tetrachords can be equal or unequal by their structure.
Combination of equal tetrachords forms consequent succession of degrees in the order of scales. When the 1-st way of combination is applied to perfect tetrachords, identical in structure, it forms a scale consisted of gradual succession of perfect quartes.

This way of "tagging" on the various tetrachords together reminds me of the Greek method of systematizing their varieties of four note and five note scales to create their families of scale genus. Itis common knowledge that the Makam is really the closest surviving cultural method that preserves the Pythagorean ratios of dividing the octave, but it also heir to the Greek idea of "Conjunct" & "Disjunct" combination. For example, this is from the philosopher Aristoxenous's "Harmonika Stoicheia":

Successive Tetrackords are either Conjunct or Disjunct.
WE shall employ the term conjunction when two succès
sive tetrachords, similar in figure, have a common note ; the
term disjunction, when two successive tetrachords similar in
figure are separated by the interval of a tone. That successive
tetrachords must be related in either of these ways, is evident
from our axioms. For a series, in which each note forms
a Fourth with the fourth note in order from it, will constitute
conjunct tetrachords; while disjunct tetrachords result, when
each note forms a Fifth with the fifth from it. Now as all
successions of notes must fulfil one or other of these conditions,
so all successive similar tetrachords must be either
conjunct or disjunct.
Difficulties have been raised by some of my hearers on
the question of succession. It has been asked, Firstly,
what is succession in general? Secondly, does it appear in
one form only, or in several? Thirdly, are conjunct and
disjunct tetrachords equally successive ? To these questions
the following answers have been given. In general, scales
are continuous, whose boundaries either are successive or
coincide. There are two forms of succession in scales ; in
the one, the upper boundary of the lower scale coincides
with the lower boundary of the upper scale ; in the other,
the lower boundary of the higher scale is in the line of
succession with the higher boundary of the lower scale. In
the first of these forms, the scales of the successive tetrachords
have a certain space in common, and are necessarily
similar in figure. In the other form, they are separated
from one another, and the species of the tetrachords may
be similar, only on condition, however, that the separating
interval is one tone. Thus we are led to conclude that two
similar tetrachords are successive, if they are either separated
by a tone, or if their boundaries coincide. Consequently
similar successive tetrachords are either conjunct or disjunct.
We also assert that two successive tetrachords either
60 must be separated by no tetrachord whatsoever, or must not
be separated by a tetrachord dissimilar to themselves.
Tetrachords similar in species cannot be separated by a
dissimilar tetrachord, and dissimilar but successive tetrachords
cannot be separated by any tetrachord whatsoever.
Hence we see that tetrachords similar in species can be
arranged in succession in the two forms above mentioned.
The interval contained by successive notes is simple.
For if the containing notes are successive, no note is
wanting; if none is wanting, none will intrude; if none
intrudes, none will divide the interval. But that which
excludes division excludes composition. For every composite
is composed of certain parts into which it is divisible.

Rast according to Hadjibeyov

clipped from PRINCIPLES OF AZERBAI JAN FOLK MUSIC
by Uzier Hadjibeyov

Peoples of the Middle East used the valuable "debris" of this collapsed "palace of music". They erected their own "temple of music", in a style peculiar to that people only, using own "mode construction" material. Naturally, the names of 12 classic mugams, as well as the mugams themselves, were subjected to great perturbations. Those once considered as independent mugams, turned into the sections of those mugams. And on the contrary, those that once were sections, turned into independent mugams. In this way, the names of one and the same mugams and their sections started to denote quite different notions at various peoples. The only mugam that could stand against the crushing influences of time and events was "Rast". Foundations of this mugam are so firm and logical that they fully deserve and justify the name and the meaning of "Rast". The word "rast" means "straight", "right", "true". Ancient musicologists called "Rast" mother of all mugams. The mugam "Rast" has retained up to now not only its name and the structure of its scale, but the pitch of its tonic, as well.

Amongst all the Middle Eastern peoples the mugam "Rast" has one structure, and one pitch of tonic. This tonic is sol of minor octave. The following comparison shows that the tone we call sol of minor octave, referred to the pitch of the "Rast" mode even in antiquity. So, Arabian - Iranian and European musicologists assert that according to the ancient Greeks, 7 tones invented by Pythagoras correspond to 7 celestial bodies.

Here is a list of the seven tones:

In Gгeek	In Arabic and Iranian
1. mi - Moon	1. Nava
2. fa - Mercury	2. Busalik
3. sol - Venus	3. Rast
4. la - Sun	4. Iraq
5. si - Mars	5. Ushshag
6. do - Jupiter	6. Zirafkand
7. re - Saturn	7. Rahavi

leap year

this is my new thing, using what is called "an adapted" guitar, ie; by placing 'extra' bridges onto the neck of the instrument one can play it like a zither or a koto. This also allows for a different set of pitches to be generated that aren't dependent upon the tempered nature of the frets. The drawback, or variously, the benefit, is that fewer pitches are actually available for use - only six notes in this case. But, who says a pentatonic scale is a drawback anyway?

My inspiration is obviously gamelon music, which is music of Indonesia. The rhythmic flow in their pieces has always been intoxicating for me. The tuning I've used is: A Bb (+20 cents sharp) D (+20 cent sharp) Eb F Bb

I have another piece awaiting in the wings, too - I think I am stirring up for larger scale things, perhaps I will try to incorporate other voices as well, inshallah.

Fire eating Iranian Sufi Women

Mevlam Nurdan Yaratmış

Sufis sing songs, here I trash the beautiful lyrics by the wali & beloved sufi poet Yunus Emre. The pictures on the wall behind me are of my Pirs, the 'saints' of our Sufi Order. Abdul Qadir Gilani, Ahmeder Rifai, Muhammad Ansari, his son Muhyiddin Anasari, Nuriddin Ozal & my murshid, Shaykh Taner Ansari. May Allah increase their light and bless their families.

Çalap nurdan yaratmış canını Muhmmed'in
Aleme rahmet saçmış adını Muhammed'in

Dostum demiş yaratmış hem onun kaydın yemiş
Ümmetten yana komuş yönünü Muhammed'in

Muhammed bir denizdir alemi tutup durur
Yetmiş bindir peygamber gölünde Muhammed'in

Dünya malın tutmamış hiç emanet artmamış
Terzi biçip dikmemiş donunu Muhammed'in

Tanrı arslanı Ali sağında Muhammed'in
Hasan ile Hüseyin solunda Muhammed'in

Yılda yetmiş bin hacı her biri niyet eder
Varır ziyaret eder nurunu Muhammed'in

Yunus Emre'm aşıkdır eksiklidir miskindir
Her kim yemez mahrumudur honını Muhammed'in

Some sufic numerical meditations...

Bismallahir Rahmanir Rahim

10 is a solid number. Not as solid as 1, but pretty solid. Each number has its charm. Been musing on the significances of 7, too. Ten seems to be a number of solidness and form.


1 = point
2 = line
3 = plane
4 = solid

See? Solidness.


Now, seven has appeared to me as something to be traversed, a ladder, levels to be gained, a cycle to witness, the curve of DNA... The seven heavens of the Quran, the seven layers of the nafs:

1. Nafs-i-Ammara, the Commanding Nafs
Behold! The commanding nafs encourages evil,
except when my Lord bestows mercy. (Qur'an 12:53)
2. Nafs-i-Lawwama: Blaming Nafs
But I swear by the accusing nafs that this Scripture is true. (Qur'an 75:2)
3. Nafs-i-Mulhama: Inspired Nafs
And a nafs and Him who gave order to it and inspired it
with a sense of what is wrong for it and what is right for it. (Qur'an 91:8)
4. Nafs-i-Mutmaina: Tranquil Nafs
To the righteous soul will be said, "O, you nafs in complete
peace and satisfaction!" (Qur'an 89:27)
5. Nafs-i-Radziyya: Satisfied Nafs
Return to your Lord, content (Qur'an 89:28)
6. Nafs-i-Mardziyya: Satisfying Nafs
for His being pleased with you! (Qur'an 89:28)
7. Nafs-i-Safiyya: Purified Nafs
This day have I perfected your religion for you,
completed My favor to you, and have chosen for
you as your religion Islam. (Qur'an 5:3)

Seven is also the number of a great many musical scales, ie; the heptatonic scale or more commonly known as a diatonic scale. Do Re Me Fa Sol La Ti. For Westerners, C D E F G A B.
In my studies in Ancient Greek musics, I found that the seemingly general way they strung their lyre was, in common western terms:

So La Ti Do Re Me Fa

The emphasis on Do is reflective of the Babylonian method of naming this their middle pitch as "The One Enki Made" or Ea, the Creator. Do, the mese note of the Greeks, is our home, our base pitch that we return to when making music. So, why is it in the middle and not at the beginning?

My studies in Tasawwuf, under my Shaykh, has taught me that murids, students in spiritual growth are brought to the fourth level of nafs, Nafs-i-Mutmaina or the Tranquil Nafs, and then after that it is considered "extra credit" so to speak to go onto the higher levels of attainment.

So La Ti DO

A gradation, a ladder to be led and then to the higher steps one must wait upon Allah's Will.

Here's my meditation, my dream:

In Sufism, Tasawwuf, the Science and School of attaining true knowledge of the Absolute begins with the four doors of Sharia, Tariqa, Marifa & Haqqiqa. Spiritual Law, Spiritual Path, Wisdom and Truth. Boom, there you are, you have learned what Allah wants from you, you know how to manifest it in your life here on Earth, you have some access to Why and you've begun to Taste What Is.

So La Ti DO


1 = point
2 = line
3 = plane
4 = solid

See? Solidness. You've become cooked and ready.


Now comes seven. What is Seven?

Certainty.

ilm al-yaqin (The Knowledge of Certainty) - You've read about it.
‘ayn al-yaqin (The Eye of Certainty) - You've seen it.
haqq al-yaqin (The Truth of Certainty) - Allah sends it directly to your heart.

The goal is to be in unlimited direct contact with one's Lord. It is, what we all seek. With the four doors of Sharia, Tariqa, Marifa & Haqqiqa. Spiritual Law, Spiritual Path, Wisdom and Truth and the three levels of certainty So La Ti DO

Re Me Fa!

Seven begets the effect of the Octave, the octave is the harmonization of the "home" pitch, the root, the beginning returns to it's Source, but at a higher frequency, ie; cooked.

In the imperfection and variance of the musical scale, the sequence of Fifths, the lopsided return of the lunar months, the calendar skipping with the leap year - is the sign, an ayat, of Allah's Infinite Vastness spiraling into a never beginning never ending greatness.

Do we have a leap year to climb the ladder to our higher pitch?

Hisar Buselik Pesrev