Makams (muslim music scales) must be avoided by Orthodox sacred singers because are not proper for Orthodox hymnology, as well european music - must be avoided - because symbolises Orthodox Church subordination to western heresies.
We can not avoid using a scale simply because the Arabs are using it too. There are so many makam scales (over 60 I think) that both the modern minor and major scales as well as all church modes have correspondences among the Arabic version of the makams (1=bayati, 2=sikah baladi, 3=ajem, 4=sikah, 5=husseini, 6=hijaz kar, 7diatonic=iraq, 8=rast). It all depends on how the scales are used not that they are good or bad by themselves. One mouth can be used to praise the God and to make sins.
On the other hand people perceive the music accordingly to their past experience. The best church music for Arabic Christians is not necessarily best for Russian Christians and vice versa.
The orthodox chanters have a great tradition to follow and preserve so I don't know whether what I wrote in my previous post about the intervals performed by non-orthodox musicians is useful or not. Nevertheless, I'd like to add something more about the lowered Vu as it is or was used by non-orthodox musicians.
As I wrote in my previous post, there are some regional differences of Vu — in some places it is lowered more (with respect to the equally tempered Vu of the western music) and in other places it is lowered less. However in the past there were talented musicians who were able to change the pitch of Vu in order to affect the mood of the scale. I have read about this from Arabic Muslim and Coptic Christian (monophysite) authors.
When Ni is tonic (8th mode) then the higher is Vu, the brighter is the mood and the lower is Vu, the more suppressed is the mood.
When Vu or Di is tonic (2nd and 4th mode) then the relation is the opposite — the lower is Vu, the brighter is the mood and the higher is Vu, the more suppressed is the mood.
I haven't read what happens when Pa is tonic (as in 1st and 5th mode). Since in this case Vu is neither tonic nor dominant tone and is subject to attractions, I can suppose that in this case Vu doesn't affect the mood as much.
I'm sorry for have to travel homeless and use internet access in municipal libraries when it's possible, and delay to reply.
As long I know intervals of Orthodox Church music, have been measured by Patriarchal Commission on Music by 1881, in ratios. Tempered intervals in tmemata were introduced just to be used by patriarchal musical organ that doesn't exist. Compouters are able to perform ratio intervals. In this forum one can read, in pdf, Patriarchal Commission's teaching book in greek. I don't know any translation in english. Any way there are websites with these intervals in english.
As long I know intervals of Orthodox Church music, have been measured by Patriarchal Commission on Music by 1881, in ratios. Tempered intervals in tmemata were introduced just to be used by patriarchal musical organ that doesn't exist. Compouters are able to perform ratio intervals.
From what I have read (but unfortunately I am almost unable to use Greek sources, so I can be wrong) the Patriarchal Commission determined the intervals not by theoretical computations but by experiment. They built an instrument that was able to play 36 notes in one octave. By this instrument they determined the intervals (in 36-equally tempered scale). I haven't read that they determined ratios too. If they did so, then I would be interested to know what was the method they used to determine the ratios.
I will be glad if someone corrects me and provides more information on this subject. As I wrote my sources of information are limited.
In this forum one can read, in pdf, Patriarchal Commission's teaching book in greek.
Mr Zinoviev you need help from greek speaking person for find it, at greek part of this forum by mr Zacharis. Ypoenothta: "Patriarchiki Epitroph 1881". (update: electronic address is gigven below by mr Emmanuil Giannopoulos).
As for your formula T=K log(x)/log(2), is good when we choose some subdivision K of octave. More general form: T=K log(x) / log(a) where (a) is any ratio interval. For example: I prefer for unit, one cent (1/100) of a great tone (9/8), then tempered interval of any ratio interval (x) is given by T=100 log(x) / log(9/8). My formula is the most general one.
Patriarchal Commission on music (1881) not only did measure Church music intervals but - also did - many more, as it's stated in preface of its handbook. One, must get a good knowledge of 19th century greek to read - and understand - it.