Oh my goodness!
Again this theory about conjunct 4chords in authentic modes!
This is wrong and useless! But some people, like tho one who advised you, don't know or don't observe the praxis or don't want to get rid of this mistake.
In classical pieces of Byzantine chant, the chromatic modes have always disjunct and not conjunct 4chords, ie. for 2nd mode:
Ni' 12 Pa' 8 etc.
If you want to put the intervals in a program in order to generate the sound, the intervals 9 and12 are pretty good but for better result in both soft and hard chromatic instead of 9 and 12 try 8 and 13
The intervals of the soft chromatic scale, as described by the Patriarchate Commission of 1883 (which is the official byzantine music intervals), are:
NI 8 PA 14 VOU 8 GA 12 DI 8 KE 14 ZO' 8 NI'
So the scale is based on tetrachords 8-14-8, which of course are disjunct, as mr. Arvanitis (Laosynaktis) stated correctly. After NI' you follow the same scheme: disjunct tone (12) and soft chromatic tetrachord (8-14-8). So:
NI' 12 PA' 8 VOU' 14 GA' 8 DI'
Although this is the typical scale, the intervals after NI' depend on the melodic phrases: if you reach VOU', the intervals are as stated above. If you reach GA', many time there is a diatonic "pthora" (sign of interval change) on PA', so you sing chromatic intervals DI-PA' and diatonic PA'-GA' (similar phenomenon with plagal B' mode, which often has a chromatic PA-DI and diatonic DI-ZO'). Be careful, this phtora may not be written in some cases, but you understand the intervals by the melodic phrase. Same intervals (diatonic) if you reach DI' with diatonic pthora. But if you reach DI' without diatonic pthora, the intervals PA'-DI' are the ones of the typical scale (8-14-8).
A few comments about the different scales stated in your message and other ones:
a) 6-15-7 tetrachord: This gives 28 parts of the tetrachord. But this leads to a scale with 68 parts and not 72, which is the scale we use today. But 15/68 = 16/72. This is considered hard chromatic interval and not soft.
b) 8-16-6 tetrachord: This was proposed by Simon Karas (more correctly, by his students, as Georgios Konstantinou, which changes Karas' tetrachord 7.5-16-6.5 to 8-16-6, to be easier). But this is also hard and not soft chromatic. It also has another disadvantage: it gives a ZO'-NI'=6, which is different of diatonic ZO'-NI' (8). This is not accepted by the majority of ancient and new theoretical approaches (Chrysanthos, Patriarchate Commission etc.), which all consider diatonic ZO' similar to soft chromatic (Chrysanthos writes it directly).
c) 9-12 or 8-13 trichord: This is a modification of what Chrysanthos proposed on his theoretical book ("Mega Theoreticon") on the 19th century (1832). Chrysanthos proposed a succession of similar trichords with major and minimum tone of his 68 part scale (7-12. On 72 part scale the intervals are 8-12). But this succession does not form a full scale (7-12/7-12/7-12/7 = 64 and not 68, on the other hand 8-12/8-12/8-12/8 = 68 and not 72), that's why it was rejected by posterior theorists. So today some people propose trichords which form a full scale. But, in my opinion, these are problematic, because the 9-12 trichord changes the minimum tone (8) to neutral (9), so provides on the second mode a VOU-GA and ZO'-NI' different from diatonic ones, which cannot be accepted. The 8-13 trichord changes the major tone and provides a GA-DI tone major than the diatonic one, which also cannot be accepted. On the contrary, Chrysanthos' trichord intervals 7-12/68 or 8-12/72 are more proper, because they can (and must) be applied in some cases (the most typical example, when you descend the scale, you reach on NI and you turn immediately on PA. These phrases were common on older melodies mainly and -probably- that's why Chrysanthos supports this trichord accession in his scale). So Chrysanthos' intervals are right, but they cannot be implemented in the whole scale, but only in special melodic phrases. Be careful: 9-12/72 is NOT Chrysanthine approach, as Chrysanthos clearly writes the similar tricords by the numbers 7-12/68 (which is 8-12/72) and says that VOY and ZO are minimum tones 7/68 in the soft chromatic and diatonic genre. Supporters of similar "neutral" trichord theories consider that the right Chrysanthos' intervals are not the ones discribed by numbers many times in his book, but the ones discribed by fractions (9/8-12/11 etc), which are different and truly mean 8-12/68 and 9-12/72 trichords. But these fractions are Al Farabi's ones, which Chrysanthos simply reports one time, only to give a mathematical proof for his intervals, but he does obviously wrong. The intervals of similar trichord of the second mode in Chysanthos' theoretical works are always discribed by the numbers 7-12 and by the words "major" and "minimum" (and NOT neutral) tone.
The "oral tradition" that mr. Giannoukakis stated above, concerns the special melodic phrases I just explained and not the whole second mode scale.
The supporters of 9-12/8-13 theories bypass the problem of the discord with the diatonic intervals by supporting the 9-12/8-13 intervals on... diatonic scales too! According to my opinion (and not only mine) this cannot be accepted at all (well, 12-9-9/12/12-9-9 scale is obviously a diatonic one, but this is which Arabs use today, not a byzantine one -although some times byzantine singers use the 9 neutral tone interval, but this is only an exception and not the main interval of a scale-. Another problem with 9-12 soft chromatic intervals theory is that the major tone (12), cannot be easily accepted as a characteristic interval in a chromatic tetrachord).
PS The second mode does not usually use below NI intervals. Personally I don't know any psalm that forms a whole tetrachord/pentachord below NI. In this case, theoretically the typical scheme should be applied. More convenient is to put a pthora, to show directly the intervals. The only widely known case of intervals below NI without pthora that I know, is the phrase "Eleison imas" of "Dynamis Syneithismenon", that reaches KE below NI. This is similar melodic phrase with the one I stated above, when you are on VOU and you reach NI without staying on it, but immediately returning on VOU. In this case, you are on NI (natural) and you reach on KE below without staying on it, but immediately returning on NI. It's obviously a trichord scheme where Chrysanthos' intervals must be applied (NI 12 ZO 8 KE, similar to VOU 12 PA 8 NI trichord of the first case). So Chrysanthos' soft chromatic intervals, with a minimum and major tone succession, may not be applied on a whole scale, but they are not useless! This is the more physical way for the voice to sing these specific melodic phrases (older times these phrases were more often). The flat that many writers put on PA when descending and not staying on NI, is not right. (I had thoroughly speaking about the issue of Chrysanthos' soft chromatic intervals on the 4th Musicological Conference of the Institute of Byzantine Musicology, you can find my announcement here, unfortunately in greek only -sorry, I cannot and have not the time to translate the whole document in english language-).
There is no discord between diatonic and soft chromatic trichords because Chrysanthos gave specific ratios for the major the minor tones which are used in both genders. So there are two kind of intervals in natural scale: the major tone(12) with ratio 9/8 and the minor tone(9) with ratio 12/11. The 88/81 tone is essentially equal to 12/11 and Chrysanthos use it typically, only in order to complete the geometry of a perfect tetrachord (9/8) *(12/11)*(88/81) = 4/3
The intervals that also Arabs used are inspired by Claudius Ptolemy’s scales. The byzantine (or better the east roman) music is based in ancient Greek music but Arabs also developed it by the same way they developed mathematics. Mathematics and music have the same origins and tradition in east. Chrysanthos knew well which ratios to use for natural scale.
The second mode uses the similar trichord system. The vou9ga12di9ke12zo is not the only one instance of this scale. There are many instances that the second mode is mixed with other modes and the intervals get different. This mix is called diploparallage (διπλοπαραλλαγή). The Patriarchate Commission of 1883 soft chromatic scale represents one of these diploparallage instances, the instance that the upper trichord is larger than the lower one (8+12<8+14). But there is not only this one. It can also be for example the upper trichord smaller than the lower one (8+14<8+12 or even 10+14<6+12). The last case is used when the second mode is mixed with first mode as in ancient chant of “Christ is Risen” (αρχαίο Χριστός Ανέστη). You can note this if you monitor old traditional chanters for example Iakovos Naypliotis and his students.
There are also many other instances of diploparallage. I have described them (for the moment) only in Greek section and represented in many conferences in the past. I’m looking forward to give a translation also in English.
I have made also a program in excel that you can practice in intervals, you can find it here. The menus are in Greek but I will translate it in English when I have time.
I will not disagree that, when there is a mixture with other modes, the intervals may vary. That's also a natural process, because the voice transition among different modes and genres has to be normal, not brutal. So when you sing 8-14-8 tetrachord and you have to transform it immediately to 12-10-8 due to a "pthora", you will probably go slightly to this scheme and sing some of the intervals you mentioned above. But, in my opinion, this cannot lead us to accept basic scales almost similar in all genres. You may accept a slightly different intervals scheme, which is executed in case of mode change (as Aristoxenus accepted the semi-chromatic genre between chromatic and enharmonic in ancient greek music -the genres are in many cases different than byzantine music ones-. I also have some theories to propose about this issue of mode change phrases, based on ancient greek theorists' practice, but they are not final yet). But we cannot take the special case of mode change (or "diploparallagi", as you say) to create the standard mode intervals.
As for the true Chrysanthos intervals, there is a long disagreement among us in the greek section of the forum, as you know... I will insist at the fact that Chrysanthos understands (as all of us do) that 9/68 is different than 7/68 and characterises the first as minor tone and the second as minimum and uses these numbers every time he speaks about intervals in his book. The ratios are used only 2 times, if I remember correctly: one for the mathematical proof and a second to another chapter, in order to compare with just intonation "european" ratios. It's not a stuff of his basic theory. In his Introduction Theory book, that was used by the students, ratios are not mentioned at all and the students learnt the theory with the numbers 12-9-7/68 scale, until Patriarchate Commitee corrected them to 12-10-8/72, because of the musical problems of the 68 scale (I have analyzed them in the greek section of the forum).
The point is not the intervals but the parallage and only this. Parallage is the way how the tones change each-other using all systems, basically by five(trochos- wheel) and also by four and by three. In papadike pro-theory is mentioned which tone is mixed with other and how. Parallage is a greek word that means to change the intervals in order to be a tone similar to an other. I have understand this how it works and I chant on this way. Now I can chant many "difficult" melodies and thesis that before I couldn't.
So I do not discuss it here anymore.
I just wanted to give a help to English-speak people, to make their research easier. This is it. So make your chanting and your life easier and learn how to apply diploparallage. It is magic It is wonderful!
For more do not hesitate to send me message or skype me.