Extending Scales

Reader Nick

Νέο μέλος
#1
Hi,
I'm not sure if this has been discussed elsewhere in english, but as of yet I have not been able to find something written definitively.

How does one extend the scales of byzantine chant? Specifically, I'm wondering about the scales that occupy a full octave. For example:
In the Diatonic scale, one can proceed from Ni to Ni' as (using commas):
12-10-8-12-12-10-8
Does this restart on Ni', proceeding again with 12-10-8 from Ni' to Vou'? Or do we insert another disjunctive note of 12 before restarting?

It seems, from random sources I've looked at, that the diatonic scale from Ni to Vou' should proceed:
12-10-8-12-12-10-8-12-10-8

Although, it seems like the Chromatic scales proceed with another disjunctive note added at the octave (for Soft Chromatic from Ni-Vou'):
8-14-8-12-8-14-8-12-8

Am I incorrect here? I'm just curious as to how to extend the scales above and below an octave and if there is any reason for the extension.

Also, is there any way to known how to extend the "mini" scales (Kliton, Spathi, and Zygos) beyond their "limits"?

Thanks!
-Nick
 

nikosthe

Νίκος Θεοτοκάτος
#2
How does one extend the scales of byzantine chant? Specifically, I'm wondering about the scales that occupy a full octave
That depends:
- on the way your scale is constructed in theory
- on the "system" you use in practice
"System" in byzantine music is a way of repeating the same notes. The basics systems are:
"dia tessaron" = by 4 notes (tetrachord)
"dia pente" = by 5 notes (pentachord or "trohos")
"dia pason" = by 8 notes (octave)
There is also "dia trion" = by 3 notes (trichord), but, as it's generally believed today, it is used in specific cases only (there is a dispute on this point of theory, as some believe that this is the basic system of byzantine music, but it's not something we can discuss here). The name of those systems are taken from ancient greek music and can be easily explained, if you want.
For example:
In the Diatonic scale, one can proceed from Ni to Ni' as (using commas):
12-10-8-12-12-10-8
Does this restart on Ni', proceeding again with 12-10-8 from Ni' to Vou'? Or do we insert another disjunctive note of 12 before restarting?
Each scale can be constructed by different ways. Theory says that the Ni-Ni' scale (plagal fourth mode) is constructed by two tetrachords that are separated from a major tone called "diazefktikos" = disjunctive (it's a common construction way of byzantine scale, we call these tetrachords "diazevgmena" = separated): Ni-Ga=12-10-8, Ga-Di=12, Di-Ni'=12-10-8. If now you want to extend the scale upper (same on lower):
- if you use the octachord or "dia pason" system (by octaves), you repeat the same intervals after Ni' and you have an high octave Ni'-Ni'' exactly the same as the lower one Ni-Ni'
- if you use the tetrachord or "diatessaron" system, you have Ni-Ga=12-10-8 and Ga-Zo'=12-10-8
- if you use pentachord or "trohos" or "dia pente" (by pentachords) you have Ni-Di=12-10-8-12 and Di-Pa'=12-10-8-12.
If at dia tessaron and dia pente you extend the second tetrachord or pentachord, you repeat the same intervals (actually this is done for 2-3 notes more). Plagal fourth mode uses the pentachord system generally. So, in that case you have a Di as a Ni and Ni-Pa' = 12, Pa'-Vou'=12 (same as Ga-Di and Di-Ke), Vou-Ga'= 10, Ga'-Di'=8 (same as Ke-Zo' and Zo'-Ni'). This is not strange, you sing a plagal fourth mode from Di, actually. But in some psalms or music phrases of plagal fourth mode we use the diapason (octachord) system. This happens when the mode is "eptaphon" = begins its melodic development 7 voices over the basis, that means from Ni'. In that case we use the same intervals of the lower scale (Ni'-Di'=12-10-8-12). Finally, there is a case we use the tetrachord system, so Ni-Ga=12-10-8, Ga-Zo=12-10-8 (ie. at Virgin's "paraklisis").

These schemas may seem a little complicated, but if you apply them at the psalms you sing, you will realize that it's simple: at first the human voice sings and then you set the intervals and systems at theory. In many cases we also use the "fthoras" to set the system we use. So:
- if you sign having Di as pentachord basis and you extend the scale until Vou' and maybe you reach Ga', the Pa-Vou' interval is generally a major tone (12), because you use the pentachord system (which happens in most cases) and this interval is identical to Di-Ke and the Vou'-Ga' interval is identical to Ke-Zo (so the Vou'-Ga' is 10 theoritically, like Ke-Zo', but in practice it's less, because Zo' is flatted when you reach until it in diatonic modes, so if Ke-Zo'=6, Vou'-Ga'=6 similarly).
- if you sign having Ni' as octachord basis and you extend the scale until Ga' or Di', you have Ni'-Di'=12-10-8-12, like normal Ni-Di.
In both cases we can use the "fthora" of Ni and we met it at Di or Ni', so the intervals you will follow are obvious.
So, now you better understand that this conclusion:
It seems, from random sources I've looked at, that the diatonic scale from Ni to Vou' should proceed:
12-10-8-12-12-10-8-12-10-8
...is for diapason system (octachord) and not for trohos (pentachord).
Although, it seems like the Chromatic scales proceed with another disjunctive note added at the octave (for Soft Chromatic from Ni-Vou'):
8-14-8-12-8-14-8-12-8
Your previous extension was based on octachord system, but this extension uses the pentachord system. Ni-Di is the same as Di-Pa'. This scale is used on second mode, as you know, that uses generally the pentachord system. In some cases it also uses the rare trichord system, but for now this is a detail you don't have to know. After Pa', the Pa'-Vou' interval must be 8, following the pentachord rule. But the Vou'-Ga' interval depends on the system that uses the musical phrase: if the phrase is based on Pa', you repeat the pentachord interval on Pa'-Di' (8-14-8-12). But if the phrase is based on Di and you reach until Ga' (which is more common), the interval above Ni' are not soft chromatic but diatonic. So you have Ni'-Ga'=12-10-8. We usually use at Pa' the diatonic "fthora" of Pa to set the intervals. The hearing of this mode is like a second plagal mode from Pa and diatonic intervals after Di. Generally, when 2nd mode from Di uses the 4th note as dominated (Ni'), which is a characteristic of its plagal mode, has a tendency to harden its intervals. And when 2nd plagal mode from Pa uses the 3rd note as dominated (Ga#), which is a characteristic of its main 2nd mode, has a tendency to soften its intervals.
Also, is there any way to known how to extend the "mini" scales (Kliton, Spathi, and Zygos) beyond their "limits"?
There are many details for the intervals above and below the limits of these mini scales (or "hroai"). In VERY GENERAL terms, Kliton and Zygos go above their basis diatonically and Spathi chromatically (hard). Below the limits, Zygos goes with Ga# and Pa# until Ni, Kliton with Di-Ga#-Vou#-Pa. So Vou#-Pa is an interval about two major tones, like singing Di-Ga##-Ga#-Pa, which is close to the original enharmonic genre of ancient Greece: 3-3-24. But when melody goes up again, Pa-Vou is a major tone. It' like you sing Ni'-Zo-Ke#-Di. Spathi goes below using hard chromatic intervals, like when going above.
 
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