Notes on the music of China and Japan

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Notes on the music of China and Japan

Post by Pāṇini »

Spoiler:
For convenience’s sake, I’ll write out all Sinospheric concepts in Hànyǔ Pīnyīn (漢語拼音, ‘Transcription System for the Chinese Language’), followed by a parenthetical with traditional characters, the Japanese reading in Hepburn (sometimes *conjectural), and a translation in single quotation marks. If I feel it would not be practical to provide a Japanese reading, it will not be given. Partially translated names, especially proper names, will be written in the text first, then followed by Traditional Characters and Pīnyīn in a parenthetical. I will admit that I was tempted to write out all Chinese terms in a non-Mandarin lect—either Cantonese or Norman’s reconstruction of Common Dialectal Chinese—but this may not be the time or place. I for one nearly yelled when a work I was referencing used Guóyǔ Luómǎzì (國語羅馬字, ‘National Language Romanization’) rather than Pīnyīn or the (still discomfort-inducing) Wade-Giles. Either way, I will not budge on using tone marks.
Before I begin, I would like to make a massive caveat. I am not an expert in Chinese musicology, nor music theory in general. I am not a practicioner of any Sinospheric musical tradition, though I am an amateur musician. I do not speak nor read Chinese beyond a passing familiarity with the basics of Literary Chinese. The Vietnamese and Korean musical traditions are unknown to me. Consequently, I am absolutely no authority on any of the things I am about to state, and am only confident in writing anything that I consider transparent in its sourcing. That being said, enjoy! [<3]

Pitches: the bare essentials

The first thing that Westerners tend to notice about the music of the Hàn (漢) Chinese is the pentatonic scale upon which it is structured. The pentatonic scale has been in China for a very long time: biānzhōng (編鐘, ‘organized bells’) dating back to the Zhōu (周) dynasty are based around the same wǔshēng (五聲, *goshō, ‘five tones’) as the instruments of today [1]: gōng (宮, kyū, ‘do’), shāng (商, shō, ‘re’), jué (角, kaku, ‘mi’), zhī (徵, chi, ‘so’), and (羽, ū, ‘la’). These are relative, rather than absolute, pitch names, and are equivalent to degrees 1, 2, 3, 5, and 6 of the Western major scale, respectively. These names were likely codified following their appearance in the Ěryǎ (爾雅, ‘Approaching Elegance’, as per Mair), a 3rd century BCE dictionary enshrined early on in the Confucian canon [Thrasher 84][3]. Both the Chinese [Thrasher 85] and Japanese [Garfias 60] traditions recognize two more additional accidental tones, referred to in much of the Japanese literature as “exchange tones”: biàngōng (變宮, henkyū, ‘si’, lit. altered gōng’) and biànzhī (變徵, henchi, ‘fi, lit. altered zhī’)—our Western degrees ♯4 and 7. The Japanese tradition furthermore has relative names for all twelve tones relative to a tonic—more on that later. I’ll refer to these using movable-do solfége.

These relative pitches exist in reference to a theoretical absolute pitch system: the Chinese tradition, much like that of the West, divides the octave into twelve tones. These shí’èrlǜ (十二律, jūniritsu, ‘twelve laws, twelve pitches’) also date back to the Zhōu period—the biānzhōng of Marquis Yǐ of Zēng (曾侯乙, Zēng hóu Yǐ) are capable of producing the whole gamut [1]. Legend tells that the generating pitch of the shí’èrlǜ, huángzhōng (黃鐘, “yellow bell’), was a length of bamboo changing with every dynasty [2], upon which Pythagorean fifths were stacked and then tempered. Scholars refuse to agree on historical pitch values for huángzhōng, or the precise equivalence between the Japanese jūniritsu and the Chinese shí’èrlǜ. Garfias equates huángzhōng with the Japanese pitch ōshiki, written with the same characters [Garfias 59], while Steven G. Nelson [Tokita 21] concurs with Intō citing Tominaga [5] in equating huángzhōng with the Japanese pitch ichikotsu (壱越), citing evidence of Táng (唐) era modal practice. In any case, modern (and likely Edo-period) Japanese practice tunes ōshiki to 440 Hz and ichikotsu to D (referencing A=440 Hz). Competing claims as to the pitch of huángzhōng in the Táng dynasty range between C [Tokita 21] and G [Thrasher 95]. I wash my hands of this debate, and will refer to any concrete pitches using Western letter names.

On our next episode, modes. [:D]

References

1. http://www.neuroscience-of-music.se/Zengbells.htm —Seems reputable enough, considering that I don’t have access to von Falkenhausen’s book.
2. Thrasher, Alan. Sīzhú instrumental music of south China: Ethos, theory and practice.
3. Ěryǎ 7:1, reading 「宮謂之重,商謂之敏,角謂之經,徴謂之迭,羽謂之柳。」I have precious little Classical Chinese, or Chinese of any sort, for that matter, and the definitions of each note are unclear to me.
4. Garfias, Robert. Music of a thousand autumns: the Tōgaku style of Japanese court music.
5. Intō, Kazuhiro. “Tominaga Nakamoto (1715-46) and gagaku (court music)”, in The Tokugawa World, edited by Leupp and Tao.
6. Tokita, Alison McQueen and Hughes, David. The Ashgate research companion to Japanese music.
天含青海道。城頭月千里。
/tʰiæn ɣɑm tsʰieŋ.hɑ́i dʱɑ́u ‖ ʑʱeŋ dʱəu ᵑgyæɾ tsʰiæn lí/
The sky swallows the road to Kokonor. On the Great Wall, a thousand miles of moonlight.
—/lí ɣɑ̀/ (李賀), tr. A. C. Graham
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Re: Notes on the music of China and Japan

Post by Pāṇini »

Just anticipating a question or two (I finished this far too late last night to expect any sort of completeness).

Tuning practice is often separate from tuning theory in East Asia. One can almost always expect scale degrees 1, 2, and 5 to be stacked perfect fifths in the Pythagorean sense [Thrasher 99], matching the traditional derivation of the shí’èrlǜ. As theorists generally see Chinese and Japanese modes as revolving around tetrachords [Thrasher 99][Tokita 19, citing Koizumi], a Pythagorean tuning serves this purpose well. Scale degrees 3 and 6 are relatively stable; Southern Chinese practice appears to place mi at a just-intoned major third above do, and la at a just-intoned minor third below do [Thrasher 102]. Scale degrees 4 and 7 are microtonally inflected in South China, and varyingly so—they tend to be at around fa half-sharp (near the 11th harmonic approximating the wolf fourth of Pythagorean fame) and ti half-flat (i.e., forming a neutral seventh with do). Japanese gagaku (雅樂, ‘refined music’) uses different microtonal alterations depending on mode, and dissonances of a semitone or more between instruments playing the same written note are common [Tokita 55].

I thought I'd do modes next, as sort of a comparative overview of the Sinospheric traditions I'm familiar with, but I feel like that structure might be both difficult to follow and divorced of some important (and interesting!) context. Any thoughts on an alternative?

1. Thrasher, Alan. Sīzhú instrumental music of south China: Ethos, theory and practice.
2. Tokita, Alison McQueen and Hughes, David. The Ashgate research companion to Japanese music.

EDIT: revised an original guess as to the just interval identity of scale degree 4.
Last edited by Pāṇini on 20 May 2022 05:24, edited 1 time in total.
天含青海道。城頭月千里。
/tʰiæn ɣɑm tsʰieŋ.hɑ́i dʱɑ́u ‖ ʑʱeŋ dʱəu ᵑgyæɾ tsʰiæn lí/
The sky swallows the road to Kokonor. On the Great Wall, a thousand miles of moonlight.
—/lí ɣɑ̀/ (李賀), tr. A. C. Graham
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Re: Notes on the music of China and Japan

Post by Salmoneus »

Thank you so much for this!
Pāṇini wrote: 19 May 2022 06:03 Both the Chinese [Thrasher 85] and Japanese [Garfias 60] traditions recognize two more additional accidental tones, referred to in much of the Japanese literature as “exchange tones”: biàngōng (變宮, henkyū, ‘si’, lit. altered gōng’) and biànzhī (變徵, henchi, ‘fi, lit. altered zhī’)—our Western degrees ♯4 and 7.
Ahh! I didn't know that! I will be interested to hear more...
The Japanese tradition furthermore has relative names for all twelve tones relative to a tonic—more on that later. I’ll refer to these using movable-do solfége.
Personally, I'd prefer plain C-D-E etc, since it's easier to remember what order they come in, but that may just be me...
These relative pitches exist in reference to a theoretical absolute pitch system: the Chinese tradition, much like that of the West, divides the octave into twelve tones. These shí’èrlǜ (十二律, jūniritsu, ‘twelve laws, twelve pitches’) also date back to the Zhōu period—the biānzhōng of Marquis Yǐ of Zēng (曾侯乙, Zēng hóu Yǐ) are capable of producing the whole gamut [1]. Legend tells that the generating pitch of the shí’èrlǜ, huángzhōng (黃鐘, “yellow bell’), was a length of bamboo changing with every dynasty [2], upon which Pythagorean fifths were stacked and then tempered.
Interesting - the wikipedia article implies that the octave was untempered (by saying the method could not produce pure octaves - but I suppose maybe they just mean the method was abandoned in order to produce pure octaves by tempering).

The wikipedia table also claims something surprising: that the Chinese only tuned in one direction. This is surprising because it means that the wolf lives on the fourth degree, and by extension that the fourth on the tonic is itself wolf. By contrast, the Western system [but maybe not the original Greek?] aiui usually tunes in both directions, which places the wolf on the tritone, way out into the weeds, leaving the main consonant intervals available for use. The Chinese seem to keep their wolves on their doorsteps!

On the other hand, this would explain why the fourth is not used in the '12356' pentatonic mode you mention: if you build your mode on the same tonic that you tuned from in this system, the fourth would be wolf. Then again, maybe this doesn't need to be explained, since 12356 is the pentatonic scale you automatically create by tuning in fifths.

[for those following along who don't understand what I'm talking about, quick explainer:
Spoiler:
if you tune up in fifths (and back down in octaves), you end up with a scale of 12 notes to the octave, but... not quite. The 13th note is not quite the octave, but slightly above it, by about a quarter of a semitone. A tempered pythagorean scale pretends that this is not the case, and shrinks the 'octave' back down to a real octave, but in the process also shrinks the 13th fifth to a point where it is audibly out-of-tune. This is known as the "wolf" fifth (lurking in the harmonic shadows to devour unsuspecting musicians who accidentally wander into its territory). If you tune 'out' from your base note, then the wolf fifth is directly 'opposite' your base, i.e. on the tritone, and will rarely be encountered except in very adventurous music, but if you tune in only one direction your wolf will be between your base note and a fifth either up or down (the opposite of the way you tuned). Since your base note and the notes a fifth away in either direction are probably notes you're going to want to play a lot, this is kind of a bugger...
]

----

On another note: this is just from wikipedia, but I'll throw it in here for context: they claim that the first references to standardisation of pitches is from 600BC, and the first surviving explanation of how to tune the pitches is from around 240AD. The bells you mention are from 433BC, in between. Pythagoras lived ~570-495. If the Zhou bells really are tuned in PT, that would demonstrate that the Chinese independently discovered it. [likewise, Europe and China appear to have independently discovered ET two thousand years later]
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Re: Notes on the music of China and Japan

Post by Salmoneus »

Pāṇini wrote: 19 May 2022 18:12 Just anticipating a question or two (I finished this far too late last night to expect any sort of completeness).

Tuning practice is often separate from tuning theory in East Asia. One can almost always expect scale degrees 1, 2, and 5 to be stacked perfect fifths in the Pythagorean sense [Thrasher 99], matching the traditional derivation of the shí’èrlǜ. As theorists generally see Chinese and Japanese modes as revolving around tetrachords [Thrasher 99][Tokita 19, citing Koizumi], a Pythagorean tuning serves this purpose well.
I'm not entirely sure what you mean by this (wouldn't pentatony have trichords instead? and why is 2 particularly relevant for tetrachords?), but expect it will become clear.
Scale degrees 3 and 6 are relatively stable; Southern Chinese practice appears to place mi at a just-intoned major third above do, and la at a just-intoned minor third below do [Thrasher 102]. Scale degrees 4 and 7 are microtonally inflected in South China, and varyingly so—they tend to be at around fa half-sharp (near the 11th harmonic) and ti half-flat (i.e., forming a neutral seventh with do). Japanese gagaku (雅樂, ‘refined music’) uses different microtonal alterations depending on mode, and dissonances of a semitone or more between instruments playing the same written note are common [Tokita 55].
I worked this out to get my head around it, so I'll put it down for anyone else who is following along, in the format [pythagorean value in cents : value you give in cents : JI value in cents]

1 - 0 : 0 : 0
2 - 113.69 : 113.69 : 111.73
3 - 407.82 : 386.31 : 386.31
4 - 521.51 : 551:32 : 498.04
5 - 701.96 : 701.96 : 701.96
6 - 905.87 : 884.36 : 884.36
7 - 1109.78 : (somewhere between 1050 and 1070?) : 1088.27

Interesting how some notes are tuned closer to just, and others are intentionally made worse!

I wonder (I don't suppose it's possible to know) whether this tuning is derived from PT, or whether PT is a later theoreticisation. A pentatonic scale is naturally created in two different ways - by splitting fourths into two parts, or by tuning in fifths until you hit the third ditonic scale (the fourth is heptatonic and the fifth is dodecatonic pythagorean temperament). It's certainly suggestive that the 12356 mode is the one given as the 'base' scale, given that this is what you get by doing the latter, and would easily develop into pythagorean tuning. On the other hand, the Greeks seem to have proceeded by splitting the fourth first, and only discovering pythagorean temperament later on. So...
I thought I'd do modes next, as sort of a comparative overview of the Sinospheric traditions I'm familiar with, but I feel like that structure might be both difficult to follow and divorced of some important (and interesting!) context. Any thoughts on an alternative?
I don't know enough about the music to know how best to describe it and in what order! Modes seem a natural next step, but maybe they're not, I don't know.
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Re: Notes on the music of China and Japan

Post by Pāṇini »

Salmoneus wrote: 20 May 2022 01:27 Thank you so much for this!
Pāṇini wrote: 19 May 2022 06:03 Both the Chinese [Thrasher 85] and Japanese [Garfias 60] traditions recognize two more additional accidental tones, referred to in much of the Japanese literature as “exchange tones”: biàngōng (變宮, henkyū, ‘si’, lit. altered gōng’) and biànzhī (變徵, henchi, ‘fi, lit. altered zhī’)—our Western degrees ♯4 and 7.
Ahh! I didn't know that! I will be interested to hear more...
The Japanese tradition furthermore has relative names for all twelve tones relative to a tonic—more on that later. I’ll refer to these using movable-do solfége.
Personally, I'd prefer plain C-D-E etc, since it's easier to remember what order they come in, but that may just be me...
I'm always glad to share! I'll be using the letter note names for absolute pitches moving forward—the movable-do thing will be mostly for talking about scale degrees without referencing a particular absolute pitch, though I suspect that simply stating the scale degree number will suffice.
Salmoneus wrote: 20 May 2022 01:57
Pāṇini wrote: 19 May 2022 18:12 Just anticipating a question or two (I finished this far too late last night to expect any sort of completeness).

Tuning practice is often separate from tuning theory in East Asia. One can almost always expect scale degrees 1, 2, and 5 to be stacked perfect fifths in the Pythagorean sense [Thrasher 99], matching the traditional derivation of the shí’èrlǜ. As theorists generally see Chinese and Japanese modes as revolving around tetrachords [Thrasher 99][Tokita 19, citing Koizumi], a Pythagorean tuning serves this purpose well.
I'm not entirely sure what you mean by this (wouldn't pentatony have trichords instead? and why is 2 particularly relevant for tetrachords?), but expect it will become clear.
It shall indeed [:D].
Scale degrees 3 and 6 are relatively stable; Southern Chinese practice appears to place mi at a just-intoned major third above do, and la at a just-intoned minor third below do [Thrasher 102]. Scale degrees 4 and 7 are microtonally inflected in South China, and varyingly so—they tend to be at around fa half-sharp (near the 11th harmonic) and ti half-flat (i.e., forming a neutral seventh with do). Japanese gagaku (雅樂, ‘refined music’) uses different microtonal alterations depending on mode, and dissonances of a semitone or more between instruments playing the same written note are common [Tokita 55].
I worked this out to get my head around it, so I'll put it down for anyone else who is following along, in the format [pythagorean value in cents : value you give in cents : JI value in cents]

1 - 0 : 0 : 0
2 - 113.69 : 113.69 : 111.73
3 - 407.82 : 386.31 : 386.31
4 - 521.51 : 551:32 : 498.04
5 - 701.96 : 701.96 : 701.96
6 - 905.87 : 884.36 : 884.36
7 - 1109.78 : (somewhere between 1050 and 1070?) : 1088.27

Interesting how some notes are tuned closer to just, and others are intentionally made worse!
I'll add some lightly abstracted temperaments cited in Thrasher for comparison, in the format [Cantonese lute temperament : Hakka/Cantonese xiāo (簫) flute temperament : 24-EDO–based Cantonese temperament : the cent values of what I had in mind]. All of them have been rounded to the tens place (if not further).

1 - 0 : 0 : 0 : 0
2 - 200 : 200 : 200 : 205.91
3 - 380 : 380 : 400 : 386.31
4 - 520 : 530 : 550 : 551.32*
5 - 700 : 700 : 700 : 701.96
6 - 880 : 880 : 900 : 884.36
7 - 1060 : 1050 : 1050 : 1049.36

Sal, I think the values you gave for scale degree 2 were for a minor, rather than major second over the tonic. Either way, I'd like to revise my initial identification of scale degree 4 with the 11th harmonic—it seems more likely to correlate to the very wolf fourth (around 519.55 cents) that the Pythagorean system generates! The wolf tuning certainly *sounds* more correct in reference to traditional recordings of Southern Chinese chamber music. Either way, Thrasher argues that the theory of the sīzhú (絲竹, 'silk and bamboo') music he describes shouldn't be correlated to that of the ancient wǔshēng, and the slipperiness of scale degree 7 does little to refute that claim. I think that placing sīzhú practice within the context of the ancient modes is helpful, however, and Chinese scholars appear to do the same.
I wonder (I don't suppose it's possible to know) whether this tuning is derived from PT, or whether PT is a later theoreticisation. A pentatonic scale is naturally created in two different ways - by splitting fourths into two parts, or by tuning in fifths until you hit the third ditonic scale (the fourth is heptatonic and the fifth is dodecatonic pythagorean temperament). It's certainly suggestive that the 12356 mode is the one given as the 'base' scale, given that this is what you get by doing the latter, and would easily develop into pythagorean tuning. On the other hand, the Greeks seem to have proceeded by splitting the fourth first, and only discovering pythagorean temperament later on. So...
Given that the ancient biàngōng (scale degree 7) and biànzhī (♯4) are the next stacked fifths after 1-5-2-6-3, it seems likely, though not certain, that the ancient Chinese system derives originally from stacked fifths rather than divided fourths.
天含青海道。城頭月千里。
/tʰiæn ɣɑm tsʰieŋ.hɑ́i dʱɑ́u ‖ ʑʱeŋ dʱəu ᵑgyæɾ tsʰiæn lí/
The sky swallows the road to Kokonor. On the Great Wall, a thousand miles of moonlight.
—/lí ɣɑ̀/ (李賀), tr. A. C. Graham
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Re: Notes on the music of China and Japan

Post by Davush »

Thank you for this thread! It’s great – I like the inclusion of characters and Pinyin.

A lot of the more technical aspects of the theory go over my head, so I may have misunderstood some things but some comments/questions I have:

– Is transposition to different tonics/keys common? Especially as you mention the note names refer to the relative degrees of the scale? Or are certain modes associated with particular tonics? (I might add a section about the Arabic note names in the Arabic music thread actually!)

– Could you please explain the stacked fifths tuning in more layman’s terms? For example, how does the tuning of the 1–2 interval relate to a stacked fifth? How does one tune “2” by ear (in relation to what note?)?

– Also to echo Sal’s question (I know you’ve mentioned this will become clear, but I’d also be interested to hear more): How do tetrachords work within a strongly pentatonic system, where fourths seem quite marginal?

– Very interesting that degrees 3 and 6 are stable – this is kind of the opposite of the Arabic system!

– The half-sharp fourth as the “default” is also quite surprising (and again opposite to the Arabic system where perfect fourths are generally very stable)! I’d be interested to hear some examples if you know of any?

– Also I’m with Sal that using C-D-E and 1-2-3 makes it easier to visualize the relationship between notes.

– Is the tuning referring to tuning of open strings, or is it also the exact “manual intonation” of the notes ? For example, are there instruments where only a few open strings are tuned (maybe the erhu)? On such instruments (if they exist), is the “wolf fourth” still preferred when “manually” intonated (or does it depend on the mode/region/player)? If you have the time, could you give an example of how an instrument(s) would be tuned “in practice” in simple terms?
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Re: Notes on the music of China and Japan

Post by Salmoneus »

Davush wrote: 20 May 2022 10:16 – Could you please explain the stacked fifths tuning in more layman’s terms? For example, how does the tuning of the 1–2 interval relate to a stacked fifth? How does one tune “2” by ear (in relation to what note?)?
I think I can quickly save Panini from answering this one!

The Pythagorean system is said to tune in fifths, but it actually tunes in fifths and octaves (i.e. it assumes octave equivalency*). If you're tuning upward, you just subtract an octave every time you end up more than an octave above the tonic.

So, starting from C:

C [up a 5th] G [up a 5th down an octave] D [up a fifth] A [up a fifth down an octave] E [up a fifth]

i.e. 1-5-2-6-3, to give a 1-2-3-5-6 pentatonic scale. [and then likewise on to B, Fs, Cs etc]

Which comes to think of it sort of explains the tritony fourth Panini mentions - if it's seen not as a fourth at all, but simply the 7th pythagorean note tuning upwards. The system really does seem more fundamentally Pythagorean than the Indo-Greek system...


And because I can't restrain myself any longer, I'll just go into a tangent I learnt recently, on the subject: why would you stop at 5 notes!?
Spoiler:
We normally think of Pythagorean tuning going round the octave in fifths (or fourths, equivalently), and it does. But we should also look at the intervals that it creates. As we build a scale in this way (1-5-2-6-3-7... etc), how many types of interval are there between adjacent notes? It turns out, mathematics demands that there can never be more than three sizes of interval between two adjacent notes in an octave formed by stacking a given size of interval (in this case a fifth) - and if you ever have three intervals, the largest inteval must always be equal to the sum of the first two intervals! What this means is that (other than monotonic scales!), there are only two types of scale produced in this way: ditonic (having two interval sizes) and tritonic (having three interval sizes). And people will quickly realise that in a tritonic scale the 'big' interval can simply be 'cracked' back down into the two small intervals by adding one more of the generating interval. In a sense, then, tritonic scales (in this sense) are likely to be seen as 'unstable', with 'missing' notes - people will ask "why can't I just play the note in the middle of that big gap? it's obvious what it is!" Whereas with a ditonic scale, adding an additional note will always create an additional smaller (and more dissonant) size of interval, which will sound 'wrong' to people not used to it.

So in practical terms which scales are which?

2 notes - ditonic (one fifth, one fourth)
3 notes - ditonic** (9:8, fourth, fourth) (big interval gets cracked)
4 notes - tritonic (9:8, fourth, 9:8, major third) (wait, can't that big fourth there be cracked the same way? yes!)
5 notes - ditonic (9:8, 9:8, third, 9:8, third) (great, nothing here can be cracked into known intervals, so no 'missing notes')

6 notes - tritonic (9:8, 9:8, third, 9:8, 9:8, 256:243) (oh I see, there IS an interval smaller than a third! doesn't that mean we can crack the othe third too?)
7 notes - ditonic (9:8, 9:8, 9:8, 256:243, 9:8, 9:8, 256:243) (there we go, no missing notes any more!)

similarly, if you continue on beyond 7 notes you crack on of the 9:8s into a 256:243 and a 17:16, so it's tritonic again. Keep adding notes and you crack each 9:8 in turn, so that you end up with a 12-tone scale comprising only 256:243s and 17:16s.

And then you carry on further and crack one of those 17:16s into a 256:243 and a spare 531441:524288, our good old friend the Pythagorean comma. Split all the 17s and you get a 17-note ditonic scale (as traditionally theorised in Arabic music at one point) of 256s and commas. Continue on and you discover new ditonic scales at 29-tone, 41-tone and 53-tone scales. This was known to the Chinese by at least the 1st century AD (and was adopted by Ottomans in the 19th). There's no point going beyond 53 in this way, because with 53 notes in the scale, the two different types of interval are indistinguishable to the human ear, so you've effectively reached equal temperament. [Boethius believed that 53tet matched all the 12-tone pythagorean intervals, which it doesn't mathematically but does to the human ear]

Anyway, this is probably why the most common scales (other than those with fewer thn 5 notes) have 5, 7, 12 or occasionally 17 notes to the octave...





*which is ironic because in a true, untempered, open-ended extended Pythagorean tuning, the octaves AREN'T equivalent...

**although obviously tritonic in a literal sense...
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Re: Notes on the music of China and Japan

Post by Torco »

Jupiter's balls, what wealth of musical insight have I found after going 'I wonder what's up in the cbb'. thank you so much for this thread, and I look forwards to moar. And the chinese are so... writy! I bet their musical history is relatively well documented.
The first thing that Westerners tend to notice about the music of the Hàn (漢) Chinese is the pentatonic scale upon which it is structured. The pentatonic scale has been in China for a very long time: biānzhōng (編鐘, ‘organized bells’) dating back to the Zhōu (周) dynasty are based around the same wǔshēng (五聲, *goshō, ‘five tones’) as the instruments of today [1]: gōng (宮, kyū, ‘do’), shāng (商, shō, ‘re’), jué (角, kaku, ‘mi’), zhī (徵, chi, ‘so’), and yǔ (羽, ū, ‘la’). These are relative, rather than absolute, pitch names, and are equivalent to degrees 1, 2, 3, 5, and 6 of the Western major scale, respectively.
the wiki says chinese music is almost always based on the 12356 pentatonic. I guess I'm thinking about this from the lens of western music, and it's comparisons with arabic (for obvious reasons I guess lmao)... is it really that focused on the pentatonic? especially in light the fact that they do have 12 names for 12 pitch classes, or is that like a stereotype? cause from a layman's view, it sure does sound like it. that wouldn't make it super unique, though, plenty of cultures really like the pentatonic.

Personally, I'd prefer plain C-D-E etc, since it's easier to remember what order they come in, but that may just be me...
seconded, especially since we hispanics don't use moveable do, but I mean, whatever's more comfortable for Panini we can, surely, adjust to.
I thought I'd do modes next, as sort of a comparative overview of the Sinospheric traditions I'm familiar with, but I feel like that structure might be both difficult to follow and divorced of some important (and interesting!) context. Any thoughts on an alternative?
I'm all for context, but if you're taking requests, I can mention the aspects of traditional chinese music that have most struck me: none of these observations are like proper musicology or anything, just vibes I get.

* traditional chinese music feels very impresionistic, as opposed to western which feels quite narrative: a lot more satie than mozart, so to speak. I know, I know, it's an ethnocentric comparison, but hey, we do what we can: besides, arabic, indian, mapuche, persian... they all have this quality of having the melody and the rythm sort of "push" them forward. by contrast, it feels like what I get when I search for chinese classical is a lot more... like, "look at this sonority, isn't this a cool sonority? check this other sound. are they not beautiful? does this other thing not sound super banging in contrast?". like, I guess what I'm trying to say is that it doesn't feel so much concerned with resolution. this is probably limited exposure and a particular taste for the guqin 古琴, tho.
Spoiler:
if someone doesn't know it, the guqin is like a zyther you pluck and use the body of the instrument as a a fingerboard. it's fretless, so harmonics and glisandi and vibrato are used a lot. the thing itself is a long sort of long rounded box thing, very specific shape, whith a bridge and a nut on each sidea and strings, tuned to the pentatonic, running up and down it. it sounds resonant and mellow at the same time, which is super dope, and though it's not loud it looks like a wonderful instrument to just noodle around: the music people traditionally play on it is lovely, you owe it to yourself to give it a google
* perhaps relatedly, I perceive chinese music as being on the lower side of the spectrum if we're to order various musical traditions from most to least concerned with rhythm: the pulses of the music are relatively simple, and there's a lot of what westerners call rubatos, accelerandi and ritardandi: like the beat of the internal metronome is constantly shifting, following the music rather than the music following it. this gives it some of its stereotypical associations with 'pleasantness' and 'contemplativeness'.

perhaps these things make sense in the context of its history and its sociology?
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Re: Notes on the music of China and Japan

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Heptatonic modes

NB: The sources I’ve consulted use two different pitch equivalencies between the Sinospheric shí’èrlǜ (十二律, jūniritsu, ‘twelve tones’) and our twelve-tone chromatic scale. Scholars dealing with Chinese music tend to arbitrarily assign the generating pitch huángzhōng (黃鐘, ‘yellow bell’) to C, mostly for convenience’s sake; I’ll refer to this as academic pitch. However, as the Japanese gagaku tradition appears to be the only major modern tradition which uses shí’èrlǜ pitch names, I’ll be using Japanese pitch, in which huángzhōng = ichikotsu (壹越, ‘first crossing over (?)’) = D in reference to an A at 440 Hz.

The oldest modal tradition in the Sinosphere likely underlies the various traditions of ritual and courtly music referred to as yǎyuè (雅樂, gagaku, ‘refined music’). In China itself, yǎyuè went extinct in the mid-20th century, having suffered the tragedies of the Civil War and Cultural Revolution. Still, quite a number of medieval and early modern treatises survive, as do the Japanese, Korean, and Vietnamese traditions of the same name. The modal theory that is revealed by comparing these sources is heptatonic in nature, based firmly in the twelve tones of the shí’èrlǜ.

First, some definitions. For the purposes of these posts, when I refer to a system, I mean the 123♯4567 scale that can be derived by stacking seven fifths above a particular absolute pitch serving as scale degree 1. For example, when I refer to the system based on C, I mean the pitch collection C-D-E-F♯-G-A-B. When I refer to a mode, on the other hand, I refer to a particular interval pattern built upon a finalis or tonic within a key. D Mixolydian (D-E-F♯-G-A-B-C) for instance, is here in the system based on C. Due to the ♯4, this is fairly unintuitive for everybody, but it's the only vaguely recognizable nomenclature that doesn't completely distort the underlying concepts of these musical traditions.

In theory, one could play in a system based on any of the twelve shí’èrlǜ pitches, and any of the seven pitches within those systems could serve as a finalis. Therefore, scholars of the Tàng and Sòng recognized eighty-four possible mode-system combinations, or diàozi (調子, chōshi), in which yǎyuè could be played [Pian 43]. A subset of twenty-eight diàozi were referred to as ‘popular’, as they were used in the súyuè (俗樂, *zokugaku, ‘popular, vernacular music’) of the time. The twelve systems were pared down to seven (based on D, E♭, F, G, A, B♭, and C*), and only degrees 1, 2, 3, and 6 of the system could serve as finales [Pian 50][Tokita 22 (though this chart has some mistakes)], producing equivalents to the Western Lydian, Mixolydian, Aeolian, and Dorian modes.

In contemporary Japanese gagaku, only seven of the original eighty-four chōshi** have survived, many of them modified in transmission. Japanese music theory divides these modes into a ryo (呂, , originally 'even-numbered note of the gamut') type and ritsu (律, , originally 'odd-numbered note of the gamut') type. The ritsu chōshi are Dorian modes with finales on A, E, and B: respectively, they are ōshiki-chō (黄鐘調, 'chōshi in A'), hyō-jō (平調, 'chōshi in E'), and banshiki-chō (盤渉調, 'chōshi in B'). The ryo chōshi on the other hand are Mixolydian modes with finales on D, A, E, and G***: respectively, they are ichikotsu-chō (壹越調, 'chōshi in D'), sui-chō (水調, lit. 'water chōshi'), taishiki-chō (太食調, lit. 'great eclipse chōshi(?)'), and sō-jō (雙調, lit. 'double chōshi') [1][4]. Although the ritsu chōshi are less numerous than the ryo chōshi, more repertoire has been written in the former and that repertoire is more frequently played (Garfias 63). The latter emphasize their pentatonic origins, while the former are more solidly heptatonic; each chōshi has a different microtonal inflection on every degree, with more ornamentation in the ritsu types.

*In Japanese pitch.
**I am using the Japanese reading so as to keep gagaku terms in their native language.
***Sort of. At some point, the fixed-pitch instruments used in gagaku stopped being able to play F♮, and the few pieces in sō-jō were changed to G Aeolian.

1. Tokita, Alison McQueen and Hughes, David. The Ashgate research companion to Japanese music.
2. Pian, Rulan Chao. Sonq dynasty musical sources and their interpretation.
3. http://gagaku.stanford.edu/en/theory/pitch/
4. Garfias, Robert. Music of a thousand autumns: The Tōgaku style of Japanese court music.

EDIT: Changed the term 'key' to 'system' based on Salmoneus' reply, and changed some phrasing to clarify.
Last edited by Pāṇini on 28 May 2022 02:12, edited 5 times in total.
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Re: Notes on the music of China and Japan

Post by Pāṇini »

Davush wrote: 20 May 2022 10:16 Thank you for this thread! It’s great – I like the inclusion of characters and Pinyin.
I'm so glad I can share [:D]! This particular romanization style/format was principally inspired by Zompist's China Construction Kit, in which all Pīnyīn consistently has tone diacritics and words are first introduced next to their characters.
– The half-sharp fourth as the “default” is also quite surprising (and again opposite to the Arabic system where perfect fourths are generally very stable)! I’d be interested to hear some examples if you know of any?
[...]
– Is the tuning referring to tuning of open strings, or is it also the exact “manual intonation” of the notes ? For example, are there instruments where only a few open strings are tuned (maybe the erhu)? On such instruments (if they exist), is the “wolf fourth” still preferred when “manually” intonated (or does it depend on the mode/region/player)? If you have the time, could you give an example of how an instrument(s) would be tuned “in practice” in simple terms?
I can likely kill two birds with one stone here. The Teochew sízhū composition Hányā Xìshuí (寒鴉戲水, lit. 'Winter Ravens Playing in the Water') is in a mode which traditionally emphasizes both the wolf fourth and neutral seventh. In cipher notation, the first four bars of the composition are written:
| 5 46 5 65 | 45 25 4 — | 5 46 5 43 | 2. 1̱ 7̣1 2 — |
Traditional recordings such as this one* by Chén Lěishì (陳蕾士) and Zhèng Sīsēn (鄭思森) or this one by the Su family ensemble** emphasize the microtonal tuning, while newer recordings such as this one*** use equal temperament. To some degree, this is a question of the difficulty of using the older system on new fretted instruments, which have been manufactured to use equal temperament. Chinese conservatories also teach the "friendlier" equal temperament system over the older microtonal one.

1. https://www.youtube.com/watch?v=rU-yMwpduA8
2. https://www.youtube.com/watch?v=3e3EV7BU93Q
3. https://www.youtube.com/watch?v=MN2Gx0GZdY0

EDIT: Changed the last link.
Last edited by Pāṇini on 25 May 2022 14:30, edited 2 times in total.
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The sky swallows the road to Kokonor. On the Great Wall, a thousand miles of moonlight.
—/lí ɣɑ̀/ (李賀), tr. A. C. Graham
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Re: Notes on the music of China and Japan

Post by Pāṇini »

Torco wrote: 21 May 2022 06:51 Jupiter's balls, what wealth of musical insight have I found after going 'I wonder what's up in the cbb'. thank you so much for this thread, and I look forwards to moar. And the chinese are so... writy! I bet their musical history is relatively well documented.
I'm enjoying myself [:P]. I'd really dive into the primary sources if I had more Literary Chinese, but alas.
The first thing that Westerners tend to notice about the music of the Hàn (漢) Chinese is the pentatonic scale upon which it is structured. The pentatonic scale has been in China for a very long time: biānzhōng (編鐘, ‘organized bells’) dating back to the Zhōu (周) dynasty are based around the same wǔshēng (五聲, *goshō, ‘five tones’) as the instruments of today [1]: gōng (宮, kyū, ‘do’), shāng (商, shō, ‘re’), jué (角, kaku, ‘mi’), zhī (徵, chi, ‘so’), and yǔ (羽, ū, ‘la’). These are relative, rather than absolute, pitch names, and are equivalent to degrees 1, 2, 3, 5, and 6 of the Western major scale, respectively.
the wiki says chinese music is almost always based on the 12356 pentatonic. I guess I'm thinking about this from the lens of western music, and it's comparisons with arabic (for obvious reasons I guess lmao)... is it really that focused on the pentatonic? especially in light the fact that they do have 12 names for 12 pitch classes, or is that like a stereotype? cause from a layman's view, it sure does sound like it. that wouldn't make it super unique, though, plenty of cultures really like the pentatonic.
I think the key phrase here is "based on". Chinese music certainly stresses pentatonic scales, but the traditions with which I'm familiar go past the pentatonic into a quasi-heptatonic system. For a Western analogue, the tunes "Danny Boy" and "Oh Susanna" are mostly pentatonic, but occasionally hit scale degrees 4 and 7. Most Chinese music is like that.
Personally, I'd prefer plain C-D-E etc, since it's easier to remember what order they come in, but that may just be me...
seconded, especially since we hispanics don't use moveable do, but I mean, whatever's more comfortable for Panini we can, surely, adjust to.
Mano, también soy hispano [:D]. One of the books that I was referencing used movable-do solfege, but I've stuck with degree numbers since then. They're even more convenient as they very easily translate to cipher notation (簡譜, jiǎnpǔ, 'simple notation').
I thought I'd do modes next, as sort of a comparative overview of the Sinospheric traditions I'm familiar with, but I feel like that structure might be both difficult to follow and divorced of some important (and interesting!) context. Any thoughts on an alternative?
I'm all for context, but if you're taking requests, I can mention the aspects of traditional chinese music that have most struck me: none of these observations are like proper musicology or anything, just vibes I get.

* traditional chinese music feels very impresionistic, as opposed to western which feels quite narrative: a lot more satie than mozart, so to speak. I know, I know, it's an ethnocentric comparison, but hey, we do what we can: besides, arabic, indian, mapuche, persian... they all have this quality of having the melody and the rythm sort of "push" them forward. by contrast, it feels like what I get when I search for chinese classical is a lot more... like, "look at this sonority, isn't this a cool sonority? check this other sound. are they not beautiful? does this other thing not sound super banging in contrast?". like, I guess what I'm trying to say is that it doesn't feel so much concerned with resolution. this is probably limited exposure and a particular taste for the guqin 古琴, tho.
Spoiler:
if someone doesn't know it, the guqin is like a zyther you pluck and use the body of the instrument as a a fingerboard. it's fretless, so harmonics and glisandi and vibrato are used a lot. the thing itself is a long sort of long rounded box thing, very specific shape, whith a bridge and a nut on each sidea and strings, tuned to the pentatonic, running up and down it. it sounds resonant and mellow at the same time, which is super dope, and though it's not loud it looks like a wonderful instrument to just noodle around: the music people traditionally play on it is lovely, you owe it to yourself to give it a google
* perhaps relatedly, I perceive chinese music as being on the lower side of the spectrum if we're to order various musical traditions from most to least concerned with rhythm: the pulses of the music are relatively simple, and there's a lot of what westerners call rubatos, accelerandi and ritardandi: like the beat of the internal metronome is constantly shifting, following the music rather than the music following it. this gives it some of its stereotypical associations with 'pleasantness' and 'contemplativeness'.

perhaps these things make sense in the context of its history and its sociology?
As a non-practitioner and observer, I absolutely agree. In the words of Thrasher, "Traditional Chinese musical accomplishment must be measured almost entirely in melodic sophistication. Where other world cultures have developed complex harmonic and rhythmic systems, Chinese musicians have felt that development of the melodic line was of paramount importance, and that melodic enrichment was best achieved by varying the melodic parameters themselves" [76].

The music of the gǔqín (古琴, kokin, 'ancient string instrument') is tied to a very particular sociocultural context; the qín* is the traditional instrument of the Confucian gentleman and scholar. Mastering it is one of the literatus' four arts (四藝, sìyì), along with the board game Go, calligraphy, and painting. Yǎyuè is even more important in the Confucian tradition, which stresses ritual music as essential for social order.

*Short form.
天含青海道。城頭月千里。
/tʰiæn ɣɑm tsʰieŋ.hɑ́i dʱɑ́u ‖ ʑʱeŋ dʱəu ᵑgyæɾ tsʰiæn lí/
The sky swallows the road to Kokonor. On the Great Wall, a thousand miles of moonlight.
—/lí ɣɑ̀/ (李賀), tr. A. C. Graham
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Re: Notes on the music of China and Japan

Post by Salmoneus »

Thank you again for all this. There's several things I'd like to ask about or comment on, but it'll have to wait until tomorrow now (or the day after?). Instead, I'll just share a few historical notes from Grove on the topic of gagaku, which may or may not be true:


- 'yayue' originally referred to the ancient music of confucian rituals, but 'gagaku' didn't. By the time the term was borrowed into Japanese, its meaning had changed to mean, essentially, contemporary Chinese pop music. Much of this in turn was not originally Chinese, since foreign music was very much in fashion, and most Chinese pop music of the time was a localised version of Indian, Central Asian, or sometimes Korean music.

- however, the earliest layers of gagaku weren't even Chinese, but rather Korean (although Grove suspects heavy Chinese influence - this was probably Chinese music via Korea (or Korean music via China and then Korea again in some cases)). Music direct from China arrived centuries later: 'Korean' music arrived in the 6th and 7th centuries, whereas direct contact with China began in the 8th. When it did, however, Chinese music became the biggest part of the gagaku repertoire.

- the Japanese government set up a government department to regulate music and dance in 701

- gagaku did contain a small repertoire of pre-Korean actual Japanese music, 'wagaku', but Grove doesn't say anything about it or ever mention it again

- Japan subsequently cut off cultural contact with China, so that as musical culture developed in China, it remained fossilised in Japan for many centuries (the Heian, basically). The Japanese were also much better at writing it down, so that Japanese sources (even from centuries later) are more useful than domestic Chinese sources in learning about Tang music.

- however, modern gagaku is completely different from the original gagaku. The Kamakura saw a reduction in the number of court events, and "by the early 14th century" there's evidence of massive reworking: "the melodies for the two key melodic instruments, the ryūteki and hichiriki, began to be transformed into the new formula-based melodies that dominate modern performances, and the original melodies began to fade into the overall texture". [there's some explanation of this (including a to-me stunning fact!) but that would be getting ahead of you!]. The modern tunes "bear no audible resemblance" to original gagaku melodies, and depart from the original Chinese modal rules.

- there have also been two more intentional reworkings. During the Sengoku period, some genres were lost entirely, while the main ones were "severely damaged"; the Tokugawa subsequently worked to "restore" or "reconstruct" gagaku, but this was not complete for some genres until the early 19th century

- however, this process of restoration led to (my words, not Grove!) worrying signs of diversity and creativity, so during the Meiji Restoration the new government summoned all the gagaku musicians and forced them to form a committee to develop new, universal music, with only one compromise version of each piece, and to then record and promulgate the new, approved music. At this time, it was also considered advantageous to develop an ideology of permanence and ancient authority, which claimed that gagaku had remained unchanged since the Asuka period.
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Re: Notes on the music of China and Japan

Post by Pāṇini »

Salmoneus wrote: 26 May 2022 02:22 Thank you again for all this. There's several things I'd like to ask about or comment on, but it'll have to wait until tomorrow now (or the day after?). Instead, I'll just share a few historical notes from Grove on the topic of gagaku, which may or may not be true:
The pleasure is all mine [:D]. Everything you've mentioned in Grove lines up with the history of gagaku write-ups I've seen in the different sources. It especially makes sense that Japanese gagaku is a descendant of Chinese súyuè rather than yǎyuè, though it seems likely that they weren't all that different from a theoretical standpoint by the Táng era.
天含青海道。城頭月千里。
/tʰiæn ɣɑm tsʰieŋ.hɑ́i dʱɑ́u ‖ ʑʱeŋ dʱəu ᵑgyæɾ tsʰiæn lí/
The sky swallows the road to Kokonor. On the Great Wall, a thousand miles of moonlight.
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Re: Notes on the music of China and Japan

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Pāṇini wrote: 25 May 2022 02:59 In theory, one could play in the key of any of the twelve shí’èrlǜ pitches, and any of the seven pitches within those keys could serve as finalis. Therefore, scholars of the Tàng and Sòng recognized eighty-four possible mode-key combinations, or diàozi (調子, chōshi, ‘mode-key combination’), in which yǎyuè could be played [Pian 43]. A subset of twenty-eight diàozi were referred to as ‘popular’, as they were used in the súyuè (俗樂, *zokugaku, ‘popular, vernacular music’) of the time. The twelve keys were pared down to seven (D, E♭, F, G, A, B♭, and C*), and only scale degrees 1, 2, 3, and 6 could serve as finales [Pian 50][Tokita 22 (though this chart has some mistakes)].

In contemporary Japanese gagaku, only seven of the original eighty-four chōshi** have survived, many of them modified in transmission.
Could you clarify some things for me here? When you talk about possible finales, and about modes, are you equating those two? And when you list the allowable finales, are these relative to the absolute system, or to the individual mode?

To expand the first question: in the European version of this system, there is a distinction between octave species and finalis.

In early Europe, in so far as I think I understand it, there is only one 'key' as you use the term (Grove seems to use 'system'). All seven degrees can be the finalis. But to define the modes, we then need to also know the 'ambitus' of the music, relative to the finalis - the ambitus being the range of notes that are actually used in that music (an octave). The finalis is not necessarily the lowest note of the ambitus - it can alternatively be the fourth note of the ambitus. Therefore there are eight modes rather than seven, and they can be divided into four pairs of modes that share exactly the same notes, but have different finales - 'authentic' if the finalis is the first note, and 'plagal' if it is the fourth. [specifically, the finalis may be on I, II, III or IV (using roman numerals to name degrees of the absolute 'key' or 'system') if the mode is authentic, hence yielding plagal modes with the finalis on IV, V, VI or VII]. [the authentic and plagal modes are further distinguished by different notes having different functions, but finalis+ambitus is enough to define them]. We can also speak of the authentic and plagal modes sharing the same species, meaning a specific order of intervals between notes in the scale (1234567 vs 2345671, etc), which I think is what you mean when you say 'mode'.

[species and ambitus are equivalent (though differently-defined) concepts in early European music, I think, since the ambitus plus the fixed system implies the species. However, if the system is not fixed - as in China, or as in modern European music - then the species and the ambitus can be changed independently of one another]

Am I right in thinking that you're implying that in the Chinese system ALL the permitted diàozi are 'authentic' in this sense, of having the finalis as the lowest note in their ambitus (and hence being definable just by the key note plus the finalis)?

And on the second question, which is of course related: when you say 'scale degrees 1, 2' etc, do you mean degrees of what you're calling the 'key', or of what you're calling the 'mode'? (if my assumption in the last question was correct, it must be the former, but I might be wrong).


... I hope my questions made sense, because now I'm confusing myself again...

Japanese music theory divides these modes into a ryo (呂, , originally 'even-numbered note of the gamut') type and ritsu (律, , originally 'odd-numbered note of the gamut') type. The ritsu chōshi are Dorian modes built off of A, E, and B: respectively, they are ōshiki-chō (黄鐘調, 'chōshi in A'), hyō-jō (平調, 'chōshi in E'), and banshiki-chō (盤渉調, 'chōshi in B'). The ryo chōshi on the other hand are Mixolydian modes built off of D, A, E, and G***
So just to be clear, the ritsu choshi are pure transpositions of one another, and have the same 'species' (order of intervals) but different 'ambitus' (pitch range) relative to an absolute pitch? And likewise the ryo choshi with the exception of so-jo?



And just to throw in some context here that those following along may not know: 'ritsu' and 'ryo' are vital political terms from the era, together defining the Japanese national structure. (where ritsu was the criminal code, and ryo was the administrative code and constitutional structure). Ritsuryo was introduced by the taika reforms about half a century before the creation of the gagaku department.
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Re: Notes on the music of China and Japan

Post by Pāṇini »

Salmoneus wrote: 28 May 2022 00:50
Pāṇini wrote: 25 May 2022 02:59 In theory, one could play in the key of any of the twelve shí’èrlǜ pitches, and any of the seven pitches within those keys could serve as finalis. Therefore, scholars of the Tàng and Sòng recognized eighty-four possible mode-key combinations, or diàozi (調子, chōshi, ‘mode-key combination’), in which yǎyuè could be played [Pian 43]. A subset of twenty-eight diàozi were referred to as ‘popular’, as they were used in the súyuè (俗樂, *zokugaku, ‘popular, vernacular music’) of the time. The twelve keys were pared down to seven (D, E♭, F, G, A, B♭, and C*), and only scale degrees 1, 2, 3, and 6 could serve as finales [Pian 50][Tokita 22 (though this chart has some mistakes)].

In contemporary Japanese gagaku, only seven of the original eighty-four chōshi** have survived, many of them modified in transmission.
Could you clarify some things for me here? When you talk about possible finales, and about modes, are you equating those two? And when you list the allowable finales, are these relative to the absolute system, or to the individual mode?
I've reworked my original post using terminology closer to yours (which I hadn't come across and actually like much better [:D]). Maybe this'll answer a couple questions:

In theory, one could play in a system based on any of the twelve shí’èrlǜ pitches, and any of the seven pitches within those systems could serve as a finalis. Therefore, scholars of the Tàng and Sòng recognized eighty-four possible mode-system combinations, or diàozi (調子, chōshi), in which yǎyuè could be played [Pian 43]. A subset of twenty-eight diàozi were referred to as ‘popular’, as they were used in the súyuè (俗樂, *zokugaku, ‘popular, vernacular music’) of the time. The twelve systems were pared down to seven (based on D, E♭, F, G, A, B♭, and C*), and only degrees 1, 2, 3, and 6 of the system could serve as finales [Pian 50][Tokita 22 (though this chart has some mistakes)], producing equivalents to the Western Lydian, Mixolydian, Aeolian, and Dorian modes.
Am I right in thinking that you're implying that in the Chinese system ALL the permitted diàozi are 'authentic' in this sense, of having the finalis as the lowest note in their ambitus (and hence being definable just by the key note plus the finalis)?
Mostly. All of the permitted diàozi are definable by just the note on which the system is based plus the finalis, but ambitus (as far as I understand) may well be a non-issue, as in modern European art music or modal jazz. Garfias doesn't mention ambitus at all when dealing with gagaku, and Pian writes that her primary sources give all their diàozi with an ambitus between D/E♭ and C/C♯.
天含青海道。城頭月千里。
/tʰiæn ɣɑm tsʰieŋ.hɑ́i dʱɑ́u ‖ ʑʱeŋ dʱəu ᵑgyæɾ tsʰiæn lí/
The sky swallows the road to Kokonor. On the Great Wall, a thousand miles of moonlight.
—/lí ɣɑ̀/ (李賀), tr. A. C. Graham
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