harmonic vs. melodic notation

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cmloegmcluin
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harmonic vs. melodic notation

Post by cmloegmcluin »

I'm working on a tutorial video for Sagittal right now, and to illustrate a particular point I needed an example of two alternative tunings that diverge from standard tuning but with deeply different agendas. So for one alternative tuning I chose JI, and for the other alternative tuning I sought an (the?) EDO which could least be said to be an effective tool for approximating JI and similarly could most be said to be an aesthetic unto itself. I'll always remember when my friend Kit called 23-EDO a "meme tuning", and indeed I think it fits the bill here: according to Wikipedia, it is "the largest EDO that has an error of at least 20 cents for the 3rd (3:2), 5th (5:4), 7th (7:4), and 11th (11:8) harmonics".

If you look on its Wikipedia page, it proposes an interesting dichotomy: between a "harmonic notation" and a "melodic notation". The latter is dumber, treating sharps and flats more as instructions to move up or down by one scale step, respectively. The former is more in line with how Sagittal approaches notation, at least in that it recognizes that based on their definition with respect to a chain of fifths, apotomes (sharps/flats, or chromatic semitones) are negative in 23. Sagittal, of course, reasonably figures you shouldn't use the symbol at all, if its meaning is so distorted, and instead bases steps on fractions of a limma (diatonic semitone, or distance from E to F).

Anyway, I just wanted to bring the dichotomy up here, because I couldn't find any information elsewhere online about the distinction, nor could I find any info about "conversion notation" which is given as another term for the "harmonic notation" because you can translate from other EDOs into it. I was wondering if perhaps anyone is aware of melodic pitch notations having much cache in the alternative tuning world. Or if maybe they would or should only be entertained for extreme outlier EDOs and the like. And harmonic notations are and should be the standard.

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Re: harmonic vs. melodic notation

Post by yahya.abdal-aziz »

cmloegcmluin wrote: Fri Feb 19, 2021 8:49 am
… 23-EDO … according to Wikipedia, …

If you look on its Wikipedia page, it proposes an interesting dichotomy: between a "harmonic notation" and a "melodic notation". The latter is dumber, treating sharps and flats more as instructions to move up or down by one scale step, respectively. The former is more in line with how Sagittal approaches notation, at least in that it recognizes that based on their definition with respect to a chain of fifths, apotomes (sharps/flats, or chromatic semitones) are negative in 23. Sagittal, of course, reasonably figures you shouldn't use the symbol at all, if its meaning is so distorted, and instead bases steps on fractions of a limma (diatonic semitone, or distance from E to F).

Anyway, I just wanted to bring the dichotomy up here, because I couldn't find any information elsewhere online about the distinction, nor could I find any info about "conversion notation" which is given as another term for the "harmonic notation" because you can translate from other EDOs into it. I was wondering if perhaps anyone is aware of melodic pitch notations having much cache [sic (¿=cachet?)] in the alternative tuning world. Or if maybe they would or should only be entertained for extreme outlier EDOs and the like. And harmonic notations are and should be the standard.
Your last statement seems unnecessarily prescriptive! Why should any harmonic notion prevail over a melodic? That smacks rather of cultural imperialism … ! ;)

A primarily melodic tradition, such as classical Hindustani (i.e. North Indian) or Karnatic (i.e. South Indian) music, whilst being fully aware of the harmonic implications of any tuning, would naturally choose names (and thus notations, which are essentially arrangements of abbreviated names) that reflect the melodic use of accidentals. Specifically, the Sargam nomenclature (Sa, Ri, Ga, Ma, Pa, Dha, Ni, [sa]) recognises both single and double (Ati) sharps (Tivra) and flats (Komal) to any of these diatonic scale degrees; thus a raga may be learnt as, e.g. Sa, Ri komal, Ga, Ma tivra, Pa, Dha komal, Ni komal, [sa] ascending, and as [sa], Ni ati komal, Dha ati komal, Pa, Ma, Ga komal, Ri komal, Sa descending. (This example describes a fictitious raga; I know of no traditional raga of either North or South India with exactly this distribution of melodic steps (called variously "sruti" = tones or "varna" = colours, though I can easily envision using it.))

You can see the Sargam system in use in the recent web applications Apotome and Leimma, along with the ratios usually chosen for these different varna.

Personally, I like the dichotomy between melodic and harmonic notations, since it lets the practitioner place the emphasis where they feel it belongs, in their own music (or musical tradition). How one goes about reconciling the two in a single system, I haven't a clue! Ravi Shankar used to inveigh against the corrupting influence of Western harmonic practice, and particularly its fixed-tuning instruments, such as the simple reed harmonium (usually tuned in 12-EDO rather than any other meantone), on the Hindustani music tradition. More than 50 years after hearing him rant on this topic, I'm no closer to having any useful answer, and am rather less inclined now than then to believe one possible.

Regards,
Yahya

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Re: harmonic vs. melodic notation

Post by cmloegmcluin »

Thanks for being gentle with me, Yahya! Cultural imperialism was just the sort of thing I was worried about, and re-reading what I wrote, I can see that perhaps with the final sentence I wrote (pretty hastily) I was flirting with it myself rather than being open about why I was interested in the issue in the first place. What I was trying to do was figure out to what extent, if at all, I could get away with a statement along the lines of: Sagittal could be a lingua franca for pitch notation. I'm thinking now it wouldn't be entirely fair. I already have some disclaimers, e.g. recognizing that there completely other pitch notation strategies like proportional/spatial notation (like David Canright's "rational notaiton", or Andrew Killick's "global notation"), but that to use Sagittal is to at least buy in to the whole 5-line staff, 7-nominals situation. But I now think I should expand the disclaimer on that statement to include how Sagittal's assumptions about how people perceive pitch are primarily harmonic, and so it may not be the best choice for representing music from certain musical traditions which approach pitch from a primarily melodic perspective.

Certainly Sagittal can't work for everyone. I myself resisted Sagittal for many years because I thought its assumptions about music ran counter to mine (at least some of the time: trying to avoid JI at all costs, or avoid using simple JI anyway, like no octaves, or no fifths). I don't entirely not think that, but I see other benefits to using it anyway.

I certainly don't mean to speak as an expert here... still very much learning. Thanks for enlightening me.

And to be clear, I don't think melodic notation is dumb, in general. Perhaps I should have chosen a different word altogether. I chose it in haste. What I really meant was "straightforward". As a software engineer, I often use "dumb" as a compliment, meaning straightforward, where I would use "clever" as its antonym, as a critique :)

I think the more subtle point, which I may not have the space to make in such a brief introduction to Sagittal, but might like to make in a longer form piece, is the one you've already made: that melodic and harmonic notations wouldn't necessarily conflict (as those two 23-EDO notations would) but could compliment each other (as Sagittal and Sargam would).

As for how to reconcile the two in a single system... I'm not even going to go there. Perhaps @Dave Keenan has some thoughts on it. I think he's on a hike for the next few days, though.

By the way, I came across that Leimma & Apotome tool thing recently on Facebook but at the time I only managed to see the Apotome half of it. I spent a little while this morning playing around with Leimma. Very interesting and particularly well-crafted, I must say! Looks like the creator Khyam Allami was recently interviewed by a hero of mine, Holly Herndon.

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Re: harmonic vs. melodic notation

Post by Dave Keenan »

AFAIK, that choice between harmonic and melodic notations is specific to 23-edo and two other edos on the right of the periodic table, namely 16 and 9, sometimes called the Mavila EDOs.

Every sagittal notation is both melodically and harmonically consistent in the sense of that 23-edo article. We achieve that in the case of the Mavila EDOs, by not using sharps or flats at all. Sagittal never uses a symbol to notate a given temperament if that symbol represents a comma whose tempered size is negative in the given temperament.

There is also the option of notating 23-edo using its second-best fifth — the 23b equal temperament. This uses sharps and flats but is not yet shown on the periodic table. It will be positioned immediately to the left of 25edo and will use the same sagittals as 30edo and will have #=6, CD=5 and not use F and B. It could also be notated as a subset of 46edo.

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Re: harmonic vs. melodic notation

Post by cmloegmcluin »

Ah, okay. So Sagittal is harmonically-based, but still quite suitable in terms of melody in almost all cases. Could anything else cause harmonic and melodic disagreement besides a negative chromatic semitone?

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Re: harmonic vs. melodic notation

Post by Dave Keenan »

cmloegcmluin wrote: Sun Feb 28, 2021 4:43 am Ah, okay. So Sagittal is harmonically-based, but still quite suitable in terms of melody in almost all cases. Could anything else cause harmonic and melodic disagreement besides a negative chromatic semitone?
Yes. A negative anything. Including F being lower in pitch than E. None of which we do in Sagittal.

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