Talk:Mason Green's New Common Practice Notation

From Xenharmonic Wiki
Jump to navigation Jump to search

The standard notation with which I am familiar has the major scale designated as 1 2 3 4 5 6 7, so, I believe, the major seventh should be 7, not 7#, as this page currently (24 April 2019) has it. Maybe there is another sort of notation with which I'm unfamiliar, that looks similar to the notation taught in the USA, though.

Also, and I know this is a can of worms to open, but I have qualms with an EDO using any sort of notation that references a diminished octave or augmented unison. Unison is unison; either two tones have the same fundamental frequency or not. Saying "augmented unison" seems like a self-contradictory reference. In this case, wouldn't it be more appropriate to refer to a small interval as a diminished second? I think there is more wiggle room, logically with a "diminished octave," but again, there could be, in this particular tuning, an augmented seventh, which seems to make more sense. If you break down the major diatonic scale into components: 1 2 3 4 5 6 7, and you have three types of components:

1, which is your point of reference, where you define the scale as starting. 2 3 and 6 7, which are tonal components that can come in a wide variety of tonal flavours, including major, minor, augmented, and diminished (and some others, maybe, that don't have much relation to 19-EDO). 4 and 5, which have a narrower variety: either perfect, augmented, or diminished.

In 19-EDO, you satisfy a finite set of the tonal options (keeping in mind the spelling of the major diatonic scale is WWHWWWH). Define four step sizes (that's sufficient to cover every tone):

1. One quantum is a diminished step (XS) 2. Two quanta are a half step (S) 3. Three quanta are a whole step (L) 4. Four quanta are an augmented step (XL)

If you start with 1 as being defined as the starting point (again, that major diatonic scale is WWHWWWH or, in quantum notation 3 3 2 3 3 3 2):

bb2 = 1 + XS (diminished second) b2 = 1 + S (minor second) 2 = 1 + L (major second) #2 = 1 + XL (augmented second) bb3 = 2 + XS = #2 (diminished third) b3 = 2 + S (minor third) 3 = 2 + L (major third) #3 = 2 + XL (augmented third) b4 = 3 + XS = #3 (diminished fourth) 4 = 3 + S (perfect fourth) #4 = 3 + L (augmented fourth) b5 = 4 + S (and so on...) 5 = 4 + L #5 = 4 + XL bb6 = 5 + XS = #5 b6 = 5 + S 6 = 5 + L #6 = 5 + XL bb7 = 6 + XS = #6 b7 = 6 + S 7 = 6 + L #7 = 6 + XL 8 = 7 + S (since the tuning references the octave, like I said above, there is no need to subdivide the octave into tonal varieties)

From those tones, you can spell any scale possible in western music theory. Major 1 2 3 4 5 6 7, natural minor 1 2 b3 4 5 b6 b7, phrigian ("saturated minor") 1 b2 b3 4 5 b6 b7, locrian ("half diminished") 1 b2 b3 4 b5 b6 b7, full diminished 1 b2 b3 b4 b5 b6 bb7, saturated diminished 1 bb2 bb3 b4 b5 bb6 bb7, augmented 1 2 3 #4 #5 6 7, saturated augmented 1 #2 #3 #4 #5 #6 #7, or any admixture you can dream up, with the only complication being that some augmented-to-diminished steps leave you with no interval change, so, for example, 1 #2 bb3 4 5 #6 bb7 doesn't make a whole lot of sense in this tuning, since you have #2 enharmonically equivalent to bb3, so the two are in unison; same goes for #6 and bb7.


1) I strongly agree that the major 7th should be 7 not #7.

2) "Augmented unison" is not a self-contradictory reference, it's a standard music theory term. It even has its own wikipedia page. In some 19edo contexts, it could be called a dim 2nd and written bbII. But in other contexts, #I makes the most sense. For example, I - III - #Im - VI - I. Likewise bI is best for Im - bI - Im (actual musical example from Pink Floyd's Shine On You Crazy Diamond verse).

3) WWHWWWH doesn't makes sense in 19-edo. Better to say LLsLLLs (large and small).

4) What you call quanta are better called edosteps, a more self-explanatory term.

Everything else you said I agree with :) By the way, "2 3 and 6 7... come in a wide variety of tonal flavours," these are called imperfect degrees, 1, 4 & 5 are perfect degrees. --TallKite (talk) 02:17, 25 April 2019 (UTC)

2) If you say so. With all due respect, though, I'm not convinced from a fundamental level, though. First off, I and 1 are not the same exact thing, but maybe I'm splitting hairs. I is a chord and 1 is a note. The 1 note refers to the start of the scale and the I chord is the tonic chord based off of the root of the key... I don't see how an accidental can be placed on the root note of the scale in purely general terms where the context of 1 2 3 degrees would be used. Secondly, the Verse of "Shine On You Crazy Diamond" is Gm F# Bb, no? The chorus is Gm/F# Gm/F... neither are what I would ever notate as Im bI Im, more like i #VII iii... or i i/maj7 i/m7... but maybe I misunderstood. At any rate, some sort of change going Im bI Im would be more clearly notated as Im #VII Im, no (I know there are different schools for roman numeral notation)? Since, for example, the harmonic minor scale is notated with a major seventh degree. It really doesn't make any sense to me, from any context I can imagine, where a song (standard non xen tuning) in C minor has a C flat in it, rather than a B natural. And 19-edo is a tuning that fits very well within the context of diatonic scales and harmonic minor scales and such. There are lots of differing schools of thought, though. But, some of my theory professors at uni would cringe anytime someone would use an accidental in any sort of unclear way, like writing bI or #I instead of VII or bII. Maybe those people are wrong. And I never heard of augmented unison outside of the online microtuning groups. I explained why I don't like it. My word on it is, by no means, authoritative.

3) Why not use W and H? Just about everyone knows that notation. I did use those to work toward explaining L and S, anyway.

4) My mistake. EDO steps is much clearer.


2) Suppose a 12-edo song is in A minor, the chords go Am - Ab (or G#) - Am, and the melody uses a C note over all chords. If the 2nd chord is G# major, since the melody note is the 3rd of the chord, the note would logically be spelled B#. (If it weren't, you would have a G# - C - D# chord, which would logically be called a "sus-dim-4th chord", which is silly.) Calling the 2nd chord Ab major allows the melody note to remain C. Which it should, because it's better if a single note doesn't have two names. Thus the chords go Am - Ab - Am, which in relative notation is Im - bI - Im.

3) W and H mean whole and half, and imply that the L/s ratio is 2:1. But in 19-edo, the ratio is 3:2. L and s are better names because they don't imply an incorrect L/s ratio. --TallKite (talk) 09:44, 26 April 2019 (UTC)

Thanks for the response. I listened to the Pink Floyd song again, and I'm pretty sure that the tonal center is Bb for the passage in question, not Gm. The change from Gm to Gbmaj, then, being vi - bVI - I, so I was wrong earlier.

Since when is a "whole step" exactly two times the distance of a "half step," though? Isn't it still common to refer to those steps as such in the context of a just major scale? Under that umbrella, there is more than one type of whole step and a half step is not exactly half of either. Maybe my knowledge ofvthe jargonnis just too outdates.


Also, the other pages on this wiki for 19-EDO are consistent with the same sort of notation with which I am comfortable. For example:

As I pointed out earlier, it's confusing for newcomers if the wiki itself uses conflicting sets of notation for the same thing without any sort of cross-reference.

--Bozu (talk) 13:45, 1 May 2019 (UTC)

Published Sources

Ok, I've done a literature search, and I'm going to double down on the "b1" or "1b" and "bI" / "Ib" notation as being generally unacceptable...

Please review any and/or all of the following literature:

Friedrich Wilhelm Marpurg, Anfangsgründe der theoretischen Musik (Leipzig: Johann Gottlieb Immanuel Breitkopf, 1757): 34.

Arthur Foote and Walter Raymond Spalding (1905). Modern Harmony in Its Theory and Practice, p. 5. Arthur P. Schmidt.

W. S. B. Mathews (1909). "Editorial: Prof. White's Harmony and Ear-Training", The Journal of School Music 1, no. 9 (June): 260–63.

Smith, Uselma Clarke (1916). Keyboard Harmony, p. 15. The Boston Music Company.

Stefan Kostka and Dorothy Payne (2004). Tonal Harmony (Boston: McGraw-Hill): 21. ISBN 978-0-07-285260-8.

Jim Aikin (2004). A Player's Guide to Chords & Harmony (San Francisco: Backbeat Books): 32. ISBN 978-0-87930-798-1.

Michael Pilhofer and Holly Day (2006). Music Theory for Dummies (Hoboken, NJ: John Wiley & Sons, Inc.): 113. ISBN 978-0-7645-7838-0.

Andrew Surmani, Karen Farnum Surmani, and Morton Manus (2009). Alfred's Essentials of Music Theory: A Complete Self-Study Course for All Musicians (Alfred Music Publishing): 135. ISBN 0-7390-3635-1.

I suggest, that, for the sake of clarity, and given the context of the article, being that it is entitled "Chord Progressions in the 19edo-family scales," that the table be edited to reflect more clear terminology. If we wish to expand the table to include some alternative nomenclature, that's fine, too, but might make things a bit untidy.

I suppose all of this is because, as I see it, the table included with this particular article is the prime example of why I feel so stupid when I try to read this wiki. The terminology used here is the polar opposite of self-explanatory. For example, the term "hygrant" is used here for the mediant chord. There is no need, in this particular context, to make up a new word for something, and I did a text search - as of 30 April 2019, the term "hygrant," out of all the internet, only exists on this one particular page. On it's own, sure, no problem, but this sort of thing is rampant on this wiki. I see it often enough browsing here that I begin to wonder if we are trying to willfully obfuscate the information to confuse newcomers to xenharmonicity. Hey, there's an example of a self-explanatory term "xenharmonic." I didn't have to look that one up the first time I saw it. On the other hand, when I see something like "caesiant," I have no idea if it has something to do with cheese, roman emperors, or the periodic table, then I see that it's a "blue" chord. And... I feel stupid again, since I have no idea what that means, either. Does anyone actively use these sorts of terms?

Bozu (talk) 20:55, 30 April 2019 (UTC)

12-EDO Roman Numeral Notation

This is the way I learned roman numeral chord notation. If other people learned by another set of symbols (I understand that the notation most common in the USA is different from that of some other countries, as is most musical notation and naming conventions, but let's talk about that...):

You choose a diatonic key, then you have to have an understanding of what that key is, otherwise, none of this has enough context to make sense. I believe the idea when the notation was developed was to make everything universal, so that a musician could decide on a key, then proceed using the roman numeral notation as a framework around the decided key, and if another musician wanted to use the same framework in a different key, it'd be very easy to move that frame work to overlay any arbitrary key.

Superscripts/post(arabic)numerals can be used to indicate dominant (I7), or a degree symbol for diminished (i°), or a plus sign for augmented (I+). "Chord colourations," that is, expanded chords, are indicated with arabic numerals, with the understanding that dominant chords are default, so major chords have a post-text of "maj" before the arabic numeral.

Then, there are exactly seven possible chords, based off the fact that western music has seven notes per scale by default. They are indicated by roman numerals indicative of the scale degree:

I, the tonic (tonic being the root key of the song, the precedent is that the "tonic" term is the same root word used in "diatonic," "pentatonic," etc.) ii, the supertonic (super meaning beyond or above) iii, the mediant ("mediant" meaning half way between the tonic and dominant chords) IV, the subdominant (sub meaning below) V (some theory books indicate V7 by default), the dominant (dominant, because this is the primary chord pushing into the tonic chord in the old way ("classical") of thinking about music theory) vi, the submediant (half way between the subdominant and tonic) viiø, the subtonic (sub being below, again - sometimes listed as vii°, but technically, the diminished seventh is out of key)

If the key of the song is a natural minor key, the chords become:

i, still called the tonic iiø, still called the supertonic bIII, still called the mediant iv, still called the subdominant v, still called the dominant bIV, still called the submediant bIIV7, still called the subtonic

Whether the chord is III or bIII or bbIII or #III or bbiii°(no 3rd)b9, it is still called the "mediant," according to the conventions I learned in school. As I said, I am open to the idea that there are most definitely other systems of terminology and notation. With that on the table, though, I still don't understand the notation and terminology proposed in this article, because there are some things inconsistent with the underlying framework of why this sort of notation works in the first place.

So, what I propose for 19-EDO, to be consistent with the notation with which I am most familiar (and the notation many musicians in the US are familiar):

Keep the same terminology listed above. Any chord associated with the first scale degree is the tonic. It could be "I" or "i" or whatever.

If your scale is something somewhat xenharmonic, like kleismic symmetrical 1 #2 b3 #4 b5 6 bb7, your chords are:

i° (tonic) #ii° (supertonic) biii°aug7 (mediant) #iv° (subdominant) bv(no 5) (dominant) vi° (submediant) NC (no subtonic)

Spelling out the dominant chord would be (from the tonic): b5 bb7 #2, and transposing that to it's own tonal center, it would be 1 b3 x5, which is a nonsense chord in classical theory, but being xenharmonic folk, we like this sort of thing... you could name it something if you like. A minor triad is 1 b3 5, and a #5 is an augmented fifth, so an x5 could be a superaugmented fifth. Maybe it's a minor superaugmented chord? The subtonic would be even more interesting in this key, bb7 #2 #4, transposed to it's own tonal center: 1 x3 x5. A triad with a superaugmented third and superaugmented fifth might be a saturated superaugmented chord or, maybe, something else.

And if you want to start doing chords for scales with more than seven notes, then you have to, in my mind, establish some sort of general rules around how to spell chords out of those extra notes. Maybe you stick to 1 2 3 4 5 6 7 8 for scale degrees and spell the tonic out of 1 3 5, but, since the 9th is now the octave, intervals are smaller, so there would ostensibly be more chances to spell diminished chords. Or maybe you spell the scale 1 2 3 4 5 6 7 with an alternate scale degree (or two) and spell the chords with different optional variations. For example 1 2 b3 3 4 5 6 7 could have both major and minor tonic chords. But, I think that, if you want to be strict about developing a new fundamental paradigm in terminology, you have to be clear about how you wish to go about doing so. And the terminology on this page isn't clear to me at what it's trying to accomplish, which is why I am so confused and proposing something else. Either I don't understand it because it sets out to do something that wasn't clearly communicated to me (maybe it's me), or maybe I don't understand it because it doesn't know what it's trying to accomplish. Either way, new terminology won't catch on unless it describes something useful for communicating to other people.

And maybe there is a gap there in terms of the musical terminology already in use. For example, in German, the lower case roman numerals are never (to my knowledge) used to indicate a minor chord, and the "mediant" is called the parallel. In Russian, sometimes lower case roman numerals are used, and the mediant is called the mediant, but the subtonic is something like opening tone and the supertonic is something like higher leading tone. In general, roman numeral notation is something that I've found doesn't translate well across cultures or languages, so maybe it's easier to simply scrap altogether.

--Bozu (talk) 13:41, 1 May 2019 (UTC)

Changes to the article

Reading the title of the article, the article digresses off the stated topic almost immediately. Perhaps the title of the article should have been "Chord progressions in 19-note systems," but that's not what it is, either. I think the article is simply missing the information that ties back to the first section, which doesn't tie back to the title of the article anyway. The first section is also not written to any formal standard. Who is Mason Green, and why does it matter which is his favourite scale? The first section doesn't tie into anything else in the article, and doesn't summarize the article, and to me, it doesn't offer any useful information relating to the title, so I propose deletion of the first section.

The second section is entitled "New intervals," but proposes an entirely new notation for intervals already presented in a much clearer fashion in the main 19-EDO article, as well as proposing this "NCP" notation. The first sentence confuses me. Is "these scales" the three listed in the first section? If so, I strongly believe that the statement is not true. The sentences that follow don't seem to matter in reference to the table, or, from what I can tell, anything else in the article nor on the wiki, and, perhaps the statement about the harmonic seventh is unclear to me, but I don't believe that it contributes anything to the topic. The statement above the table has an asterisk that doesn't seem to correspond to anything. The table itself has some problems I've discussed at length in previous comments, and the paragraphs following the table as well. But my main problem with the notation is that it is visually identical to a conflicting notation. I believe that the proposed NCP notation would merely confuse people familiar with more widely understood notation standards. Do we really want to propose a notation standard for 19-EDO that is visually identical to standard notation, and impossible to use with other EDO tunings? So, here are my proposition is to create a new article with this NCP notation explained the best we can explain it and remove it entirely from the article entitled "Chord progressions in 19edo-family scales."

The next section: Expanding Beyond Triads...

"In 12edo, triads containing the tonic, mediant (third) and fifth are considered the basic chordal harmonies." Only in 12-EDO? "Occasionally tetrads (seventh chords) appear but they are wildly out of tune and considered unstable." In 12-EDO?! At any rate, this is entirely untrue! "In NCP, triads may be considered incomplete depending on the context, and pentads, hexads, and even higher-order chords can appear and sound great." This is unclear to me. Why are triads incomplete? What context? The fact that pentads and hexads can appear is an obvious statement, and how "great" they sound is just opinion. "Also, there are many different possible chords, rather than just the major and minor." Same as any literally other tuning. "As a result, generalizing Roman numeral analysis presents problems." Based on thelack of accuracy of the arguments presented, I don't think it does. "My solution is to add a string of subscripted lowercase letters to the Roman numeral." Whose solution? Mason Green?

I propose cleaning this up and moving the remaining information into the new NCP article.

The last section: Chord progressions

"Porting is the process of translating chord progressions from 12edo to enneadecimal. Most chord progressions can be ported in some way, although it's important to note that some commas are not tempered out anymore, and there are chord progressions that close in 12edo that don't close in 19 (so that you will end up one semitone higher or lower than where you started). Most of the time, however, this can easily be remedied."

I think that's pretty good. I think one nit to pick about the wording is that it could be generalized. For example, porting could attempt to translate a chord progression from any tuning system into any other tuning system arbitrarily, and the same sorts of challenges could exist, or not, depending solely on the natures of the tuning systems and the chord progressions.

"For instance, the Coltrane changes no longer work as before because three major thirds do not make an octave. However, a variant can be constructed in which one of the major thirds is replaced with a supermajor third; this version does close."

That's very interesting, and I wish there was more of that sort of thing in the article.

"Porting the following progressions is trivial:

All progressions using only I, IV, and V. The circle progression (vi - ii- V - I). The following progressions can be ported in more than one way:

The 50s progression (can become I – vi - IV - V, or I - vi# - IV - V) "Axis of Awesome" (can become I - V - vi - IV, or I - V - vi# - IV). Pachelbel (several ways, some of which close and some don't)"

I disagree. The vi chord clearly translates to the vi chord, not the #vi chord. I cannot believe this is anything short of a mistake. Pachelbel's Canon ports very nicely in one very specific way into 19-EDO. Since the piece wasn't written in 12-EDO in the first place, I think that is also a mistake. Since these statements are not true, they need to be removed, but then there are frankly no examples of why this notation is at all necessary.

So, I propose replacing this entire section with some other information, but since I believe it is necessary for this article to be completely rewritten, this section needs to reflect that.

Furthermore, I get the feeling that the NCP notation is probably something developed solely by Mason Green for his own purposes, whatever those may be. Perhaps other people would find the notation useful, perhaps not, but, either way, it clearly doesn't belong here. If you remove NCP from this article, and then remove the mistakes, there is literally nothing left of the article. Here are the options:

1. Leave the article as is. 2. Delete the article. (Could be options to recreate the article or not) 3. Move the article to a new article for NCP.

  a. Do or don't create a new article for 19-EDO chord progressions
  b. Do or don't remove the errant information in this article from the resultant NCP article.

I really don't like option one. There are too many problems with this article, which I've outlined. Perhaps you disagree with the assessment that some of these are problems. I'd like to hear from you if that's the case. I don't think Mason Green would be particularly keen on option 2, since he was interested enough in NCP to take the time to create the article for it, albeit with a misleading title. So, that leaves option 3. Since I came here looking for an article about 19-EDO chord progressions, I'd appreciate "do" to option 3a and since I made this comment, I'd appreciate "do" to option 3b. Thoughts?

--Bozu (talk) 12:58, 2 May 2019 (UTC)

Bozu, as a quick note, I would say this should be moved to "Mason Green's 19-EDO notation," or whatever, and then this page should be edited however you see fit. I share your view there are some issues with the existing notation as written - having the augmented second be "bIII," for instance, totally breaks the pattern in 19-EDO... Mike Battaglia (talk) 16:41, 2 May 2019 (UTC)
Thanks Mike! I moved the page, as you can see, if you are reading this. I'll make a few edits, but I'll try not to mess this up any worse. --Bozu (talk) 18:55, 2 May 2019 (UTC)