Talk:Gregorian mode

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Article Title[edit]

I was surprised to come upon this article titled Gregorian Mode. While these modes were/are used for Gregorian Chant (initially, far from exclusively), I have never in all my years of music research (I hold a masters) heard them called "Gregorian modes." The common name for them are "Church Modes" (see Grove Music Online "Mode, §II: Medieval modal theory"; "Church Modes", etc.). Since it is wikipedia policy to use the most common name for an article title, I assert that we must change this article's title to comply. Pitchperfect (talk) 17:14, 5 January 2010 (UTC)[reply]

I agree. The correct term for an article with this universal content, that the first author of "Gregorian mode" had not in mind, would be "Church tone". For an article "mode", it is not universal enough. --Platonykiss (talk) 15:45, 2 December 2014 (UTC)[reply]
Invoking WP:COMMONNAME is tricky in this case. The expression "Church tone" is indeed the correct academic formulation, but it is likely to be misunderstood by ordinary readers. After all, isn't "tone" a synonym for "note"? Seen from this perspective, "Gregorian mode" is probably the more familiar term to the human being of either gender in the street, even if incorrect from a scholar's point of view.—Jerome Kohl (talk) 16:51, 2 December 2014 (UTC)[reply]

Gregorian, authentic, plagal: propose merger[edit]

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section. A summary of the conclusions reached follows.
The result of this discussion was confusion. Please stay on-topic and don't throw out other merge ideas in a discussion. The discussion has been restarted in a new section below D O N D E groovily Talk to me 02:15, 15 March 2012 (UTC)[reply]

The articles Gregorian mode, Authentic mode and Plagal mode are small and lacking information. They are also closely related; indeed any expansion would probably start by explaining their close inter-relationship. I propose merging them. Feline Hymnic (talk) 19:38, 14 March 2009 (UTC)[reply]

  • Concur, I find the close inter-relationship a compelling argument. I would have said that the present situation is like having separate articles on the different major and minor keys, instead of just one article for major and one for minor, only I see that in fact there are separate articles for every key! However, we also have separate articles on Mixolydian mode, Hypodorian mode, etc., but there are no separate article on, say, major keys with flats in the signature and major keys with sharps. The only complication I can see has to do with the inter-Wiki links to the similarly separate articles in other languages, but that shouldn't be an insuperable difficulty.—Jerome Kohl (talk) 20:07, 14 March 2009 (UTC)[reply]

Related to the above: I wonder whether it might go a step further? There seems already to be a reasonably good description of authentic and plagal modes in Gregorian chant (sections 'Organisation' and the latter part of 'Modality'). Is there scope for some sort of merger into that? Feline Hymnic (talk) 21:59, 14 March 2009 (UTC)[reply]

Hmm. There are certainly too many articles for too few actual topics here. I believe I was assuming Gregorian mode and Musical mode to be one and the same. This creates a small problem, inasmuch as there is an issue whether to merge the "Plagal mode" and "Authentic mode" articles into "Gregorian mode" or "Musical mode". Since the latter has a section on "Western Church modes", it might even be possible to merge "Gregorian mode" (after it has first absorbed the Plagal and Authentic articles) into "Musical mode" (instead of into "Gregorian chant", which of course should be cross-referenced to "musical mode" if this option is taken). The "Musical mode" article is broader than "Gregorian mode", including sections on Ancient Greek and modern modal theory, as well on "Analogues in different musical traditions".—Jerome Kohl (talk) 00:32, 15 March 2009 (UTC)[reply]

Good thoughts. Musical mode covers a range of different mode types (Greek, Gregorian, jazz, etc.). So perhaps its angle should be of "compare and contrast" nature across those types rather than a detailed exploration into any of them. Gregorian chant is already a large article and covers a range of different Gregorian topics of which the modes comprise just one. I'm inclined towards retaining (in principle, at least) a Gregorian mode article. Then the relevant sections of "Musical mode" and "Gregorian chant" can be relieved of heavy-duty explanation of Gregorian modes which, via '{{main|Gregorian mode}}', would then gravitate here. Might that structure work? Allowing various articles to play to their various strengths? Feline Hymnic (talk) 13:57, 15 March 2009 (UTC)[reply]

I've also just proposed merging Final (music), Cofinal (music) and Ambitus (music) into here. (But not reciting tone, because that topic is common across several chant types.) Feline Hymnic (talk) 19:27, 15 March 2009 (UTC)[reply]
This all sounds very sensible to me. I look forward to seeing how it plays out with other editors.—Jerome Kohl (talk) 19:34, 15 March 2009 (UTC)[reply]

No dissent, so I've just started the first stages of the merger: cofinal and final now redirect to Gregorian mode. Feline Hymnic (talk) 12:21, 21 March 2009 (UTC)[reply]

With reference to the further proposal to merge Ambitus (music) into this article, I see a big problem, and therefore must oppose this merger. As it is currently written, that article is in fact eminently mergeable. However, the term "ambitus" is also applicable far outside of the realm of chant (it may refer simply to "the range of a voice, instrument or piece", to quote the New Grove article "Ambitus"), so the problem really is that the article as it stands is too restrictive. (See also the use of the word in the New Grove articles on Andrieu Contredit d'Arras, Neidhart von Reuental, David Kellner, Philippe Verdelot, Benedetto Marcello, Brahms [§8: Chamber music], Morocco, Mohammad Omar, and Louis Armstrong, for example.) If it is merged with "Gregorian mode", then a redirect will be put in place that would require a different (clumsy) article title—such as "Ambitus (music: non-Gregorian)"—in order to accommodate a future, better-written article.—Jerome Kohl (talk) 20:19, 21 March 2009 (UTC)[reply]
Coincidentally during the last few days I, too, am inclining against the ambitus merger that I had originally proposed, for just the reasons you outline. Feline Hymnic (talk) 20:42, 21 March 2009 (UTC)[reply]
I've made a start at correcting the "Ambitus" article, which I think now does not appear so completely attached to chant theory.—Jerome Kohl (talk) 20:48, 21 March 2009 (UTC)[reply]
The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Article development[edit]

As mentioned above, I've just started expanding the article. I notice that the other articles about modes have ended up being almost impenetrable to the beginner. I suggest:

  • introducing some terminology relatively early in the article (in-depth exploration should be later)
  • being consistent with terminology (trouble already looms: are the terms "cofinal", "dominant", "tenor" and "reciting tone") equivalent?)
  • relating examples to familiar "white-note" scales (even the the development of the keyboard was far later)

Feline Hymnic (talk) 15:27, 21 March 2009 (UTC)[reply]

I think you've made a good start. With reference to your concern about articles "impenetrable to the beginner", I can see one major problem here that needs dealing with. The scale examples of modes 5 and 6 (Lydian and Hypolydian) each have B-flat instead of B-natural, and there is no explanation given for why this should be so. It would only add to the beginner's confusion, but mode 4 (Hypophrygian) really ought to have B-flat instead of B-natural on the top note only, since in chant this note must be flatted as a turning note at the top of a melodic line (only in cases of an upward extension to C is it possible to use B-natural), and a cautionary natural sign on the low B which, similarly, must always be B-natural. In addition, the example does not include the option of B-flat/B-natural found in mode 1 (Dorian). I don't know how to edit this music example but, even if I did, I'm not sure how I would address these issues. Harold Powers gives a much better example in his New Grove article, but it requires several paragraphs of explanatory material.—Jerome Kohl (talk) 19:54, 21 March 2009 (UTC)[reply]

Agreed, I spotted that this afternoon and wondered. The image was in musical mode, and seems to have been made about four years ago (2005-02-19). Someone queried it about two years ago (2007-02-03) on that article's talk page. Looks like a refresh is needed. Feline Hymnic (talk) 21:00, 21 March 2009 (UTC)[reply]

Error which needs correcting[edit]

I note that this article says:

"An authentic mode has its final as the lowest note of the scale (it may occasionally go one note below). These four modes correspond to the modern modal scales starting on D (Dorian), E (Phrygian), F (Lydian), and G (Mixolydian)."

Then it shows a .gif image of the various modes notated. If you look at the notated modes, even though the names of the modes may SAY "Lydian", it's not a Lydian mode, and there are no Lydian modes present in that picture/notation. Instead we find 6 unique modes (all BUT the Lydian mode) and 2 duplicates (the mixolydian and the dorian).

I'm not sure which is right/wrong, the words or the pitch-notation, so I didn't want to make an edit, but would prefer someone more knowledgeable to do so.

I also note that under the sub-article "Authentic Modes", this needs correcting also. Hope it gets fixed someday.

Rasselas21 (talk) 23:50, 21 May 2010 (UTC)[reply]

There is no error, but the Lydian mode is not correctly (or perhaps I should say, "fully") explained in this article, as it is in the Lydian mode article. The historical (as opposed to the modern) Lydian mode has a variable fourth scale degree. When untransposed, the authentic Lydian runs from F to F an octave higher, and may have either a "hard" or "soft" B (that is, B or B). "Many theorists of the period, however, recognized that in fact it is B rather than B that is characteristic of this mode" (citing Harold Powers's article "Lydian", from the New Grove). Consequently, the usual Medieval/Renaissance Lydian scale is indistinguishable from the modern major key (which, after all, frequently sharps degree 4 to produce a secondary dominant of the dominant). The modern Lydian scale is another matter altogether, but the concepts of authentic and plagal have no place there. Neither does the modern Lydian scale have much to do with the specifically Gregorian modes (the subject of this article). This certainly could use some clarification here, but because this is a duplicated article which should probably be merged to Musical modes (where all of this is explained in greater detail), it hardly seems worth the bother.—Jerome Kohl (talk) 01:10, 22 May 2010 (UTC)[reply]

final, cofinal, reciting tone, mediant and participant[edit]

The section "Tonality" attempts to describe five terms: final, cofinal, reciting tone, mediant and participant. But the description leaves the poor beginner, even intermediate, reader confused. Any chance of a real example, please? For instance, near the top of the article is the notation of part of "Quasi modo geniti". Might, perhaps, some of these terms be illustrated with reference to that? (Of course, there may well be better examples elsewhere in Wikipedia.) Feline Hymnic (talk) 16:19, 25 April 2011 (UTC)[reply]

Requested example added at long last. Apologies for the delay.—Jerome Kohl (talk) 04:05, 5 January 2012 (UTC)[reply]

Additional citations[edit]

Why and where does this article need additional citations for verification? What references does it need and how should they be added? Hyacinth (talk) 10:32, 3 January 2012 (UTC)[reply]

I agree that the banner is no longer applicable, and have removed it. Thanks, Hyacinth, for calling attention to this.—Jerome Kohl (talk) 20:08, 3 January 2012 (UTC)[reply]

Gregorian, authentic, plagal: propose merger 2[edit]

I'm restarting the discussion about merging Gregorian mode, Authentic mode and Plagal mode. The last discussion went horribly off-topic, in the end having seven or eight different merges proposed, and it's hard to find a consensus in that. Please stick to these three articles, and note you opinion with the words merge or don't merge. Thanks, D O N D E groovily Talk to me 02:11, 15 March 2012 (UTC)[reply]

Merge all articles are related enough to merge. Consider renaming the merged article Into church modes or something like that Paradoxical 0^2 (talk) 02:42, 18 March 2012 (UTC)[reply]
I find the fork with Mode (music)#Western church more worrisome; shouldn't Gregorian mode be developed into the main article? Sparafucil (talk) 05:41, 7 March 2018 (UTC)[reply]

Pitch terminology[edit]

I'm not sure that, although Powers may use lettering to describe the pitches of the Gregorian modes, that this is appropriate. Chant is not organised along these principles, since it is a relative system:

"It must be clearly understood that in Plainsong the notation is not and was never meant to indicate the absolute but only the relative pitch of the melodic intervals. The two clefs of Doh and Fah, and their different positions, have no other aim than to make possible or easier the writing of the melodies on the stave. Often these clefs could be interchanged, their positions could be different, as, in fact, is the case in the Manuscripts of Plainsong. It must, therefore, be well understood that the notes read on the stave are to be sung at the pitch which is within the compass of the singers, according to the size of the building, and the special character of the piece."[1]

I would then question using a nomenclature that references absolute pitches, even if it does appear in Grove, which is why I would suggest that using Relative Sol-fa syllables is a more appropriate way to express this information.

Where I am afraid that the article is currently wrong completely is in the assertion that expressing the finalis in solfége is only true with reference to 'modern fixed-Do solfége'. In the editing history, Jerome Kohl asserts that 'in modern movable-do solfège the Dorian mode is do, re, me, fa, sol, la, te, do (and so on'). This isn't correct, solfége syllables in the moveable system denote the relationships between intervals.[2] The Dorian mode begins on Re, the Phrygian on Mi, the Lydian on Fa, and the Myxolydian on So, and so on. To sing a semitone between re and mi completely changes the relationship between the two syllables. In Tonic Sol-fa, do-re is always a major second, mi-fa is always a semitone, etc.

What I think would be worth talking about, however, and this came up in the editing history, is whether the modes should be described with modern notational systems, or whether it should be described using hexachords, which is why Jerone Kohl described the leading note as 'fi' instead of 'ti'. I am inclined to the opinion that if the article will be more easily accessible if it uses modern terms. Therefore I think a choice must be made between using a system of relative solmisation, which is very close to the practical and theoretical application of chant, or the Anglophone system of lettering, in which case the article must emphasise that the Do clef does not mean that the singer is obliged to treat Do as a C.

Finally, as far as 'sticking to the source' goes, I wouldn't have thought it possible to write an article on Gregorian modality without reference to the Liber Usualis, which whilst it may be technically flawed in certain academic ways, is the only source for the current standard performance practice of the chants.

Arthurjameswright 23/04/2020 (12:45 BST)

With reference to my supposedly "incorrect" use of movable-do solfège (the accent, by the way, is grave, not aigu), I suggest you read the relevant portion of the Wikipedia article on the subject. The main reason, I suspect, that Powers avoids using solfège syllables is that they are almost certain to lead to confusion, not only because of the difference between fixed-do (which simply substitutes syllables for letter names, as is the standard practice in French, for example) and movable-do, but because in the historical context of Gregorian chant there is also the Guidonian hexachordal system of solfège (from which the modern systems descend, of course).—Jerome Kohl (talk) 17:46, 23 April 2020 (UTC)[reply]

Thank you for correcting my spelling, and I am sure there may be many more!

Firstly, the article you have referred me to does not contain any information about how one expresses the Dorian mode, or any mode for that matter, in a moveable-Do system. It is strictly limited to the diatonic scales. Secondly, with reference to your comment in the editing, I think it rather unlikely that Vinden is presenting incorrect information. He is after all a professor of the Guildhall School of Music, as well as being on the board of the International Kodály Society.

It simply isn't necessary to alter the sol-fa syllables to sing the modern modes in Solfège. No matter which pitch of the chromatic scale you begin on, if you sing re mi fa so la ti do re, you will have sung an ascending Dorian modal scale. So why are you insisting that in Gregorian chant, where there is no key signature, that the Dorian mode must begin on Re only in a fixed-Do system? Please can you provide sources with your answer that are not Wikipedia pages.

Arthurjameswright 23/04/2020 (21:59 BST) — Preceding unsigned comment added by 82.34.17.195 (talk) 20:59, 23 April 2020 (UTC)[reply]

"No matter which pitch of the chromatic scale you begin on, if you sing re mi fa so la ti do re, you will have sung an ascending Dorian modal scale". Yes, but that is either fixed-do, or a variant of movable-do in which do is attached to the tonic of what would be the major (Ionian) scale in that particular set of notes. The first variant described in that article (and the one I was taught in school) makes do the tonic of whatever scale is at hand. For C minor, do is C; for D Phrygian, do is D, and so on; for the variant you describe, do would be E and B, respectively.—Jerome Kohl (talk) 21:49, 23 April 2020 (UTC)[reply]

You are quite correct, do would indeed be E in a C minor scale, as I understand it. My understanding is of the second system in that article which is that of the Sarah Golver, John Curwen, Zoltán Kodály variety, which is in turn an adaptation of Guido d'Arezzo. In that system, do is the tonic of the diatonic major scale, and the minor scale begins on la. An understanding of the minor scale (beginning on la) is therefore predicated on knowing that la is the tonic of the major (Ionian) scale. The same is true of the modern modes in this system. Do is not only the tonic of the Ionian mode, but also the leading note of the Dorian where re is the finalis, the submediant of the Phyrigian where mi is the finalis, the dominant of the Lydian.

So I think we probably have two different understandings of the word 'moveable'. It would appear that your conception of 'moveable' is related to which degree of the scale do can be used to express; do in your understanding is moveable because it can relate to the tonic, the dominant, the mediant, or any other note of the scale. But in the Tonic Sol-fa system 'moveable' indicates that in a modulation, do becomes a different absolute pitch. Do is C when the tonality rests in C major, but when a modulation to G major occurs do then becomes G. Much in the same way that Ut can exist on C, F, or G, do can also exist on any of these notes, as well as the other nine notes of the chromatic scale. So in a sense you are right, this is similar to fixed-do, but only in as far as both systems would be exactly the same in C major.

The major advantage of approaching solfège from this perspective is that the need to make alterations to the vowel sounds is largely eradicated, and this is where I see your conception of moveable-do being closer to the fixed-do system where there may be as many as thirty-five syllables to express every possible permutation. To sing re mi fa so la ti do re only requires a knowledge of the semitone intervals mi-fa and ti-do to be performed successfully, whereas a more specialist knowledge is required to memorise the different permutations of each sol-fa syllable when do is the tonic note in any given scale. Of course, there are instances where altered syllables appear in Tonic sol-fa, in the harmonic minor scale for instance: la ti do re mi fa si la. Ta is another common one, as is fi. The major disadvantage of this way of expressing pitch is when music is polytonal or atonal, but this is true I think in every system of solfège, and in Gregorian chant we need not be troubled by that anyway.

I hope this helps to clear up any confusion. It should now be clear that I am not describing fixed-do solfège.

The reason why I regard this as a necessary subject for conversation is because in my experience as a choral singer I have met far too many people who simply see the do clef as C major. If we use absolute pitches to describe chant, or indeed fixed-do solfège, that perception will continue to be propogated if those people turn to this page for their information. As a case in point, let us consider Missa Cum Jubilo (Mass IX in the Liber). If you treat the Kyrie and the Gloria of that Mass setting as being in the same key, and in C, then you are left with the most extraordinary range, A2-A4, and unless one expects only Basses to perform the Kyrie and only Tenors to perform the Gloria then it's simply asking too much of an ordinary choir, monastic or otherwise. Even if you 'transpose' the chants down to F2-F4, the lower notes will be utterly unreachable by the tenors, assuming they were not already, and the upper notes will still be unreachable for some basses. So the point I am trying to make is the one made in the explanatory notes of the Liber, that pitch in Gregorian notation is relative, and so we should be using a relative system to demonstrate that fact. Nevertheless, I now appreciate that there are two differing ideas about relative solmisation, so I might just finish by saying that the Glover-Curwen-Kodály system is something more deeply rooted in English musical culture and also very popular in the US and Australia through its use in the Kodály educational approach. I think we should seriously consider using solfège, and perhaps acknowledging this difficulty in the article. Arthurjameswright 24/02/2020 (00:49 BST)

You seem to believe that notes with letter names have fixed pitches, whereas solfège syllables do not. The latter is of course true for either variety of movable-do solfège. Speaking as a musician without absolute pitch, and one accustomed to performing at a variety of pitch standards, the exact placement of the notes labeled F and B are entirely relative. One note will be a perfect fourth or fifth away from the other, and singers can choose to sing higher or lower as they like. I fail to see why substituting solfège syllables for note names is an advantage, especially in a theoretical discussion, where the ambiguities of three or even four different systems of solfège can easily lead to confusion that letter-names never will. Let me correct one thing: for me, using movable-do solfège by definition precludes attaching do to the dominant, mediant, or any other scale degree. It always signifies the tonic. This has obvious problems when modulations occur (as you mention), since there may be extended passages that may be understood in at least two different keys simultaneously.—Jerome Kohl (talk) 00:55, 24 April 2020 (UTC)[reply]

Yes, and what you describe is transposition, but I think it's a strange claim to assert that letter names do not have fixed pitches.

Let me put it another way. If you are looking at a chant in Mode 1, what is the clef called? It is usually a do clef. If not, then it is a fa clef. In a chant in Mode 1 where the do clef is on the top line of the four, where will the finalis fall? On the bottom line of the four. If the top line is do, the bottom line is therefore re. Do you see? User:Arthurjameswright 08:53, 24 April 2020 (UTC)

First, I am not describing transposition, I am describing the application of a different frequency standard for one and the same written note. For example, A=440Hz, A=392Hz, A=550Hz. What you are describing (for singers, at least) only holds for those afflicted with "absolute pitch". Second, I have never heard a C clef described (in English) as a do clef, nor an F clef as a fa clef, and I see no reference to such terminology in the Wikipedia article Clef. This is of course the usual nomenclature in the Romance languages, but this is English Wikipedia.—Jerome Kohl (talk) 17:17, 24 April 2020 (UTC)[reply]

I'll answer both points you raise seperately, starting with the clef.

Please refer to the English translation of the Liber Usualis (1961, pp.xvii), to the English academic Sr. Mary Berry's Plainchant for Everybody (1979, p.7)[3], and to various American sources published on the Musica Sacra website, including Basic Gregorian Chant and Sight Reading: Moveable Do edition (Gregorian Institute of America, 1960, p.13) for references to 'Doh clef' and 'Fah clef'.[4] Referring to these clefs thus is standard in English, and this should be reflected in the Wikipedia entry.

Just to briefly comment on temperament: I was not referring to temperament. Yes, I am referring to those who are "afflicted", as you put it, with absolute or 'perfect' pitch. Those people read Wikipedia entries as well. If you describe the do clef as a C clef without stating that this only indicates which degree of the scale the clef falls on then they will take that to mean that most chant is written in C major. This does matter in this subject, because a lot of singers have absolute pitch.

I invite you, again, to cite sources outside of Wikipedia. So far you are yet to do so, and may I ask, have you actually read the sources I have provided? Arthurjameswright (talk) 14:01, 25 April 2020 (UTC)Arthurjameswright 25/04/2020 (15:01 BST)[reply]

My take on this subject is at Talk:Clef#Gregorian_clefs. Sparafucil (talk) 21:21, 25 April 2020 (UTC)[reply]
The discussion above is a bit exhausting, but what I think I understand is that there are conflicting definitions of "movable do" and that "re mi fi sol la ti di" is either a fixed-do major scale or a 'movable-do' Locrian with upbeats (for me the minor scale always starts on "la"). As to what "transposition" means, though I rarely go I've never before gone wrong assuming Jerome knows what he's talking about, I feel I'm having to give him the benefit of a doubt here. In learning Goehr's Pomfret in a key suited to my voice I've gradually come to believe that I've mastered a curious new instrument with middle C on the rightmost of 3 black keys. Am I still transposing anymore? :-)
Btw, the 1961 Liber has two preferatory essayists who both explain the rule for accidentals: the one on p. xv speaks of "B-flat" while the 'Do-clef'-ist on p. xviii says "Ta". Sparafucil (talk) 01:41, 27 April 2020 (UTC)[reply]

I agree it's a bit exhausting, and I have written far too much text! Is there a way that the argument can be summarised in a new section, and this one be consigned to history?

But to answer your points, if you've learned a piece in a different key to the one it is written in, that's perfectly sensible, but it does not mean that Middle C has moved. Surely you have described transposition. Otherwise we're in a whole new world of pain where C=233.0819Hz, and surely that's not a conversation we want to add to the above? What Jerome was describing was temperament; notes sound at different Hz depending on different eras or regions.

Locrian scales begin on ti in a moveable-do system (or the one I understand), being characterised by a semitone between the first and second degrees of the scale.

I had not noticed that within the Liber there was a divergence in terminology! I think the guiding principle is that the notation does not indicate absolute pitch, which is something that the monks of Solemne would have had to deal with given their musical culture is based on fixed-do. Anyway, this conversation has obviously arisen out of the inconsistencies in nomenclature between the sources (and even with one source). — Preceding unsigned comment added by Arthurjameswright (talkcontribs) 08:59, 27 April 2020 (UTC)[reply]

Not wishing to add to an already overlong discussion, I am nevertheless obliged to point out that temperament is a system of tuning of the notes in a scale, not a pitch standard. I was not describing any temperament (such as mean-tone, one of the Werckmeister temperaments, or twelve-equal). What we can agree on is that there is no fixed frequency reference for the written notes.—Jerome Kohl (talk) 18:24, 27 April 2020 (UTC)[reply]

References

  1. ^ Catholic Church (1961). The liber usualis: with introduction and rubrics in English. Tournai, Belgium: Society of St. John the Evangelist, Desclée & Co. pp. xix.
  2. ^ Levine, Art (1 July 2016). "Movable Do and Fixed Do: What they are, what they aren't..." The IFCM Magazine. Retrieved 23 April 2020.
  3. ^ Berry, Sr. Mary (1979). Plainchant for Everyone: An Introduction to Plainsong. Croydon, UK: The Royal School of Church Music. pp. 7, 17.
  4. ^ Demetria, Sr. Mary (13 October 2016). "Basic Gregorian Chant and Sight Reading" (PDF). Musica Sacra. Retrieved 25 April 2020.