The Hatter's Diary
16 Oct 2024
The singalong took place, and I'm so grateful. The thing could be evolving into a stage production, which means I should, perhaps, write more parts. I plan to add a part to Walrus (I hear Tweedledum, a countertenor/soprano, in some descants) and a couple lines to the chorus of Looking-Glass (for at present, there aren't "hundreds of voices"), but that's barely a writing assignment - more like dusting a cake with a sprinkling of powdered sugar. 'Tis the business for mornings of leisure and tea, tea and leisure. And chocolates.
But more clearly than ever before, I realized that Lobster and William don't work. Lobster needs to go faster - it's manic, and I've clearly failed as a performer, but not necessarily as a composer. Time and ambition will clarify this suspicion.
But William, dear William! William is a total flop!!
Nobody minds the parallel fifths. Nobody is absolutely horrified by a SEQUENCE of TRITONES. Nobody thinks it sounds like Byrd, and what's more, nobody even cares about Byrd. Nobody cleared their throat to say, "Why, William! What ever are you doing here in Wonderland, with us?" Nobody even thinks the plagal cadence is blasphemous. Everyone just wants it to be over with.
Surely I'm not mistaken in the notion that this concept - that Father William is William Byrd - is the correct approach, and everyone ought to be delighted by a piece by Byrd from Wonderland. And unfortunately, that means I have not done my job.
I need to do Byrd better. And the first step in remedying that problem is to drop the piano. William must break in and out of Byrdian vocal polyphony. (The idea of rescoring some of these pieces has arrived with impeccable timing.)
I could scrap everything and start all over, but most of me doesn't want to totally erase the original composition, because I believe there's some magic trapped inside, even if nobody else can see it.
There's no real reason to rewrite the son's part (which does need the piano accompaniment) even though I'm not particularly attached to it, and some of the father's part might be salvageable.
Before I get started on that, I'll have to know some things that I don't know.
The first order of business is to review my own composition notes from a few years back.
To imitate Dowland/Byrd, I wrote William's accompaniment in a three-voice texture thatMostly avoided doubling the melody
Mostly stayed on root position and first inversion triads
Mostly avoided parallel 5ths and 8ves, and
Mostly treated 2nds, 4ths, & 7ths from the bass as unaccented passing tones or suspensions.
William's phrases are punctuated with 4-3 suspensions on G major and D major cadences.
Each of William's melodic phrases appears in rhythmic augmentation in the bass.
Also, there's always some middle voice imitation.
Each of William's verses has four phrases.
The first phrase remains relatively untouched throughout the verses to set the stage.
The second verse ruins its 2nd phrase:
The words, "I kept all my limbs very supple," are illustrated with a diverging melodic line.
The third verse ruins its 2nd and 3rd phrases:
The word "argued" is illustrated with a series of 3 ascending tritones in the 2nd phrase.
The word "strong" displays strength with a high 5-beat note in the 3rd phrase.
The fourth verse ruins its 2nd, 3rd, and 4th phrases, all of which have blatant parallel 5ths.
As Dr. David Neumeyer put it, "[parallel] fifths will irritate the pedantically minded."
That was worked out towards the beginning of 2021, when I was a being a big fat stupid crybaby. "Dr. Neumeyer, help me! Whatever shall I do?" A lot of good that did me - now I'm sitting here, at the end of 2024 with a flop on my hands. It's time to roll up my sleeves. A really big girl would commence a massive interval analysis project on a hundred pieces by Byrd, but I'm not that independent just yet.
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The Hatter's Diary17-18 Oct 2024
In case it helps, I watched five lectures on 16th century 2-voice counterpoint by Kevin Ure to learn a little bit about species counterpoint, which I don't remember studying in school. It's not the same as what I've set out to do, but it's a mindset. A starting place. I'm addressing the situation.
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In case it helps, I watched five lectures on 16th century 2-voice counterpoint by Kevin Ure to learn a little bit about species counterpoint, which I don't remember studying in school. It's not the same as what I've set out to do, but it's a mindset. A starting place. I'm addressing the situation.
Chapter 1: Introductory Notes
Cantus Firmus - "fixed voice," (CF).
Teacher usually provided the CF, and it may not be changed.
Counterpoint - the "solution" to the CF by the student; can be above or below.
In counterpoint, horizontal voice leading is the point, not harmony.
---
Fux wrote Gradus ad Parnassum (1725, Latin), a tutorial on 16th-century species counterpoint.
First species - whole notes against whole notes.
Second species - whole notes against half notes.
Third species - whole notes against quarter notes.
Fourth species - whole notes against tied half notes/syncopated whole notes.
Fifth species combines the first four species.
None of them actually have to be based on whole notes.
As we move through the five species, more dissonances are permitted.
Dissonance is a tool to create tension and move the piece forward.
Although it must be treated carefully, it should be used as much as possible.
Dissonances may not be exposed on strong beats.
---
Steps - 2nds, skips - 3rds, leaps - 4ths or greater.
Perfect consonances are unisons, 8ves, and 5ths.
Imperfect consonances are 3rds and 6ths.
Dissonances are 2nds, 4ths, 7ths, and tritones.
The 4th is only considered a consonance if it fits in the harmonic series.
(Fundamental, 8ve, 5th, 4th, M3rd, m3rd, so C G C is okay but C F C is not.)
Diminished intervals, 4ths, and m7ths should be resolved inwards.
Augmented intervals and M7ths should be resolved outwards.
Always count intervals from the lowest sounding voice, even if voices have crossed.
---
Modal counterpoint - all church modes except Locrian (tritone).
Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian
Tonal counterpoint - major or minor scales (not used in 16th or 18th centuries).
---
Types of motion: similar, contrary, parallel, oblique.
Both similar and parallel motion are called direct motion.
Contrary is best, similar is next, and parallel and oblique are less desirable.
Use a mix of different types of motion.
---
Four Rules of Motion:
Perfect consonance to perfect consonance - contrary or oblique motion.
Imperfect consonance to perfect consonance - contrary or oblique motion.
Perfect consonance to imperfect consonance - any motion.
Imperfect consonance to imperfect consonance - any motion.
In other words, never move in direct motion to a perfect consonance.
Parallel motion into perfect consonances results in parallel 5ths or 8ves.
Similar motion into perfect consonances results in hidden/direct 5ths or 8ves.
In 4-part harmony, direct motion to an octave is "fixed" by stepwise motion in the soprano.
---
Two-voiced counterpoint should stay within a 12th; 10th is better; 8ve is even better.
Entire range (four parts) must be within F2-A5.
Chapter 2: Melodic Principles
Establish tonality immediately; 1st scale degree begins and ends the piece.
1st, 4th, and 5th scale degrees should be emphasized early.
Aim for a V-I cadence.
Avoid unresolved leading tones or tendency tones.
---
Melodies have a natural contour of rise and fall.
They should have one high point, which is consonant to the tonic (final).
The high point is best placed between the halfway point and three quarters through the piece.
Ideally, melodies should also have a low point, but this is less important.
The low point should also be consonant to the final.
---
Conjunct - stepwise
Disjunct - skips or leaps.
Counterpoint melodies should consist mostly of conjunct motion.
Avoid conjunct motion that is followed by a leap in the same direction.
---
Skips can be resolved by a step in either direction.
Avoid consecutive skips unless outlining a triad.
Dissonant leaps were not used in 16th or 18th-century counterpoint.
Avoid melodic tritones, descending m6ths, M6ths, 7ths, and 9ths.
Leaps should be resolved by a step in the opposite direction.
Leaps can also be resolved by smaller skips or leaps in the opposite direction.
---
Melodic range should not exceed a 10th.
Melodic leaps should not exceed an 8ve, and even 8ves are used rarely.
Avoid consecutive skips and leaps that expand the melody over an 8ve.
Avoid consecutive 4ths and 5ths.
Avoid three or four intervals of the same type.
---
With minor scales, use melodic (raised ascending, natural descending).
Avoid chromatic relationships outside of the mode.
Bb to B natural would not be acceptable in Ionian.
Bb to B natural could be used in Lydian or Dorian (musica ficta).
At least one measure should be placed between such tones.
---
In Fux's CF, the last 3 bars are often stepwise and the last 2 bars are 2-1.
When writing counterpoint, begin with the opening, cadence, and high point.
With all 2-voiced openings,
If the CF is in the bass, begin with a unison, 5th or 8ve.
If the CF is in the soprano, begin with a unison or 8ve.
Fill in remaining voices with a lot of imperfect consonances.
Chapter 3: First Species
Whole notes against whole notes.
Dissonances are not acceptable.
Avoid two unisons, 5ths, or 8ves on consecutive accented beats.
5ths can move to 8ves and vice-versa, but only in contrary motion.
---
Battuta - a 10-8 progression from downbeat to downbeat.
Battutas are forbidden in the middle of a counterpoint because they sound like cadences.
They're okay from a strong beat to a weak beat, and only forbidden in the first species.
10-8-6 contrary motion is acceptable (voice exchange, 8ve is passing tones).
Rests, Unisons, Repeated Notes
Do not begin with a rest.
Unisons to the CF may only be used in the first and last measures.
Repeated notes are permitted.
Cadences
The cadence above and below the CF uses the modal degrees 1-7-1.
This 7 is always sharped except in Phrygian mode.
The third to last note cannot ascend by a 3rd to the leading tone.
If the CF is in the bass, the cadence is M6-8.
If the CF is in the soprano, the cadence is m10-8 or m3-unison.
Chapter 4: Second Species
Whole notes against half notes.
All downbeats must be consonant.
Dissonance can be used on weak beats, but only when moving by step.
Passing tones must begin and end with strong beat consonance.
Consonant neighbor tones must also begin and end with strong beat consonance.
All dissonances are passing tones, and they should be used often.
---
Intervening thirds don't erase parallel fifths or octaves.
However, leaps correct parallel 8ves - they "make the ear forget."
Leaps also correct hidden 5ths or 8ves.
---
If voices are too close together, 8ves or ascending m6th leaps can be used.
If the counterpoint crosses voices with the CF, it must stay crossed.
Rests, Unisons, Repeated Notes
The first half of the measure may use a rest.
Unisons are permitted on weak beats, beginning, and ending tones.
Repeated notes are not permitted.
Cadences
The final 2 or 3 notes may revert to first species whole notes.
If the CF is in the bass, penultimate measure is P5-M6 to an 8ve in the final measure.
If the CF is in the soprano, penultimate measure is P5-m3 to an 8ve in the final measure.
Avoid consecutive skips or leaps that outline a 7th.
Chapter 5: Third Species
Whole notes against quarter notes.
There should be about 2-4 skips and 1-3 leaps in 10-12 measures of CF.
Melodic high point should be on a strong beat (1 or 3).
It's still best to make the high point consonant with final, but less important than before.
If the counterpoint crosses voices with the CF, it crosses back quickly.
---
Avoid ascending skips from a strong beat.
Descending skips from a strong beat are permitted.
The disconnect - skipping or leaping and continuing in the same direction; avoid this.
---
Downbeat to downbeat consecutive 8ve and 5th rules:
There should be three intervening tones between consecutive 8ves and 5ths.
Avoid emphasizing 8ves and 5ths with leaps, sequences, or devices.
When one voice skips or leaps, the other voice should step.
With 4 quarter notes between consecutive unisons, 5ths, or 8ves, you will always be safe.
With 2-3, perfect consonances must not be emphasized with skips or leaps.
---
Cambiata - "changing tone"
If the CF is in the bass, 8-7-5-6 or 3-4-6-5 (first is preferred).
If the CF is in the soprano, 3-4-6-5.
The cambiata begins with a consonant interval and steps to a dissonance.
The resolution to the dissonance is delayed with an interjected consonant interval.
The 2nd beat note is often repeated on the next downbeat, consonant to the CF.
Avoid outlining a tritone (B-A-F-G, F-G-B-A).
Avoid creating a harmonic tritone, which sounds like a leading tone/cadence.
---
Dissonant double neighbor tones begin and end with same consonance.
They create dissonances on beats 2 and 3 (3-2-4-3, 8-9-7-8).
Consonant neighbor tones can be used freely.
---
Cambiatas and dissonant neighbor tones are "devices," and therefore exceptions.
But contrary to Fux's teachings, there should generally be no dissonance on strong beats.
Stranded dissonances are dissonances that are not passing or neighbor tones; avoid them.
Rests, Unisons, Repeated Notes
A quarter rest may be used on the first beat.
Unisons are permitted on the downbeats of the first and last measure.
Otherwise, they should be used sparingly and only on weak beats.
Repeated notes are not permitted.
Cadences
Cadences - if the CF is in the bass, 3-4-5-6-8 or 8-7-5-6-8 cadences are most conventional.
If the CF is in the soprano, use 3-5-4-3-1.
The leading tone must be on the fourth beat, against scale degree 2 in the CF.
Chapter 6: Fourth Species
Whole notes against tied half notes/syncopated whole notes.
Because half notes are tied over downbeats, dissonances are now permitted on strong beats.
Suspensions have three parts:
consonant preparation, suspension, consonant resolution.
The suspension (the middle part) can be dissonant or consonant.
Dissonant suspensions are preferable to consonant suspensions.
Dissonant suspensions always resolve down by step; consonant suspensions don't have to.
Never use more than 3 dissonant suspensions in a row.
If the CF is in the bass, use 7-6 or 4-3 suspensions.
If the CF is in the soprano, use 2-3 suspensions.
If the CF is in the bass, 9-8, 2-1 are also possible, but must be handled more carefully.
Chains of 9-8 and 2-1 suspensions cause chains of parallel 5ths or 8ves.
Therefore, they must be used one at a time with contrary motion (10-9-8, 3-2-1).
Retardations (resolving upwards) were never used in the 16th century.
Rests, Unisons, Repeated Notes
A half note rest must be used at the beginning.
Unisons are permitted at the beginning and the downbeat of the last measure.
Repeated notes are not permitted.
Cadences
If the CF is in the bass, use a 7-6 sus to an 8ve.
If the CF is in the soprano, use a 2-3 (not 9-10) sus to a unison.
Second species cadences can be used as well.
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The Hatter's Diary
19-20 Oct 2024
After taking those notes, I looked up a bunch of similar stuff and started taking even more notes on species counterpoint. But I stopped dead in my tracks and erased all of those when I suddenly ran into this book:
The Technique of Byrd's Vocal Polyphony
by Herbert Kennedy Andrews, 1966.
The discovery instantly created two problems. The first is that when not enough people are reading The Technique of Byrd's Vocal Polyphony from 1966, it does not get digitized, or at least does not remain so, and the last thing I want is another book cluttering up a house that is shared by a gaggle of hoarders. The second problem is that everybody who knows me, knows that I swore off reading and writing in the beginning of 9th grade. But I would wager there have been a few exceptions to the reading claim, and I'm violating the writing principle this very moment, so the discomforts of owning another thing and the reading of a book are to be overruled. It will arrive "between November 5th and November 21st," which gives me plenty of mornings for leisure and tea, tea and leisure. And chocolates.
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The Hatter's Diary
21-23 Oct 2024
I was going to stop taking notes on all the different species rules. But of course I downloaded the English translation of Gradus because I was hoping to take notes on the fifth species' clausula vera. "What's that?" you may be wondering. Well, I don't actually know, because the English translation floating around from about 1750 is partial. So until my Andrews comes, I'll be taking a look at A Study of Counterpoint from Johann Joseph Fux's Gradus ad Parnassum, translated and edited by Alfred Mann, 1943.
Fux (1660-1698) was an Austrian composer and theorist. Gradus is made up of play-like dialogue, which you'd never have guessed from the bad (partial) translation. Aloysius is the master (Palestrina), and Josephus is the pupil (the Hatter channeling the world Byrd visited before he came to Wonderland to write Father William). This is as close as I come to reading graphic novels.
As I'm making my way through the first species, it's becoming clear that Kevin Ure did a pretty good job, because these conversations between Aloysius and Josephus are hardly giving me pause. It's not a particularly fast read, but that doesn't mean it's not a page turner. And for what it's worth, Aloysius and Josephus are a great deal more charismatic than Kevin. I would recommend this approach - bore yourself with a college professor and then sit back and relax as Fux's play unfolds before you. (Mann also translated all the movable C clefs to treble and tenor clefs, bless him.)
Page numbers are based on the 1971 copyright edition.
First Species
p. 32 Fux explains why direct 5ths and 8ves are offensive [by imagination].
Stepwise motion to the perfect consonances would reveal parallel 5ths or 8ves.
p. 39 Avoid progressing to or from a unison with a skip or a leap in either voice.
(Similarly, avoid skipping/leaping inwards to an 8ve, which also presents a range problem.)
p. 39 Using a sharp before an upwards resolution (musica ficta) is encouraged.
Second Species
p. 46 When cadencing in Phrygian, a B against the F in the CF is a tritone; use C instead.
Third Species
p. 50 Indeed, Fux approves dissonant passing tones on beat 3.
p. 52 Similarly to p. 32, Fux explains why the cambiata should be pardoned [by imagination].
Stepwise eighths on beat 2 results in 7-6-5-6, which is so much nicer than 7-5-6.
p. 54 musica ficta examples in Lydian, resulting in transposed Ionian.
Fourth Species
p. 56 Nothing is new, but Fux explains why suspensions are permitted [by imagination].
Syncopated whole notes can be shifted a half note to the right to check their consonances.
p. 58 If the CF is in the soprano, 4-5 and 9-10 suspensions are possible in addition to 2-3s.
p. 58 7-8 suspensions are off limits simply because the masters did not use them.
p. 60 It is possible to cut off a tie for good reasons, like avoiding melodic repetition.
Fifth Species
p. 62 Ornamentation - can add stepwise eighths on weak beats.
p. 62 7-6 suspensions can be decorated with two eighths on beat 2 (7-6-5-6).
p. 62 7-6 suspensions can be decorated with leaps to and from a consonance on beat 2 (7-3-6).
p. 62 Fifth Species is called florid counterpoint.
p. 65 Ties over the downbeat "brings about the greatest beauty in counterpoint."
p. 65 Sneakily, three voiced examples started popping up with the CF in the middle.
p. 67 This is not a rule, but a piece of advice.
A measure of quarter quarter half isn't that great, so consider one of these alternatives:
Half quarter quarter, all quarters, or tying the half over the barline to a quarter or half.
The Hatter's Diary
28 Oct - 04 Nov 2024
I've been on sabbatical to celebrate two birthdays and Halloween, make my daughter a witch's dream-catcher, carve a jack-o-lantern, paint a Heawood conjecture mug, give some haircuts, and design a holiday card. The art that has simply demanded my attention. The projects creep up onto my shoulder and whisper into my ear, "If not for you, I will never exist."
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The Hatter's Diary
05 Nov 2024
Three Voice First Species
p. 71 Three voiced counterpoint is the "most perfect of all" because triads have three parts.
Fux's triads are 5/3/1 (no inversions of triads are considered triads).
p. 71 Both upper voices must be consonant with the lowest.
p. 72 To avoid parallel perfects, 6/3/1, 8/3/1, or 8/6/1 might be used instead of 5/3/1.
p. 73 Voice leading principles are much more important than the completion of triads.
p. 74 If the CF is in the bass and moving by step, it's better to harmonize with a 6th than a 5th.
p. 76 Rules (such as no tritones) should be followed between upper voices if possible.
However, in three voices, rules must sometimes be broken for good reasons.
p. 77 Ascending 6ths on downbeats sound harsh, but they work on upbeats.
p. 78 Sometimes adhering to a rule forces more awkwardness further along.
p. 79 8ves are preferred to unisons.
p. 80 In a scale with a m3rd from the final, cadence without any 3rd.
Picardy 3rds are considered disturbing and m3rds are considered inconclusive.
If you must choose a 3rd to avoid parallel 5ths and tritones, choose the M3rd.
Three Voice Second Species
p. 86 Two voices of whole notes in consonance, one voice of half notes.
p. 86 In three voices, parallel 5ths can be "fixed" with a third to promote harmonic triads.
p. 87 Examples use suspensions at the cadences.
p. 87 Downbeats should have triads.
p. 88 It is often necessary to end with M3rds.
p. 90 In this species, write only when considering 1-2 measures ahead.
Three Voice Third Species
p. 91 Two voices of whole notes in consonance, one voice of quarter notes.
p. 91 Downbeats should have triads, but if they cannot, triads should be on beats 2 or 3.
p. 93 One voice of whole notes, one of half notes, one of quarters.
Three Voice Fourth Species
p. 94 Wait, what?
What a rejection of democracy.
What a rejection of women.
What a rejection of progress.
What a shithole of a country.
What an absolute and utter disgrace.
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The Hatter's Diary
06 Nov 2024
It's a good thing my mild interest in Fux outweighs my attachment to the US, or I'd be broken.
(Cries herself to sleep.)
(Clears throat. "The Ligature.")
Three Voice Fourth Species
p. 94 Two voices of whole notes in consonance.
Third voice must be consonant whole notes and then pushed a half note forward.
p. 95 Are chains of 6-5 suspensions acceptable, or are they parallel 5ths?
p. 96 Well, parallel 8ves are worse than parallel 5ths.
p. 97 And higher parallel 5ths are worse than lower ones.
"For highness accentuates and lowness subdues."
p. 98 If the bass is on a pedal point, the first note of the ligature need not be consonant.
p. 99 7ths should be set with 3rds.
p. 100 When placing the ligature in the bass, the opening note should be above the tenor.
p. 103 If direct 8ves or 5ths cannot be avoided, use rests.
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The Hatter's Diary
07 Nov 2024
As I was saying, it's a really good thing.
(Cries herself to sleep.)
(Clears throat. "Florid Counterpoint.")
Three Voice Fifth Species
p. 104 This is a combination of all four species in as beautiful and singable a way as possible.
p. 106 In this species, oblique motion should be used in every measure.
From here, Fux goes on to teach about four voices. I've skimmed through it, and the play ends very dramatically with Aloysius on his death bed, too tired to continue his teachings in five voices.
There is a perfection to three voiced writing that Dr. Neumeyer and Fux have hinted on, for any more, and we're entering the world of doubling. This is the right time to review, for understanding this kind of theory on a deeper level is not bloggable anyway.
The long and short of it, as I gather, is this: there are quite a few guidelines, and maintaining all of them all the time is totally impossible. We therefore have to use our ears, not our brains, to decide which rules to break and how to break them. And to practice that stuff, we need to listen to all of the examples I couldn't copy into this post. It would be gratuitous and unproductive to continue taking notes when the real work that needs to be done right now is not that.
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The Hatter's Diary
Nov 2024
The Technique of Byrd's Vocal Polyphony
