The Solitaire "arrange stacks" are made to be descending chromatic cards instead of descending alternating red and black cards. The Spit "collective piles" must be constructed in ascending order according to the theory lesson of the round. So before a round, I have to be able to calculate any of what's listed below beginning on any pitch, in order to define the collective piles. It all got me thinking - I'm not that fast. I need to fix that.
This post will be written from the point of view of somebody who understands these things, but has never had to calculate them quickly. Shame is the stuff mid-life crises are made of, so I really have no choice but to write this post.
Dominant 9th♭5
Major 9th
Major 9th ♯11
Minor 9th
Minor 11th
Dominant 13th ♯9
Major 13th
Major 13th ♯11
Intervals
P1/P8
m2/m9
M2/M9
m3/m10
M3/M10
P4/P11
Tritones/+4ths/+11ths/°5ths/°12ths
P5/P12
m6/m13
M6/M13
m7/m14
M7/M14
Musings
Amongst my own friends, the topic of 12ths or 14ths has never come up. Come on. Who thinks in those? The odd compound intervals are used in extended chords, but let's be real: 12ths and 14ths are 5ths and 7ths. In general, I guess I know intervals well enough that I don't have to worry about this category. I'm not the best at reading ledger lines, but I have a few "landmarks" that make calculations pretty fast. The notion of the number of half steps per interval is similar; here are my landmarks.
m3 - 3
P5 - 7
M6 - 9
P8 - 12
That's all I know by heart, and it's enough.
Basic Chords
Major Triad
Minor Triad
Diminished Triad
Augmented Triad
Dominant 7th
Major 7th
Minor 7th
Fully Diminished 7th
Half Diminished 7th
Augmented 7th
Minor Major 7th
Musings
These are fine too, because I only have to know up to 4 pitches at a time. Playing the piano makes you learn them. In terms of thirds, they're:
Mm mM mm MM
Mmm MmM mMm mmm mmM MMm mMM
No big deal.
Chord Inversions
(53) Triad root position
6(3) Triad first inversion
64 Triad second inversion
7(53) 7th chord root position
65(3) 7th chord first inversion
(6)43 7th chord second inversion
(6)42 7th chord third inversion
Musings
Again, you have to learn these for school. I've never played figured bass, which is admittedly a bit embarrassing, but there are 3 pieces of information necessary for each calculation: the root, the pitches, and the bass note.
The slow way to calculate each is to find the chord and count the actual inversions to find the bass note. This way, a third inversion chord takes longer to figure out than a second inversion, which takes longer still than a first inversion. (I imagine root position chords to be fastest even for figured bass readers.) I realize that I've somehow internalized the bass notes for triad inversions (6 and 64), but for seventh chords, I have not! So what I really need to know are these bass notes:
65 - 3rd
43 - 5th
42 - 7th
Or even better:
65 - 6 triad, add in 7th
43 - 64 triad, add in 7th
42 - root, add in 7th a whole step or M9 lower!
I can do that.
Chord Qualities
I Tonic
ii Supertonic
iii Mediant
IV Subdominant
V Dominant
vi Submediant
vii° Leading Tone
i Tonic
ii° Supertonic
III, III+ Mediant
iv Subdominant
v Dominant
VI, vi° Submediant
VII Subtonic
Musings
I just know these. Moving on.
Altered & Extended Chords
Sus - add 4th, sometimes drop the 3rd
(voicing the 3rd above the 4th is less dissonant than the 4th above the 3rd)
Major 6th - add M6th
Major 6/9 - add M6th and M9th
Dominant 7th sus
Dominant 7th ♭5
Dominant 7th ♯9Dominant 9th♭5
Major 9th
Major 9th ♯11
Minor 9th
Minor 11th
Dominant 13th ♯9
Major 13th
Major 13th ♯11
Musings
Ugh, I am NOT good at this. These are jazz chords and I don't read them. The trick I use right now to speed up my processing is having instant access to what the dominant 13th is.
There are three ways I like to do this.
First, thinking horizontally, the pitches are that of the mixolydian scale.
Second, I combine two 7th chords to get the thirds stacked quickly. First I build a dominant 7th chord, and then I build a major 7th chord using the original 7th as my root. So for example, A13 is (A C♯ E G) plus (G B D F♯). Both of those calculations are very fast because I'm never thinking beyond 7th chords, which is within my realm.
My third method combines both lines of thinking. First I build a dominant 7th chord, and then I superimpose a supertonic (minor) triad onto that collection of pitches. The result is a scale, but still mentally organized in thirds. This way, A13 is (A C♯ E G) plus (B D F♯), all in the same octave.
From here, I still have to do whatever the chord symbol tells me to do. So in the case of a Amaj9♯11, the first step is to drop the 13th (A C♯ E G B D). The second step is to raise the 7th for the "maj" (A C♯ E G♯ B D). Finally, I have to sharp the 11th (A C♯ E G♯ B D♯). It's not as bad as it sounds; having an instant 13th template to alter is a lot faster than stacking thirds from scratch in the first place.
From here, I still have to do whatever the chord symbol tells me to do. So in the case of a Amaj9♯11, the first step is to drop the 13th (A C♯ E G B D). The second step is to raise the 7th for the "maj" (A C♯ E G♯ B D). Finally, I have to sharp the 11th (A C♯ E G♯ B D♯). It's not as bad as it sounds; having an instant 13th template to alter is a lot faster than stacking thirds from scratch in the first place.
Scales & Modes
Pentatonic Scales
Major Pentatonic
Minor Pentatonic
Egyptian/Suspended
Musings
There's a lot to unpack in the scales, so I had better do this section by section. I should mention that anything in blue font isn't actually from Oom-Pah, which makes it extra credit.
Pentatonic scales are either hemitonic (containing at least one half step) or anhemitonic (not). I'll only cover the most popular ones, which happen to be anhemitonic.
The main pentatonic scale is made from 5 consecutive pitches from the circle of fifths. That's also the relationship of the 5 black keys, which are scale degrees 1 2 3 5 6 in F♯ major (or any major scale).
From this pentatonic scale, as with any scale, we can pick different starting pitches and generate different modes. When the last note (D♯) is selected, the resulting mode is the minor pentatonic scale. These are also the natural minor scale degrees 1 3 4 5 7. The scale degrees trick is pretty efficient, but I also find it helpful to remember that the five notes of the minor pentastonic scale create a palindrome of sorts, the intervals being m3 M2 M2 m3.
The second mode of the major pentatonic scale is called the Egyptian or Suspended scale, which is like a minor pentatonic scale with a lowered second pitch, or natural minor scale degrees 1 2 4 5 7. It's also a sus dominant 9th chord.
The remaining two modes have blues names, and favoring hexatonic blues scales, I do not wish to acknowledge them.
Hexatonic Scales
Whole Tone
Prometheus
Major Blues
Minor Blues
Major Hexatonic
Minor Hexatonic
Augmented
Tritone
Musings
For the whole tone scale, it's helpful to think of the black notes as divided into two groups: 2 black keys and 3 black keys. Any whole tone scale will include one of these groups and all the white notes surrounding the other group. That makes it faster.
The Prometheus scale is based on the "mystic chord": C F♯ B♭ E A D. When stacked as a scale, it ends up as whole tone with a raised fifth scale degree: C D E F♯ A(♮) B♭.
The major and minor blues scales are just the major and minor pentatonic scales, but with an added "blue" note. In the black key example of F♯ above, an A♮is the blue one! It's easiest for me to start with a pentatonic scale and just add in the blue note - the chromatic note between the upper of the two consecutive M2's.
The major hexatonic scale is a major scale with no 7th scale degree. That seems easy enough to remember. Its second mode is the minor hexatonic scale. So a major hexatonic scale can be built from triads I and ii, and a minor hexatonic scale can be built from triads i and ♭VII. Both have a folk-like sound. Oh, there are more modes, but I've reached my limit for the moment.
The augmented scale alternates between minor thirds and half steps, but it amounts to an augmented triad with a leading tone under each pitch: C E♭ E♮ G♮ G♯ B.
Much in the way I defined the major and minor hexatonic scales as two triads, the tritone scale is two major triads with roots a tritone apart. C E G G♭ B♭ D♭. When stacked in order, they alternate between one triad and the next like this C D♭ E G♭ G B♭. Fun fact: the tritone scale is enharmonically equivalent to the "Petrushka chord": C C♯ E F♯ G A♯.
Heptatonic Scales
Major/ Ionian (mode)
Dorian (mode)
Phrygian (mode)
Lydian (mode)
Mixolydian (mode)
Aeolian (mode)
Locrian (mode)
Melodic Minor/ Minor-Major (mode)
Phrygian-Dorian [Phrygian ♯6] (mode)
Lydian Augmented [Lydian ♯5] (mode)
Lydian Dominant [Lydian ♭7] (mode)
Mixolydian♭6 (mode)
Locrian ♯2 (mode)
Locrain♭4/ Altered/ Diminished Whole-Tone (mode)
Natural Minor
Harmonic Minor
Musings
As is usual, I know three minor scales and a major scale for each pitch quite well. The major scale modes are fairly familiar but not immediate; I'll start with those.
Dorian - natural minor ♯6
Phrygian - natural minor ♭2
Lydian - major ♯4
Mixolydian - major ♭7
Locrian - natural minor♭2 ♭5
But I realized something else. Envisioning the circle of fifths, it becomes clear that you can track clock hand movements to 12:00, which is C major. Lydian (F, 11:00) needs 1♯ added to its key signature to get to 12:00. So if you add 1♯ to any scale, you get that scale in Lydian. Ex. E♭ with 2♭s instead of 3 is E♭ Lydian, or B with 6♯s is B Lydian. Naturally, that trick works with any of the modes. So for Locrian (B, 5:00), you must add 5 ♭s to any major key signature. C major with 5 ♭s is C Locrian. A major with 2 ♭s is A Locrian. I like this trick, and I wouldn't have discovered it if I weren't writing this post.
Regarding the melodic minor modes, I've hardly ever thought about any of them. I can't use my clock trick because only the natural minor scale conforms to the circle of fifths. It's interesting that simply lowering the third from the major scale to get to the melodic minor scale breeds such a wealth of unfamiliarity! The Locrian ♭4, also known as the altered or diminished whole tone, is the only one with three alterations from a scale I know well, so it requires my attention first.
Octatonic Scales
Octatonic/Diminished
Bebop Dominant
Bebop Dorian
Bebop Major
Bebop Melodic Minor
Musings
If I didn't know what I was talking about with the heptatonic scales, things just got a lot worse. Luckily, everything in this section is very easily defined. The octatonic/diminished scale is a series of alternating half steps and whole steps, and it's okay to start with either. It works out that there are only 3 distinct sets of pitches for them. Any octatonic scale is made of all the notes except a fully diminished chord. I've never in my life tried to play one. Maybe today is the day.
Bebop Dominant - Mixolydian, add M7.
Bebop Dorian - Dorian, add M3.
Bebop Major - Major, add ♯5.
Bebop Melodic Minor - Melodic Minor, add ♯5.
None of that is hard to memorize, but I should probably start with trying to play an octatonic scale. What will my fingerings be? How annoying - to be this old and to think about playing a brand new scale.
Chromatic Scale
Musings
Oh thank goodness. We learn this one as mere babes.
Cadences
V I Perfect Authentic, major
V i Perfect Authentic, harmonic minor
IV I Plagal, major
iv i Plagal, minor
I V Half (sometimes called Imperfect), major
ii V Half (sometimes called Imperfect), major
iv V Half (sometimes called Imperfect), harmonic minor
V vi Deceptive (sometimes called Interrupted), major
v VI Deceptive (sometimes called Interrupted), minor
I IV Plagal Half Cadence, major
iv6 V, Phrygian Half Cadence, minor
♯iv6 V, Lydian Cadence, minor
IVadd6 I6 Moravian Cadence, major
Musings
I know most of this, but sometimes I worry about remembering the requirements for perfect authentic cadences. There are only 3: dominant to tonic progression; both chords in root position; ending highest note is the tonic. Otherwise, the V I is an imperfect authentic cadence.
The fact that half cadences are sometimes called imperfect cadences is awful indeed.
The Plagal half cadence is rare.
The Phrygian half cadence has a most misleading name - someone believed that the bass movement from a iv6 to a V, being a half step, was reminiscent of the ii I (with a picardy third) Phrygian cadence and named it so. I do not care for this naming.
Lydian cadence and Moravian cadences are new to me, and I must learn them posthaste!
Common Chord Progressions
I IV V, major
ii V I, major
I vi7 ii7 V7, major/ I VI7 ii7 V7/ iii7 vi7 ii7 V7, major/ III7 VI7 II7 V7, major
I V vi IV, major
vi ii V vii° I, major
I ii iii IV, major
i iv v, natural minor
i VI III VII, natural minor
VI VII i, natural minor
i ii° V, harmonic minor
Musings
I should probably pay a little attention to this, but surely, there are other progressions of importance. And are these really the most common? It's such a hard thing to quantify, and I don't think this category even belongs in the board game. They should have cut it and included an 8-sided die for the categories (they divide scales and modes into two separate piles of cards) as well as a 12-sided die for the pitches. Good thing it's pretty easy to leave this stack of cards in the box and I just dropped a Jackson on some very pretty dragon dice.
GROUP WIN ROLLS, ROLLED ONLY AT BEGINNING OF GAME
Icosahedron (1-20) = number of total rounds to be played
Two Pentagonal Trapezohedrons (0-99) = number of mins total rounds must be completed
GAME ROLLS, RE-ROLLED EVERY 1-4 ROUNDS
Hexahedron (1-6) = number of active compose stacks allowed at once
Tetrahedron (1-4) = number of rounds before [hexa/tetra/octa/dodeca] re-rolls
COMPOSE STACK ROLLS, RE-ROLLED WITH GAME ROLLS
Octahedron (1-8) = to select a category
1 = Intervals
2 = Basic Chords
3 = Chord Inversions
4 = Chord Qualities
5 = Altered & Extended Chords
6 = Scales
7 = Modes
8 = Cadences
Dodecahedron (1-12) = to select a starting note/Oom-Pah card
1 = C♯/D♭
2 = D
3 = D♯/E♭
4 = E
5 = F
6 = F♯/G♭
7 = G
8 = G♯/A♭
9 = A
10 = B♭
11 = B
12 = C
The End.
