H!P COMPLETE Album Cover and Track Listing

The long-awaited remix album by DJ Kirarin☆Snow ☃ is … still long-awaited. Hopefully it’ll be out in November.

In the meantime, here is a preview of the cover:

The official album art, consisting of 100% vector graphics, is in PostScript, and the design is actually randomly generated every time you load the file (this randomness doesn’t carry over to most other image formats, hence the PDF, PNG, and JPEG alternatives are poor substitutes, in order of strictly increasing poorness). The background image on the front cover is taken from a screenshot from the “Koko ni Iruzee!” PV, which was sampled and replicated as a fractal consisting of about 350,000 circles. This information is stored in the PostScript file. When you load the PostScript file, each of those circles has a 1/4 probability of being drawn. Below is an animated GIF screencap of the GhostScript interpreter loading the background image:

I may have spent more time designing and programming the album art (in plain text!) than I’ve spent actually working on the remixes themselves. But hey, randomized album art is always awesome. Interior and back cover images will be released with the final version of the album tracks.

And here’s a track listing, which I believe is finalized but may be subject to last-minute changes. Official track titles are in Japanese; Romanized renditions are given in blue, and English translations (of dubious accuracy) are given in red.

H!P-COMPLETE — DJ Kirarin☆Snow ☃

01.	ザ☆Kiss!☆Kiss!☆ピ～ス！ ∈ Buono! × モーニング娘。	The☆Kiss!☆Kiss!☆Peace! (The Kiss! Kiss! Peace!) ∈ Buono! × Morning Musume.
02.	ピリリとチャンス！ ∈ 月島きらり starring 久住小春(モーニング娘。) × Berryz工房	Piriri to Chance! (Chance with Briskness!) ∈ Tsukishima Kirari starring Kusumi Koharu (Morning Musume.) × Berryz Koubou
03.	告白のリゾナント ブルー ∈ モーニング娘。 × Berryz工房	Kokuhaku no Resonant Blue (The Resonant Blue Color of Confessions) ∈ Morning Musume. × Berryz Koubou
04.	でっかい宇宙に涙が歩いてるぜぇ！ ∈ (モーニング娘。 + モーニング娘。 + (モーニング娘。おとめ組 ∩ モーニング娘。さくら組)) × モーニング娘。	Dekkai Uchuu ni Namida ga Aruiteru zee! (In This Huge Universe, Tears Go Walking!) ∈ (Morning Musume. + Morning Musume. + (Morning Musume. Otome Gumi ∩ Morning Musume. Sakura Gumi)) × Morning Musume.
05.	AS FOR ONE DAY 好きでいいですか ∈ 松浦亜弥 × モーニング娘。	AS FOR ONE DAY Suki de Ii desu ka (Is It OK to Love You for One Day?) ∈ Matsuura Aya × Morning Musume.
06.	ブギーはNS '03 ∈ きら☆ぴか × 藤本美貴	Boogie wa NS '03 (The Boogie Is NS '03) ∈ Kira☆Pika × Fujimoto Miki
07.	VERY 風信子(ヒヤシンス) ∈ 松浦亜弥 × Berryz工房	VERY Hyacinth (Very Hyacinth) ∈ Matsuura Aya × Berryz Koubou
08.	大阪 恋のバカンス ∈ W × モーニング娘。	Osaka Koi no Vacance (Osaka Love Vacation) ∈ W × Morning Musume.
09.	そうだ！トロピカ〜ル スクランブ〜ル モード ∈ (藤本美貴 + 後藤真希 + モーニング娘。) × 松浦亜弥	Souda! Tropica~l Scramb~le Mode (That’s Right! Tropical Scramble Mode) ∈ (Fujimoto Miki + Goto Maki + Morning Musume.) × Matsuura Aya
10.	ファイティングポーズはみんなだいすき！ ∈ Buono! × Berryz工房	Fighting Pose wa Minna Daisuki! (The Fighting Pose Loves Everyone!) ∈ Buono! × Berryz Koubou
11.	カッチョイイゼ！TOUCH ∈ 美勇伝 × 後藤真希	Kacchoii ze! TOUCH (It’s Cool! Touch) ∈ v-u-den × Goto Maki
12.	21時までの恋なんて ∈ 安倍なつみ＆矢島舞美(°C-ute) × Berryz工房	21ji Made no Koi Nante (A Love Until 21:00) ∈ Abe Natsumi & Yajima Maimi (°C-ute) × Berryz Koubou

This is a total of 12 tracks, 5 of which (Tracks 3, 5, 6, 10, and 12) are brand new (to the public; I’ve shared a few previews in private), including Tracks 3 and 12, which are inverses of mixes previously released. The remaining tracks have previously been released in some form, but all of them have had significant changes, including the addition of new source vocals to Tracks 4 and 9.

A note on the mathematical notation used in the bylines:

Previously I used the plus symbol (+) for indicating which groups or artists performed the original songs being mixed together. This was more-or-less idiosyncratic, as mashups are commonly denoted “X vs. Y”. But I don’t like “versus”; it gives the remix a confrontational feel, and I don’t see the combinatorial nature of mashups as necessarily antagonistic.

The problem with “+” is that in math, it represents addition of objects, which is commutative. The combining of tracks X and Y is in general not commutative. In this case, one track is used for its vocals, and the other is used primarily for its instrumentals. If you switch X and Y, the roles they play become reversed, but indicating this as “Y + X” sort of implies that it’s the same as “X + Y”.

Hence I have replaced the “+” with “×”, which represents a product of objects. For complex numbers, this is just multiplication, which is commutative, but products in general need not be commutative. If we’re talking about groups (in the mathematical sense, which is the part of the motivation for adopting mathematical notation to use with musical groups), then for two groups X and Y, “X × Y” represents the direct product of X and Y. “×” is also used to denote the Cartesian product of sets and the cross product of vectors, and this “crossing” aspect of the meaning is also intended. Thus “W × Morning Musume.” means, informally, the crossing of W with Morning Musume., in that order.

Of course, when applied to non-mathematical objects, the meaning of specific operators becomes quite fuzzy, so my use of mathematical notation is primarily intended for semantic resonance and should not be interpreted as technical statements.

The “∈” symbol means set membership, and in this case, the group names are intended to refer to collections of works by a group rather than collections of artists. So one could interpret “Koi no Vacance ∈ W” as “Koi no Vacance is a work by W”. Then “Osaka Koi no Vacance ∈ W × Morning Musume.” means Osaka Koi no Vacance is a work in the crossing of W and Morning Musume. In general, you can read “A ∈ B × C” as “A is an element of B crossed with C” or “A is one of the pairings of B and C” or just “A is a product of B and C”.

Then we get into more complicated stuff like multiple tracks being used for their vocals, hence the reintroduction of “+” in a different context. Here “+” is commutative, and when used with sets, refers to the disjoint union of sets. I’ve appropriated this symbol to indicate the union of vocals from different tracks placed disjointly in time. For example, “Souda! Tropica~l Scramb~le Mode ∈ (Fujimoto Miki + Goto Maki + Morning Musume.) × Matsuura Aya” means that Fujimoto, Goto, and Morning Musume. all contribute vocals to the resulting remix, but their contributions are disjoint and don’t overlap.

And finally, there’s the monster of a MoMusu megamix “Dekkai Uchuu ni Namida ga Aruiteru zee! ∈ (Morning Musume. + Morning Musume. + (Morning Musume. Otome Gumi ∩ Morning Musume. Sakura Gumi)) × Morning Musume.”, in which Morning Musume. Otome Gumi and Morning Musume. Sakura Gumi contribute overlapping vocals in the same section. Since this is intuitively different from a disjoint union, we need a different operator. And here, I’ve adopted the “∩” symbol denoting set intersection, so that “(Morning Musume. Otome Gumi ∩ Morning Musume. Sakura Gumi)” represents the set of works that both groups have performed.

Overall, the notation may be a bit sloppy, but at least it’s semantically motivated and makes sense if you’re familiar with the mathematical usage of these symbols. I don’t know if I can say that for some of H!P’s own mathematical notation abuse, as in “C\C (Cinderella\Complex)” (if “\” denotes the set-theoretic complement, then C\C is ironically the empty set), Sakura → Nyuugakushiki (a function mapping cherry blossoms to school entrance ceremonies??), or “Yuki / Ai × Anata ≥ Suki” (I don’t even know where to begin…).

I should write a blog entry on H!P math notation….