recursal/Fanatic-Fandom huggingface dataset:
Christian (Cyberstars)

Christian, as Trayvon, in Online Gaming

**Christian**, a.k.a **The Stoner**, was one of the main characters of *Cyberstars* in season one. He is portrayed by, and a fictional version of, Christian Parker.

## Appearances

### Season 1

* “Online Gaming” (as Trayvon)
* "Pocket Chocolate" (as Matthew)
* "How We Play"
* "Codename: Kids Next Door - Next Generation" (as Cameron / Numbah 420)

## Trivia

* Christian's *Cyberstars* title is, **The Stoner**, due to his frequent use of marijuana.
* Christian left the group in 2015 (before the series officially premiered) due to personal reasons.
	+ This is the reason for his absence in *The Interview* and subsequent dedication message in *Love Sucks.*

* In *#StormArea51*, Christian has a cameo on a newspaper as a "Florida Man" that RKO'd a 15-foot alligator.
* David, Cortez and Christian reconnected in January 2020.
10L 11s

This is the MOS which splits its large steps 1-1-1-1-1-1-1-1-1-2 between its small steps. It is the simplest MOS which is really useful for Miracle temperament, placing the low estimate for the boundary of "practicality" at 41edo (L:s = 3:1). Its diatonic semitone generator is no smaller than 2/21edo (114.286 cents).
1171edo

The 1171 equal division divides the octave into 1171 parts of size 1.0248 cents each. It is a very strong 5-limit division, being the first one past 612 with a lower 5-limit relative error. It has a 5-limit comma basis consisting of the monzisma, |54 -37 2> and whoosh, |37 25 -33>. While not a strong higher-limit system, it is uniquely consistent through the 27-limit, and is very strong on the 2.3.5.11 subgroup. We might also note that 1171 is a prime number.
Episode List

## **Season One**

* Episode 01: “The Worlds, Perhaps, of Spirits”
* Episode 02: “The Impending Shades”
* Episode 03: “Thither to Burn”
* Episode 04: “A Momentary Crimson”
* Episode 05: “Their Frozen Horrors”
* Episode 06: “Beyond the Reach of Human Thought”
* Episode 07: “In the Distant Obscurity”
* Episode 08: “That Still Hour”
* Episode 09: “These Dark Battlements”
* Episode 10: “A Track of Blood”
* Episode 11: “The Silence of the Night”
* Episode 12: “This Dark Sojourn”
* Episode 13: “These Imperfect Images”
* Episode 14: “The Wild and Solitary”
* Episode 15: “This Solitary Shore”
* Episode 16: “The Shadows of a Moment”
* Episode 17: “Here is a Traitor”
* Episode 18: “The Vastness of the Sea”
* Episode 19: “In Deep Shadow”
* Episode 20: “In Absentia”
* Episode 21: “Cumulous”
* Episode 22: “Such a Place as This”
* Episode 23: “Pour Death and Defeat Upon Them”
* Episode 24: “At Midnight’s Spectred Hour”
* Episode 25: “Time’s Imperious Voice”
* Episode 26: “And Trembling Stars Below the Waves”
Peter Slate

> "I just hope you find what you’re looking for out there, and… Once you do, I’ll still be here." - Peter Slate, "Come in Under the Shadow"
>
>

### Relatives

Kate Sheridan (Wife - Alive) Andrew Sheridan-Slate (Son - Alive)

Anna Sheridan (Sister-in-Law - Missing/Unknown)

Mrs. Sheridan (Mother-in-Law - Alive)

### Affiliation

Kate Sheridan (Wife- Alive) Andrew Sheridan-Slate (Son - Alive)

## Appearances

### Debut

TST - Episode 28: "Come in Under the Shadow"

Peter Slate is Kate Sheridan's loving husband and the father of their son, Andrew Sheridan-Slate.

## **Personality**

Peter's main personality trait is he is an excellent father and loves his wife deeply - these are the best personality traits if you ask me.
He is the ultimate wife-guy.

## **Relationships**

**Kate Sheridan:** Kate is Peter's wife. He loves her very much. When Kate goes away to find clues about Anna he is nothing but supportive though he misses her terribly.
112/75

Interval information

**112/75**, the marvelous fifth (694.7¢), is 225/224 (7.7¢) below the just fifth 3/2. It often arises in just intonation scales, for instance as the interval from 15/14 to 8/5, or 5/7 to 16/15. Tempering out 225/224 from the scale can be used to make it much less flat, but it is usable as it is, being only half a cent flat from the 19edo fifth of 11\19. Considered as a meantone fifth, it is approximately 5/14-comma meantone.
14-3reduced-limit

**3reduced-limits:**

* 1-3reduced-limit
* 2-3reduced-limit
* 4-3reduced-limit
* 5-3reduced-limit
* 7-3reduced-limit
* 8-3reduced-limit
* 10-3reduced-limit
* 11-3reduced-limit
* 13-3reduced-limit
* **14-3reduced-limit**
* 16-3reduced-limit
* 17-3reduced-limit
* 19-3reduced-limit
* 20-3reduced-limit
* 22-3reduced-limit
* 23-3reduced-limit
* 25-3reduced-limit
* 26-3reduced-limit
* 28-3reduced-limit
* 29-3reduced-limit
* 31-3reduced-limit
* 32-3reduced-limit
* 34-3reduced-limit
* 35-3reduced-limit
* 37-3reduced-limit
* 38-3reduced-limit
* 40-3reduced-limit
* 41-3reduced-limit
* 43-3reduced-limit
* 44-3reduced-limit
* 46-3reduced-limit
* 47-3reduced-limit
* 49-3reduced-limit
* 50-3reduced-limit
* 52-3reduced-limit

 In 14-3reduced-limit we have tritave equivalence, and the following 3reduced harmonics: 2, 4, 5, 7, 8, 10, 11, 13, 14

* 15/14, 14/5
* 14/13, 39/14
* 13/12, 36/13
* 12/11, 11/4
* 11/10, 30/11
* 10/9, 27/10
* 9/8, 8/3
* 8/7, 21/8
* 15/13, 13/5
* 7/6, 18/7
* 13/11, 33/13
* 6/5, 5/2
* 11/9, 27/11
* 5/4, 12/5
* 14/11, 33/14
* 9/7, 7/3
* 13/10, 30/13
* 4/3, 9/4
* 15/11, 11/5
* 11/8, 24/11
* 18/13, 13/6
* 7/5, 15/7
* 10/7, 21/10
* 13/9, 27/13
* 3/2, 2/1
* 14/9, 27/14
* 11/7, 21/11
* 8/5, 15/8
* 21/13, 13/7
* 13/8, 24/13
* 18/11, 11/6
* 5/3, 9/5
* 12/7, 7/4
1600edo

The **1600** equal division divides the octave into 1600 equal parts of exactly 0.75 cents each. It is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller relative error than anything else with this property until 4501. It is also the first division past 311 with a lower 43-limit relative error. One step of it is the relative cent for 16.
125cET

This nonoctave tuning uses equal steps of 125 cents each. This could be considered dividing the 500 cent perfect fourth into 4 equal parts.

! E:\cakewalk\scales\125cent.scl
!

125 cent tuning

4
!

125.00000

250.00000

375.00000

500.00000

Example music with this tuning

Canyon Diablo Fall

File:Http://micro.soonlabel.com/125cent/20130317 125cent.mp3

Crossing Over

File:Http://micro.soonlabel.com/125cent/20141011 125ct crossing over.mp3
Cortez Andre

Andre in 2016.

**Cortez Andre Crawley** (born June 20, 1995), known professionally simply as **Cortez Andre**, is an American actor, director and writer, and was the one of Cyberstars Entertainment's Board of Directors. He is one of the creators of *Cyberstars*, as well as the creator of *Tez TV.*

As an actor, he portrayed the main antagonist Switchblade in the *Graffiti* series, and plays various roles, including a fictional version of himself, on *Cyberstars*.

## **Biography**

Cortez was born in Dearborn, Michigan in 1995. He has three sisters: Alyssa, Alieya and Alexis.

He began acting professionally in 2012, and shortly after joined the Creative Arts Spirit of Excellence (CASOE) Group along with his sisters. Through CASOE, he would meet David Ragin, Demonte Thompson, Christian Parker, Johnny Docs and Jovante Gray.

In 2015, Andre, Ragin and Thompson would create *Cyberstars*, and bring on Ragin's longtime friend DK Williams, fellow CASOE member Christian Parker, and Andre's sister Alyssa to form the original cast of *Cyberstars*, with Cortez acting as the main writer for the group.

## **External Links**

* *IMDb*
* *Official YouTube*

* *Official Facebook*

* *Official Instagram*
1-3reduced-limit

**3reduced-limits:**

* **1-3reduced-limit**
* 2-3reduced-limit
* 4-3reduced-limit
* 5-3reduced-limit
* 7-3reduced-limit
* 8-3reduced-limit
* 10-3reduced-limit
* 11-3reduced-limit
* 13-3reduced-limit
* 14-3reduced-limit
* 16-3reduced-limit
* 17-3reduced-limit
* 19-3reduced-limit
* 20-3reduced-limit
* 22-3reduced-limit
* 23-3reduced-limit
* 25-3reduced-limit
* 26-3reduced-limit
* 28-3reduced-limit
* 29-3reduced-limit
* 31-3reduced-limit
* 32-3reduced-limit
* 34-3reduced-limit
* 35-3reduced-limit
* 37-3reduced-limit
* 38-3reduced-limit
* 40-3reduced-limit
* 41-3reduced-limit
* 43-3reduced-limit
* 44-3reduced-limit
* 46-3reduced-limit
* 47-3reduced-limit
* 49-3reduced-limit
* 50-3reduced-limit
* 52-3reduced-limit

 The only tritave–reduced 1-3reduced-limit interval is 1/1.
Curse of the Red Beanie

***Curse of the Red Beanie*** is the twelfth episode of the first season of *Cyberstars*. It was written by Jovante Gray and directed by David Ragin. It was released on January 13, 2017 on YouTube as the premiere of the second half of season one.

## Synopsis

The gang tries to convince David that his outfit, which has been previously worn by both Soulja Boy and Meek Mill, is a bad idea.

## Cast

### *Cyberstars* Cast

* David Ragin as David
* Jovante Gray as Jovante
* Johnny Docs as Johnny
* Cortez Andre as Cortez
* DK Williams as DK

## External Links

* *YouTube Episode Link*
* *IMDb Page Link*
Try Not to Laugh

***Try Not to Laugh*** (also known as ***Try Not to Laugh (with okaayminnie and LyonSage Productions)*** or ***Try Not to Laugh #1***) is the twenty-fifth episode and season finale of the first season of *Cyberstars*. It was directed by David Ragin. It was released on September 29, 2017.

## Synopsis

In the season one finale, David, Cortez and J Gray participate in a "Try Not to Laugh" challenge with special guests okaayminnie and Dominique Lyons of Lyon Sage Productions.

## Cast

### *Cyberstars* Cast

* David Ragin
* Cortez Andre
* Jovante Gray

### **Featured Cast**

* Miniece Ragin (okaayminnie)
* Dom Lyons (LyonSage Productions)

## External Links

* *YouTube Episode Link*
* *IMDb Page Link*
1-3 Syntonic Comma Meantone

de:Drittelkomma-mitteltönig
In **1/3-comma meantone** temperament, each perfect fifth is tempered by a third of a syntonic comma from its just value of 3/2. This results in minor thirds being exactly 6/5 (and major sixths being exactly 5/3).

In other words, 1/3-comma meantone is the specific tuning of meantone temperament with an eigenmonzo of 6/5.

The fifth is 694.786 cents in size, and the major third 379.145 cents, which is about 7 cents flatter than in 1/4-comma meantone.

1/3-comma meantone is practically identical to the closed system of 19edo (although technically there is a slight difference).

# External links

Die mitteltönige Stimmung mit reinen kleinen Terzen (explanation of 1/3 comma meantone, in german)
1-6 Syntonic Comma Meantone

1/6 comma meantone is the tuning of meantone temperament which tunes the fifth as the sixth root of 45/4, or in other words 698.371 cents. This means the fifth is flattened by 1/6 of the syntonic comma (81/80 ratio) of 21.506 cents, which is to say by 3.584 cents, hence the name 1/6-comma meantone. In 1/6-comma meantone, the diatonic tritone 45/32 is tuned justly, and it can be characterized fully as the regular tuning tempering out 81/80 and tuning 2 and 45/32 justly. It is closely related to 55edo in terms of its tuning.

# Fractional projection matrix

The fractional projection map defining 7-limit 1/6 comma meantone is

 [2/3
 [-4/3
 [-19/3

# Links

Baroque Ensemble Tuning in Extended 1/6 Syntonic Comma Meantone by Ross W. Duffin permalink

Mozart's tuning: 55-EDO and its close relative, 1/6-comma meantone by Joe Monzo permalink
Dub (Cyberstars)

**Dub**, a.k.a **The Profound**, is one of the main characters of *Cyberstars Detroit*. He is portrayed by, and a fictional version of, Dubby Davito.

## Appearances

### Season 2

* "Netflix Exclusive"
* "That's What She Said" (as Jay)

## Trivia

* Creech's *Cyberstars* title is **The Profound** due to his seemingly wise insight.
* Dub was hired by DK to replace Creech in Cyberstars; however, he would join the group and Creech would retain his role in the group.
The Good Ol' Days

***The Good Ol' Days*** is the eighteenth episode of the first season of *Cyberstars*. It was both written and directed by Cortez Andre. It was released on March 10, 2017.

## Synopsis

A young boy’s uncle (ironically known as “Grandad”) attempts to lecture him on “good music”, but soon gets his own lecture on how he embarrasses his nephew.

## Cast

### *Cyberstars* Cast

* Cortez Andre as Grandad
* Demonte Thompson as Lemont
* Alyssa Crawley as Dareta
* Johnny Docs as Lemont's friend
* David Ragin as Buckles
* DK Williams as Clifford
* Jovante Gray as Freddie

## External Links

* *YouTube Episode Link*
* *IMDb Page Link*
13平均律

# 最も2.5.9.11.13.17.19.21に近似する音律

13平均律は周波数比2のオクターブを13個の均等なパートに分割するシステムを参照する。それは6番目の素数平均律であり、11平均律の後であり17平均律の前の平均律である。600セントより小さいステップ（6ステップ、553.84セント）は、最も近い12平均律の近似よりも狭い。そして600セントより大きいもの（7ステップ、646.15セント）は幅広い。これは巧妙な耳のトリックを起こす。12平均律から連想されるメロディーは、慣れていない場所へ素早くたどり着く。

21アドリミットJIのテンペラメントとしてみなすと、13平均律は素晴らしい11番目と21番目の倍音に近似する。そして5、9、13、17、19倍音にもそれなりに近づくことができる。一番の目的は、3、7、15倍音の近似と認識するものを与えないことである。3倍音の響きとそれなりに近い響きが発生しないということは、13平均律が慣習的な音楽に適していないということを示す。しかし11、13、21の周波数とはとても良い近似値であり、とてもゼンハーモニックチューニングを作り出す。これらの独自性は12平均律の表現から離れはしないけれども。評価は不協和であるものの、それは2.5.9.11.13.17.19.21サブグループであり、素晴らしいランク1のテンペラメントである。そして小さいサイズのための、複雑に一致する多くのレパートリーを持つ。

# 13平均律の音程と近似値

「The “neighborhood” of JI」の一覧はこちら（huygens-fokker）を参照のこと。各周波数比の大きさが16以内で表現される純正音程は以下のようになる。これはedjirulerを用いて、[number of equal divisions=13, interval of equivalence=2, integer limit=16, threshold of JI pitch inclusion=0.2]というパラメータで生成したものである。

# 13平均律の音階

13という素数の特徴によって、13平均律はいくつかのゼンハーモニックMOS音階（moment of symmetry scales）を形作る。下のダイアグラムはMOS音階の5音「ファミリー」を示す。これらは2*13**（13平均律の2音程）、3*13、4*13**、5*13、6//13のチェーンによって作成される。

13edo\_horograms.jpg

13edo horograms.pdf

Ery Wilsonが先駆者となったホラグラムをもとに、Andrew Heathwaiteが作成したダイアグラム。

13平均律のもう一つのきちんとした様相として、余分な半音を加えるか、現在の半音を全音に変えることで、どんな12平均律の音階も13平均律の音階に「変えられる」ということである。このため、13平均律のメロディーはとても不思議で、類似した方法でフレーズを始めると、即座に予想外の何かに導かれる。

# 13平均律のハーモニー

一般的な考えとは逆に、13平均律で協和音は可能である。しかし12平均律やピタゴラス、ミーントーンなどをベースとしたチューニングの使い方とは徹底的に異なったアプローチを要求する。一般的な12平均律の長3和音や短3和音の近似値を13平均律の中で試みるとき、ゴールを0-3-7、0-4-7、0-3-8、0-4-8とするなら、13平均律では荒くなるので通常断念せざるを得ない。13平均律で通常最も協和するハーモニーは、「3度の積み重ね」ではない。13平均律の最も強い不協和は、オクターブのミドルトーン、つまり音程が6、7、8ステップに近い時である。代わりに、全音の積み重ね、または全音と短3度のミックスの積み重ねで、しばしば良い結果が生み出される。たとえば、13平均律をハーモニック2.5.9.11.13のテンペラメントサブグループとしてみなす方法である。これは実際見事に演じる。そして4:5:9:11:13に近い0-4-15-19-22のコードはとても人を納得させる。より大きなサブグループは、2\*13 subgroup2.9.5.21.11.13である。13は26ETのようなコンマとチューニングをもつ。

この場合、私たちは13平均律の長9度が12平均律の完全5度や他のミーントーン平均律と似ていると想定することができる。これは11/8や5/4などが続く13平均律において、長2度や長9度が2/1に次いで最も協和することを意味する。4:5:9コードはそれゆえ基本的な13平均律のトライアドであると考えることができる。

2.9.5.11.13サブグループは、45/44と65/64,そして81/80コンマを持ち、POTEジェネレーター185.728セントとともにリニアーテンペラメントを導く。それは非常に2//13に近い。これをジェネレーターとして使うと、そして7音（6L1s）の2つの完全なペンタを利用する。同様に2つの4:5:9:11テトラと、1つの4:5:9:13テトラも利用できる。これらのトライアドとテトラは、13平均律の中でおそらくもっとも協和するベースソノリティーであり、長3和音や短3和音と似た手法を演じるという想定ができる。しかしながら、ほかのOrwellコードのようなソノリティーも同時に感じられる。

のアプローチは特定の作曲家と理論家によって探求されており、大まかなものは下に示される。

Play the 4:5:9 chord:

File:13 edo 459 chord.wav

Play the 4:5:9:11 chord:

File:13 edo 45911 chord.wav

Play the 4:5:9:13 chord:

File:13 edo 45913 chord.wav

Play the 4:5:9:21 chord:

File:13 edo 45921 chord.wav

# 13平均律の記譜法と作曲のアプローチ

13平均律は多くの作曲家や理論家から興味を持たれており、何人かは記譜法と作曲に関するアプローチの提案を行っている。

# コンマをなだらかにする

13平均律を<13 21 30 36 45 48|ヴァルとみなした時、次のリストのコンマをテンパーアウトする。
154edo

The ***154edo*** divides the octave into 154 equal parts of 7.79221 cents each. It is a contorted 77et in the 7-limit; in the 11-limit, it tempers out 126/125, 1029/1024 and 243/242, which define the 11-limit 31&123 temperament, for which 154 provides a good tuning, though 185edo gives the patent val. In the 13-limit, it tempers out 196/195, 364/363 and 676/675.

154 = 2 \* 7 \* 11, with divisors 2, 7, 11, 14, 22 and 77.
10/7

Interval information

Type: Utonal

In 7-limit Just Intonation, 10/7 is a high tritone measuring about 617.5¢. It has a similar sound to its inversion, 7/5, but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third (5/4) appears above the harmonic seventh (7/4), such as 4:6:7:10. (This particular chord is well-approximated in 88cET, which has a good approximation of 10/7 -- but no 7/5.)

*See also Gallery of Just Intervals*
101edo

***101-EDO*** divides the octave into 101 equal parts of 11.881 cents each. It can be used to tune the grackle temperament. It is the 26th prime edo. The 101cd val provides an excellent tuning for witchcraft temperament, falling between the 13 and 15 limit least squares tuning.

7-limit commas: 126/125, 32805/32768, 2430/2401

## Some important MOS scales:

**25 13 25 25 13:** *3L2s MOS* (Pentatonic)

 38
 63
 88

**17 17 8 17 17 17 8:** *5L2s MOS* (Diatonic Pythagorean)

**13 13 13 13 13 13 13 10:** *7L1s MOS* (Grumpy Octatonic)

 26
 39
 52
 65
 78
 91

**13 13 13 5 13 13 13 13 5:** *7L2s MOS* (Superdiatonic 1/13-tone 13;5 relation)

**10 10 7 10 10 10 7 10 10 10 7:** *8L3s MOS* (Improper Sensi-11)

**7 7 7 8 7 7 7 7 8 7 7 7 7 8:** *3L11s MOS* (Anti-Ketradektriatoh)
13ed5

What is known as "father" has a large 3:2 which warps the heptatonic scale to an octatonic.

Analogously, in hyperpyth, 13ed5 has an analogously large "13:5" which warps the scale similarly. I haven't figured out what it approximates well, but it sounds good.

18ed5 also does this; the "13:5" is actually 50 cents sharp, while 8:3 is much closer. Interesting.
106edo

The 106 equal division divides the octave into 106 equal parts of 11.321 cents each. Since 106 = 2\*53 it is closely related to 53edo, and is contorted through the 7-limit, tempering out the same commas (32805/32768, 15625/15552, 1600000/1594323, 2109375/2097152 in the 5-limit, 3125/3097, 225/224, 4000/3969, 1728/1715, 2430/2401, 4375/4374 in the 7-limit) as the patent val for 53edo. In the 11-limit it also tempers out 243/242, 3025/3024 and 9801/9800, so that it supports spectacle temperament and borwell temperament.

The division is notable for the fact that it is related to the turkish cent, ot türk sent, which divides 106edo into 100 parts just as ordinary cents divides 12edo into 100 parts, thereby making it the relative cent division for 106edo.

Artists using 106 et:

* Dolores Catherino -- her website, YouTube profile: dolomuse
* Still Life in 106 Notes Per Octave « Music & Techniques by Chris Vaisvil
127edo

**127edo**, which divides the octave into 127 parts of 9.45 cents each, is another equal division interesting because of its approximations, defined by the commas it tempers out. In the 5-limit, it tempers out the würschmidt comma, 393216/390625 and hence supports würschmidt temperament. In the 7-limit, it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the 11-limit, it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the optimal patent val and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

127edo is the 31st prime edo.

MOS Scales of 127edo
11L 1s

This MOS, with its diatonic minor second generator, is the dodecatonic scale of Ripple (9:8=+2 generators) and Passion (6:5=+3 generators) temperaments. However, it feels markedly more hendecatonic to listeners used to the equally divided chromatic scale because of its unbroken chain of eleven equal steps–never mind that the 12th degree is actually less than the octave. This hendecatonic feel is especially pronounced above 2/23edo, where the octave feels like a comma shift of the 12th degree rather than an independent note.
15ED4

# Basics

15ED4 is a macrotonal tuning system that divides the double-octave (4/1) into 15 equally spaced pitches each about 160 cents apart. It can be viewed as a subset of 15 EDO that repeats at two octaves rather than one. It has a big xen appeal as it is non octave but at the same time contains the double octave allowing for a sort of best of both worlds approach. 15ED4 doesn't do Just Intonation well for the most part but it does represent 7/4 and 11/8 rather well.

# MOS Scales

There are a variety of Mos scales available. William Lynch considers the symmetrical MOS: LsLsLsLs to be the most consonant scale in 15ED4. There is also a LsLLsLLLs scale which is more spacey sounding than the symmetrical MOS. The symmetrical MOS can be harmonized with c
0edo

# Zero equal divisions of the octave

There are two ways to approach this idea.

Given that *n*-edo means that you are dividing the octave into 1*/n* equal divisions and that 1/0 is sometimes considered undefined, it would follow that 0edo would be similarly undefined and thus would comprise no sounds at all (or intervals from unison are undefined, so 1 note is there).

The other way of looking at it is to see what happens as *n* gets smaller. At 1-edo you have one note per octave. At 0.5-edo you have 1/0.5 which is one note every two octaves. As *n* gets smaller you reach a point where you only have one note within an audible octave range and any other notes outside of this range. Taking this to its conclusion, and assuming you want 0edo to be defined, you would conclude that 0edo is just one note without any octaves.

An example of a trivial temperament, 0edo tempers out all commas and is consistent in all limits.
StormArea51: The Anthem

***#StormArea51: The Anthem*** is the first episode of *Cyberstars Detroit*, the second season of *Cyberstars*. It was written and directed by David Ragin. It was released on September 13, 2019 on YouTube, the first *Cyberstars* skit in almost two years.

## Synopsis

The full team reunite and team up with singer Chris Thomas to provide the theme song for the *Area 51 Raid* on September 20th in this parody of "I'll Make a Man Out of You".

## Cast

### *Cyberstars* Cast

* David Ragin as David
* Cortez Andre as Cortez
* Indiana Rose as India
* DK Williams as DK
* Alyssa Crawley as Alyssa
* Johnny Docs as Johnny
* Jovante Gray as Jovante
* Jameer "B Cyde" DeAndre as B Cyde

### **Featured Cast**

* Christopher A. Thomas
* Derrick Jackson, Jr.
* Michele Clark
* Dom Lyons
* Bryndyn Williams
* Lambert Greaves
* Amir Walker
* Antisha Williams
* Crystal Wright
* Rhondee Palmer
* Rachelle Ragin
* Gianna Rose

## Trivia

* *#StormArea51: The Anthem* features the most *Cyberstars* members than any other skit, with 10 of the 12 members appearing in some way.
	+ Christian Parker and Demonte Thompson make cameo appearances on a newspaper that Cortez holds up.
	+ Ashley McClellan and Jay Creech are the only *Cyberstars* members not to appear in the skit in any capacity.
		- Creech was meant to appear, but was unable to due to scheduling conflicts.

## External Links

* *YouTube Episode Link*
* *IMDb Page Link*
16/15

**16/15**

111.73129 cents

File:Jid 16 15 pluck adu dr220.mp3 sound sample

The 5-limit just diatonic semitone is the superparticular interval 16/15 -- the difference between the major third 5/4 and the fourth 4/3, and between 3/2 and 8/5.

When this ratio is taken as a comma to be tempered, it produces father temperament, where 4/3 and 5/4 are equated. In this temperament, major thirds and fifths become octave-inverses of each other.
150edo

The *150 equal division* divides the octave into 150 equal steps exactly 8 cents each. This means eleven such steps are 88 cents, relating 150edo to the 88cET nonoctave tuning. It tempers out 245/243, 4000/3969 and 2401/2400 in the 7-limit, 896/891, 385/384 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675 and 1575/1573 in the 134-limit. It is contorted in the 5-limit, tempering out the same commas as 75edo, including 20000/19683 and 2109375/2097152. It provides a good tuning for Tetracot family, for which 88 cents provides a generator.
11/8

Interval information

In 11-limit Just Intonation, 11/8 is an undecimal (11-based) superfourth of about 551.3¢. Falling about halfway between 12edo's perfect fourth and tritone, it is very xenharmonic. It is the simplest superfourth in JI. As an octave-reduced overtone, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the much stronger and more familiar consonances of 10 (5) and 12 (3). It is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12.

*See also Gallery of Just Intervals*
de:Alphorn-Fa
11-3reduced-limit

**3reduced-limits:**

* 1-3reduced-limit
* 2-3reduced-limit
* 4-3reduced-limit
* 5-3reduced-limit
* 7-3reduced-limit
* 8-3reduced-limit
* 10-3reduced-limit
* **11-3reduced-limit**
* 13-3reduced-limit
* 14-3reduced-limit
* 16-3reduced-limit
* 17-3reduced-limit
* 19-3reduced-limit
* 20-3reduced-limit
* 22-3reduced-limit
* 23-3reduced-limit
* 25-3reduced-limit
* 26-3reduced-limit
* 28-3reduced-limit
* 29-3reduced-limit
* 31-3reduced-limit
* 32-3reduced-limit
* 34-3reduced-limit
* 35-3reduced-limit
* 37-3reduced-limit
* 38-3reduced-limit
* 40-3reduced-limit
* 41-3reduced-limit
* 43-3reduced-limit
* 44-3reduced-limit
* 46-3reduced-limit
* 47-3reduced-limit
* 49-3reduced-limit
* 50-3reduced-limit
* 52-3reduced-limit

 11-3reduced-limit could be considered the tritave equivalent to 11-odd-limit.

In 11-odd-limit we have octave equivalence, and the following odd harmonics: 3, 5, 7, 9, 11

In 11-3reduced-limit we have tritave equivalence, and the following 3reduced harmonics: 2, 4, 5, 7, 8, 10, 11

* 12/11, 11/4
* 11/10, 30/11
* 10/9, 27/10
* 9/8, 8/3
* 8/7, 21/8
* 7/6, 18/7
* 6/5, 5/2
* 11/9, 27/11
* 5/4, 12/5
* 9/7, 7/3
* 4/3, 9/4
* 15/11, 11/5
* 11/8, 24/11
* 7/5, 15/7
* 10/7, 21/10
* 3/2, 2/1
* 11/7, 21/11
* 8/5, 15/8
* 18/11, 11/6
* 5/3, 9/5
* 12/7, 7/4
1-odd-limit

**Odd limits:**

* **1-odd-limit**
* 3-odd-limit
* 5-odd-limit
* 7-odd-limit
* 9-odd-limit
* 11-odd-limit
* 13-odd-limit
* 15-odd-limit
* 17-odd-limit
* 19-odd-limit
* 21-odd-limit
* 23-odd-limit
* 25-odd-limit
* 27-odd-limit
* 29-odd-limit
* 31-odd-limit
* 33-odd-limit
* 35-odd-limit
* 37-odd-limit
* 39-odd-limit
* 41-odd-limit
* 43-odd-limit
* 45-odd-limit
* 47-odd-limit
* 49-odd-limit
* 51-odd-limit

 The only octave–reduced 1-odd-limit interval is 1/1.
11/10

**11/10**

165.00423 cents

File:Jid 11 10 pluck adu dr220.mp3 sound sample

11/10, the large neutral second, is an interval favored by Ptolemy. Three of them are less than 4/3 by the wizardharry comma, 4000/3993.

Coincidentally, the interval between the most common tuning frequency (A440) and the second most common AC electrical frequency (50hz) is exactly 44/5, or three octaves above an 11/10.

See: Gallery of Just Intervals
149edo

The *149 equal division* divides the octave into 149 equal parts of 8.054 cents each. It provides the optimal patent val for 7- 11- 13- and 17-limit heinz temperament and the rank three temperament ominous in the 13- and 17- limits. It has a generally flat tendency, with the fifth 1.28 cents flat, but the major third is a quarter of a cent sharp. In the 5-limit it tempers out the sensipent comma, 78732/78125; in the 7-limit, 1029/1024, 3136/3125 and 19683/19600; in the 11-limit 385/384 and 441/440; in the 13-limit 351/350 and 676/675; in the 17-limit 273/272 and 561/560; in the 19-limit 286/285 and 343/342.

149edo is the 35th prime edo.
164edo

The *164 equal division* divides the octave into 164 equal parts of 7.317 cents each. In the 5-limit it tempers out the würschmidt comma, 393216/390625, and supplies the optimal patent val for würschmidt temperament. In higher limits, also supplies the optimal patent val for the 7-limit, 1/41 octave period 41&123 temperament, and the 13-limit momentous temperament, the rank-three temperament tempering out 196/195, 352/351, 385/384 and 441/440.

164 = 4 \* 41, with divisors 2, 4, 41, 82
12L 2s

This MOS, being two periods of 6L 1s, is always proper. It appears as the mega chromatic scale of Injera temperament, meaning that its harmonic entropy is where +4 generators equals 5/4 (simple) or +10 generators equals 5/3 (complex).

Its generator is a neutral semitone of 1/14edo (85.714 cents) to 1/12edo (100).
16808edo

The 16808 division divides the octave into 16808 steps of size 0.0714 cents each. It is distinctly consistent and highly accurate through the 35 limit, and can be used as a measure of interval size (the jinn) for most intervals which occur in practice. It is a very, very strong 31-limit division, and a zeta peak, zeta integral and zeta gap tuning. In the 23, 29 and 31 limits it has the lowest logflat badness up until at least 200000; in the 19 limit it is beaten out by 8539edo, and in the 17 limit by 72edo, 1506edo, 3395edo and 7033edo.

Among the enormous list of 31-limit commas it tempers out, the simplest are 43681/43680, 49011/49010, 52326/52325 and 53361/53360. In the 13-limit it tempers out 123201/123200 and1990656/1990625; in the 17-limit 194481/194480 and 336141/336140; in the 19-limit 43681/43680,89376/89375 and104976/104975. Since 43681/43680 is both the simplest comma it tempers out and the limit is as low (in this context) as 19, it may be regarded as rather characteristic of 16808.

16808 has proper divisors 1, 2, 4, 8, 11, 22, 44, 88, 191, 382, 764, 1528, 2101, 4202 and 8404, among which 22edo and 764edo are particularly notable. One step of 22edo is 764 jinns, and one step of 764edo is 22 jinns.
120edo

120edo means division of the octave into equal parts of 10 cents each. Its patent val is contorted only through the 3-limit and does not temper out 81/80 in the 5-limit or 64/63 and 5120/5103 in the 7-limit. However, 5120/5103 is done about as badly as this interval can be done relative to an equal division, falling close to exactly in the middle of a step (1\120 is ~42.42 relative cents sharp of it). Being the simplest division of the octave by the Germanic long hundred, it has a unit step which is the fine relative cent of 1edo
112edo

112EDO has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which is identical to the perfect fifth of 56edo, a slightly large fifth where +5 fifths gives a near-just 27:28 while -8 fifths gives a near-just 32:39 (identical to 2 degrees of 7edo) and +9 fifths gives a close approximation to 17:21.

One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from 17edo, but sharing a similar structure.

# Music in 112EDO

Circulating 2.3.7.11.13 Floaty Piano Improv by Cam Taylor
The Echo

The Echo is supernatural entity made of pure radio waves that can mimic and take on the form of humans it encounters. It can copy multiple people at once. While it never states its personal goal, it is assumed that it desires to replace humanity with its self.

It has currently taken the preferred form of horror writer Anna Sheridan.

## **History**

Anna Sheridan first encountered the Echo in Spirit Mountain Cave, Wyoming.
149edt

**149edt** is pretty much the tritave equivalent to 94edo. Like 94edo is consistent in 23-odd-limit, **149edt** is consistent in 23-3reduced-limit. It has a step size of 12.764798663526 cents, nearly identical to 94edo with 12.765957446809 cents, and the simulated octave is of 1199.8910743715 cents. It achieves this accuracy naturally because 94edo is a sum of 41edo and 53edo so it naturally too has accurate proportions of 2 to 3.
143edo

143edo is a scale which divides the octave into 143 equal divisions of approximately 8.392¢. The 143b val provides a tuning almost identical with that of the POTE tuning for 7-limit meantone (quarter comma meantone).

As 143 is 11\*13, 143edo allows the polymicrotonal juxtaposition of 11edo and 13edo, that is, it can be used to play 11edo and 13edo music at the same time with the 143/13 and 143/11 vals respectively. The resulting scale would have 23 tones in the octave. It's impossible to have 24, because the scales will always overlap.
118edo

In the 7-limit it is particularly notable for tempering out the gamelisma, 1029/1024, and is an excellent tuning for the rank three gamelismic temperament, and for guiron, the rank two temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the hemimean comma, but 99edo does better with that.

In the 11-limit, it tempers out 385/384 and 441/440, and is an excellent tuning for portent, the temperament tempering out both, and for the 11-limit version of guiron, which does also.
1012edo

The 1012 equal division divides the octave into 1012 equal parts of 1.1858 cents each. It is a strong 13-limit system, distinctly consistent through the 15 limit. It is a zeta peak edo, though not zeta integral nor zeta gap. A basis for the 13-limit commas is 2401/2400, 4096/4095, 6656/6655, 9801/9800 and | 2 6 -1 2 0 4 >. 1012 is divisible by 22, 46 and 253.
15-odd-limit

**Odd limits:**

* 1-odd-limit
* 3-odd-limit
* 5-odd-limit
* 7-odd-limit
* 9-odd-limit
* 11-odd-limit
* 13-odd-limit
* **15-odd-limit**
* 17-odd-limit
* 19-odd-limit
* 21-odd-limit
* 23-odd-limit
* 25-odd-limit
* 27-odd-limit
* 29-odd-limit
* 31-odd-limit
* 33-odd-limit
* 35-odd-limit
* 37-odd-limit
* 39-odd-limit
* 41-odd-limit
* 43-odd-limit
* 45-odd-limit
* 47-odd-limit
* 49-odd-limit
* 51-odd-limit

 This is a list of 15-odd-limit intervals. It has proven helpful for showing JI properties of medium-sized edo systems (~15 .. 41 steps). To 13-odd-limit, it adds four additional interval pairs involving 15.

* 16/15, 15/8
* 15/14, 28/15
* 14/13, 13/7
* 13/12, 24/13
* 12/11, 11/6
* 11/10, 20/11
* 10/9, 9/5
* 9/8, 16/9
* 8/7, 7/4
* 15/13, 26/15
* 7/6, 12/7
* 13/11, 22/13
* 6/5, 5/3
* 11/9, 18/11
* 16/13, 13/8
* 5/4, 8/5
* 14/11, 11/7
* 9/7, 14/9
* 13/10, 20/13
* 4/3, 3/2
* 15/11, 22/15
* 11/8, 16/11
* 18/13, 13/9
* 7/5, 10/7
11-odd-limit

**Odd limits:**

* 1-odd-limit
* 3-odd-limit
* 5-odd-limit
* 7-odd-limit
* 9-odd-limit
* **11-odd-limit**
* 13-odd-limit
* 15-odd-limit
* 17-odd-limit
* 19-odd-limit
* 21-odd-limit
* 23-odd-limit
* 25-odd-limit
* 27-odd-limit
* 29-odd-limit
* 31-odd-limit
* 33-odd-limit
* 35-odd-limit
* 37-odd-limit
* 39-odd-limit
* 41-odd-limit
* 43-odd-limit
* 45-odd-limit
* 47-odd-limit
* 49-odd-limit
* 51-odd-limit

 This is a list of 11-odd-limit intervals. To 9-odd-limit, it adds 5 additional interval pairs involving 11.

* 12/11, 11/6
* 11/10, 20/11
* 10/9, 9/5
* 9/8, 16/9
* 8/7, 7/4
* 7/6, 12/7
* 6/5, 5/3
* 11/9, 18/11
* 5/4, 8/5
* 14/11, 11/7
* 9/7, 14/9
* 4/3, 3/2
* 11/8, 16/11
* 7/5, 10/7
12/7

Interval information

In 7-limit Just Intonation, 12/7 is the septimal supermajor sixth of about 933.1¢. It represents the interval between the 12th and 7th harmonics and appears in chords such as 4:5:7:9:12. It differs from the 5-limit major sixth of 5/3 by 36/25 -- the septimal quartertone -- a superparticular interval of about 48.8¢. It differs from the Pythagorean major sixth of 27/16 by 64/63 -- Archytas' comma -- about 27.3¢. And finally, it differs from the harmonic seventh -- 7/4, about 968.8¢ -- by 49/48 -- the large septimal diesis or slendro diesis -- about 35.7¢. 12/7 is the inversion of the septimal subminor third of 7/6.

See: Gallery of Just Intervals]]
17-3reduced-limit

**3reduced-limits:**

* 1-3reduced-limit
* 2-3reduced-limit
* 4-3reduced-limit
* 5-3reduced-limit
* 7-3reduced-limit
* 8-3reduced-limit
* 10-3reduced-limit
* 11-3reduced-limit
* 13-3reduced-limit
* 14-3reduced-limit
* 16-3reduced-limit
* **17-3reduced-limit**
* 19-3reduced-limit
* 20-3reduced-limit
* 22-3reduced-limit
* 23-3reduced-limit
* 25-3reduced-limit
* 26-3reduced-limit
* 28-3reduced-limit
* 29-3reduced-limit
* 31-3reduced-limit
* 32-3reduced-limit
* 34-3reduced-limit
* 35-3reduced-limit
* 37-3reduced-limit
* 38-3reduced-limit
* 40-3reduced-limit
* 41-3reduced-limit
* 43-3reduced-limit
* 44-3reduced-limit
* 46-3reduced-limit
* 47-3reduced-limit
* 49-3reduced-limit
* 50-3reduced-limit
* 52-3reduced-limit

 **17-3reduced-limit** is the tritave equivalent of 17-odd-limit.

In 17-odd-limit we have octave equivalence, and the following odd harmonics: 3, 5, 7, 9, 11, 13, 15, 17

In 17-3reduced-limit we have tritave equivalence, and the following 3reduced harmonics: 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17

* 18/17, 17/6
* 17/16, 48/17
* 16/15, 45/16
* 15/14, 14/5
* 14/13, 39/14
* 13/12, 36/13
* 12/11, 11/4
* 11/10, 30/11
* 10/9, 27/10
* 9/8, 8/3
* 17/15, 45/17
* 8/7, 21/8
* 15/13, 13/5
* 7/6, 18/7
* 13/11, 33/13
* 6/5, 5/2
* 17/14, 42/17
* 11/9, 27/11
* 16/13, 39/16
* 21/17, 17/7
* 5/4, 12/5
* 14/11, 33/14
* 9/7, 7/3
* 13/10, 30/13
* 17/13, 39/17
* 21/16, 16/7
* 4/3, 9/4
* 15/11, 11/5
* 11/8, 24/11
* 18/13, 13/6
* 7/5, 15/7
* 24/17, 17/8
* 17/12, 36/17
* 10/7, 21/10
* 13/9, 27/13
* 16/11, 33/16
* 3/2, 2/1
* 17/11, 33/17
* 14/9, 27/14
* 11/7, 21/11
* 27/17, 17/9
* 8/5, 15/8
* 21/13, 13/7
* 13/8, 24/13
* 18/11, 11/6
* 5/3, 9/5
* 27/16, 16/9
* 17/10, 30/17
* 12/7, 7/4
12L 1s

This MOS, the Grumpy tridecatonic, apparently belongs to no particularly important temperament. However, it becomes a compressed 12ed scale when you ignore the octave (this obviously does not work when the generator is very near 12edo (within -7/24¢ of it), for the 13th degree of the scale registers as identical to the octave for human listeners, and it becomes indistinct from 13edo or the Happy dodecatonic (1L 11s) in the 1.75¢ above 1/13edo because the large and small steps register as identical to one another for human listeners).
12平均律

12平均律はおそらく12ETとしてよく知られている。明らかにテンペラメントである。今日、世界でも有力なチューニングである。5リミットハーモニーの響きを強く主張する、最小の均等分割であるため、この地位を獲得した。1/12ピタゴラスコンマ（およそ1/11のシントニックコンマ）ミーントーンのように、それはミーントーンを代表する。

オクターブが縮小または拡大されていない限り、オクターブを100セントで均等に分割し、12個のパートを作る。12平均律は2セントフラットされたとてもよい5度を持っている。長3度は13+2/3セントシャープされており、いくつかの音楽スタイルで十分に機能し、それ以外の音楽スタイルでは機能しない。そして短3度は15+2/3セントフラットされる。ヨーロッパのチューニングがだんだんと12ETに向かって近づいて行ったのはたぶん偶然ではない。12ETの欠陥はあまり目立たずあらわれるように、音楽スタイルが変わったのである。けれども実際のパフォーマンスではしばしば、パフォーマーによるチューニングの操作により、12ETの欠陥は減少されたことを心にとどめておくべきだ。

不完全な7度（7/4、968.83cent）は、31セントよりも大きくシャープされた音程であることを「示す」。そしてテトラコードの心地良さから明確に突出している。そのようなテトラコードはしばしばドミナントセブンスコードの機能で使われた。5リミットJIバージョンはおそらく1/1 - 5/4 - 3/2 - 16/9であり、12ETははっきりと7リミットミーントーンのことを、<12 19 28 34|ヴァル（val）を経由してサポートしている。この7リミットの範囲における信用性は、疑いようもなく陳腐なものとなる。17と、そしてより19においては信用できるが、11と13で繰り返し信用できるかといえば全くそうではない。関連するチューニングの正確性はとても高いにもかかわらず、12平均律は4番目のゼータインテグラル平均律である（zeta integral edo）。

次のコンマがテンパーアウトされる。3^12/2^19のピタゴラスコンマ、81/80のディディモスコンマ、128/125のディエシス、2048/2025のディアシスマ、64/63のアルキュタスコンマ、36/35の7リミットの4分音、50/49のジュビリスマ、126/125の7リミットのセミコンマ、225/224の7リミットのクレイスマ。特定の手法によりそれぞれは12ETの構造に影響を与える。そして問題のコンマを共有するチューニングシステムは、正確にそれらの方法で12ETに近づく。

# ランク2テンペラメント

悪い12ETランク2テンペラメントのリスト

複雑な12ETランク2テンペラメントのリスト

平均律とは異なった12fランク2テンペラメントのリスト

per octave

# 12平均律の音程と近似値

「The “neighborhood” of JI」の一覧はこちら（huygens-fokker）を参照のこと。各周波数比の大きさが16以内で表現される純正音程は以下のようになる。これはedjirulerを用いて、[number of equal divisions=12, interval of equivalence=2, integer limit=16, threshold of JI pitch inclusion=0.2]というパラメータで生成したものである。

# コンマをなだらかにする

12平均律を< 12 19 28 34 42 44 |ヴァルとみなした時、次のリストのコンマをテンパーアウトする。
13-notwos-3reduced-limit

**Notwos-3reduced-limits:**

* 1-notwos-3reduced-limit
* 5-notwos-3reduced-limit
* 7-notwos-3reduced-limit
* 11-notwos-3reduced-limit
* **13-notwos-3reduced-limit**
* 17-notwos-3reduced-limit
* 19-notwos-3reduced-limit
* 23-notwos-3reduced-limit
* 25-notwos-3reduced-limit
* 29-notwos-3reduced-limit
* 31-notwos-3reduced-limit
* 35-notwos-3reduced-limit

**13-notwos-3reduced-limit** is used in notwos tunings. It is naturally based on 13-notwos-limit, which utilizes the following primes: 3, 5, 7, 11, 13. 13-notwos-3reduced-limit however assumes tritave equivalence and restricts the remaining factors to a maximum of 13. Here is the interval list:

* 15/13, 13/5
* 13/11, 33/13
* 11/9, 27/11
* 9/7, 7/3
* 15/11, 11/5
* 7/5, 15/7
* 11/7, 21/11
* 13/9, 27/13
* 21/13, 13/7
* 5/3, 9/5
136edo

Welcome to 136edo

## 136edo = 8edo × 17edo

Distinctively interesting choice for an edo, due to its divisibility by both 8 and 17. This means it can be used to play 8edo music and 17edo music at the same time, using the 136/17 and 136/8 vals respectively.

## 8.824

136edo has a step size of 8.8235294117647 cents. It is a commatonal EDO, because the step size represents commas like 91/90.

## Selected just intervals by error

The following table shows how some prominent just intervals are represented in 136edo (ordered by absolute error).
1178edo

The 1178 equal tuning divides the octave into 1178 parts of 1.0187 cents each. It is a very strong 19-limit system, and is a zeta peak, integral and gap edo. It is also distinctly consistent through to the 21 odd limit, and is the first edo past 742 with a lower 19-limit relative error. It is also notable for being divisible by both 19 and 31. A basis for its 19-limit commas is 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4375/4374, 4914/4913 and 5985/5984.
102edo

**102edo** is the equal division of the octave into 102 steps of size 11.765 cents each. In the 5-limit it tempers out the same commas (2048/2025, 15625/15552, 20000/19683) as 34edo. In the 7-limit it tempers out 686/675 and 1029/1024; in the 11-limit 385/384, 441/440 and 4000/3993; in the 13-limit 91/90 and 169/168; in the 17-limit 136/135 and 154/153; and in the 19-limit 133/132 and 190/189. It is the optimal patent val for 13-limit echidnic temperament, and the rank five temperament tempering out 91/90.
103edo

**103edo** is the equal division of the octave into 103 steps of size 11.6505 cents each. It is a good miracle tuning, especially for the 7- and 13- limits and benediction and hemisecordite, two of the 13-limit extensions of miracle. It tempers out 78732/78125 in the 5-limit; 225/224, 1029/1024 and 2401/2400 in the 7-limit; 243/242, 441/440 and 540/539 in the 11-limit; 351/350 and 847/845 in the 13-limit. In the 13-limit it provides the optimal patent val for marvel temperament as well as benediction and hemisecordite.

103edo is the 27th prime edo.
145edo

The *145 equal division* divides the octave into 145 equal parts of 8.276 cents each. It is the optimal patent val for 11-limit mystery temperament and 11-limit rank three temperament pele temperament. It tempers out 1600000/1594323 in the 5-limit; 4375/4374 and 5120/5103 in the 7-limit; 441/440 and 896/891 in the 11-limit; 196/195, 352/351 and 364/363 in the 13-limit; 595/594 in the 17-limit; 343/342 and 476/475 in the 19-limit. The 145c val provides a tuning for magic which is nearly identical to the POTE tuning. It also supports and provides a good tuning for 13-limit mystery, and because it tempers out 441/440 it allows werckismic chords, because it tempers out 196/195 it allows mynucumic chords, because it tempers out 352/351 it allows minthmic chords, and because it tempers out 847/845 it allows the cuthbert triad, making it a very flexible harmonic system. The same is true of 232edo, the optimal patent val for 13-limit mystery.

# Music

Chromatic piece in magic 16 Chris Vaisvil
11-Hendrix diamond

The **11-'***Hendrix diamond'* is the tonality diamond generated from the ratios 1/1, 5/4, 11/8, 3/2 and 11/6.

All notes in the Hendrix diamond are also found in the 15-limit tonality diamond, because 1/1:5/4:11/8:3/2:11/6 is a 15-limit anomalous saturated suspension.

## Symmetry group

The symmetry group of the 11-Hendrix diamond has 16 elements. Its generators are:

* 3:2, 5:4, 11:8 → 11:6, 5:3, 11:9
* 3:2, 5:4, 11:8 → 3:2, 15:11, 18:11
* 3:2, 5:4, 11:8 → 4:3, 8:5, 16:11
125edo

The *125 equal temperament* divides the octave into 125 equal parts of exactly 9.6 cents each. It defines the optimal patent val for 7- and 11-limit slender temperament. It tempers out 15625/15552 in the 5-limit; 225/224 and 4375/4374 in the 7-limit; 385/384 in the 11-limit; and 275/273 in the 13-limit. It is notorious for a very accurate 10/9, being 0.0037121340600743 cents flat, and a very accurate 9/5, being 0.0037121340598745 cents sharp. Because the 9/5 maps to an even 106\125, it can split into a half-comma 4/3, approximating half-comma meantone.
114edo

**114edo** is the equal division of the octave into 114 parts, each of 10.52632 cents. In the 5-limit it tempers out 2048/2025, in the 7-limit 245/243, in the 11-limit 121/120 and 176/175, in the 13-limit 196/195 and 325/324, in the 17-limit 136/135 and 154/153, in the 19-limit 286/285 and 343/342. These commas make for 114edo being an excellent tuning for shrutar temperament; it is in fact the optimal patent val for shrutar in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.
11/9

Interval information

In 11-limit Just Intonation, **11/9** is a neutral third of about 347.4¢, falling in between "major third" and "minor third" territory. It is the simplest neutral third in just intonation, but of course, only one of persony (others include 16/13, 27/22, 49/40 and 60/49). It is nearly halfway between two intervals of 12edo, implying that it is both very xenharmonic and well-represented in 24edo.

In the 11-limit theyxad 4:5:6:7:9:11, 11/9 appears between the harmonic 11th and the harmonic 9th. A triad can also be built with a 3/2 fifth and 11/9 third: this would be 18:22:27. This introduces a second neutral third, 27/22, which together make a perfect fifth. Persony temperaments, including 17edo, 24edo, 31edo, 41edo, 58edo, 72edo, 130edo, 202edo, miracle, harry, and sesquart, conflate these two neutral thirds, allowing one neutral third interval to be stacked to generate a perfect fifth. 11/9 differs from 27/22 by 243/242, but also from 49/40 by 441/440 and 60/49 by 540/539, with varied consequences when one or more of them are tempered out. Tempering out all of them leads to the 11-limit rank three temperament jove.

*See also Gallery of Just Intervals*
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