The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2235: "Bathian"

Scale 2235: Bathian, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

41161837294116105072918310504116183
Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Bathian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,5,7,11}
Forte Number7-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2979
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 375
Deep Scaleno
Interval Vector443532
Interval Spectrump3m5n3s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsC{0,4,7}321
Minor Triadscm{0,3,7}221.2
em{4,7,11}221.2
Augmented TriadsD♯+{3,7,11}231.4
Diminished Triadsc♯°{1,4,7}131.6
Parsimonious Voice Leading Between Common Triads of Scale 2235. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ c#° c#° C->c#° em em C->em D#+->em

view full size

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter3
Radius2
Self-Centeredno
Central Verticescm, C, em
Peripheral Verticesc♯°, D♯+

Modes

Modes are the rotational transformation of this scale. Scale 2235 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3165
Scale 3165: Mylian, Ian Ring Music TheoryMylian
3rd mode:
Scale 1815
Scale 1815: Godian, Ian Ring Music TheoryGodian
4th mode:
Scale 2955
Scale 2955: Thorian, Ian Ring Music TheoryThorian
5th mode:
Scale 3525
Scale 3525: Zocrian, Ian Ring Music TheoryZocrian
6th mode:
Scale 1905
Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian
7th mode:
Scale 375
Scale 375: Sodian, Ian Ring Music TheorySodianThis is the prime mode

Prime

The prime form of this scale is Scale 375

Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian

Complement

The heptatonic modal family [2235, 3165, 1815, 2955, 3525, 1905, 375] (Forte: 7-13) is the complement of the pentatonic modal family [279, 369, 1809, 2187, 3141] (Forte: 5-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2235 is 2979

Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2235 is chiral, and its enantiomorph is scale 2979

Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian

Transformations:

T0 2235  T0I 2979
T1 375  T1I 1863
T2 750  T2I 3726
T3 1500  T3I 3357
T4 3000  T4I 2619
T5 1905  T5I 1143
T6 3810  T6I 2286
T7 3525  T7I 477
T8 2955  T8I 954
T9 1815  T9I 1908
T10 3630  T10I 3816
T11 3165  T11I 3537

Nearby Scales:

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 2233Scale 2233: Donimic, Ian Ring Music TheoryDonimic
Scale 2237Scale 2237: Epothian, Ian Ring Music TheoryEpothian
Scale 2239Scale 2239: Dacryllic, Ian Ring Music TheoryDacryllic
Scale 2227Scale 2227: Raga Gaula, Ian Ring Music TheoryRaga Gaula
Scale 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian
Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
Scale 2203Scale 2203: Dorimic, Ian Ring Music TheoryDorimic
Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian
Scale 2299Scale 2299: Phraptyllic, Ian Ring Music TheoryPhraptyllic
Scale 2107Scale 2107, Ian Ring Music Theory
Scale 2171Scale 2171, Ian Ring Music Theory
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 2491Scale 2491: Layllic, Ian Ring Music TheoryLayllic
Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
Scale 3259Scale 3259, Ian Ring Music Theory
Scale 187Scale 187, Ian Ring Music Theory
Scale 1211Scale 1211: Zadian, Ian Ring Music TheoryZadian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.