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Scale 2455: "Bothian"

Scale 2455: Bothian, 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
Bothian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,4,7,8,11}
Forte Number7-Z18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3379
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 755
Deep Scaleno
Interval Vector434442
Interval Spectrump4m4n4s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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}331.5
E{4,8,11}331.5
G{7,11,2}242
Minor Triadsc♯m{1,4,8}242
em{4,7,11}331.5
Augmented TriadsC+{0,4,8}331.5
Diminished Triadsc♯°{1,4,7}242
g♯°{8,11,2}242
Parsimonious Voice Leading Between Common Triads of Scale 2455. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E c#°->c#m em->E Parsimonious Voice Leading Between Common Triads of Scale 2455. Created by Ian Ring ©2019 G em->G g#° g#° E->g#° G->g#°

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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.

Diameter4
Radius3
Self-Centeredno
Central VerticesC, C+, em, E
Peripheral Verticesc♯°, c♯m, G, g♯°

Modes

Modes are the rotational transformation of this scale. Scale 2455 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3275
Scale 3275: Mela Divyamani, Ian Ring Music TheoryMela Divyamani
3rd mode:
Scale 3685
Scale 3685: Kodian, Ian Ring Music TheoryKodian
4th mode:
Scale 1945
Scale 1945: Zarian, Ian Ring Music TheoryZarian
5th mode:
Scale 755
Scale 755: Phrythian, Ian Ring Music TheoryPhrythianThis is the prime mode
6th mode:
Scale 2425
Scale 2425: Rorian, Ian Ring Music TheoryRorian
7th mode:
Scale 815
Scale 815: Bolian, Ian Ring Music TheoryBolian

Prime

The prime form of this scale is Scale 755

Scale 755Scale 755: Phrythian, Ian Ring Music TheoryPhrythian

Complement

The heptatonic modal family [2455, 3275, 3685, 1945, 755, 2425, 815] (Forte: 7-Z18) is the complement of the pentatonic modal family [179, 779, 1633, 2137, 2437] (Forte: 5-Z18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2455 is 3379

Scale 3379Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2455 is chiral, and its enantiomorph is scale 3379

Scale 3379Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending

Transformations:

T0 2455  T0I 3379
T1 815  T1I 2663
T2 1630  T2I 1231
T3 3260  T3I 2462
T4 2425  T4I 829
T5 755  T5I 1658
T6 1510  T6I 3316
T7 3020  T7I 2537
T8 1945  T8I 979
T9 3890  T9I 1958
T10 3685  T10I 3916
T11 3275  T11I 3737

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 2453Scale 2453: Raga Latika, Ian Ring Music TheoryRaga Latika
Scale 2451Scale 2451: Raga Bauli, Ian Ring Music TheoryRaga Bauli
Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian
Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
Scale 2439Scale 2439, Ian Ring Music Theory
Scale 2447Scale 2447: Thagian, Ian Ring Music TheoryThagian
Scale 2471Scale 2471: Mela Ganamurti, Ian Ring Music TheoryMela Ganamurti
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
Scale 2519Scale 2519: Dathyllic, Ian Ring Music TheoryDathyllic
Scale 2327Scale 2327: Epalimic, Ian Ring Music TheoryEpalimic
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 2199Scale 2199: Dyptimic, Ian Ring Music TheoryDyptimic
Scale 2711Scale 2711: Stolian, Ian Ring Music TheoryStolian
Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic
Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian

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. Special thanks to Richard Repp for helping with technical accuracy.