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Scale 1357: "Takemitsu Linea Mode 2"

Scale 1357: Takemitsu Linea Mode 2, 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

Named After Composers
Takemitsu Linea Mode 2
Takemitsu Tree Line Mode 2
Zeitler
Katonimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,2,3,6,8,10}
Forte Number6-34
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1621
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 683
Deep Scaleno
Interval Vector142422
Interval Spectrump2m4n2s4dt2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {5,6,7}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation1.667
Maximally Evenno
Maximal Area Setno
Interior Area2.482
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
Heliotonicno

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 TriadsG♯{8,0,3}131.5
Minor Triadsd♯m{3,6,10}221
Augmented TriadsD+{2,6,10}131.5
Diminished Triads{0,3,6}221
Parsimonious Voice Leading Between Common Triads of Scale 1357. Created by Ian Ring ©2019 d#m d#m c°->d#m G# G# c°->G# D+ D+ D+->d#m

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 Verticesc°, d♯m
Peripheral VerticesD+, G♯

Modes

Modes are the rotational transformation of this scale. Scale 1357 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1363
Scale 1363: Gygimic, Ian Ring Music TheoryGygimic
3rd mode:
Scale 2729
Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
4th mode:
Scale 853
Scale 853: Epothimic, Ian Ring Music TheoryEpothimic
5th mode:
Scale 1237
Scale 1237: Salimic, Ian Ring Music TheorySalimic
6th mode:
Scale 1333
Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic

Prime

The prime form of this scale is Scale 683

Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic

Complement

The hexatonic modal family [1357, 1363, 2729, 853, 1237, 1333] (Forte: 6-34) is the complement of the hexatonic modal family [683, 1369, 1381, 1429, 1621, 2389] (Forte: 6-34)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1357 is 1621

Scale 1621Scale 1621: Scriabin's Prometheus, Ian Ring Music TheoryScriabin's Prometheus

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1357 is chiral, and its enantiomorph is scale 1621

Scale 1621Scale 1621: Scriabin's Prometheus, Ian Ring Music TheoryScriabin's Prometheus

Transformations:

T0 1357  T0I 1621
T1 2714  T1I 3242
T2 1333  T2I 2389
T3 2666  T3I 683
T4 1237  T4I 1366
T5 2474  T5I 2732
T6 853  T6I 1369
T7 1706  T7I 2738
T8 3412  T8I 1381
T9 2729  T9I 2762
T10 1363  T10I 1429
T11 2726  T11I 2858

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 1359Scale 1359: Aerygian, Ian Ring Music TheoryAerygian
Scale 1353Scale 1353: Raga Harikauns, Ian Ring Music TheoryRaga Harikauns
Scale 1355Scale 1355: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 1349Scale 1349: Tholitonic, Ian Ring Music TheoryTholitonic
Scale 1365Scale 1365: Whole Tone, Ian Ring Music TheoryWhole Tone
Scale 1373Scale 1373: Storian, Ian Ring Music TheoryStorian
Scale 1389Scale 1389: Minor Locrian, Ian Ring Music TheoryMinor Locrian
Scale 1293Scale 1293, Ian Ring Music Theory
Scale 1325Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic
Scale 1421Scale 1421: Raga Trimurti, Ian Ring Music TheoryRaga Trimurti
Scale 1485Scale 1485: Minor Romani, Ian Ring Music TheoryMinor Romani
Scale 1101Scale 1101: Stothitonic, Ian Ring Music TheoryStothitonic
Scale 1229Scale 1229: Raga Simharava, Ian Ring Music TheoryRaga Simharava
Scale 1613Scale 1613: Thylimic, Ian Ring Music TheoryThylimic
Scale 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
Scale 333Scale 333: Bogitonic, Ian Ring Music TheoryBogitonic
Scale 845Scale 845: Raga Neelangi, Ian Ring Music TheoryRaga Neelangi
Scale 2381Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
Scale 3405Scale 3405: Stynian, Ian Ring Music TheoryStynian

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.