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Scale 545

Scale 545, 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).

Analysis

Cardinality3 (tritonic)
Pitch Class Set{0,5,9}
Forte Number3-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 137
Hemitonia0 (anhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes2
Prime?no
prime: 137
Deep Scaleno
Interval Vector001110
Interval Spectrumpmn
Distribution Spectra<1> = {3,4,5}
<2> = {7,8,9}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setno
Interior Area1.183
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyStrictly Proper
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 TriadsF{5,9,0}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 545 can be rotated to make 2 other scales. The 1st mode is itself.

2nd mode:
Scale 145
Scale 145: Raga Malasri, Ian Ring Music TheoryRaga Malasri
3rd mode:
Scale 265
Scale 265, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 137

Scale 137Scale 137: Ute Tritonic, Ian Ring Music TheoryUte Tritonic

Complement

The tritonic modal family [545, 145, 265] (Forte: 3-11) is the complement of the nonatonic modal family [1775, 1915, 1975, 2935, 3005, 3035, 3515, 3565, 3805] (Forte: 9-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 545 is 137

Scale 137Scale 137: Ute Tritonic, Ian Ring Music TheoryUte Tritonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 545 is chiral, and its enantiomorph is scale 137

Scale 137Scale 137: Ute Tritonic, Ian Ring Music TheoryUte Tritonic

Transformations:

T0 545  T0I 137
T1 1090  T1I 274
T2 2180  T2I 548
T3 265  T3I 1096
T4 530  T4I 2192
T5 1060  T5I 289
T6 2120  T6I 578
T7 145  T7I 1156
T8 290  T8I 2312
T9 580  T9I 529
T10 1160  T10I 1058
T11 2320  T11I 2116

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 547Scale 547: Pyrric, Ian Ring Music TheoryPyrric
Scale 549Scale 549: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
Scale 553Scale 553: Rothic 2, Ian Ring Music TheoryRothic 2
Scale 561Scale 561: Phratic, Ian Ring Music TheoryPhratic
Scale 513Scale 513, Ian Ring Music Theory
Scale 529Scale 529: Raga Bilwadala, Ian Ring Music TheoryRaga Bilwadala
Scale 577Scale 577, Ian Ring Music Theory
Scale 609Scale 609, Ian Ring Music Theory
Scale 673Scale 673, Ian Ring Music Theory
Scale 801Scale 801, Ian Ring Music Theory
Scale 33Scale 33: Honchoshi, Ian Ring Music TheoryHonchoshi
Scale 289Scale 289, Ian Ring Music Theory
Scale 1057Scale 1057: Sansagari, Ian Ring Music TheorySansagari
Scale 1569Scale 1569, Ian Ring Music Theory
Scale 2593Scale 2593, Ian Ring Music Theory

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.