The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1545

Scale 1545, 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

Cardinality4 (tetratonic)
Pitch Class Set{0,3,9,10}
Forte Number4-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 525
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes3
Prime?no
prime: 75
Deep Scaleno
Interval Vector112011
Interval Spectrumpn2sdt
Distribution Spectra<1> = {1,2,3,6}
<2> = {3,5,7,9}
<3> = {6,9,10,11}
Spectra Variation4
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 1545 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 705
Scale 705, Ian Ring Music Theory
3rd mode:
Scale 75
Scale 75, Ian Ring Music TheoryThis is the prime mode
4th mode:
Scale 2085
Scale 2085, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 75

Scale 75Scale 75, Ian Ring Music Theory

Complement

The tetratonic modal family [1545, 705, 75, 2085] (Forte: 4-13) is the complement of the octatonic modal family [735, 1785, 1995, 2415, 3045, 3255, 3675, 3885] (Forte: 8-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1545 is 525

Scale 525Scale 525, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1545 is chiral, and its enantiomorph is scale 525

Scale 525Scale 525, Ian Ring Music Theory

Transformations:

T0 1545  T0I 525
T1 3090  T1I 1050
T2 2085  T2I 2100
T3 75  T3I 105
T4 150  T4I 210
T5 300  T5I 420
T6 600  T6I 840
T7 1200  T7I 1680
T8 2400  T8I 3360
T9 705  T9I 2625
T10 1410  T10I 1155
T11 2820  T11I 2310

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 1547Scale 1547, Ian Ring Music Theory
Scale 1549Scale 1549, Ian Ring Music Theory
Scale 1537Scale 1537, Ian Ring Music Theory
Scale 1541Scale 1541, Ian Ring Music Theory
Scale 1553Scale 1553, Ian Ring Music Theory
Scale 1561Scale 1561, Ian Ring Music Theory
Scale 1577Scale 1577: Raga Chandrakauns (Kafi), Ian Ring Music TheoryRaga Chandrakauns (Kafi)
Scale 1609Scale 1609: Thyritonic, Ian Ring Music TheoryThyritonic
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
Scale 1801Scale 1801, Ian Ring Music Theory
Scale 1033Scale 1033, Ian Ring Music Theory
Scale 1289Scale 1289, Ian Ring Music Theory
Scale 521Scale 521, Ian Ring Music Theory
Scale 2569Scale 2569, Ian Ring Music Theory
Scale 3593Scale 3593, 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, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.