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Scale 75

Scale 75, 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{0,1,3,6}
Forte Number4-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2625
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes3
Prime?yes
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
Maximal Area Setno
Interior Area1.183
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
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
Diminished Triads{0,3,6}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 75 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode:
Scale 2085
Scale 2085, Ian Ring Music Theory
3rd mode:
Scale 1545
Scale 1545, Ian Ring Music Theory
4th mode:
Scale 705
Scale 705, Ian Ring Music Theory

Prime

This is the prime form of this scale.

Complement

The tetratonic modal family [75, 2085, 1545, 705] (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 75 is 2625

Scale 2625Scale 2625, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 75 is chiral, and its enantiomorph is scale 2625

Scale 2625Scale 2625, Ian Ring Music Theory

Transformations:

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

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 73Scale 73, Ian Ring Music Theory
Scale 77Scale 77, Ian Ring Music Theory
Scale 79Scale 79, Ian Ring Music Theory
Scale 67Scale 67, Ian Ring Music Theory
Scale 71Scale 71, Ian Ring Music Theory
Scale 83Scale 83, Ian Ring Music Theory
Scale 91Scale 91, Ian Ring Music Theory
Scale 107Scale 107, Ian Ring Music Theory
Scale 11Scale 11, Ian Ring Music Theory
Scale 43Scale 43, Ian Ring Music Theory
Scale 139Scale 139, Ian Ring Music Theory
Scale 203Scale 203, Ian Ring Music Theory
Scale 331Scale 331: Raga Chhaya Todi, Ian Ring Music TheoryRaga Chhaya Todi
Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic
Scale 1099Scale 1099: Dyritonic, Ian Ring Music TheoryDyritonic
Scale 2123Scale 2123, 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.