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Scale 175

Scale 175, 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

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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

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,3,5,7}
Forte Number6-9
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3745
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes5
Prime?yes
Deep Scaleno
Interval Vector342231
Interval Spectrump3m2n2s4d3t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,4,6,7}
<3> = {3,4,5,7,8,9}
<4> = {5,6,8,9,10}
<5> = {7,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.866
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
Minor Triadscm{0,3,7}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 175 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2135
Scale 2135, Ian Ring Music Theory
3rd mode:
Scale 3115
Scale 3115, Ian Ring Music Theory
4th mode:
Scale 3605
Scale 3605, Ian Ring Music Theory
5th mode:
Scale 1925
Scale 1925, Ian Ring Music Theory
6th mode:
Scale 1505
Scale 1505, Ian Ring Music Theory

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [175, 2135, 3115, 3605, 1925, 1505] (Forte: 6-9) is the complement of the hexatonic modal family [175, 1505, 1925, 2135, 3115, 3605] (Forte: 6-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 175 is 3745

Scale 3745Scale 3745, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 175 is chiral, and its enantiomorph is scale 3745

Scale 3745Scale 3745, Ian Ring Music Theory

Transformations:

T0 175  T0I 3745
T1 350  T1I 3395
T2 700  T2I 2695
T3 1400  T3I 1295
T4 2800  T4I 2590
T5 1505  T5I 1085
T6 3010  T6I 2170
T7 1925  T7I 245
T8 3850  T8I 490
T9 3605  T9I 980
T10 3115  T10I 1960
T11 2135  T11I 3920

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 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 171Scale 171, Ian Ring Music Theory
Scale 167Scale 167, Ian Ring Music Theory
Scale 183Scale 183, Ian Ring Music Theory
Scale 191Scale 191, Ian Ring Music Theory
Scale 143Scale 143, Ian Ring Music Theory
Scale 159Scale 159, Ian Ring Music Theory
Scale 207Scale 207, Ian Ring Music Theory
Scale 239Scale 239, Ian Ring Music Theory
Scale 47Scale 47, Ian Ring Music Theory
Scale 111Scale 111, Ian Ring Music Theory
Scale 303Scale 303: Golimic, Ian Ring Music TheoryGolimic
Scale 431Scale 431: Epyrian, Ian Ring Music TheoryEpyrian
Scale 687Scale 687: Aeolythian, Ian Ring Music TheoryAeolythian
Scale 1199Scale 1199: Magian, Ian Ring Music TheoryMagian
Scale 2223Scale 2223: Konian, Ian Ring Music TheoryKonian

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.