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Scale 751

Scale 751, 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

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,5,6,7,9}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3817
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?yes
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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
Major TriadsD{2,6,9}341.9
F{5,9,0}341.9
Minor Triadscm{0,3,7}242.3
dm{2,5,9}242.1
f♯m{6,9,1}341.9
Augmented TriadsC♯+{1,5,9}341.9
Diminished Triads{0,3,6}242.3
d♯°{3,6,9}242.1
f♯°{6,9,0}242.1
{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 751. Created by Ian Ring ©2019 cm cm c°->cm d#° d#° c°->d#° cm->a° C#+ C#+ dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m D D dm->D D->d#° D->f#m f#° f#° F->f#° F->a° f#°->f#m

view full size

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 751 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2423
Scale 2423, Ian Ring Music Theory
3rd mode:
Scale 3259
Scale 3259, Ian Ring Music Theory
4th mode:
Scale 3677
Scale 3677, Ian Ring Music Theory
5th mode:
Scale 1943
Scale 1943, Ian Ring Music Theory
6th mode:
Scale 3019
Scale 3019, Ian Ring Music Theory
7th mode:
Scale 3557
Scale 3557, Ian Ring Music Theory
8th mode:
Scale 1913
Scale 1913, Ian Ring Music Theory

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [751, 2423, 3259, 3677, 1943, 3019, 3557, 1913] (Forte: 8-Z29) is the complement of the tetratonic modal family [139, 353, 1553, 2117] (Forte: 4-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 751 is 3817

Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 751 is chiral, and its enantiomorph is scale 3817

Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic

Transformations:

T0 751  T0I 3817
T1 1502  T1I 3539
T2 3004  T2I 2983
T3 1913  T3I 1871
T4 3826  T4I 3742
T5 3557  T5I 3389
T6 3019  T6I 2683
T7 1943  T7I 1271
T8 3886  T8I 2542
T9 3677  T9I 989
T10 3259  T10I 1978
T11 2423  T11I 3956

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 749Scale 749: Aeologian, Ian Ring Music TheoryAeologian
Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian
Scale 743Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian Inverse
Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic
Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic
Scale 719Scale 719: Kanian, Ian Ring Music TheoryKanian
Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 687Scale 687: Aeolythian, Ian Ring Music TheoryAeolythian
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic
Scale 1007Scale 1007: Epitygic, Ian Ring Music TheoryEpitygic
Scale 239Scale 239, Ian Ring Music Theory
Scale 495Scale 495: Bocryllic, Ian Ring Music TheoryBocryllic
Scale 1263Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic
Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic
Scale 2799Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic

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.