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Scale 1777: "Saptian"

Scale 1777: Saptian, 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).

Common Names

Zeitler
Saptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,4,5,6,7,9,10}
Forte Number7-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 493
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 367
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsC{0,4,7}231.4
F{5,9,0}231.4
Minor Triadsam{9,0,4}221.2
Diminished Triads{4,7,10}142
f♯°{6,9,0}142
Parsimonious Voice Leading Between Common Triads of Scale 1777. Created by Ian Ring ©2019 C C C->e° am am C->am F F f#° f#° F->f#° F->am

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
Radius2
Self-Centeredno
Central Verticesam
Peripheral Verticese°, f♯°

Modes

Modes are the rotational transformation of this scale. Scale 1777 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 367
Scale 367: Aerodian, Ian Ring Music TheoryAerodianThis is the prime mode
3rd mode:
Scale 2231
Scale 2231: Macrian, Ian Ring Music TheoryMacrian
4th mode:
Scale 3163
Scale 3163: Rogian, Ian Ring Music TheoryRogian
5th mode:
Scale 3629
Scale 3629: Boptian, Ian Ring Music TheoryBoptian
6th mode:
Scale 1931
Scale 1931: Stogian, Ian Ring Music TheoryStogian
7th mode:
Scale 3013
Scale 3013: Thynian, Ian Ring Music TheoryThynian

Prime

The prime form of this scale is Scale 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Complement

The heptatonic modal family [1777, 367, 2231, 3163, 3629, 1931, 3013] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1777 is 493

Scale 493Scale 493: Rygian, Ian Ring Music TheoryRygian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1777 is chiral, and its enantiomorph is scale 493

Scale 493Scale 493: Rygian, Ian Ring Music TheoryRygian

Transformations:

T0 1777  T0I 493
T1 3554  T1I 986
T2 3013  T2I 1972
T3 1931  T3I 3944
T4 3862  T4I 3793
T5 3629  T5I 3491
T6 3163  T6I 2887
T7 2231  T7I 1679
T8 367  T8I 3358
T9 734  T9I 2621
T10 1468  T10I 1147
T11 2936  T11I 2294

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 1779Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
Scale 1781Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic
Scale 1785Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
Scale 1761Scale 1761, Ian Ring Music Theory
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1713Scale 1713: Raga Khamas, Ian Ring Music TheoryRaga Khamas
Scale 1649Scale 1649: Bolimic, Ian Ring Music TheoryBolimic
Scale 1905Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian
Scale 2033Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic
Scale 1265Scale 1265: Pynimic, Ian Ring Music TheoryPynimic
Scale 1521Scale 1521: Stanian, Ian Ring Music TheoryStanian
Scale 753Scale 753: Aeronimic, Ian Ring Music TheoryAeronimic
Scale 2801Scale 2801: Zogian, Ian Ring Music TheoryZogian
Scale 3825Scale 3825: Pynyllic, Ian Ring Music TheoryPynyllic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.