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Scale 713: "Thoptitonic"

Scale 713: Thoptitonic, 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).

Common Names

Zeitler
Thoptitonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,3,6,7,9}
Forte Number5-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 617
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes4
Prime?no
prime: 587
Deep Scaleno
Interval Vector114112
Interval Spectrumpmn4sdt2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5,6}
<3> = {6,7,8,9}
<4> = {9,10,11}
Spectra Variation2
Maximally Evenno
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
Heliotonicno

Modes

Modes are the rotational transformation of this scale. Scale 713 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 601
Scale 601: Bycritonic, Ian Ring Music TheoryBycritonic
3rd mode:
Scale 587
Scale 587: Pathitonic, Ian Ring Music TheoryPathitonicThis is the prime mode
4th mode:
Scale 2341
Scale 2341: Raga Priyadharshini, Ian Ring Music TheoryRaga Priyadharshini
5th mode:
Scale 1609
Scale 1609: Thyritonic, Ian Ring Music TheoryThyritonic

Prime

The prime form of this scale is Scale 587

Scale 587Scale 587: Pathitonic, Ian Ring Music TheoryPathitonic

Complement

The pentatonic modal family [713, 601, 587, 2341, 1609] (Forte: 5-31) is the complement of the heptatonic modal family [731, 1627, 1739, 1753, 2413, 2861, 2917] (Forte: 7-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 713 is 617

Scale 617Scale 617: Katycritonic, Ian Ring Music TheoryKatycritonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 713 is chiral, and its enantiomorph is scale 617

Scale 617Scale 617: Katycritonic, Ian Ring Music TheoryKatycritonic

Transformations:

T0 713  T0I 617
T1 1426  T1I 1234
T2 2852  T2I 2468
T3 1609  T3I 841
T4 3218  T4I 1682
T5 2341  T5I 3364
T6 587  T6I 2633
T7 1174  T7I 1171
T8 2348  T8I 2342
T9 601  T9I 589
T10 1202  T10I 1178
T11 2404  T11I 2356

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 715Scale 715: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 717Scale 717: Raga Vijayanagari, Ian Ring Music TheoryRaga Vijayanagari
Scale 705Scale 705, Ian Ring Music Theory
Scale 709Scale 709: Raga Shri Kalyan, Ian Ring Music TheoryRaga Shri Kalyan
Scale 721Scale 721: Raga Dhavalashri, Ian Ring Music TheoryRaga Dhavalashri
Scale 729Scale 729: Stygimic, Ian Ring Music TheoryStygimic
Scale 745Scale 745: Kolimic, Ian Ring Music TheoryKolimic
Scale 649Scale 649: Byptic, Ian Ring Music TheoryByptic
Scale 681Scale 681: Kyemyonjo, Ian Ring Music TheoryKyemyonjo
Scale 585Scale 585: Diminished Seventh, Ian Ring Music TheoryDiminished Seventh
Scale 841Scale 841: Phrothitonic, Ian Ring Music TheoryPhrothitonic
Scale 969Scale 969: Ionogimic, Ian Ring Music TheoryIonogimic
Scale 201Scale 201, Ian Ring Music Theory
Scale 457Scale 457: Staptitonic, Ian Ring Music TheoryStaptitonic
Scale 1225Scale 1225: Raga Samudhra Priya, Ian Ring Music TheoryRaga Samudhra Priya
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic

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.